| 1. |
- Bellomo, Nicola, 1943, et al.
(författare)
-
The generalized-kinetics-based equilibrium distribution function for composite particles
- 2003
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Ingår i: Comptes Rendus - Mecanique. - : Elsevier Science B.V., Amsterdam.. - 1631-0721 .- 1873-7234. ; 331:7, s. 461-467
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Tidskriftsartikel (refereegranskat)abstract
- This work is devoted to the equilibrium distribution function for a fluid of mutually non-interacting identical composite point particles in three-dimensional physical space. The distribution function is derived within the generalized-kinetics (GK) vision from the proposed probabilistic model based on quantum-mechanical bosons and fermions. The first GK advantage is that the derivation does not involve any assumption on the interpolation between bosons and fermions whereas the resulting function provides this interpolation. The second GK advantage is that composons, the particles described with the GK-based distribution function, are considerably less schematic and more consistent physically than quons. Composons correspond to a specific case of Isakov's general q-commutation relation involving an infinite number of the q-coefficients. Connection of the composon concept to previous results in the literature is pointed out. A few directions for future research on the topic are formulated. The results of the work can be used in the composite-particle fluid problems where the Maxwell–Boltzmann description is not valid, for instance, in dense populations of not too massive point-like particles of a complex, composite nature at not too high temperatures. FRENCH: Ce travail s'intéresse à la fonction de distribution d'équilibre pour un fluide mutuellement non agissant, composé de particules points dans un espace de dimension trois. La fonction de distribution provient, d'un point de vue de CG, d'un modèle probabiliste issu de la mécanique quantique des fermions et des bosons. Le premier avantage de CG est que la dérivation ne nécessite aucune hypothèse sur l'interpolation entre les bosons et les fermions alors que la fonction résultante fournit cette interpolation. Le second est que les composons, les particules décrites par ce procédé sont considérablement moins schématiques et plus consistantes, physiquement, que les quons. Les composons correspondent à un cas particulier de la relation générale de q-commutation d'Isakov, pour un nombre infini de q-coefficients. Les résultats antérieurs liés au concept de composon sont signalés et quelques directions de recherches futures sont proposées. Les résultats de ce travail peuvent servir pour l'étude de fluides composés, où la description Maxwell–Boltzmann n'est pas valable, par exemple, pour une dense population de particules, pas trop lourdes et a des températures pas trop élevées, et d'une comoposition de nature complexe.
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| 2. |
- Berbyuk, Viktor, 1953, et al.
(författare)
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Ice detection for smart de-icing of wind turbines
- 2017
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Icing on a wind turbine rotor blade is a problem in the operation of wind turbines in cold climates. Ice detection is a critical process to get a workable cost-effective wind turbine de-icing system. The paper presents the theoretical models, methods, algorithms, principles, and a demonstrator that are the basis for developing a new technique for detecting icing on rotor blades of a wind turbine based on acoustic wave propagation in composite structures. Two methods have been proposed: guided acoustic wave propagation and bulk acoustic wave propagation in composite structures. Analysis of computer simulations and the results of experimental study obtained by using the developed demonstrator in cold climate lab has shown that the integration of the guided acoustic wave propagation and the bulk acoustic wave propagation methods provides an efficient scientific approach to be used for the design of new ice detection system for wind turbines in cold climate regions. In particular, the guided acoustic wave propagation method makes it possible to detect ice and icing area location on the rotor blades. Several criteria (Icing Index, Frequency Factor Index, others) have been proposed for ice detection of composite structures. Bulk acoustic wave propagation method makes it possible to identify the time-varying spatially heterogeneous “landscapes” over the blade surface for each of the following eight ice parameters: thickness, the volumetric bulk density, bulk and shear moduli, stress relaxation time, porosity, and volume and shear viscosities. These data are necessary for smart, energy-efficient de-icing systems. The identification algorithm is computationally efficient and can be implemented in the real-time mode. A LIDAR (Light Detection And Ranging) for the detection of early ice growth on the wind turbine blades has also designed, tested and evaluated in this project. LIDAR uses laser pulses that emit at two different wavelengths and is capable of distinguishing between a thin layer of ice and water covering the turbine blades. The results of the tests that have been carried out in the project are undeniable. LIDAR detects early ice growth by measuring the difference in reflectivity of a surface by using two different laser wavelengths. The limitation of LIDAR is that it cannot be used to determine the amount of ice on the sheet, only if there is ice or not. The obtained results can be used to develop smart de-icing systems for wind turbines operating in cold climates, and can lead to new future products that are sought after by wind power industry. Since the efficient ice detection systems can increase wind turbine profitability, the results contribute to an increased ability to establish multiple wind turbines in cold regions.
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| 3. |
- Carlsson, Tobias, 1975, et al.
(författare)
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Irreducible memory function and slow dynamics in disordered systems.
- 2007
-
Ingår i: Phys. Rev. E. - 1539-3755. ; 75:031109, s. 1-8
-
Tidskriftsartikel (refereegranskat)abstract
- We show how the irreducible memory function can be obtained in a rather straightforward way, and that it can be expressed in terms of two contributions representing two parallel decay channels. This representation should be useful for treating systems with a slow time dependence and where eventually some internal degrees of freedom enters in the relaxation process, and cuts off an underlying ideal ergodic to nonergodic transition. We also show how the irreducible memory function under certain mild conditions defines a regenerative stochastic process, or a two level stochastic system. This leads to a picture with dynamical heterogeneities, where the statistical properties asymptotically are ruled by limit processes. This can explain the universal behavior observed in many glass-forming systems.
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| 4. |
- Mamontov, Eugen, 1955, et al.
(författare)
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A Scalar Acoustic Equation for Gases, Liquids, and Solids, Including Viscoelastic Media
- 2014
-
Ingår i: Journal of Applied Mathematics and Physics. - : Scientific Research Publishing, Inc.. - 2327-4379 .- 2327-4352. ; 2, s. 960-970
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Tidskriftsartikel (refereegranskat)abstract
- The work deals with a mathematical model for real-time acoustic monitoring of material parameters of media in multi-state viscoelastic engineering systems continuously operating in irregular external environments (e.g., wind turbines in cold climate areas, aircrafts, etc.). This monitoring is a high-reliability time-critical task. The work consistently derives a scalar wave PDE of the Stokestype for the non-equilibrium part (NEP) of the average normal stress in a medium. The explicit expression for the NEP of the corresponding pressure and the solution-adequateness condition are also obtained. The derived Stokes-type wave equation includes the stress relaxation time and is applicable to gases, liquids, and solids.
