Riemann-Hilbert approach for the NLSLab equation with nonzero **boundary**
**conditions**

**boundary**

**conditions**(NZBCs) at infinity. In order to better deal with the scattering problem of NZBCs, we introduce the two-sheeted Riemann surface of $\kappa$, then it convert into the standard complex $z$-plane. In the direct scattering problem, we study the analyticity, symmetries and asymptotic behaviors of the Jost function and the scattering matrix in detail. In addition, we establish the discrete spectrum, residual conditions, trace foumulae and theta

**conditions**for the case of simple poles and double poles. The inverse problems of simple poles and double poles are from the Riemann-Hilbert problem (RHP). Finally, we obtain some soliton solutions of the NLSLab equation, including stationary solitons, non-stationary solitons and multi-soliton solutions. Some features of these soliton solutions caused by the influences of each parameters are analyzed graphically in order to control such nonlinear phenomena.

10/10 relevant

arXiv

Cut Bogner-Fox-Schmit Elements for Plates

**boundary**

**conditions**together with addition of certain stabilization terms that enable us to establish coercivity and stability of the resulting system of linear equations. We also take geometric approximation of the

**boundary**into account and we focus our presentation on the simply supported

**boundary**

**conditions**which is the most sensitive case for geometric approximation of the

**boundary**.

4/10 relevant

arXiv

**Boundary** **Conditions** and the q-state Potts model on Random Planar Maps

**boundary**. In this paper we explore the $(q

8/10 relevant

arXiv

Non-standard anomalous heat conduction in harmonic chains with correlated isotopic disorder

**boundary**conditions, whereas for fixed

**boundary**

**conditions**$\kappa \sim N^{(\beta-1)/(2+\beta)}$; where $\beta>-1$, which is the usual power law scaling for one dimensional systems. Nevertheless, if $W$ does not scale as a power law in the low wavelength limit, the thermal conductivity may not scale in its usual form $\kappa\sim N^{\alpha}$, where the value of $\alpha$ depends on the particular one dimensional model. As an example of the latter statement, if $W(\mu)\sim \exp(-1/\mu)/\mu^2$, $\kappa \sim N/(\log N)^3$ for fixed

**boundary**

**conditions**and $\kappa \sim N/\log(N)$ for free

**boundary**conditions, which represent non-standard scalings of the thermal conductivity.

5/10 relevant

arXiv

Existence results for non-homogeneous **boundary** **conditions** in the relaxed
micromorphic model

**boundary**

**condition**in both the dynamic and the static case.

8/10 relevant

arXiv

On the behavior of the free boundary for a one-phase Bernoulli problem
with mixed **boundary** **conditions**

**boundary**for a class of solutions to a one-phase Bernoulli free

**boundary**problem with mixed periodic-Dirichlet

**boundary**

**conditions**. It is shown that if the free

**boundary**of a symmetric local minimizer approaches the point where the two different

**conditions**meet, then it must do so at an angle of $\pi/2$

10/10 relevant

arXiv

Charged Dirac perturbations on Reissner-Nordstr\"om-Anti-de Sitter
spacetimes: quasinormal modes with Robin **boundary** **conditions**

**boundary**

**conditions**, as a generic principle, are applicable not only to neutral but also to electrically charged fields. Expand abstract.

**boundary**conditions, by extending our earlier work of neutral Dirac QNMs on Schwarzschild-AdS black holes. We first derive the equations of motion for charged Dirac fields on a RN-AdS background. To solve these equations we impose a requirement on the Dirac field: that its energy flux should vanish at asymptotic infinity. A set of two Robin

**boundary**

**conditions**compatible with QNMs is consequently found. By employing both analytic and numeric methods, we then obtain the quasinormal spectrum for charged Dirac fields, and analyse the impact of various parameters, in particular of electric charge. An analytic calculation shows explicitly that the charge coupling between the black hole and the Dirac field does not trigger superradiant instabilities. Numeric calculations, on the other hand, show quantiatively that Dirac QNMs may change substantially due to the electric charge. Our results illustrate how vanishing energy flux

**boundary**conditions, as a generic principle, are applicable not only to neutral but also to electrically charged fields.

