Nonlocal Phase Research Articles

Hölder regularity results for parabolic nonlocal double phase problems

Hölder regularity results for parabolic nonlocal double phase problems

A convergence result for the derivation of front propagation in nonlocal phase field models

We prove that the mean curvature of a smooth surface in \R^{n} , n\geq 2 , arises as the limit of a sequence of functions that are intrinsically related to the difference between an n - and 1 -dimensional fractional Laplacian of a phase transition. Depending on the order of the fractional Laplace operator, we recover the fractional mean curvature or the classical mean curvature of the surface. Moreover, we show that this is an essential ingredient for deriving the evolution of fronts in fractional reaction-diffusion equations such as those for atomic dislocations in crystals.

Normalized homoclinic solutions of discrete nonlocal double phase problems

The aim of this paper is to discuss the existence of normalized solutions to the following nonlocal double phase problems driving by the discrete fractional Laplacian: [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] if [Formula: see text], [Formula: see text] if [Formula: see text], and [Formula: see text]([Formula: see text] or [Formula: see text], [Formula: see text] or [Formula: see text]) is the discrete fractional [Formula: see text]-Laplacian. By variational methods, we discuss the existence of non-negative normalized homoclinic solutions under the conditions that the nonlinear term satisfies sublinear growth or superlinear growth conditions. In particular, we establish the compactness of the associated energy functional of the problem without weights. Our paper is the first time to deal with the existence of normalized solutions for discrete double phase problems.

Nonlocal Double Phase Implicit Obstacle Problems with Multivalued Boundary Conditions

Nonlocal Double Phase Implicit Obstacle Problems with Multivalued Boundary Conditions

Nonlocal Phase Linking for Distributed Scatterer Interferometry

Nonlocal Phase Linking for Distributed Scatterer Interferometry

Energy-decreasing second order exponential time differencing Runge–Kutta methods for Nonlocal Cahn–Hilliard equation

Due to the energetic variational structure inherent in the nonlocal phase field model, the energy of the system naturally decreases over time according to the Nonlocal Cahn–Hilliard (NCH) equation. Preserving this crucial property of energy dissipation is highly desirable in numerical solutions. However, most existing numerical methods can only ensure a decrease in some modified form of energy, rather than the original energy itself. In this paper, we propose the second-order exponential time differencing Runge–Kutta (ETD-RK2) methods for solving the NCH equation. We demonstrate that this method has the ability to unconditionally preserve the original energy dissipation. Numerical experiments are included to illustrate the accuracy and energy stability of the ETD-RK2 methods.

Existence and Stability of Normalized Solutions for Nonlocal Double Phase Problems

Existence and Stability of Normalized Solutions for Nonlocal Double Phase Problems

Phase engineering of anomalous Josephson effect derived from Andreev molecules

A Josephson junction (JJ) is a key device for developing superconducting circuits, wherein a supercurrent in the JJ is controlled by the phase difference between the two superconducting electrodes. When two JJs sharing one superconducting electrode are coherently coupled and form the Andreev molecules, a supercurrent of one JJ is expected to be nonlocally controlled by the phase difference of another JJ. Here, we evaluate the supercurrent in one of the coupled two JJs as a function of local and nonlocal phase differences. Consequently, the results exhibit that the nonlocal phase control generates a finite supercurrent even when the local phase difference is zero. In addition, an offset of the local phase difference giving the JJ ground state depends on the nonlocal phase difference. These features demonstrate the anomalous Josephson effect realized by the nonlocal phase control. Our results provide a useful concept for engineering superconducting devices such as phase batteries and dissipationless rectifiers.

Nonlocal phase modulation of multimode, continuous-variable twin beams

We investigate experimentally the nonlocal phase modulation of multiple-frequency-mode, continuous-variable entangled twin beams. We use a pair of electro-optical phase modulators to modulate the entangled probe and conjugate light beams produced by four-wave mixing in hot rubidium vapor. A single phase modulator in either one of the twin beams reduces the two-mode squeezing signal. The overall quantum entanglement is preserved, however, as the modulator nonlocally distributes the beam correlations among frequency modes of the multimode fields. The two-mode squeezing can be recovered by reversing the mixing with an additional out-of-phase electro-optical phase modulator (EOM) in the other beam.