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| 5. |
- Mamontov, Eugen, 1955
(författare)
-
A specification of the Maxwell–Rayleigh–Heisenberg approach to modelling fluids for bioelectronic applications
- 2005
-
Ingår i: Mathl Comput. Modelling. - : Elsevier BV. - 0895-7177. ; 42:3-4, s. 441-470
-
Tidskriftsartikel (refereegranskat)abstract
- The key question which any version of random fluid mechanics has to resolve is how to provide continuous probability distributions for the fluid particles. Each specific way is determined by one or another set of assumptions. Statistical mechanics proceeds on the thermodynamic-limit assumption supposing that the domain occupied by the fluid is “macroscopically big” and the number of the particles in it is “statistically large”. This picture cannot be the case in mesoscopic systems. The latter are common in many modern applications including bioelectronics. The present work develops a nonstatistical way to provide the above continuous distributions. It follows the vision formed by certain results of Heisenberg, Rayleigh, and Maxwell and specifies it by means of extending nonlinear nonequilibrium stochastic hydrodynamics (NNSHD) introduced by the authors earlier. The work concentrates on the following two generalizations: first, allowing for nonzero volumes of the particles, the feature typical in the biological parts of bioelectronic problems, and, second, accounting the general kinetic-energy/momentum dependences, including the relativistic ones, which are usually necessary in the electronic parts of bioelectronic problems. The simplest case of the first generalization is exemplified with an evaluation of the electrochemical potentials and pressures of red blood cells in human blood in a recently published paper of the authors. The second generalization is illustrated in Section 10 of the present work with the relativistic distribution functions which take into account the general spin picture of composite particles by means of the model of composons, the flexible combination of bosons and fermions based on the generalized-kinetics (GK) methods. The above generalization is intended to be a framework rather than theory that inherently includes the capabilities in coupling to other fluid-modelling treatments like common hydrodynamics or stochastic kinetic equations. The issues on further extensions in line with GK and on the coupling to the latter are emphasized. A few directions for future research are discussed as well.
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| 6. |
- Mamontov, Eugen, 1955, et al.
(författare)
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An analytical-numerical method for fast evaluation of probability densities for transient solutions of nonlinear Itô’s stochastic differential equations
- 2009
-
Ingår i: International Journal of Engineering Science. - : Elsevier BV. - 0020-7225. ; 47:1, s. 116-130
-
Tidskriftsartikel (refereegranskat)abstract
- Probability densities for solutions of nonlinear Itô’s stochastic differential equations are described by the corresponding Kolmogorov-forward/Fokker-Planck equations. The densities provide the most complete information on the related probability distributions. This is an advantage crucial in many applications such as modelling floating structures under the stochastic load due to wind or sea waves. Practical methods for numerical solution of the probability-density equations are combined, analytical-numerical techniques. The present work develops a new analytical-numerical approach, the successive-transition (ST) method, which is a version of the path-integration (PI) method. The ST technique is based on an analytical approximation for the transition-probability density. It enables the PI approach to explicitly allow for the damping matrix in the approximation. This is achieved by extending another method, introduced earlier for bistable nonlinear reaction-diffusion equations, to the probability-density equations. The ST method also includes a control for the size of the time step. The overall accuracy of the ST method can be tested on various nonlinear examples. One such example is proposed. It is one-dimensional nonlinear Itô’s equation describing the velocity of a ship maneuvering along a straight line under the action of the stochastic drag due to wind or sea waves. Another problem in marine engineering, the rolling of a ship up to its possible capsizing is also discussed in connection with the complicated damping-matrix picture. The work suggests a few directions for future research.
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| 7. |
- Mamontov, Eugen, 1955, et al.
(författare)
-
Associations and dissociations with time-dependent reaction coefficients in finite polymer mixtures: The model and analytical-numerical method for solution by successive approximations
- 2017
-
Ingår i: Applied Mathematical Modelling. - : Elsevier BV. - 0307-904X. ; 51, s. 109-128
-
Tidskriftsartikel (refereegranskat)abstract
- The work deals with the association and dissociation reactions with time-dependent coef- ficients in finite mixtures of polymers dispersed in fluid media with solid components. The polymers are regarded to be formed by identical units, polymer-forming units (PFUs) and, thus, present homopolymers. The model takes into account the porosity of the dispersion- medium/polymer-mixture system. The work derives the model for the reactions in the fi- nite mixtures. The model presents a non-autonomous quadratic finite ODE system in a time-independent hyperplane and is based on the conservation law for the total num- ber of PFUs. A variety of engineering applications of the derived finite-mixture model are discussed. The simplest case of the finite mixtures, i.e., the monomer-dimer mix- tures with time-independent reaction coefficients is completely analyzed. An analytical- numerical (AN) method of the successive-approximations (SA) type is proposed for solv- ing the derived model. The AN/SA method includes explicit analytical expressions for each of the approximations in terms of the preceding approximation. The method is exact in the dissociation-only case. The approximations are expected to converge if the association- reaction coefficients are not too large and the zeroth approximations are not very far from the solution. The AN/SA method comprises two sequences of the approximations. If the first one converges uniformly in the entire time axis, then the limit function is a steady- state (or “dynamic equilibrium”) solution of the non-autonomous quadratic ODE system. The second sequence presumes that the first sequence is convergent in the above men- tioned sense. The second sequence is intended for calculation of the solutions of initial- value problems for the above ODE system in a semi-infinite time interval. The main differ- ences from common computational methods are formulated. The AN/SA method is quan- titatively illustrated with a few examples of the settings in the aforementioned case of monomer-dimer mixtures, also in comparison with the explicit Euler method. The form of the AN/SA method allows especially efficient implementation on multi-processor/multicore personal computers with graphic processing units even if the dimension of the state space is large. The developed model and method form a constructive framework for analysis or design of polymer mixtures dispersed in fluid-solid media. An application to prospective manufacturing of spatially heterogeneous polymer products is noted. A few directions for future research are proposed as well.
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| 8. |
- Mamontov, Eugen, 1955, et al.