10/10 relevant

arXiv

Inverse scattering transform and soliton solutions for the focusing
Kundu-Eckhaus equation with nonvanishing **boundary** **conditions**

**boundary**

**conditions**at infinity, under two cases: simple zeros and double zeros, is investigated systematically via Riemann-Hilbert (RH) problem. Expand abstract.

**boundary**

**conditions**at infinity, under two cases: simple zeros and double zeros, is investigated systematically via Riemann-Hilbert (RH) problem. We derive some new results for the equation including the following seven parts. (I) The analyticities and symmetries of the Jost function and the scattering matrix are analyzed with the help of the normalized Lax pair. (II) Based on the resulting symmetries, the corresponding discrete spectrum set and residue

**conditions**of scattering coefficients are further obtained, which is very important to construct the formulae of solution to the original equation. (III) A generalized RH problem is established by combining the analytic properties of Jost functions and modified eigenfunctions. (IV) The RH problem is solved by the corresponding asymptotic behavior combined with the Plemelj's formulae and Cauchy operator. The expression of the solution to the focusing KE equation is given under the

**condition**of non-reflection. (V) From the reflection coefficients and discrete spectrums, the trace formula and the corresponding theta

**condition**are given to obtain the phase difference of the initial value at the

**boundary**. (VI) For the double zeros, there is a similar framework from the set of discrete spectral points, but the operation process is much more complicated than that of simple zeros, and new results and phenomena appear. (VII) Some interesting phenomena are obtained that one of the solutions is gradually to rouge waves when the spectrum points tend to singular points by choosing appropriate parameters.

10/10 relevant

arXiv

On the **Boundary** **Conditions** of Avoidance Memory Reconsolidation: An Attractor Network Perspective

**boundary**

**conditions**that can be tested experimentally. Expand abstract.

**boundary**

**conditions**have been extensively studied. Knowing their network mechanisms may lead to the development of better strategies for the treatment of fear and anxiety-related disorders. In 2011, Osan et al. developed a computational model for exploring such phenomena based on attractor dynamics, Hebbian plasticity and synaptic degradation induced by prediction error. This model was able to explain, in a single formalism, experimental findings regarding the freezing behavior of rodents submitted to contextual fear conditioning. In 2017, through the study of inhibitory avoidance in rats, Radiske et al. showed that the previous knowledge of a context as non-aversive is a

**boundary**

**condition**for the reconsolidation of the shock memory subsequently experienced in that context. In the present work, by adapting the model of Osan et al. (2011) to simulate the experimental protocols of Radiske et al. (2017), we show that such

**boundary**

**condition**is compatible with the dynamics of an attractor network that supports synaptic labilization common to reconsolidation and extinction. Additionally, by varying parameters such as the levels of protein synthesis and degradation, we predict behavioral outcomes, and thus

**boundary**

**conditions**that can be tested experimentally.

10/10 relevant

bioRxiv

Separation property and convergence to equilibrium for the equation and
dynamic **boundary** **condition** of Cahn-Hilliard type with singular potential

**boundary**

**conditions**and the total mass, in the bulk and on the boundary, is conserved for all time. Expand abstract.

**boundary**interactions in a bounded domain with non-permeable wall. The system is characterized by certain dynamic type

**boundary**

**conditions**and the total mass, in the bulk and on the boundary, is conserved for all time. For the case with physically relevant singular (e.g., logarithmic) potential, global regularity of weak solutions is established. In particular, when the spatial dimension is two, we show the instantaneous strict separation property such that for arbitrary positive time any weak solution stays away from the pure phases +1 and -1, while in the three dimensional case, an eventual separation property for large time is obtained. As a consequence, we prove that every global weak solution converges to a single equilibrium as the time goes to infinity, by the usage of an extended Lojasiewicz-Simon inequality.

8/10 relevant

arXiv