Absorbing **boundary** **conditions** for the time-dependent Schr\"odinger-type
equations in $\mathbb R^3$

**boundary**

**conditions**are presented for three-dimensional time-dependent Schr\"odinger-type of equations as a means to reduce the cost of the quantum-mechanical calculations. The

**boundary**

**condition**is first derived from a semi-discrete approximation of the Schr\"odinger equation with the advantage that the resulting formulas are automatically compatible with the finite-difference scheme and no further discretization is needed in space. The absorbing

**boundary**

**condition**is expressed as a discrete Dirichlet-to-Neumann (DtN) map, which can be further approximated in time by using rational approximations of the Laplace transform to enable a more efficient implementation. This approach can be applied to domains with arbitrary geometry. The stability of the zeroth order and first order absorbing

**boundary**

**conditions**is proved. We tested the

**boundary**

**conditions**on benchmark problems. The effectiveness is further verified by a time-dependent Hartree-Fock model with Skyrme interactions. The accuracy in terms of energy and nucleon density is examined as well.

10/10 relevant

arXiv

Inverse square singularities and eigenparameter dependent **boundary**
**conditions** are two sides of the same coin

**boundary**

**conditions**to those with inverse square singularities, and vice versa. Expand abstract.

**boundary**

**conditions**containing rational Herglotz--Nevanlinna functions of the eigenvalue parameter with "a negative number of poles". More precisely, we treat in a unified manner one-dimensional Schr\"{o}dinger operators with either an inverse square singularity or a

**boundary**

**condition**containing a rational Herglotz--Nevanlinna function of the eigenvalue parameter at each endpoint, and define Darboux-type transformations between such operators. These transformations allow one, in particular, to transfer almost any spectral result from

**boundary**value problems with eigenparameter dependent

**boundary**

**conditions**to those with inverse square singularities, and vice versa.

10/10 relevant

arXiv

Continuum damping effects in nuclear collisions associated with twisted
**boundary** **conditions**

**boundary**conditions, which can avoid finite box-size effects of the employed 3D coordinate space, have been implemented. The prolate deformed $^{24}$Mg has been set to different orientations to study vibrations and rotations of the compound nucleus $^{48}$Cr. Our time evolution results show continuum damping effects associated with the twist-averaged

**boundary**

**condition**play a persistent role after the fusion stage. In particular, a rotational damping in continuum is presented in calculations of both twist-averaged and absorbing

**boundary**conditions, in which damping widths can be clearly extracted. It is unusual that the rotating compound nucleus in continuum evolves towards spherical but still has a considerable angular momentum.

10/10 relevant

arXiv

Wave Enhancement through Optimization of **Boundary** **Conditions**

**boundary**

**conditions**. Expand abstract.

**boundary**

**conditions**for the Laplacian from Dirichlet to Neumann can result in significant changes to the associated eigenmodes, while keeping the eigenvalues close. We present a new and efficient approach for optimizing the transmission signal between two points in a cavity at a given frequency, by changing

**boundary**

**conditions**. The proposed approach makes use of recent results on the monotonicity of the eigenvalues of the mixed

**boundary**value problem and on the sensitivity of the Green s function to small changes in the

**boundary**

**conditions**. The switching of the

**boundary**

**condition**from Dirichlet to Neumann can be performed through the use of the recently modeled concept of metasurfaces which are comprised of coupled pairs of Helmholtz resonators. A variety of numerical experiments are presented to show the applicability and the accuracy of the proposed new methodology.

10/10 relevant

arXiv

Introducing Open **boundary** **conditions** in modeling nonperiodic materials
and interfaces: the impact of the periodic assumption

**boundary**

**conditions**are omnipresent in material simulations. In this work, we intro-duce ROBIN (recursive open

**boundary**and interfaces), the first method allowing open

**boundary**

**conditions**in material and interface modeling. The computational costs are limited to solving quantum properties in a focus area which allows explicitly discretizing millions of atoms in real space and to consider virtually any type of environment (be it periodic, regular, or ran-dom). The impact of the periodicity assumption is assessed in detail with silicon dopants in graphene. Graphene was con-firmed 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. Key insight of this assessment is, assuming periodici-ty elevates a small perturbation of a periodic cell into a strong impact on the material property prediction. Periodic