(författare)
-
Asymptotic trajectory matching in self-navigation of autonomous manless interceptors: Nonsearch method and a formulation of the functional optimization of the stability of random systems
- 2006
-
Ingår i: Proc. 5th MATHMOD Vienna Conf., 8-10 February, 2006 (Vienna Univ. of Technol., Vienna, Austria). - 3901608303 ; 2
-
Konferensbidrag (refereegranskat)abstract
- In the field of self-navigation autonomous manless robots there is a noticeable interest to the robot-based target-interception problem. The interceptor trajectory is usually determined by search-based optimization algorithms. In contrast to this, the present work treats the interception as asymptotic trajectory matching and introduces a nonsearch method for the interceptor trajectory. This method is substantially simpler than the well-known proportional navigation and requires very limited computing resources. The latter feature makes the proposed method especially suitable to the interceptors based on embedded onboard computers and civil applications. An example of the latter discussed in the work is the protection of the infrastructure components against intended or unintended attacks. In a general case when parameters of the interceptor are random, the new method leads to a formulation of a new problem in stochastic optimization, namely the functional optimization of (the so-called targetal) stability of the interceptor trajectory. Certain aspects of a practical implementation of the new systems are analyzed. The work proposes the basic physical principle and schemes for innovative sensors which can make the interceptors truly autonomous, in particular, fully GPS-free. A list of the fundamental and applied topics for future research is also suggested.
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| 9. |
- Mamontov, Eugen, 1955
(författare)
-
Dynamic-equilibrium solutions of ordinary differential equations and their role in applied problems
- 2008
-
Ingår i: Appl. Math. Lett.. - : Elsevier BV. - 0893-9659. ; 21:4, s. 320-325
-
Tidskriftsartikel (refereegranskat)abstract
- The work introduces the notion of an dynamic-equilibrium (DE) solution of an ordinary differential equation (ODE) as the special (limit) version of the ODE general solution. The dynamic equilibrium is understood as independence of the initial point. The work explains the special importance of ODEs which have DE solutions. The criteria for the existence and global attraction of these solutions are developed. A few examples illustrate different aspects of the DE-solution theory and application. The work discusses the role of these solutions in applied problems (related to ODEs in both Euclidean and function Banach spaces) with the emphasis on advanced models for living systems (such as the active-particle generalized kinetic theory). This discussion also concerns a few directions for future research.
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| 10. |
- Mamontov, Eugen, 1955, et al.
(författare)
-
High-Dimensional Nonlinear Diffusion Stochastic Pprocesses. Modelling for Engineering Applications
- 2001
-
Bok (övrigt vetenskapligt/konstnärligt)abstract
- This book is the first one devoted to high-dimensional (or large-scale) diffusion stochastic processes (DSPs) with nonlinear coefficients. These processes are closely associated with nonlinear Ito's stochastic ordinary differential equations (ISODEs) and with the space-discretized versions of nonlinear Ito's stochastic partial integro-differential equations. The latter models include Ito's stochastic partial differential equations (ISPDEs). The book presents the new analytical treatment which can serve as the basis of a combined, analytical-numerical approach to greater computational efficiency in engineering problems. A few examples discussed in the book include: the high-dimensional DSPs described with the ISODE systems for semiconductor circuits; the nonrandom model for stochastic resonance (and other noise-induced phenomena) in high-dimensional DSPs; the modification of the well-known stochastic-adaptive-interpolation method by means of bases of function spaces; ISPDEs as the tool to consistently model non-Markov phenomena; the ISPDE system for semiconductor devices; the corresponding classification of charge transport in macroscale, mesoscale and microscale semiconductor regions based on the wave-diffusion equation; the fully time-domain nonlinear-friction aware analytical model for the velocity covariance of particle of uniform fluid, simple or dispersed; the specific time-domain analytics for the long, non-exponential "tails" of the velocity in case of the hard-sphere fluid. These examples demonstrate not only the capabilities of the developed techniques but also emphasize the usefulness of the complex-system-related approaches to solve some problems which have not been solved with the traditional, statistical-physics methods yet. From this veiwpoint, the book can be regarded as a kind of complement to such books as "Introduction to the Physics of Complex Systems. The Mesoscopic Approach to Fluctuations, Nonlinearity and Self-Organization" by Serra, Andretta, Compiani and Zanarini, "Stochastic Dynamical Systems. Concepts, Numerical Methods, Data Analysis" and "Statistical Physics: An Advanced Approach with Applications" by Honerkamp which deal with physics of complex systems, some of the corresponding analysis methods and an innovative, stochastics-based vision of theoretical physics. To facilitate the reading by nonmathematicians, the introductory chapter outlines the basic notions and results of theory of Markov and diffusion stochastic processes without involving the measure-theoretical approach. This presentation is based on probability densities commonly used in engineering and applied sciences.
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| 11. |
- Mamontov, Eugen, 1955
(författare)
-
Homeorhesis and evolutionary properties of living systems: From ordinary differential equations to the active-particle generalized kinetics theory
- 2006
-
Ingår i: 10th Evolutionary Biology Meeting at Marseilles, 20-22 September 2006, Marseilles, France.
