Related papers: Clasical solids dynamics as 4D statics of elastic …
We investigate the classicality of linear dipolar droplet arrays through a normal mode analysis of the dynamical properties in comparison to the supersolid regime. The vibrational patterns of isolated-droplet crystals that time-evolve after…
For the $\mathfrak{so}(4)$ free rigid body the stability problem for the isolated equilibria has been completely solved using Lie-theoretical and topological arguments. For each case of nonlinear stability previously found we construct a…
We consider nematic liquid crystals in a bounded, convex polyhedron described by a director field n(r) subject to tangent boundary conditions. We derive lower bounds for the one-constant elastic energy in terms of topological invariants.…
Deformations of conventional solids are described via elasticity, a classical field theory whose form is constrained by translational and rotational symmetries. However, flexible metamaterials often contain an additional approximate…
Starting from a general classical model of many interacting particles we present a well defined step by step procedure to derive the continuum-mechanics equations of nonlinear elasticity theory with fluctuations which describe the…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
Classical, Quantum, Relativistic and Statistical: the four branches of mechanics. However, the Quattro Donna of Physics disagree even about the entities that are supposed to be fundamental, such as space, matter and time. In order to search…
The present paper shows that Edward Nelson's stochastic mechanics approach for quantum mechanics can be derived from the two classical elastically colliding particles with masses M and m satisfying a collision momentum preserving equation.…
The mechanical response of naturally abundant amorphous solids such as gels, jammed grains, and biological tissues are not described by the conventional paradigm of broken symmetry that defines crystalline elasticity. In contrast, the…
An extended variational principle providing the equations of motion for a system consisting of interacting classical, quasiclassical and quantum components is presented, and applied to the model of bilinear coupling. The relevant dynamical…
The theory of mechanical response and stress transmission in disordered, jammed solids poses several open questions of how non-periodic networks -- apparently indistinguishable from a snapshot of a fluid -- sustain shear. We present a…
A model system for classical fluids out of equilibrium, referred to as DPD solid (Dissipative Particles Dynamics), is studied by analytical and simulation methods. The time evolution of a DPD particle is described by a fluctuating heat…
Thermodynamic equations for a solid and a solid continuum under stress are derived on the basis of a multicomponent mean field Markov process for thermofluctuation kinetics of microcracks. The resulting continuum is viscous elastoplastic…
Conventional descriptions of transverse waves in an elastic solid are limited by an assumption of infinitesimally small gradients of rotation. By assuming a linear response to variations in orientation, we derive an exact description of a…
We introduce a class of continuum mechanical models aimed at describing the behaviour of viscoelastic fluids by incorporating concepts originated in the theory of solid plasticity. Within this class, even a simple model with constant…
A new kinetic instability which results in formation of charge density waves is proposed. The instability is of a purely classical nature. A spatial period of arising space-charge and field configuration is inversely proportional to…
It is shown that the total energy of the static "field + particle" system, defined in the framework of classical, renormalized electrodynamics of particles and fields, depends in an unstable way upon the field boundary data. It is argued…
The thermodynamic equilibrium conditions for compact structures composed by mass varying particles are discussed assuming that the so-called dynamical mass behaves like an additional extensive thermodynamic degree of freedom. It then…
An attempt to explain with the classical stands a number of statements of the quantum mechanics has been done. At this the Plank constant appears as consequence of demand of nucleon stability. Proton can be imagined as a rotating disk which…
Considering deterministic classical lattice systems with continuous variables, we show that, if the initial conditions are sampled according to a probability distribution in which the dynamical variables are statistically independent, the…