Maximum principles and qualitative properties of solutions for nonlocal double phase operator

Maximum principles and qualitative properties of solutions for nonlocal double phase operator

Regularity of weak solutions for mixed local and nonlocal double phase parabolic equations

We study the mixed local and nonlocal double phase parabolic equation∂tu(x,t)−div(a(x,t)|∇u|q−2∇u)+Lu(x,t)=0 in QT=Ω×(0,T), where L is the nonlocal p-Laplace type operator. The local boundedness of weak solutions is proved by means of the De Giorgi-Nash-Moser iteration with the nonnegative coefficient function a(x,t) being bounded. In addition, when a(x,t) is Hölder continuous, we discuss the pointwise behavior and lower semicontinuity of weak supersolutions based on energy estimates and De Giorgi type lemma. Analogously, the corresponding results are also valid for weak subsolutions.

Nonlocal phase coupling in turbulence spreading across the magnetic island

We study the nonlocal phase coupling during turbulence spreading across the magnetic island. It is found that the coherent convective cells (sharing similar features to quasi-coherent mode in experiment) on both sides of the O-point boundary are accumulated during the island formation. The phase entrainment of the convective cells on the turbulence both in the inner and the outer regions of the magnetic island sets up a nonlocal phase coupling channel and leads to a fast spreading of the outer turbulence into the magnetic island by conquering the flow shear at the O-point boundary. This nonlocal coupling mechanism of turbulence spreading is analogous to a turbulence version of the well-known enhanced diffusion of passive scalars in laminar convective flows of neutral fluid system.

The Effect of Nonlocal Scale Value and Phase Lags on Thermoelastic Waves in a Multilayered LEMV/CFRP Composite Cylinder

In this study, the effect of nonlocal scale value and two phase lags on the free vibration of generalized thermoelastic multilayered LEMV (Linear Elastic Material with Voids)/CFRP (Carbon Fiber Reinforced Polymer) composite cylinder is studied using nonlocal form of linear theory of elasticity. The governing equation of motion is established in longitudinal axis and variable separation model is used to transform the governing equations into a system of differential equations. To investigate vibration analysis from frequency equations, the stress free boundary conditions are adopted at the inner, outer and interface boundaries. The graphical representation of the numerically calculated results for frequency shift, natural frequency, and thermoelastic damping is presented. A special care has been taken to inspect the effect of nonlocal parameter on the aforementioned quantities. The results suggest that the nonlocal scale and the phase lag parameters alter the vibration characteristics of composite cylinders significantly.

The Effect of Nonlocal Scale Value and Phase Lags on Thermoelastic Waves in a Multilayered LEMV/CFRP Composite Cylinder

The Effect of Nonlocal Scale Value and Phase Lags on Thermoelastic Waves in a Multilayered LEMV/CFRP Composite Cylinder

A modified damage and fracture phase field model considering heterogeneity for rock‐like materials

AbstractDamage and fracture are the most extensive failure modes of rock materials, which may easily induce disaster and instability of engineering structures. This study developed a nonlocal damage fracture phase field model for rocks considering the heterogeneity of rocks. The modified phase field model introduced the heterogeneity of fracture parameters and modified the governing equations. Meanwhile, the free energy was constructed by the elastic strain energy sphere‐bias decomposition and the plastic strain energy. As for the numerical implementation, the three layers finite elements method structure was used in the frame of the finite element method. The ability of the modified phase field model has been illustrated by reproducing the experiment results of rock samples with pre‐existing cracks under compression.

Quantum Spin Hall Effect in Two-Monolayer-Thick InN/InGaN Coupled Multiple Quantum Wells.

In this study, we present a theoretical study of the quantum spin Hall effect in InN/InGaN coupled multiple quantum wells with the individual well widths equal to two atomic monolayers. We consider triple and quadruple quantum wells in which the In content in the interwell barriers is greater than or equal to the In content in the external barriers. To calculate the electronic subbands in these nanostructures, we use the eight-band k∙p Hamiltonian, assuming that the effective spin-orbit interaction in InN is negative, which represents the worst-case scenario for achieving a two-dimensional topological insulator. For triple quantum wells, we find that when the In contents of the external and interwell barriers are the same and the widths of the internal barriers are equal to two monolayers, a topological insulator with a bulk energy gap of 0.25 meV can appear. Increasing the In content in the interwell barriers leads to a significant increase in the bulk energy gap of the topological insulator, reaching about 0.8 meV. In these structures, the topological insulator can be achieved when the In content in the external barriers is about 0.64, causing relatively low strain in quantum wells and making the epitaxial growth of these structures within the range of current technology. Using the effective 2D Hamiltonian, we study the edge states in strip structures containing topological triple quantum wells. We demonstrate that the opening of the gap in the spectrum of the edge states caused by decreasing the width of the strip has an oscillatory character regardless of whether the pseudospin-mixing elements of the effective Hamiltonian are omitted or taken into account. The strength of the finite size effect in these structures is several times smaller than that in HgTe/HgCdTe and InAs/GaSb/AlSb topological insulators. Therefore, its influence on the quantum spin Hall effect is negligible in strips with a width larger than 150 nm, unless the temperature at which electron transport is measured is less than 1 mK. In the case of quadruple quantum wells, we find the topological insulator phase only when the In content in the interwell barriers is larger than in the external barriers. We show that in these structures, a topological insulator with a bulk energy gap of 0.038 meV can be achieved when the In content in the external barriers is about 0.75. Since this value of the bulk energy gap is very small, quadruple quantum wells are less useful for realizing a measurable quantum spin Hall system, but they are still attractive for achieving a topological phase transition and a nonlocal topological semimetal phase.