-
Konferensbidrag (refereegranskat)abstract
- Advanced generalized-kinetic-theory (GKT) models for biological systems are developed for populations of active (or living) particles [1]-[5]. These particles are described with both the stochastic variables common in kinetic theory (such as time, the particle random location and velocity) and the stochastic variables related to the internal states of an active particle. Evolution of these states represents biological, ecological, or social properties of the particle behavior. Paper [6] analyzes a number of the well-known statistical-mechanics approaches and shows that the active-particle GKT (APGKT) is the only treatment capable of modelling living systems. Work [2] summarizes the significance of the notion of an active particle in kinetic models. This notion draws attention to the features distinguishing living matter from nonliving matter. They are discussed by many authors (e.g., [7]-[15], [1]-[3], [6], [16]-[18]). Work [11] considers a lot of differences between living and nonliving matters, and the limitations of the modelling approaches developed for nonliving matter. Work [6] mainly focuses on the comparison of a few theoretical mechanics treatments in terms of the key living-matter properties formulated in [15]. One of the necessary properties of the evolution of living systems is homeorhesis. It is, loosely speaking, a peculiar qualitative and quantitative insensitivity of a living system to the exogenous signals acting on it. The earlier notion, homeostasis, was introduced by W. B. Cannon in 1926 who discussed the phenomenon in detail later [7]. Homeorhesis introduced by C. H. Waddington [8, p. 32] generalizes homeostasis and is well known in biology [8], [9], [12]. It is an inherent part of mathematical models for oncogeny (e.g., [16]-[18], [6, Appendix]). Homeorhesis is also discussed in [3, Section 4] in connection with APGKT. Homeorhesis is documented in ecology (e.g., [11], [13, the left column on p. 675]) where it is one of the key notions of the strong Gaia theory, a version of the Gaia theory (e.g., [14, Chapter 8]). The strong Gaia theory “states that the planet with its life, a single living system, is regulated in certain aspects by that life” [14, p. 124]. The very origin of the name “Gaia” is related to homeorhesis or homeostasis [14, p. 118]. These notions are also used in psychology and sociology. If evolution of a system is not homeorhetic, the system can not be living. Work [6, Appendix] derives a preliminary mathematical formulation of homeorhesis in terms of the simplest dynamical systems, i.e. ordinary differential equations (ODEs). The present work complements, extended, and further specify the approach of [6, Appendix]. The work comprises the two main parts. The first part develops the sufficient conditions for ODE systems to describe homeorhesis, and suggests a fairly general structure of the ODE model. It regards homeorhesis as piecewise homeostasis. The model can be specified in different ways depending on specific systems and specific purposes of the analysis. An example of the specification is also noted (the PhasTraM nonlinear reaction-diffusion model for hyperplastic oncogeny [16]-[18]). The second part of the work discusses implementation of the above homeorhesis ODE model in terms of a special version [3] of APGKT (see above). The key feature of this version is that the components of a living population need not be discrete: the subdivision into the components is described with a general, continuous-discrete probability distribution (see also [6]). This enables certain properties of living matter noted in [15]. Moreover, the corresponding APGKT model presents a system of, firstly, a generalized kinetic equation for the conditional distribution function conditioned by the internal states of the population and, secondly, Ito's stochastic differential equations for these states. This treatement employs the results on nonstationary invariant diffusion stochastic processes [19]. The second part of the work also stresses that APGKT is substantially more important for the living-matter analysis than in the case of nonliving matter. One of the reasons is certain limitations in experimental sampling of the living-system modes presented with stochastic processes. A few directions for future research are suggested as well. REFERENCES: [1] Bellomo, N., Bellouquid, A. and Delitala, M., 2004, Mathematical topics on the modelling complex multicellular systems and tumor immune cells competition, Math. Models Methods Appl. Sci., 14, 1683-1733. [2] Bellomo, N., 2006, New hot Paper Comments, Essential Science Indicators, http://www.esi-topics.com/nhp/2006 /may- 06-NicolaBellomo.html. [3] Willander, M., Mamontov, E. and Chiragwandi, Z., 2004, Modelling living fluids with the subdivision into the components in terms of probability distributions, Math. Models Methods Appl. Sci. 14, 1495-1520. [4] Bellomo, N. and Maini, P.K., 2005, Preface and the Special Issue “Multiscale Cancer Modelling-A New Frontier in Applied Mathematics”, Math. Models Methods Appl. Sci., 15, iii-viii. [5] De Angelis, E. and Delitala, M., 2006, Modelling complex systems in applied sciences: Methods and tools of the mathematical kinetic theory for active particles. Mathl Comput. Modelling, 43, 1310-1328. [6] Mamontov, E., Psiuk-Maksymowicz, K. and Koptioug, A., 2006, Stochastic mechanics in the context of the properties of living systems, Mathl Comput. Modelling, Article in Press, 13 pp. [7] Cannon, W.B., 1932, The Wisdom of the Body (New York: Norton). [8] Waddington, C.H., 1957, The Strategy of the Genes. A Discussion of Some Aspects of Theoretical Biology (London, George Allen and Unwin). [9] Waddington, C.H., 1968, Towards a theoretical biology, Nature, 218, 525-527. [10] Cotnoir, P.-A., 1981, La compétence environnementale: Une affaire d’adaptation. Séminaire en écologie behaviorale, Univeristé du Québec, Montralé. Available online at: http://pac.cam.org/culture.doc . [11] O’Neill, R.V., DeAngelis, D.L., Waide, J.B. and Allen, T.F.H., 1986, A Hierarchical Concept of Ecosystems, Princeton: Princeton Univ. Press). [12] Sauvant, D., 1992, La modélisation systémique en nutrition, Reprod. Nutr. Dev., 32, 217-230. [13] Christensen, N.L., Bartuska, A.M., Brown, J.H., Carpenter, S., D'Antonio, C., Francis, R., Franklin, J.F., MacMahon, J.A., Noss, R.F., Parsons, D.J., Peterson, C.H., Turner, M.G. and Woodmansee, R.G., 1996, The Report of the Ecological Society of America Committee on the Scientific Basis for Ecosystem Management, Ecological Applications, 6, 665-691. Available online at: http://www.esa.org/pao/esaPositions/Papers/ReportOfSBEM.php. [14] Margulis, L., 1998, Symbiotic Planet. A New Look at Evolution (Amherst: Sciencewriters). [15] Hartwell, L.H., Hopfield, J.J., Leibler, S. and Murray, A.W., 1999, From molecular to modular cell biology, Nature, 402, C47-C52. [16] Mamontov, E., Koptioug, A.V. and Psiuk-Maksymowicz, K., 2006, The minimal, phase-transition model for the cell- number maintenance by the hyperplasia-extended homeorhesis, Acta Biotheoretica, 54, 44 pp., (no. 2, May-June, accepted). [17] Psiuk-Maksymowicz, K. and Mamontov, E., 2005, The time-slices method for rapid solving the Cauchy problem for nonlinear reaction-diffusion equations in the competition of homeorhesis with genotoxically activated hyperplasia, In: European Conference on Mathematical and Theoretical Biology - ECMTB05 (July 18-22, 2005) Book of Abstracts, Vol.1 (Dresden: Center for Information Services and High Performance Computing, Dresden Univ. Technol.), p. 429 (http://www.ecmtb05.org/). [18] Psiuk-Maksymowicz, K. and Mamontov, E., 2006, The homeorhesis-based modelling and fast numerical analysis for oncogenic hyperplasia under radiation therapy, submitted. [19] Mamontov, E., 2005, Nonstationary invariant distributions and the hydrodynamic-style generalization of the Kolmogorov-forward/Fokker-Planck equation, Appl. Math. Lett. 18 (9) 976-982.
