The nonlocal elastic response function is crucial for understanding many properties of soft solids. This may be obtained by measuring strain-strain autocorrelation functions. We use computer simulations as well as video microscopy data of superparamagnetic colloids to obtain these correlations for two-dimensional triangular solids. Elastic constants and elastic correlation lengths are extracted...

The Doi kinetic theory for flows of homogeneous, rodlike liquid crystalline polymers (LCPs) is extended to model flows of nonhomogeneous, rodlike LCPs through a nonlocal (long-range) intermolecular potential. The theory features (i) a nonlocal, anisotropic, effective intermolecular potential in an integral form that is consistent with the chemical potential, (ii) short-range elasticity as well ...

We describe a method to show short time uniqueness results for viscosity solutions of general nonlocal and non-monotone second-order geometric equations arising in front propagation problems. Our method is based on some lower gradient bounds for the solution. These estimates are crucial to obtain regularity properties of the front, which allow to deal with nonlocal terms in the equations. Appli...

This paper studies a nonlinear fractional differential equation of an arbitrary order with four-point nonlocal integral boundary conditions. Some existence results are obtained by applying standard fixed point theorems and Leray-Schauder degree theory. The involvement of nonlocal parameters in four-point integral boundary conditions of the problem makes the present work distinguished from the a...

The nonlocal correlation energy in the van der Waals density functional (vdW-DF) method can be interpreted in terms of a coupling of zero-point energies of characteristic modes of semilocal exchange-correlation (xc) holes. These xc holes reflect the internal functional in the framework of the vdW-DF method. We explore the internal xc hole components, showing that they share properties with thos...

Abstract In the paper, two existing upgrades of gradient damage model for simulations cracking in concrete are compared. The theory is made nonlocal via a enhancement to overcome mesh dependence simulation results. implicit with an averaging equation, where internal length parameter assumed as constant during strain softening analysis, gives unrealistically broadened zones. scalar can be improv...

Local and nonlocal contributions to the total strain rate tensor S(ij) at any point x in a flow are formulated from an expansion of the vorticity field in a local spherical neighborhood of radius R centered on x. The resulting exact expression allows the nonlocal (background) strain rate tensor S(ij)(B)(x) to be obtained from S(ij)(x). In turbulent flows, where the vorticity naturally concentra...

We consider coarsening in interfacial systems driven by nonlocal energies. Of particular interest are the nonlocal Cahn–Hilliard equation and models of biological aggregation. The energies considered cause the system to separate into phases. The pattern of interfaces evolves under nonlocal surfacetension-type effects. The typical length scales grow and the pattern coarsens. We prove a rigorous ...

We study synaptic plasticity in a complex neuronal cell model where NMDA-spikes can arise in certain dendritic zones. In the context of reinforcement learning, two kinds of plasticity rules are derived, zone reinforcement (ZR) and cell reinforcement (CR), which both optimize the expected reward by stochastic gradient ascent. For ZR, the synaptic plasticity response to the external reward signal...