arXiv subjects

F. E. Garbuzov

Publications and source records attributed to F. E. Garbuzov.

7 recordsLinked to original sources

arXiv2026

Nonlinear dynamic elastic moduli from equilibrium stress fluctuations

Fluctuation formulas for elastic and viscoelastic moduli allow their computation from equilibrium molecular dynamics simulations, avoiding explicit nonequilibrium deformation protocols. While such expressions are well established for the quasi-static moduli, and also the linear dynamic moduli, no fluctuation formula exists for the nonlinear time-dependent moduli that govern anharmonic viscoelastic response under finite time-dependent strains. In this work we derive transient-time correlation function expressions for both the linear and the nonlinear dynamic moduli, starting from the DOLLS/SLLOD equations of motion for irrotational motion. The resulting formulas involve equilibrium time correlations of the stress tensor and Born-kinetic terms, and they recover the known quasi-static and linear dynamic results in the appropriate limits.

cond-mat.mtrl-sci↗

arXiv2025

Slowly decaying strain solitons in nonlinear viscoelastic waveguides

This paper is devoted to the modeling of longitudinal strain waves in a rod composed of a nonlinear viscoelastic material characterized by frequency-dependent second- and third-order elastic constants. We demonstrate that long waves in such a material can be effectively described by a damped Boussinesq-type equation for the longitudinal strain, incorporating dissipation through retarded operators. Using the existing theory of solitary wave solutions in nearly integrable systems, we derive a slowly-decaying strain soliton solution to this equation. The derived soliton characteristics are shown to be in a good agreement with results from full 3D simulations. We demonstrate the importance of taking into account the frequency dependence of third-order elastic constants for the description of strain solitons.

nlin.PS↗

arXiv2024

Generalization of nonlinear Murnaghan elastic model for viscoelastic materials

This paper presents a generalization of Murnaghan elastic material to viscoelastic behavior using the Green-Rivlin multiple-integral approach. In the linear limit, the model coincides with the generalized Maxwell model. To create a nonlinear generalization, all possible second-order corrections were included in the constitutive equations written in the internal strains representation. Using this approach, we obtained expressions for the time- and frequency-dependent nonlinear dynamic moduli. We applied the developed nonlinear viscoelastic model to the description of infinitesimal strain waves superposed on finite prestrain. Furthermore, we considered the generation of higher harmonic by the nonlinear interaction of two strain waves, which we showed can provide a method to measure all viscoelastic constants of the developed model.

cond-mat.soft↗

arXiv2022

Shock Wave Evolution into Strain Solitary Wave in Nonlinearly Elastic Solid Bar

In this paper we present thorough experimental observation of the process of shock wave transformation into a bulk strain solitary wave in a nonlinearly elastic solid bar made of polystyrene. A theoretical model based on the describing propagation of a plane elastic wave in a bar is developed with account made for material nonlinearity and viscosity. Numerical modeling performed on the base of the developed model with and without regard to viscosity demonstrated formation of a long stable disturbance at proper account made for viscoelastic properties of the bar material.

cond-mat.mtrl-sci↗

arXiv2022

Nonequilibrium model of short-range repression in gene transcription regulation

Transcription factors are proteins that regulate gene activity by activating or repressing gene transcription. A special class of transcriptional repressors operates via a short-range mechanism, making local DNA regions inaccessible to binding by activators, and thus providing an indirect repressive action on the target gene. This mechanism is commonly modeled assuming that repressors interact with DNA under thermodynamic equilibrium and neglecting some configurations of the gene regulatory region. We elaborate on a more general nonequilibrium model of short-range repression using the graph formalism for transitions between gene states, and we apply analytical calculations to compare it with the equilibrium model in terms of the repression strength and expression noise. In contrast to the equilibrium approach, the new model allows us to separate two basic mechanisms of short-range repression. The first mechanism is associated with the recruiting of factors that mediate chromatin condensation, and the second one concerns the blocking of factors that mediate chromatin loosening. The nonequilibrium model demonstrates better performance on previously published gene expression data obtained for transcription factors controlling Drosophila development, and furthermore it predicts that the first repression mechanism is the most favorable in this system. The presented approach can be scaled to larger gene networks and can be used to infer specific modes and parameters of transcriptional regulation from gene expression data.

q-bio.MN↗

arXiv2021

Longitudinal bulk strain solitons in a hyperelastic rod with quadratic and cubic nonlinearities

We study long nonlinear longitudinal bulk strain waves in a hyperelastic rod of circular cross section within the scope of the general weakly-nonlinear elasticity leading to a model with quadratic and cubic nonlinearities. We systematically derive the extended Boussinesq and Korteweg - de Vries - type equations and construct a family of approximate weakly-nonlinear soliton solutions with the help of near-identity transformations. These solutions are compared with the results of direct numerical simulations of the original nonlinear problem formulation, showing excellent agreement within the range of their asymptotic validity (waves of small amplitude) and extending their relevance beyond it (to the waves of moderate amplitude) as a very good initial guess. In particular, we were able to observe a stably propagating "table-top" soliton..

nlin.PS↗

arXiv2019

On Boussinesq-type models for long longitudinal waves in elastic rods

In this paper we revisit the derivations of model equations describing long nonlinear longitudinal bulk strain waves in elastic rods within the scope of the Murnaghan model in order to derive a Boussinesq-type model, and extend these derivations to include axially symmetric loading on the lateral boundary surface, and longitudinal pre-stretch. We systematically derive two forced Boussinesq-type models from the full equations of motion and non-zero surface boundary conditions, utilising the presence of two small parameters characterising the smallness of the wave amplitude and the long wavelength compared to the radius of the waveguide. We compare the basic dynamical properties of both models (linear dispersion curves and solitary wave solutions). We also briefly describe the laboratory experiments on generation of bulk strain solitary waves in the Ioffe Institute, and suggest that this generation process can be modelled using the derived equations.

nlin.PS↗