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| 12. |
- Mamontov, Eugen, 1955, et al.
(författare)
-
Identification of Material Parameters of Thin Curvilinear Viscoelastic Solid Layers in Ships and Ocean Structures by Sensing the Bulk Acoustic Signals
- 2015
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Ingår i: 6th International Conference on Computational Methods in Marine Engineering, MARINE 2015, Rome, Italy, 15-17 June 2015. - 9788494392863 ; , s. 502-513
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Konferensbidrag (refereegranskat)abstract
- Ships and other ocean structures have components, which are thin planar or curvilinear viscoelastic solid layers surrounded by air or water. The present work deals with the identification of material parameters of these layers to extend the scope of the real-time structural health monitoring. The work proposes the approach to the parameter identification from passive sensing of acoustic signals resulting from the operational load. The identification is based on the partial integro-differential equation (PIDE) for the non-equilibrium part of the average normal stress. The PIDE is derived in the work. It includes the Boltzmann superposition integral associated with the stress-relaxation function. It is shown that, in the exponential approximation for this function, the PIDE expresses the steady-state solution (with respect to a certain variable)of the corresponding third-order partial differential equation (PDE) of the Zener type. The operators of both the equations are identical. The equations are applicable at all values of the stress-re-laxation time. The roots of the characteristic equation of this operator are consistently analyzed, and the acoustic attenuation coefficient for arbitrary high frequencies is indicated. The approach is exemplified with the identification of the layer-material stress-relaxation time and ratio of the bulk-wave speed to the layer thickness. This identification can be carried out from the acoustic acceleration normal to the layer measured by an acoustic accelerometer attached to the layer surface and is applicable to both planar and curvilinear layers. The identification method presumes the finite-difference calculation of the time derivatives of themeasured acoustic acceleration up to the third order and can be computationally efficient.
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| 13. |
- Mamontov, Eugen, 1955, et al.
(författare)
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Managing panic-stricken crowds: The need in quantitative models for social dynamics
- 2007
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Ingår i: Abstract Booklet, The 8th Annual Conference of the European Sociological Association.
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Konferensbidrag (refereegranskat)abstract
- Panics typically occur during disaster or social crisis. Panics in crowds in public sites (airports, hospitals, supermarkets, office buildings, air- or sea-liners, trains, stadiums, downtown areas, etc.) often cause stampedes leading to injuries or deaths. How can we best organize public events at existing sites in order to prevent the tragic outcomes? How can one design new public sites to avoid the consequences of panic? What methods and tools can be applied? These questions determine the focus of the present work. Obviously, experimental approaches are inapplicable. Intuitive problem solving does not assure specific and consistent solutions. Therefore, the work concentrates on the non-intuitive, model-based approaches. Evaluation of the model-based solutions involves quantitative characteristics, e.g., the time of the evacuation, the probability for individuals to get injured, the concentration of oxygen, etc. Subsequently, any suitable model must be quantitative. Moreover, the behaviour of crowds develops continuously in both space and time. Thus, the models must also be space-time continuous. The work analyzes these and other features of the models for social dynamics and emphasizes the key differences from the dynamical models in the natural sciences studying nonliving matter. The related application aspects and directions for future research are also discussed.
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| 14. |
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| 15. |
- Mamontov, Eugen, 1955
(författare)
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Modelling homeorhesis by ordinary differential equations
- 2007
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Ingår i: Mathl Comput. Modelling. - : Elsevier BV. - 0895-7177. ; 45:5-6, s. 694-707
-
Tidskriftsartikel (refereegranskat)abstract
- Homeorhesis is a necessary feature of any living system. If a system does not perform homeorhesis, it is nonliving. The present work develops the sufficient conditions for the ODE model to describe homeorhesis and suggests the structure of the model. The proposed homeorhesis model is fairly general. It treats homeorhesis as piecewise homeostasis. The model can be specified in different ways depending on the specific system and specific purposes of this analysis. An example of the specification is the PhasTraM model, the homeorhesis-aware nonlinear reaction–diffusion model for hyperplastic oncogeny in the previous works of the author. The qualitative agreement of the developed homeorhesis model with the living-system experimental results is noted. The work also shows that the basic mathematical models (such as the active-particle generalized kinetic theory) are substantially more important for the living-matter studies than in the case of nonliving matter. A few directions for future research are suggested as well.
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| 16. |
- Mamontov, Eugen, 1955, et al.
(författare)
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Nonsearch paradigm for large-scale parameter-identification problems in dynamical systems related to oncogenic hyperplasia
- 2006
-
Ingår i: Systems, Control, Modeling and Optimization. IFIP International Federation for Information Processing. - : Springer US. - 1571-5736. - 9780387338811 - 0387338810 ; 202, s. 269-278
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Konferensbidrag (refereegranskat)abstract
- In many engineering and biomedical problems there is a need to identify parameters of the systems from experimental data. A typical example is the biochemical-kinetics systems describing oncogenic hyperplasia where the dynamical model is nonlinear and the number of the parameters to be identified can reach a few hundreds. Solving these large-scale identification problems by the local- or global-search methods can not be practical because of the complexity and prohibitive computing time. These difficulties can be overcome by application of the non-search techniques which are much less computation- demanding. The present work proposes key components of the corresponding mathematical formulation of the nonsearch paradigm. This new framework for the nonlinear large-scale parameter identification specifies and further develops the ideas of the well-known approach of A. Krasovskii. The issues are illustrated with a concise analytical example. The new results and a few directions for future research are summarized in a dedicated section.
