| 1. |
- Bernhoff, Niclas, 1971-
(författare)
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Discrete Velocity Models for Polyatomic Molecules Without Nonphysical Collision Invariants
- 2018
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Ingår i: Journal of statistical physics. - New York : Springer. - 0022-4715 .- 1572-9613. ; 172:3, s. 742-761
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Tidskriftsartikel (refereegranskat)abstract
- An important aspect of constructing discrete velocity models (DVMs) for the Boltzmann equation is to obtain the right number of collision invariants. Unlike for the Boltzmann equation, for DVMs there can appear extra collision invariants, so called spurious collision invariants, in plus to the physical ones. A DVM with only physical collision invariants, and hence, without spurious ones, is called normal. The construction of such normal DVMs has been studied a lot in the literature for single species, but also for binary mixtures and recently extensively for multicomponent mixtures. In this paper, we address ways of constructing normal DVMs for polyatomic molecules (here represented by that each molecule has an internal energy, to account for non-translational energies, which can change during collisions), under the assumption that the set of allowed internal energies are finite. We present general algorithms for constructing such models, but we also give concrete examples of such constructions. This approach can also be combined with similar constructions of multicomponent mixtures to obtain multicomponent mixtures with polyatomic molecules, which is also briefly outlined. Then also, chemical reactions can be added.
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| 2. |
- Kavallaris, Nikos I., et al.
(författare)
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On the impact of noise on quenching for a nonlocal diffusion model driven by a mixture of Brownian and fractional Brownian motions
- 2024
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Ingår i: Discrete and Continuous Dynamical Systems. Series S. - : American Institute of Mathematical Sciences. - 1937-1632 .- 1937-1179. ; 17:3, s. 1222-1268
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we study a stochastic parabolic problem involving anonlocal diffusion operator associated with nonlocal Robin-type boundary conditions. The stochastic dynamics under consideration is driven by a mixtureof a classical Brownian and a fractional Brownian motion with Hurst indexH ∈ (1/2, 1). We first establish local in time existence results and then exploreconditions under which the resulting SPDE exhibits finite-time quenching. Using results on the probability distribution of perpetual integral functionals ofBrownian motion as well as tail estimates for the fractional Brownian motionwe provide analytic estimates for certain quantities of interest, such as upperbounds for quenching times and the corresponding quenching probabilities.The existence of global in time solutions is also investigated and as a consequence a lower estimate of the quenching time is also derived. Our analyticalresults demonstrate the non-trivial impact of the noise on the dynamics ofthe system. The analytic results are complemented with a detailed numericalstudy of the model under Dirichlet boundary conditions. A possible application concerning MEMS technology is considered and the implications of theresults in this context are commented upon.
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| 3. |
- Araujo-Cabarcas, Juan Carlos, 1981-, et al.
(författare)
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Shape optimization for the strong directional scattering of dielectric nanorods
- 2021
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Ingår i: International Journal for Numerical Methods in Engineering. - : John Wiley & Sons. - 0029-5981 .- 1097-0207. ; 122:8, s. 3683-3704
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Tidskriftsartikel (refereegranskat)abstract
- In this project, we consider the shape optimization of a dielectric scatterer aiming at efficient directional routing of light. In the studied setting, light interacts with a penetrable scatterer with dimension comparable to the wavelength of an incoming planar wave. The design objective is to maximize the scattering efficiency inside a target angle window. For this, a Helmholtz problem with a piecewise constant refractive index medium models the wave propagation, and an accurate Dirichlet-to-Neumann map models an exterior domain. The strategy consists of using a high-order finite element (FE) discretization combined with gradient-based numerical optimization. The latter consists of a quasi-Newton (BFGS) with backtracking line search. A discrete adjoint method is used to compute the sensitivities with respect to the design variables. Particularly, for the FE representation of the curved shape, we use a bilinear transfinite interpolation formula, which admits explicit differentiation with respect to the design variables. We exploit this fact and show in detail how sensitivities are obtained in the discrete setting. We test our strategy for a variety of target angles, different wave frequencies, and refractive indexes. In all cases, we efficiently reach designs featuring high scattering efficiencies that satisfy the required criteria.