Effect of Nonlocal Elasticity and Phase Lags on the Magneto Thermoelastic Waves in a Composite Cylinder with Hall Current

In this study, the effect of nonlocal scale value and two phases lags on the free vibration of generalized magneto thermoelastic multilayered LEMV (Linear Elastic Material with Voids)/CFRP (Carbon Fiber Reinforced Polymer) composite cylinder is studied using nonlocal form of linear theory of elasticity. The governing equation of motion is established in longitudinal axis and variable separation model is used to transform the governing equations into a system of differential equations. To investigate vibration analysis from frequency equations, the stress free boundary conditions are adopted at the inner, outer and interface boundaries. The graphical representation of the numerically calculated results for frequency shift, natural frequency, and thermoelastic damping is presented. A special care has been taken to inspect the effect of nonlocal parameter on the aforementioned quantities. The results suggest that the nonlocal scale and the phase lag parameters alter the vibration characteristics of composite cylinders significantly.

Existence for a nonlocal Penrose-Fife type phase field system with inertial term

This article presents a nonlocal Penrose-Fife type phase field system with inertial term. We do not know whether we can prove the existence of solutions to the problem as in Colli-Grasselli-Ito [3] or not. In this article we introduce a time discretization scheme, then pass to the limit as the time step h approaches 0, and obtain an error estimate for the difference between the continuous solution and the discrete solution.

Integrable Floquet systems related to logarithmic conformal field theory

We study an integrable Floquet quantum system related to lattice statistical systems in the universality class of dense polymers. These systems are described by a particular non-unitary representation of the Temperley-Lieb algebra. We find a simple Lie algebra structure for the elements of Temperley-Lieb algebra which are invariant under shift by two lattice sites, and show how the local Floquet conserved charges and the Floquet Hamiltonian are expressed in terms of this algebra. The system has a phase transition between local and non-local phases of the Floquet Hamiltonian. We provide a strong indication that in the scaling limit this non-equilibrium system is described by the logarithmic conformal field theory.

Local–nonlocal stress-driven model for multi-cracked nanobeams

Exact closed-form solutions for multi-cracked Euler–Bernoulli nanobeams are provided by proposing two equivalent approaches. The considered multi-cracked nanobeams are modeled with a well-posed local–nonlocal stress-driven model and contain an arbitrary number n of isolated damaged cross-sections. In order to simulate the damaged sections, it is assumed that the nanobeam bending flexibility contains n Dirac delta functions, with a Dirac delta located at each damaged section: this representation of cracked sections, already used in local problem, is adopted for the first time here in the local–nonlocal stress-driven model. The first approach providing closed-form solutions is based on the integral definition of the local–nonlocal stress-driven model, where the bending curvature is given by the superposition of the local and nonlocal phases, and the nonlocal phase is an integral convolution of the bending moment. This approach provides an integro-differential equation, which is solved by taking firstly the Laplace transform and then the anti-transform. In the second approach, it is shown that the integral definition of the stress-driven multi-cracked nanobeam model is equivalent to a differential equation together with suitable constitutive boundary conditions. This equation is solved by making use of Laplace transform again. The two approaches provide the same solution, with the second one resulting computationally faster. Interesting results show that a jump of the rotation at the damaged cross-sections occurs in local beam, but does not occur in pure nonlocal nanobeams (i.e. local phase is absent): contrary to the local elasticity theory, the bending curvature of pure nonlocal nanobeams has no singularity at damaged sections. The typical stiffness increase, due to the increase in nonlocal fraction of the mixture or to the increase in the length-scale parameter, also appears in multi-cracked nanobeams and this stiffening nonlocal effect is more pronounced in more constrained nanobeams.