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Treating competing fluctuations, e.g., density, spin, current, need a tractable, self-consistent approach. One method that treats particle-particle and particle-hole correlations self-consistently is the diagrammatic "crossing-symmetric equations" method. In a general calculation for pairing, non-local interaction plays an important role in enhancing certain quantum fluctuations and thereby determining the pairing symmetry.

We present a mathematical model for cell-induced gel contraction in vitro. The core of the model consists of conservation equations for the mass of the gel and the number of cells, coupled to a force balance on the gel. On the basis of previously reported experimental findings for collagen gels, which are frequently used experimentally, the gel is treated as a compressible viscous fluid while inertial effects are neglected. The flow is assumed to be isothermal, and a linear pressure–density relation is adopted. The force exerted on the gel by cells is assumed to depend upon the local environment surrounding the cell: influences can include the cell and extracellular matrix density, and the concentration of a diffusible chemical produced by the cells. We consider the simple, but experimentally relevant, case of spherically symmetric gels. For cell-free gels, we show how simple experiments might be used to determine the parameters in the model. When the cell-derived forces are given by a prescribed function of position, we are able to obtain the early time and steady-state behavior of the solution analytically. We perform numerical simulations which generate predictions of how the gel density evolves during compaction under differing assumptions concerning the factors influencing the force exerted by the cells. These results are compared with some previous observations reported in the literature.

A general theory of non-local materials, with linear constitutive equations and memory effects, is developed within a thermodynamic framework. Several free energy and dissipation functionals are constructed and explored. These include an expression for the minimum free energy and a functional that is a free energy for important categories of memory kernels and is explicitly a functional of the minimal state. The functionals discussed have a similar general form to the corresponding expressions for simple materials. A number of new results are derived for them, most of which apply equally to both types of material. In particular, detailed formulae are given for these quantities in the case of sinusoidal histories.

This paper deals with a non-local curve evolution problem in the plane which will increase both the length of the evolving curve and the area it bounds and make the evolving curve more and more circular during the evolution process. And the limiting shape of the evolving curve will be a finite circle (i.e. a circle with finite radius) as the time t goes to infinity.

We study the $\mathrm{\Gamma }$-convergence of a family of non-local, non-convex functionals in $L^p(I)$ for $p\ge 1$, where $I$ is an open interval. We show that the limit is a multiple of the $W^{1,p}(I)$ semi-norm to the power $p$ when $p>1$ (respectively, the $BV(I)$ semi-norm when $p=1$). In dimension one, this extends earlier results which required a monotonicity condition.

A scheme for realizing the non-local Toffoli gate among three spatially separated nodes through cavity quantum electrodynamics (C-QED) is presented. The scheme can obtain high fidelity in the current C-QED system. With entangled qubits as quantum channels, the operation is resistive to actual environment noise.

In this paper, a nonlocal approach for handling nonlinear heat conduction problems is developed using the peridynamic differential operator (PDDO). The boundary conditions and heat conduction equations are transformed from local differential form to nonlocal integral form by introducing peridynamic functions. The algebraic equations are established by the Lagrange multiplier method and variational analysis, which is solved with Newton–Raphson iterative method. Nonlinearities resulting from the temperature-dependence of material properties have been taken into account in irregular boundaries and cracked plates. Numerical examples demonstrate the effectiveness and accuracy of the PDDO for solving nonlinear heat conduction problems with temperature-dependent conductivity.

Treating competing fluctuations, e.g., density, spin, current, need a tractable, self-consistent approach. One method that treats particle-particle and particle-hole correlations self-consistently is the diagrammatic "crossing-symmetric equations" method. In a general calculation for pairing, non-local interaction plays an important role in enhancing certain quantum fluctuations and thereby determining the pairing symmetry.