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| 4. |
- Araujo-Cabarcas, Juan Carlos, 1981-, et al.
(författare)
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Shape optimization for the strong routing of light in periodic diffraction gratings
- 2023
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Ingår i: Journal of Computational Physics. - : Elsevier. - 0021-9991 .- 1090-2716. ; 472
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Tidskriftsartikel (refereegranskat)abstract
- In the quest for the development of faster and more reliable technologies, the ability to control the propagation, confinement, and emission of light has become crucial. The design of guide mode resonators and perfect absorbers has proven to be of fundamental importance. In this project, we consider the shape optimization of a periodic dielectric slab aiming at efficient directional routing of light to reproduce similar features of a guide mode resonator. For this, the design objective is to maximize the routing efficiency of an incoming wave. That is, the goal is to promote wave propagation along the periodic slab. A Helmholtz problem with a piecewise constant and periodic refractive index medium models the wave propagation, and an accurate Robin-to-Robin map models an exterior domain. We propose an optimal design strategy that consists of representing the dielectric interface by a finite Fourier formula and using its coefficients as the design variables. Moreover, we use a high order finite element (FE) discretization combined with a bilinear Transfinite Interpolation formula. This setting admits explicit differentiation with respect to the design variables, from where an exact discrete adjoint method computes the sensitivities. We show in detail how the sensitivities are obtained in the quasi-periodic discrete setting. The design strategy employs gradient-based numerical optimization, which consists of a BFGS quasi-Newton method with backtracking line search. As a test case example, we present results for the optimization of a so-called single port perfect absorber. We test our strategy for a variety of incoming wave angles and different polarizations. In all cases, we efficiently reach designs featuring high routing efficiencies that satisfy the required criteria.
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| 5. |
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| 6. |
- Mousavi, Abbas, et al.
(författare)
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How the waveguide acoustic black hole works: A study of possible damping mechanisms
- 2022
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Ingår i: Journal of the Acoustical Society of America. - : Acoustical Society of America (ASA). - 0001-4966 .- 1520-8524. ; 151:6, s. 4279-4290
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Tidskriftsartikel (refereegranskat)abstract
- The acoustic black hole (ABH) effect in waveguides is studied using frequency-domain finite element simulations of a cylindrical waveguide with an embedded ABH termination composed of retarding rings. This design is adopted from an experimental study in the literature, which surprisingly showed, contrary to the structural counterpart, that the addition of damping material to the end of the waveguide does not significantly reduce the reflection coefficient any further. To investigate this unexpected behavior, we model different damping mechanisms involved in the attenuation of sound waves in this setup. A sequence of computed pressure distributions indicates occurrences of frequency-dependent resonances in the device. The axial position of the cavity where the resonance occurs can be predicted by a more elaborate wall admittance model than the one that was initially used to study and design ABHs. The results of our simulations show that at higher frequencies, the visco-thermal losses and the damping material added to the end of the setup do not contribute significantly to the performance of the device. Our results suggest that the primary source of damping, responsible for the low reflection coefficients at higher frequencies, is local absorption effects at the outer surface of the cylinder.
