Valley to charge current conversion in graphene grain boundaries

**boundary**

**conditions**used. Expand abstract.

**boundary**junction with Fermi velocity mismatch are analyzed. We provide a generalization of the Dirac Hamiltonian model taking into account the Fermi velocity gradient at the interface. General

**boundary**

**conditions**for the scattering problem are derived within the framework of the matching matrix method. We show that the scattering properties of the interface, as predicted by the theory, strongly depend on the

**boundary**

**conditions**used. We demonstrate that when the valley degeneracy is broken a charge current is established at the grain

**boundary**interface. These findings provide the working principle of a valley to charge current converter, which is relevant for the emergent field of valleytronics.

4/10 relevant

arXiv

No-**boundary** prescriptions in Lorentzian quantum cosmology

**conditions**allows one to specify the Hubble rate on the

**boundary**hypersurface, and we highlight the surprising aspect that specifying the final Hubble rate (rather than the final size of the universe) significantly alters the off-shell structure of the path integral. Expand abstract.

**boundary**

**conditions**on the (minisuperspace) Lorentzian gravitational path integral. In particular we assess the implications for the Hartle-Hawking no-

**boundary**proposal. It was shown recently that when this proposal is defined as a sum over compact metrics, problems arise with the stability of fluctuations. These difficulties can be overcome by an especially simple implementation of the no-

**boundary**idea: namely to take the Einstein-Hilbert action at face value while adding no

**boundary**term. This prescription simultaneously imposes an initial Neumann

**boundary**

**condition**for the scale factor of the universe and Dirichlet

**conditions**for the anisotropies. Another way to implement the no-

**boundary**proposal is to use Robin

**boundary**

**conditions**. A sub-class of Robin

**conditions**allows one to specify the Hubble rate on the

**boundary**hypersurface, and we highlight the surprising aspect that specifying the final Hubble rate (rather than the final size of the universe) significantly alters the off-shell structure of the path integral. The conclusion of our investigations is that all current working examples of the no-

**boundary**proposal force one to abandon the notion of a sum over compact and regular geometries, and point to the importance of an initial Euclidean momentum.

7/10 relevant

arXiv

The Stokes resolvent problem: Optimal pressure estimates and remarks on resolvent estimates in convex domains

**boundary**

**conditions**is investigated. In the first part of the paper we show that for Neumann-type

**boundary**

**conditions**the operator norm of $\mathrm{L}^2_{\sigma} (\Omega) \ni f \mapsto \pi \in \mathrm{L}^2 (\Omega)$ decays like $\lvert \lambda \rvert^{- 1 / 2}$ which agrees exactly with the scaling of the equation. In comparison to that, we show that the operator norm of this mapping under Dirichlet

**boundary**

**conditions**decays like $\lvert \lambda \rvert^{- \alpha}$ for $0 \leq \alpha < 1 / 4$ and we show that this decay rate cannot be improved to any exponent $\alpha > 1 / 4$, thereby, violating the natural scaling of the equation. In the second part of this article, we investigate the Stokes resolvent problem subject to homogeneous Neumann-type

**boundary**

**conditions**if the underlying domain $\Omega$ is convex. We establish optimal resolvent estimates and gradient estimates in $\mathrm{L}^p (\Omega ; \mathbb{C}^d)$ for $2d / (d + 2) < p < 2d / (d - 2)$ (with $1 < p < \infty$ if $d = 2$). This interval is larger than the known interval for resolvent estimates subject to Dirichlet

**boundary**

**conditions**on general Lipschitz domains and is to the best knowledge of the author the first result that provides $\mathrm{L}^p$-estimates for the Stokes resolvent subject to Neumann-type

**boundary**

**conditions**on general convex domains.

7/10 relevant

arXiv

Pure and twisted holography

**boundary**

**conditions**. Expand abstract.

**boundary**and in the bulk. We define the topological bulk supergravity theory in terms of twisted

**boundary**

**conditions**. We corroborate the duality by calculating the chiral configurations in the bulk supergravity theory and by quantising the solution space. Moreover, we note that the

**boundary**calculation of the structure constants of the chiral ring carries over to the bulk theory as well. We thus construct a topological AdS/CFT duality in which the bulk theory is independent of the

**boundary**metric.

4/10 relevant

arXiv

An experimental and computational investigation of the effects of volumetric **boundary** **conditions** on the compressive mechanics of passive skeletal muscle

