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- 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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| 3. |
- Jiao, Yang, 1985, et al.
(författare)
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Signatures of van der Waals binding: A coupling-constant scaling analysis
- 2018
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Ingår i: Physical Review B. - 2469-9969 .- 2469-9950. ; 97:8
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Tidskriftsartikel (refereegranskat)abstract
- The van der Waals (vdW) density functional (vdW-DF) method [Rep. Prog. Phys. 78, 066501 (2015)RPPHAG0034-488510.1088/0034-4885/78/6/066501] describes dispersion or vdW binding by tracking the effects of an electrodynamic coupling among pairs of electrons and their associated exchange-correlation holes. This is done in a nonlocal-correlation energy term Ecnl, which permits density functional theory calculation in the Kohn-Sham scheme. However, to map the nature of vdW forces in a fully interacting materials system, it is necessary to also account for associated kinetic-correlation energy effects. Here, we present a coupling-constant scaling analysis, which permits us to compute the kinetic-correlation energy Tcnl that is specific to the vdW-DF account of nonlocal correlations. We thus provide a more complete spatially resolved analysis of the electrodynamical-coupling nature of nonlocal-correlation binding, including vdW attraction, in both covalently and noncovalently bonded systems. We find that kinetic-correlation energy effects play a significant role in the account of vdW or dispersion interactions among molecules. Furthermore, our mapping shows that the total nonlocal-correlation binding is concentrated to pockets in the sparse electron distribution located between the material fragments.
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| 6. |
- Baggioli, Matteo, et al.
(författare)
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Holographic plasmon relaxation with and without broken translations
- 2019
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Ingår i: Journal of High Energy Physics (JHEP). - : SPRINGER. - 1126-6708 .- 1029-8479. ; :9
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Tidskriftsartikel (refereegranskat)abstract
- We study the dynamics and the relaxation of bulk plasmons in strongly coupled and quantum critical systems using the holographic framework. We analyze the dispersion relation of the plasmonic modes in detail for an illustrative class of holographic bottom-up models. Comparing to a simple hydrodynamic formula, we entangle the complicated interplay between the three least damped modes and shed light on the underlying physical processes. Such as the dependence of the plasma frequency and the effective relaxation time in terms of the electromagnetic coupling, the charge and the temperature of the system. Introducing momentum dissipation, we then identify its additional contribution to the damping. Finally, we consider the spontaneous symmetry breaking (SSB) of translational invariance. Upon dialing the strength of the SSB, we observe an increase of the longitudinal sound speed controlled by the elastic moduli and a decrease in the plasma frequency of the gapped plasmon. We comment on the condensed matter interpretation of this mechanism.
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| 7. |
- Görnerup, Olof, 1977
(författare)
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Inference of Hierarchical Structure in Complex Systems
- 2008
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Hierarchical organization is a central property of complex systems. It is even argued that a system is required to be hierarchical in order to evolve complexity within reasonable time. A hierarchy of a system is defined as the set of self-contained levels at which the system operates and can be described on. Given a dynamical system there are only specific levels that are valid. This thesis mainly concerns the definition and inference of such levels. Paper I describes an algorithm for finding hierarchical levels in stochastic processes. The method systematically explores the set of possible partitions of a process' state space and statistically determines which of the partitions that impose closed dynamics. It is applicable to moderately sized systems. In Paper II an alternative approach that applies to linear dynamical systems is presented. In this case the spectral properties of the matrix that defines a system's dynamics is utilized, which allows for analysis of large systems (with on the order of thousand states). The specification and analysis of an algorithm that is based on the results in Paper II is presented in Paper III. Paper IV applies the spectral method and a complementary agglomeration method to infer aggregated dynamics in a Markov model of codon substitutions in DNA. The standard genetic code is identified as a projection that gives the hierarchical level of amino acid substitutions. Further, higher order amino acid groups that are relatively conserved under substitutions are found to define other levels of dynamics. Paper V and VI relate hierarchical organization to primordial evolution in a conceptual model that is based on the RNA world hypothesis. A well-stirred system of processes that catalyze the production of other processes is shown to successively build higher levels of organization from simple and general-purpose components by autocatalysis.