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| 7. |
- Nepal, Surendra
(författare)
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Models for capturing the penetration of a diffusant concentration into rubber : Numerical analysis and simulation
- 2024
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Understanding the transport of diffusants into rubber plays an important role in forecasting the material's durability. In this regard, we study different models, conduct numerical analysis, and present simulation results that predict the evolution of the penetration front of diffusants.We start with a moving-boundary approach to model this phenomenon, employing a numerical scheme to approximate the diffusant profile and the position of the moving boundary capturing the penetration front. Our numerical scheme utilizes the Galerkin finite element method for space discretization and the backward Euler method for time discretization. We analyze both semi-discrete and fully discrete approximations of the weak solution to the model equations, proving error estimates and demonstrating good agreement between numerical and theoretical convergence rates. Numerically approximated penetration front of the diffusant recovers well the experimental data. As an alternative approach to finite element approximation, we introduce a random walk algorithm that employs a finite number of particles to approximate both the diffusant profile and the location of the penetration front. The transport of diffusants is due to unbiased randomness, while the evolution of the penetration front is based on biased randomness. Simulation results obtained via the random walk approach are comparable with the one based on the finite element method.In a multi-dimensional scenario, we consider a strongly coupled elliptic-parabolic two-scale system with nonlinear dispersion that describes particle transport in porous media. We construct two numerical schemes approximating the weak solution to the two-scale model equations. We present simulation results obtained with both schemes and compare them based on computational time and approximation errors in suitable norms. By introducing a precomputing strategy, the computational time for both schemes is significantly improved.
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| 8. |
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| 9. |
- Kotik, Nikolai, 1971-
(författare)
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Solution to boundary-contact problems of elasticity in mathematical models of the printing-plate contact system for flexographic printing
- 2007
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Boundary-contact problems (BCPs) are studied within the frames ofclassical mathematical theory of elasticity and plasticityelaborated by Landau, Kupradze, Timoshenko, Goodier, Fichera andmany others on the basis of analysis of two- and three-dimensionalboundary value problems for linear partial differential equations.A great attention is traditionally paid both to theoreticalinvestigations using variational methods and boundary singularintegral equations (Muskhelishvili) and construction of solutionsin the form that admit efficient numerical evaluation (Kupradze).A special family of BCPs considered by Shtaerman, Vorovich,Alblas, Nowell, and others arises within the frames of the modelsof squeezing thin multilayer elastic sheets. We show thatmathematical models based on the analysis of BCPs can be alsoapplied to modeling of the clich\'{e}-surface printing contactsand paper surface compressibility in flexographic printing.The main result of this work is formulation and completeinvestigation of BCPs in layered structures, which includes boththe theoretical (statement of the problems, solvability anduniqueness) and applied parts (approximate and numericalsolutions, codes, simulation).We elaborate a mathematical model of squeezing a thin elasticsheet placed on a stiff base without friction by weak loadsthrough several openings on one of its boundary surfaces. Weformulate and consider the corresponding BCPs in two- andthree-dimensional bands, prove the existence and uniqueness ofsolutions, and investigate their smoothness including the behaviorat infinity and in the vicinity of critical points. The BCP in atwo-dimensional band is reduced to a Fredholm integral equation(IE) with a logarithmic singularity of the kernel. The theory oflogarithmic IEs developed in the study includes the analysis ofsolvability and development of solution techniques when the set ofintegration consists of several intervals. The IE associated withthe BCP is solved by three methods based on the use ofFourier-Chebyshev series, matrix-algebraic determination of theentries in the resulting infinite system matrix, andsemi-inversion. An asymptotic theory for the BCP is developed andthe solutions are obtained as asymptotic series in powers of thecharacteristic small parameter.We propose and justify a technique for the solution of BCPs andboundary value problems with boundary conditions of mixed typecalled the approximate decomposition method (ADM). The main ideaof ADM is simplifying general BCPs and reducing them to a chainof auxiliary problems for 'shifted' Laplacian in long rectanglesor parallelepipeds and then to a sequence of iterative problemssuch that each of them can be solved (explicitly) by the Fouriermethod. The solution to the initial BCP is then obtained as alimit using a contraction operator, which constitutes inparticular an independent proof of the BCP unique solvability.We elaborate a numerical method and algorithms based on theapproximate decomposition and the computer codes and performcomprehensive numerical analysis of the BCPs including thesimulation for problems of practical interest. A variety ofcomputational results are presented and discussed which form thebasis for further applications for the modeling and simulation ofprinting-plate contact systems and other structures offlexographic printing. A comparison with finite-element solutionis performed.
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