Numerical simulations of NMR relaxation in chalk using local Robin
**boundary** **conditions**

**boundary**

**conditions**for random walk simulations of NMR relaxation in digital domains were presented. Here, we have applied those

**boundary**

**conditions**to large, three-dimensional (3D) porous media samples. We compared the random walk results with known solutions and then applied them to highly structured 3D domains, from images derived using synchrotron radiation CT scanning of North Sea chalk samples. As expected, there were systematic errors caused by digitalization of the pore surfaces so we quantified those errors, and by using linear local

**boundary**conditions, we were able to significantly improve the output. We also present a technique for treating numerical data prior to input into the ESPRIT algorithm for retrieving Laplace components of time series from NMR data (commonly called $T$-inversion).

10/10 relevant

arXiv

Hydrodynamics of a particle model in contact with stochastic reservoirs

**boundary**

**conditions**on the external boundaries $x=-N$, $x=2N$ of the reservoirs. Finally, a system of Neumann and Dirichlet

**boundary**

**conditions**is derived at the interior boundaries $x=0$, $x=N$ of the reservoirs.

4/10 relevant

arXiv

Inviscid damping and enhanced dissipation of the **boundary** layer for 2D
Navier-Stokes linearized around Couette flow in a channel

**boundary**

**conditions**in the vanishing viscosity $\nu \to 0$ limit. We split the vorticity evolution into the free evolution (without a boundary) and a

**boundary**corrector that is exponentially localized to at most an $O(\nu^{1/3})$

**boundary**layer. If the initial vorticity perturbation is supported away from the boundary, we show inviscid damping of both the velocity and the vorticity associated to the

**boundary**layer. For example, our $L^2_t L^1_y$ estimate of the

**boundary**layer vorticity is independent of $\nu$, provided the initial data is $H^1$. For $L^2$ data, the loss is only logarithmic in $\nu$. Note both such estimates are false for the vorticity in the interior. To the authors' knowledge, this inviscid decay of the

**boundary**layer vorticity seems to be a new observation not previously isolated in the literature. Both velocity and vorticity satisfy the expected $O(\exp(-\delta\nu^{1/3}\alpha^{2/3}t))$ enhanced dissipation in addition to the inviscid damping. Similar, but slightly weaker, results are obtained also for $H^1$ data that is against the

**boundary**initially. For $L^2$ data against the boundary, we at least obtain the

**boundary**layer localization and enhanced dissipation.

4/10 relevant

arXiv

Gradient estimates in fractional Dirichlet problems

**boundary**

**conditions**. Expand abstract.

**boundary**for solutions to fractional elliptic problems subject to exterior Dirichlet

**boundary**

**conditions**. Our results provide, in particular, the sign of the normal derivative of such solutions near the

**boundary**of the underlying domain.

4/10 relevant

arXiv

Non-Bloch $\mathcal{PT}$ symmetry breaking in non-Hermitian Photonic Quantum Walks

**boundary**

**conditions**. Remarkably, in certain non-Hermitian lattices the bulk properties are largely affected by boundaries, leading to such major effects as the non-Hermitian skin effect and violation of the bulk-

**boundary**correspondence. Here we unveil that non-unitary discrete-time quantum walks of photons in systems involving gain and loss show rather generally non-Bloch parity-time ($\mathcal{PT}$) symmetry breaking phase transitions, and suggest a bulk probing method to detect such

**boundary**-driven phase transitions.

4/10 relevant

arXiv

Finite element modeling of micropolar-based phononic crystals

**boundary**

**conditions**are given for both translational and rotational degrees of freedom and for the associated force- and couple-traction vectors. Expand abstract.

**boundary**

**conditions**. The periodic

**boundary**

**conditions**are given for both translational and rotational degrees of freedom and for the associated force- and couple-traction vectors. Results in terms of band structures for different material cells and mechanical parameters are provided.

4/10 relevant

arXiv

Infrared renormalon in $SU(N)$ QCD(adj.) on $\mathbb{R}^3\times S^1$

**boundary**

**conditions**. We rely on the so-called large-$\beta_0$ approximation as a conventional tool to analyze renormalon, in which only Feynman diagrams that dominate in the large $n_W$ limit are kept while the coefficient of the vacuum polarization is set by hand to the one-loop beta function~$\beta_0=11/3-2n_W/3$. In the large~$N$ limit within the large-$\beta_0$ approximation, we find that the Borel singularity at~$u=2$, which exists in the system on the un-compactified~$\mathbb{R}^4$ and is expected to correspond to twice the bion action, disappears. Instead, for the compactified space~$\mathbb{R}^3\times S^1$, an unfamiliar renormalon singularity \emph{emerges\} at~$u=3/2$. Our conclusion differs from the claim by Anber and Sulejmanpasic in that the IR renormalon exists in QCD(adj.) even on the compactified space~$\mathbb{R}^3\times S^1$ with the twisted

**boundary**

**conditions**.

5/10 relevant

arXiv

Introducing Open **boundary** **conditions** in modeling nonperiodic materials
and interfaces

**boundary**

**conditions**in material and interface modeling. The new method, which we named ROBIN (recursive open

**boundary**and interfaces) allows for discretizing millions of atoms in real space, thereby not requiring any symmetry or order of the atom distribution. The computational costs are limited to solving quantum properties in a focus area. It is verified in detail that the impact of the infinite environment on that area is included exactly. Calculations of graphene with the same amount of 1) periodic (currently available methods) and 2) randomly distributed silicon atoms shows that assuming periodicity elevates a small perturbation into a strong impact on the material property prediction. Graphene was confirmed to produce a band gap with periodic substitution of 3% carbon with silicon in agreement with published periodic

**boundary**

**condition**calculations. Instead, 3% randomly distributed silicon in graphene only shifts the energy spectrum. The predicted shift agrees quantitatively with published experimental data. Periodic

**boundary**

**conditions**can be applied on truly periodic systems only. Other systems should apply an open

**boundary**method.

10/10 relevant

arXiv

Analysis of switching strategies for the optimization of periodic chemical reactions with controlled flow-rate

**boundary**

**conditions**and evaluate the cost analytically for small periods. Expand abstract.

**boundary**

**conditions**. This problem arises in chemical engineering as the maximization of the product of non-isothermal reactions by consuming a fixed amount of input reactants. It follows from the Pontryagin maximum principle that the optimal controls are piecewise constant in the considered case. We focus on a parametrization of optimal controls in terms of switching times in order to estimate the cost under different switching strategies. We exploit the Chen-Fliess functional expansion of solutions to the considered nonlinear system with bang-bang controls to satisfy the

**boundary**

**conditions**and evaluate the cost analytically for small periods. In contrast to the previous results in this area, the system under consideration is not control-affine, and the integrand of the cost depends on the state. This approach is applied to non-isothermal chemical reactions with simultaneous modulation of the input concentration and the volumetric flow-rate.

4/10 relevant

arXiv

Parabolic equations with dynamic **boundary** **conditions** and drift terms

**boundary**

**conditions**by using the approach of sesquilinear forms, and secondly for its backward adjoint equation using the Galerkin approximation and the extension semigroup to a negative Sobolev space.

10/10 relevant

arXiv