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Nonclassical Linear Theories of Continuum Mechanics
We present a brief survey of nonclassical linear theories of continuum mechanics. Thus, we give a concise characterization of the Eringen–Edelen...
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Density Functional Kinetic Theory for Soft Matter
In the last decades kinetic theory has developed into a very elegant and effective framework to handle a broad spectrum of problems involving complex...
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A Geometric Field Theory of Dislocation Mechanics
In this paper, a geometric field theory of dislocation dynamics and finite plasticity in single crystals is formulated. Starting from the...
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Toward local Madelung mechanics in spacetime
It has recently been shown that relativistic quantum theory leads to a local interpretation of quantum mechanics wherein the universal wavefunction...
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Quantum mechanics, radiation, and the equivalence proof
This paper re-evaluates the formative year of quantum mechanics—from Heisenberg’s first paper on matrix mechanics to Schrödinger’s equivalence...
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Modeling Problems of Dynamics and Development of Scientific Areas of Mechanics and Applied Mathematics
AbstractThe paper discusses the development of scientific areas of mechanics in the research by the honorary professor of St. Petersburg State...
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General Relativistic Lagrangian Continuum Theories Part I: Reduced Variational Principles and Junction Conditions for Hydrodynamics and Elasticity
We establish a Lagrangian variational framework for general relativistic continuum theories that permits the development of the process of Lagrangian...
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Introduction to Rigid Body Mechanics
The goal of this chapter is to introduce students to the rudiments of the theory of rigid bodies. Rigid bodies, sometimes also called solid bodies,...
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The turbulence theory of P. Wehrlé and G. Dedebant (1934–1948): a forgotten probabilistic approach?
The development of the statistical theory of turbulence mainly take places between 1920 and 1940, in a context where emerging theories in fluid...
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Balance Equations and First Integrals in Mechanics
The aim of this chapter is to introduce certain physical quantities relative to point-particle systems entering particular “balance equations” and...
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Advanced Topics in Lagrangian Mechanics
In this chapter we consider more advanced topics in Lagrangian Mechanics that have had a tremendous impact on the later development of Mathematical...
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On the statistical background of quantum mechanics: generalities and a concrete example
We revisit our description of randomness in quantum processes that began in collaboration of Jean Ginibre. The calculations were performed on a...
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Breaking Consensus in Kinetic Opinion Formation Models on Graphons
In this work, we propose and investigate a strategy to prevent consensus in kinetic models for opinion formation. We consider a large interacting...
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A Statistical Mechanics Approach to Describe Cell Reorientation Under Stretch
Experiments show that when a monolayer of cells cultured on an elastic substratum is subject to a cyclic stretch, cells tend to reorient either...
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Introduction to Continuum Mechanics
In this initial chapter, we introduce various fundamentals: description of deformation, definition and interpretation of the strain and stress...
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Gas kinetic flux solver based finite volume weighted essentially non-oscillatory scheme for inviscid compressible flows
A high-order gas kinetic flux solver (GKFS) is presented for simulating inviscid compressible flows. The weighted essentially non-oscillatory (WENO)...
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On Dynamics and Thermodynamics of Moving Media
AbstractIn this paper, recent results regarding generalized continuum mechanics on oriented Riemannian manifolds are reviewed and summarized. The...
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Dissipative Soliton Resonance: Adiabatic Theory and Thermodynamics
We present the adiabatic theory of dissipative solitons (DS) of complex cubic-quintic nonlinear Ginzburg–Landau equation (CQGLE). Solutions in the...
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Bending and wave propagation analysis of axially functionally graded beams based on a reformulated strain gradient elasticity theory
A new size-dependent axially functionally graded (AFG) micro-beam model is established with the application of a reformulated strain gradient...
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Mathematical Model of Flow Past a Sphere with Modified Boundary Slip Condition
AbstractThe problem of a slow Stokes flow past a sphere with modified slip condition on its surface is solved. The new boundary condition on the...
