相关论文: Causality and Passivity in Elastodynamics

The existence and uniqueness of weak solutions is shown for a system related to the Willis model of elastodynamics. Both the whole space case and the case of a bounded smooth domain are studied. To this end the equations are reformulated as…

Spatial symmetries and invariances play an important role in the behaviour of materials and should be respected in the description and modelling of material properties. The focus here is the class of physically symmetric and positive…

During the normal operation of a power system all the voltages and currents are sinusoids with a frequency of 60 Hz in America and parts of Asia, or of 50Hz in the rest of the world. Forcing all the currents and voltages to be sinusoids…

We analyze the dynamical generation of entanglement in systems of two interacting spins initially prepared in a product of spin coherent states. For arbitrary time-independent Hamiltonians, we derive a semiclassical expression for the…

The important consequence of the Kramers-Kronig relations (KKrs) is that dissipative behavior in material media inevitably implies the existence of dispersion, i.e., a frequency dependence in the constitutive equations. Basically, the…

The behaviour of elastic structures undergoing large deformations is the result of the competition between confining conditions, self-avoidance and elasticity. This combination of multiple phenomena creates a geometrical frustration that…

The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…

The role of thermodynamics in continuum mechanics and the derivation of the proper constitutive relations is a discussed subject of Rational Mechanics. The classical literature did not use the accumulated knowledge of thermostatics and was…

It is discussed that the classical effective medium theory for the elastic properties of random heterogeneous materials is not congruous with the effective medium theory for the electrical conductivity. In particular, when describing the…

A soft solid is said to be initially stressed if it is subjected to a state of internal stress in its unloaded reference configuration. Developing a sound mathematical framework to model initially stressed solids in nonlinear elasticity is…

Magnetic gels and elastomers are promising candidates to construct reversibly excitable soft actuators, triggered from outside by magnetic fields. These magnetic fields induce or alter the magnetic interactions between discrete rigid…

Electrostatic actuators are simple but important switching devices for MEMS applications. Due to the difficulties associated with the electrostatic nonlinearity, precise mathematical description is often hard to obtain for the dynamics of…

The modeling of the elastic properties of disordered or nanoscale solids requires the foundations of the theory of elasticity to be revisited, as one explores scales at which this theory may no longer hold. The only cases for which…

We propose an explanation for the quadratic dependence on the momentum $Q$, of the broadening of the acoustic excitation peak recently found in the study of the dynamic structure factor of many real and simulated glasses. We ascribe the…

Testing whether a probability distribution is compatible with a given Bayesian network is a fundamental task in the field of causal inference, where Bayesian networks model causal relations. Here we consider the class of causal structures…

Mechanical densification of granular bodies is a process in which a loose material becomes increasingly cohesive as the applied pressure increases. A constitutive description of this process faces the formidable problem that granular and…

It is shown that, in the non-relativistic limit, causal fermion systems give rise to an effective collapse theory. The nonlinear and stochastic correction terms to the Schr\"odinger equation are derived from the causal action principle. The…

There have been some interesting recent advances in understanding the notion of mechanical disorder in structural glasses and the statistical mechanics of these systems' low-energy excitations. Here we contribute to these advances by…

Except for very particular and artificial experimental configurations, linear transformations of the state of polarization of an electromagnetic wave result in a reduction of the intensity of the exiting wave with respect to the incoming…

The adiabatic elastic modulus is often useful in the high frequency response of materials. Unfortunately, it can be much more difficult to directly measure the adiabatic elastic modulus of material than the isothermal elastic modulus. We…