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| 17. |
- Mamontov, Eugen, 1955
(författare)
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Nonstationary invariant distributions and the hydrodynamic-style generalization of the Kolmogorov-forward/Fokker-Planck equation
- 2005
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Ingår i: Appl. Math. Lett.. - : Elsevier BV. - 0893-9659. ; 18:9, s. 976-982
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Tidskriftsartikel (refereegranskat)abstract
- The work deals with nonstationary invariant probability distributions of diffusion stochastic processes (DSPs). A few results on this topic are available, such as theoretical works of Il’in and Has’minski and a recent more practical contribution of Mamontov and Willander. This is in disproportion to the importance of nonstationary invariant DSPs which have a potentially wide application to the natural sciences and mathematics, in particular, stability in distribution, the least restrictive type of stochastic stability. The nontransient analytical recipes to determine an invariant probability density are available only if the density is stationary and the so-called detailed-balance condition holds. If the invariant density is nonstationary, the recipes are unknown. This is one of the fundamental problems still unsolved in theory of DSPs. The present work proposes a solution of the problem and illustrates the solution with the new results on the Il’in–Has’minski example. The work also discusses the developed recipe in connection with stability in distribution and the uniform boundedness in time, and suggests a few directions for future research in mathematics and biology.
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| 18. |
- Mamontov, Eugen, 1955, et al.
(författare)
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Oncogenic hyperplasia caused by combination of various factors: A decision-support software for radionuclide therapy
- 2007
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Ingår i: Workshop "Mathematical Modelling and Analysis of Cancer Invasion of Tissues", Mar 26, 2007 - Mar 30, 2007, Dundee, Scotland.
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Konferensbidrag (refereegranskat)abstract
- The present work deals with the software based on the PhasTraM model [1] for oncogenic hyperplasia, the first stage of formation of any solid tumor. The work generalizes the related results of [2]-[6] and discusses application of the software for decision support in radionuclide therapy. The software capabilities to allow for combinations of various causes of oncogeny are emphasized. The causes comprise inflammation, immune dysfunction, and chronic psychological stress. The immune dysfunction is represented with hypogammaglobulenimia expressed in terms of the concentration of the immunoglobulin-G molecules. The level of chronic pychological stress is described with the concentration of the interleukin-6 molecules. The work considers how application of the software can support decisions on the specific radionuclide-therapy setting depending on the tissue-, organ-, and patient-specific data. This is illustrated by a number of numerical-simulation results, also the ones which include the effects of common and fractionation-based radionuclide-therapy modalities. A proper attention is paid to how specifically the input data can be prepared by prospective users of the software, i.e. the specialists who apply radionuclide therapy. The work also formulates a few directions for future research in connection with the features of the everyday work of the prospective users. REFERENCES: [1] E. Mamontov, K. Psiuk-Maksymowicz, A. Koptioug, 2006, Stochastic mechanics in the context of the properties of living systems, Mathl Comput. Modelling, 44(7-8) 595-607. [2] E. Mamontov, A. V. Koptioug, K. Psiuk-Maksymowicz, 2006, The minimal, phase-transition model for the cell-number maintenance by the hyperplasia-extended homeorhesis, Acta Biotheoretica, 54(2) 61-101. [3] K. Psiuk-Maksymowicz and E. Mamontov, 2006, The homeorhesis-based modelling and fast numerical analysis for oncogenic hyperplasia under radiotherapy, Mathl Comput. Modelling, Special Issue
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| 19. |
- Mamontov, Eugen, 1955
(författare)
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Ordinary differential equation system for population of individuals and the corresponding probabilistic model
- 2008
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Ingår i: Mathl. Computer Modelling. - : Elsevier BV. - 0895-7177.
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Tidskriftsartikel (refereegranskat)abstract
- The key model for particle populations in statistical mechanics is the Bogolyubov–Born– Green–Kirkwood–Yvon (BBGKY) equation chain. It is derived mainly from the Hamilton ordinary differential equation (ODE) system for the vectors of the particle states in the particle position-momentum phase space. Many problems beyond physics or chemistry, for instance, in the living-matter sciences (biology, medicine, ecology, and scoiology) make it necessary to extend the notion of a particle to an individual, or active particle. This challenge is met by the generalized kinetic theory. It implements the extension by extending the phase space from the space of the position-momentum vectors to more rich spaces formed by the state vectors with the entries which need not be limited to the entries of the position and momentum: they include other scalar variables (e.g., those associated with modelling homeorhesis or other features inherent to the individuals). One can assume that the dynamics of the state vector in the extended space, i.e. the states of the individuals (rather than common particles) is also described by an ODE system. The latter, however, need not be the Hamilton one. The question is how one can derive the analogue of the BBGKY paradigm for the new settings. The present work proposes an answer to this question. It applies a very limited number of carefully selected tools of probability theory and common statistical mechanics. It in particular uses the well-known feature that the maximum number of the individuals which can mutually interact simultaneously is bounded by a fixed value of a few units. The present approach results in the finite system of equations for the reduced many-individual distribution functions thereby eliminating the so-called closure problem inevitable in the BBGKY theory. The thermodynamic-limit assumption is not needed either. The system includes consistently derived terms of all of the basic types known in kinetic theory, in particular, both the “mean-field” and scattering-integral terms, and admits the kinetic equation of the form allowing a direct chemical-reaction reading. The present approach can deal with Hamilton’s equation systems which are nonmonogenic and not treated in statistical mechanics. The proposed modelling suggests the basis of the generalized kinetic theory and may serve as the stochastic mechanics of population of individuals.
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| 20. |
- Mamontov, Eugen, 1955, et al.
(författare)
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Passive acoustic signal sensing approach to detection of ice on the rotor blades of wind turbines
- 2015
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- In cold seasons, irregular layers of atmospheric ice (AI) are usually accreted on the rotor blades of wind turbines. These layers can cause unexpected downtimes and increase the maintenance cost reducing the efficiency. AI presents an unpredictable mixture of crystalline and amorphous ices including such forms as dense snow frozen to the surface, soft rime, hard rime, clear ice, and glaze. The parameters of the AI-layer e.g., the thickness, mass volumetric density, porosity, elastic moduli, viscosities, and stress relaxation time, vary significantly, from a half on order to a few orders, depending on the parameter and type of AI.To solve the icing problem for wind turbines, the ice-detection and de-icing systems are needed. The ice detection systems (IDSs) should not only detect the AI-layer on the blade skin but also provide the data allowing identification of the AI-layer parameters, which are sufficient for the cost-efficient de-icing. The identification method is, thus, in the focus of the IDS development, which deals with the following main features. (1) The operational load in a blade creates irregular space-time distributions of acoustic variable (e.g., strain, stress, and displacement) which depend on the acceleration, deceleration, and speed of rotation of the rotor, the blade-pitch angle, the wind, the presence of the AI layer on the skin, and other factors. The corresponding experimental data are well documented. (2) The blade skin is a layer of a complex, curvilinear shape, which, in the course of the turbine operation, varies in space and time. This feature is also well documented. (3) The AI stress-relaxation time can be in an interval of a few orders. (4) The AI-layer parameters should be identified by means of an appropriate acoustic model from the data of the sensors, which are located on the inner surface of the blade skin and wirelessly controlled in the real-time mode by a computer and gateways. The present work develops an acoustic model and method for identification of four of the AI-layer parameters: the thickness, mass density, bulk-wave speed, and stress-relaxation time. Due to Point (1), the identification method presumes passive rather than active sensing. The method is based on measurements of the acoustic accelerations at different points on the inner surface of the skin. The challenge in Point (2) is met by the generalizing the thin-planar-disk approximation from a single solid layer to the system of the blade-skin/AI layers. The proposed identification method is computationally efficient and suitable for the use indicated in Point (4). It extends the scope of the structural health monitoring techniques.