**conditions**. Expand abstract.

**conditions**and (3) determine the extent to which different assumptions of volumetric behavior affect model results. Muscle in confined compression exhibited stiffer behavior, agreeing with previous assumptions of near-incompressibility. Stress relaxation was found to be faster under unconfined compression, suggesting there may be different mechanisms that support load these two

**conditions**. Finite element calibration was achieved through nonlinear optimization (normalized root mean square error

8/10 relevant

engrXiv

Semiclassical limit of Gross-Pitaevskii equation with Dirichlet **boundary**
**condition**

**boundary**

**condition**. Expand abstract.

**boundary**

**condition**on the 3-D upper space under the assumption that the leading order terms to both initial amplitude and initial phase function are sufficiently small in some high enough Sobolev norms. We remark that the main difficulty of the proof lies in the fact that the

**boundary**layer appears in the leading order terms of the amplitude functions and the gradient of the phase functions to the WKB expansions of the solutions. In particular, we partially solved the open question proposed in \cite{CR2009, PNB2005} concerning the semiclassical limit of Gross-Pitaevskii equation with Dirichlet

**boundary**

**condition**.

7/10 relevant

arXiv

On the transfer matrix of the supersymmetric eight-vertex model. II.
Open **boundary** **conditions**

**boundary**

**conditions**is investigated. It is shown that for vertex weights $a,b,c,d$ that obey the relation $(a^2+ab)(b^2+ab)=(c^2+ab)(d^2+ab)$ and appropriately chosen $K$-matrices $K^\pm$ this transfer matrix possesses the remarkably simple, non-degenerate eigenvalue $\Lambda_L = (a+b)^{2L}\,\text{tr}(K^+K^-)$. For positive vertex weights, $\Lambda_L$ is shown to be the largest transfer-matrix eigenvalue. The corresponding eigenspace is equal to the space of the ground states of the Hamiltonian of a related XYZ spin chain. An essential ingredient in the proofs is the supersymmetry of this Hamiltonian.

10/10 relevant

arXiv

Fluctuations around a homogenised semilinear random PDE

**boundary**

**condition**. If the amplitude of the oscillations has the right size compared to its typical spatiotemporal scale, then the solution of our equation converges to the solution of a deterministic homogenised parabolic PDE, which is a form of law of large numbers. Our main interest is in the associated central limit theorem. Namely, we study the limit of a properly rescaled difference between the initial random solution and its LLN limit. In dimension $d=1$, that rescaled difference converges as one might expect to a centred Ornstein-Uhlenbeck process. However, in dimension $d=2$, the limit is a non-centred Gaussian process, while in dimension $d=3$, before taking the CLT limit, we need to subtract at an intermediate scale the solution of a deterministic parabolic PDE, subject (in the case of Neumann

**boundary**condition) to a non-homogeneous Neumann

**boundary**

**condition**. Our proofs make use of the theory of regularity structures, in particular of the very recently developed methodology allowing to treat parabolic PDEs with

**boundary**

**conditions**within that theory.

7/10 relevant

arXiv

On the torsion function with mixed **boundary** **conditions**

**boundary**$\partial D$, with finite Lebesgue measure $|D|$, and which satisfies a parabolic Harnack principle. Let $K$ be a compact, non-polar subset of $D$. We obtain the leading asymptotic behaviour as $\varepsilon\downarrow 0$ of the $L^{\infty}$ norm of the torsion function with a Neumann

**boundary**

**condition**on $\partial D$, and a Dirichlet

**boundary**

**condition**on $\partial (\varepsilon K)$, in terms of the first eigenvalue of the Laplacian with corresponding

**boundary**

**conditions**. These estimates quantify those of Burdzy, Chen and Marshall who showed that $D\setminus K$ is a non-trap domain.

10/10 relevant

arXiv

A Liouville theorem for fully nonlinear problems with infinite **boundary**
**conditions** and applications

**boundary**blow up rates for ergodic functions in bounded domains related to degenerate/singular operators, and, as a further consequence, we deduce the uniqueness of the ergodic functions. Expand abstract.

**boundary**value problems related to fully nonlinear, uniformly elliptic operators. We then apply the result in order to obtain gradient

**boundary**blow up rates for ergodic functions in bounded domains related to degenerate/singular operators, and, as a further consequence, we deduce the uniqueness of the ergodic functions.

9/10 relevant

arXiv