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| 8. |
- Sun, Bing, et al.
(författare)
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Ion transport in polycarbonate based solid polymer electrolytes : experimental and computational investigations
- 2016
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Ingår i: Physical Chemistry, Chemical Physics - PCCP. - : Royal Society of Chemistry (RSC). - 1463-9076 .- 1463-9084. ; 18:14, s. 9504-9513
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Tidskriftsartikel (refereegranskat)abstract
- Among the alternative host materials for solid polymer electrolytes (SPEs), polycarbonates have recently shown promising functionality in all-solid-state lithium batteries from ambient to elevated temperatures. While the computational and experimental investigations of ion conduction in conventional polyethers have been extensive, the ion transport in polycarbonates has been much less studied. The present work investigates the ionic transport behavior in SPEs based on poly(trimethylene carbonate) (PTMC) and its co-polymer with epsilon-caprolactone (CL) via both experimental and computational approaches. FTIR spectra indicated a preferential local coordination between Li+ and ester carbonyl oxygen atoms in the P(TMC20CL80) co-polymer SPE. Diffusion NMR revealed that the co-polymer SPE also displays higher ion mobilities than PTMC. For both systems, locally oriented polymer domains, a few hundred nanometers in size and with limited connections between them, were inferred from the NMR spin relaxation and diffusion data. Potentiostatic polarization experiments revealed notably higher cationic transference numbers in the polycarbonate based SPEs as compared to conventional polyether based SPEs. In addition, MD simulations provided atomic-scale insight into the structure-dynamics properties, including confirmation of a preferential Li+-carbonyl oxygen atom coordination, with a preference in coordination to the ester based monomers. A coupling of the Li-ion dynamics to the polymer chain dynamics was indicated by both simulations and experiments.
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| 9. |
- Alizadehheidari, Mohammadreza, 1987, et al.
(författare)
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Nanoconfined Circular and Linear DNA: Equilibrium Conformations and Unfolding Kinetics
- 2015
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Ingår i: Macromolecules. - : American Chemical Society (ACS). - 0024-9297 .- 1520-5835. ; 48:3, s. 871-878
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Tidskriftsartikel (refereegranskat)abstract
- Studies of circular DNA confined to nanofluidic channels are relevant both from a fundamental polymer-physics perspective and due to the importance of circular DNA molecules in vivo. We here observe the unfolding of confined DNA from the circular to linear configuration as a light-induced double-strand break occurs, characterize the dynamics, and compare the equilibrium conformational statistics of linear and circular configurations. This is important because it allows us to determine to what extent existing statistical theories describe the extension of confined circular DNA. We find that the ratio of the extensions of confined linear and circular DNA configurations increases as the buffer concentration decreases. The experimental results fall between theoretical predictions for the extended de Gennes regime at weaker confinement and the Odijk regime at stronger confinement. We show that it is possible to directly distinguish between circular and linear DNA molecules by measuring the emission intensity from the DNA. Finally, we determine the rate of unfolding and show that this rate is larger for more confined DNA, possibly reflecting the corresponding larger difference in entropy between the circular and linear configurations.
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| 10. |
- Thiele, Illia, 1989, et al.
(författare)
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Electron Beam Driven Generation of Frequency-Tunable Isolated Relativistic Subcycle Pulses
- 2019
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Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 122
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Tidskriftsartikel (refereegranskat)abstract
- © 2019 American Physical Society. We propose a novel scheme for frequency-tunable subcycle electromagnetic pulse generation. To this end a pump electron beam is injected into an electromagnetic seed pulse as the latter is reflected by a mirror. The electron beam is shown to be able to amplify the field of the seed pulse while upshifting its central frequency and reducing its number of cycles. We demonstrate the amplification by means of 1D and 2D particle-in-cell simulations. In order to explain and optimize the process, a model based on fluid theory is proposed. We estimate that using currently available electron beams and terahertz pulse sources, our scheme is able to produce millijoule-strong midinfrared subcycle pulses.
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