**boundary**

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

**boundary**method for reliable predictions.

10/10 relevant

arXiv

Translation constraints on quantum phases with twisted **boundary**
**conditions**

**boundary**

**conditions**as long as the boundary respects the symmetries. Expand abstract.

**boundary**

**conditions**as long as the

**boundary**respects the symmetries. Based on this physically reasonable requirement, we discuss the Lieb-Schultz-Mattis-type ingappability in two-dimensional quantum magnets under a

**boundary**

**condition**that makes evident a quantum anomaly underlying the lattice system. In particular, we direct our attention to those on the checkerboard lattice which are closely related to frustrated quantum magnets on the square lattice and on the Shastry-Sutherland lattice. Our discussion is focused on the adiabatic U(1) flux insertion through a closed path in a

**boundary**

**condition**twisted by a spatial rotation and a reflection. Two-dimensional systems in this

**boundary**

**condition**are effectively put on a nonorientable space, namely the Klein bottle. We show that the translation symmetry on the Klein-bottle space excludes the possibility of the unique and gapped ground state. Taking advantage of the flux insertion argument, we also discuss the ground-state degeneracy on magnetization plateaus of the Heisenberg antiferromagnet on the checkerboard lattice.

10/10 relevant

arXiv

Nontrivially Topological Phase Structure of Ideal Bose Gas System within
Different **Boundary** **Conditions**

**boundary**

**conditions**, which can be distinguished by the off--diagonal particle number susceptibility. Expand abstract.

**boundary**conditions, \emph{i.e.}, the periodic

**boundary**

**condition**and Dirichlet

**boundary**

**condition**in this work, in an infinite volume, is investigated. It is found that the ground states of ideal Bose gas within those two

**boundary**

**conditions**are both topologically nontrivial, which can not be classified by the traditional symmetry breaking theory. The ground states are different topological phases corresponding to those two

**boundary**conditions, which can be distinguished by the off--diagonal particle number susceptibility. Moreover, this result is universal. The

**boundary**

**condition**may play an important role in pining the critical endpoint of QCD diagram on the approach of the lattice simulations and the computation of some solvable statistical models .

10/10 relevant

arXiv

Interplay between **boundary** **conditions** and Wilson's mass in Dirac-like
Hamiltonians

**boundary**

**conditions**for the envelope functions on finite systems. Considering only Wilson's masses allowed by symmetry, we show that the $k^2$ corrections are equivalent to Berry-Mondragon's discontinuous

**boundary**

**conditions**. This allows for simple numerical implementations of regularized Dirac models on a lattice, while properly accounting for the desired

**boundary**

**condition**. We apply our results on graphene nanoribbons (zigzag and armchair), and on a PbSe monolayer (topological crystalline insulator). For graphene, we find generalized Brey-Fertig

**boundary**conditions, which correctly describes the small gap seen on \textit{ab initio} data for the metallic armchair nanoribbon. On PbSe, we show how our approach can be used to find spin-orbital coupled

**boundary**

**conditions**. Overall, our discussions are set on a generic model that can be easily generalized for any Dirac-like Hamiltonian.

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

Implementation of on-site velocity **boundary** **conditions** for D3Q19 lattice
Boltzmann

**boundary**

**conditions**are often desired for lattice Boltzmann simulations of fluid flow in complex geometries such as porous media or microfluidic devices. Expand abstract.

**boundary**

**conditions**are often desired for lattice Boltzmann simulations of fluid flow in complex geometries such as porous media or microfluidic devices. The possibility to specify the exact position of the boundary, independent of other simulation parameters, simplifies the analysis of the system. For practical applications it should allow to freely specify the direction of the flux, and it should be straight forward to implement in three dimensions. Furthermore, especially for parallelized solvers it is of great advantage if the

**boundary**

**condition**can be applied locally, involving only information available on the current lattice site. We meet this need by describing in detail how to transfer the approach suggested by Zou and He to a D3Q19 lattice. The

**boundary**

**condition**acts locally, is independent of the details of the relaxation process during collision and contains no artificial slip. In particular, the case of an on-site no-slip

**boundary**

**condition**is naturally included. We test the

**boundary**

**condition**in several setups and confirm that it is capable to accurately model the velocity field up to second order and does not contain any numerical slip.

10/10 relevant

arXiv