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| 21. |
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| 22. |
- Mamontov, Eugen, 1955, et al.
(författare)
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Stochastic mechanics in the context of the properties of living systems
- 2006
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Ingår i: Mathl Comput. Modelling. - : Elsevier BV. - 0895-7177 .- 1872-9479. ; 44:7-8, s. 595-607
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Tidskriftsartikel (refereegranskat)abstract
- Many features of living systems prevent the application of fundamental statistical mechanics (FSM) to study such systems. The present work focuses on some of these features. After discussing all the basic approaches of FSM, the work formulates an extension of the kinetic theory paradigm (based on the reduced one-particle distribution function) that exhibits all of the living-system properties considered. This extension appears to be a model within the generalized kinetic theory developed by N. Bellomo and his co-authors. In connection with this model, the work also stresses some other features necessary for making the model relevant to living systems. A mathematical formulation of homeorhesis is also derived. An example discussed in the work is a generalized kinetic equation coupled with a probability-density equation representing the varying component content of a living system. The work also suggests a few directions for future research. [All rights reserved Elsevier]
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| 23. |
- Mamontov, Eugen, 1955, et al.
(författare)
-
The minimal, phase-transition model for the cell-number maintenance by the hyperplasia-extended homeorhesis
- 2006
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Ingår i: Acta Biotheoretica. - : Springer Science and Business Media LLC. - 0001-5342 .- 1572-8358. ; 54:2, s. 61-101
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Tidskriftsartikel (refereegranskat)abstract
- Oncogenic hyperplasia is the first and inevitable stage of formation of a (solid) tumor. This stage is also the core of many other proliferative diseases. The present work proposes the first minimal model that combines homeorhesis with oncogenic hyperplasia where the latter is regarded as a genotoxically activated homeorhetic dysfunction. This dysfunction is specified as the transitions of the fluid of cells from a fluid, homeorhetic state to a solid, hyperplastic-tumor state, and back. The key part of the model is a nonlinear reaction-diffusion equation (RDE) where the biochemical-reaction rate is generalized to the one in the well-known Schlögl physical theory of the non-equilibrium phase transitions. A rigorous analysis of the stability and qualitative aspects of the model, where possible, are presented in detail. This is related to the spatially homogeneous case, i.e. when the above RDE is reduced to a nonlinear ordinary differential equation. The mentioned genotoxic activation is treated as a prevention of the quiescent G0-stage of the cell cycle implemented with the threshold mechanism that employs the critical concentration of the cellular fluid and the nonquiescent-cell-duplication time. The continuous tumor morphogeny is described by a time-space-dependent cellular-fluid concentration. There are no sharp boundaries (i.e. no concentration jumps exist) between the domains of the homeorhesis- and tumor-cell populations. No presumption on the shape of a tumor is used. To estimate a tumor in specific quantities, the model provides the time-dependent tumor locus, volume, and boundary that also points out the tumor shape and size. The above features are indispensable in the quantitative development of antiproliferative drugs or therapies and strategies to prevent oncogenic hyperplasia in cancer and other proliferative diseases. The work proposes an analytical-numerical method for solving the aforementioned RDE. A few topics for future research are suggested.
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| 24. |
- Mamontov, Eugen, 1955, et al.
(författare)
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The nonzero minimum of the diffusion parameter and the uncertainty principle for a Brownian particle
- 2002
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Ingår i: Modern physics letters B. - : World Scientific. - 0217-9849. ; 16:13, s. 467-471
-
Tidskriftsartikel (refereegranskat)abstract
- The limits of applicability of many classical (non-quantum-mechanical) theories are not sharp. These theories axe sometimes applied to the problems which axe, in their nature, not very well suited for that. Two of the most widely used classical approaches are the theory of diffusion stochastic process and Itos stochastic differential equations. It includes the Brownian-motion treatment as the basic particular case. The present work shows that, for quantum-mechanical reasons, the diffusion parameter of a Brownian paxticle cannot be arbitrarily small since it has a nonzero minimum value. This fact leads to the version of Heisenbergs uncertainty principle for a Brownian particle which is obtained in the precise mathematical form of a limit inequality. These quantitative results can help to,properly apply the theories associated with Brownian-particle modelling. The consideration also discusses a series of works of other authors.
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| 25. |
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| 26. |
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| 27. |
- Mamontov, Eugen, 1955, et al.
(författare)
-
What stochastic mechanics are relevant to the study of living systems?
- 2005
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Ingår i: Proceedings of the Latvian Academy of Sciences. Section B: Natural, Exact and Applied Sciences. - Riga, Latvia : Latvian Academy of Sciences. - 1407-009X. ; 59:6, s. 255-262
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Tidskriftsartikel (refereegranskat)abstract
- Biologists have identified many features of living systems which cannot be studied by application of fundamental statistical mechanics (FSM). The present work focuses on some of these features. By discussing all the basic approaches of FSM, the work formulates the extension of the kinetic-theory paradigm (based on the reduced one-particle distribution function) that possesses all the considered properties of the living systems. This extension appears to be a model within the generalized-kinetic theory developed by N. Bellomo and his co-authors. In connection with this model, the work also stresses some other features necessary for making the model relevant to living systems. An example is discussed, which is a generalized kinetic equation coupled with the probability-density equation which represents the varying component content of a living system. The work also suggests directions for future research.
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| 28. |
- Naess, A., et al.
(författare)
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The physical, gain-loss model for the stochasticity of the phase velocity of a wind-driven water wave
- 2012
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Ingår i: Mathematical and Computer Modelling. - : Elsevier BV. - 0895-7177. ; 55:3-4, s. 740-745
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Tidskriftsartikel (refereegranskat)abstract
- Mathematical-model study of the behavior of a ship in an irregular sea (e.g., the roll motion) includes an analysis of the particular case where the stochastic wind-driven wave is a plane wave, i.e. the wave traveling in one spatial direction. The stochasticity of a wind-driven wave is solely due to the stochasticity of wind. By using the basic physical facts on the water-surface/wind interaction, more specifically, the rates of the gain and loss of the wave energy, the present work derives a dynamical model for the phase velocity of a water wave. The model is a linear ordinary differential equation for the cubed phase velocity. This equation which includes the velocity of wind becomes stochastic when the wind is a stochastic process, for example, is described by the first-order ItÔ's stochastic differential equation (ISDE). In this case, the water-wave phase velocity appears to be a solution of the second-order ISDE. The derivation of the model implies an analytical relation which explicitly couples the parameters "alpha" and "beta" of the well-known Pierson-Moskowitz spectral function. It is shown that the derived relation agrees well with the experimentally obtained values of the parameters. The derived model can be used not only in models for the ship dynamics in a stochastic sea but also in a number of other ocean problems where the prediction of water waves by mere measurement of the wind is an advantage. These problems in particular include the real-time control of the stochastic water load on the ocean structures by sensing the stochastic wind rather than sensing stochastic waves thereby creating an alternative to more complex and expensive methods. © 2011 Elsevier Ltd.
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| 29. |
- Piotrowska, Monika, 1979, et al.
(författare)
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A model and simulation for homeorhesis in the motion of a single individual
- 2008
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Ingår i: Mathematical and Computer Modelling. - : Elsevier BV. - 0895-7177 .- 1872-9479. ; 48:7-8, s. 1122-1143
-
Tidskriftsartikel (refereegranskat)abstract
- In contrast to nonliving systems, all living systems perform homeorhesis. The system state tends to the so-called necessary path, or creode, when the exogenous signals are in a certain system-relevant range. The present work develops the homeorhesis-aware dynamical model for the motion of a single individual (e.g., human). The model allows for the purposeful behaviour of the individual, the creode, the exogenous forces, and the individual-specific sensitivity to their influences. The model also describes the homeorhetic-dysfunction movements. The transparency of the model is such that it allows a physical analogue in the form of electronic circuits. The model is a first step towards the construction of sociologically relevant models for the prediction of human behaviour. It is indispensable for analyses of dangerous scenarios where experiments are impossible, for example when predicting the behaviour of panic-stricken crowds in life-threatening situations. The work illustrates the corresponding numerical-simulation results with a series of figures and suggests topics for future research.
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| 30. |
- Psiuk-Maksymowicz, Krzysztof, 1980, et al.
(författare)
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Homeorhesis-based modelling and fast numerical analysis for oncogenic hyperplasia under radiotherapy
- 2008
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Ingår i: Mathl Comput. Modelling. - : Elsevier BV. - 0895-7177. ; 47:5-6, s. 580-596
-
Tidskriftsartikel (refereegranskat)abstract
- A few previous works of the authors derived and discussed the space–time mathematical description, the PhasTraM model, for oncogenic hyperplasia regarded as a genotoxically activated homeorhetic dysfunction. The model is based on the fluid-to-solid-and-back transitions and nonlinear reaction–diffusion equations relevant to a series of the key biomedical facts, and some distinguishing features of living systems. The first computer-simulation results have also been reported. The present work generalizes the PhasTraM model for the effect of radiation therapies (RTs), both external and internal. The resulting model also includes the autocrine mechanism promoting oncogenic hyperplasia and the suppression of this process by certain drugs. The autocrine signalling is implemented by the transforming-growth-factor-α (TGF-α) molecules released by the cells and bound to the epidermal-growth-factor receptors (EGFRs) at the cell surface. The suppression can be carried out by a drug deactivating the mentioned molecules. The work also presents and discusses examples of the computer-simulation results for four different settings of the applied RT. A few directions for future research, as well as prospective applications of the model and developed software, are also discussed.
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| 31. |
- Willander, Magnus, 1948, et al.
(författare)
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Modelling living fluids with the subdivision into the components in terms of probability distributions
- 2004
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Ingår i: Math. Models Methods Appl. Sci.. - : World Scientific. - 0218-2025. ; 14:10, s. 1495-1520
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Tidskriftsartikel (refereegranskat)abstract
- As it follows from the results of C. H. Waddigton, F. E. Yates, A. S. Iberall, and other well-known bio-physicists, living fluids cannot be modelled within the frames of the fundamental assumptions of the statistical-mechanics formalism. One has to go beyond them. The present work does it by means of the generalized kinetics (GK), the theory enabling one to allow for the complex stochasticity of internal properties and parameters of the fluid particles. This is one of the key features which distinguish living fluids from the nonliving ones. It creates the disparity of the particles and hence breaks the each-fluid-component-uniformity requirement underlying statistical mechanics. The work deals with the corresponding modification of common kinetic equations which is in line with the GK theory and is the complement to the latter. This complement allows a subdivision of a fluid into the fluid components in terms of nondiscrete probability distributions. The treatment leads to one more equationthat describes the above internal parameters. The resulting model is the system of these two equations. It appears to be always nonlinear in case of living fluids. In case of nonliving fluids, the model can be linear. Moreover, the living-fluid model, as a whole, cannot have the thermodynamic equilibrium, only partial equilibriums (such as the motional one) are possible. In contrast to this, in case of nonliving fluids, the thermodynamic equilibrium is, of course, possible. The number of the fluid components is treated as the number of the modes of the particle-characteristic probability density. In so doing, a fairly general extension of the notion of the mode from the one-dimensional case to the multidimensional case is proposed. The work also discusses the variety of the time-scales in a living fluid, the simplest quantum-mechanical equation relevant to living fluids, and the non-equilibrium nonlinear stochastic hydrodynamics option. The latter is simpler than, but conceptually comparable to, stochastickinetic equations. A few directions for future research are suggested. The work notes a cohesion of mathematical physics and fluid mechanics with the living-fluid-related fields as a complex interdisciplinary problem.
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