Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases

**boundary**

**conditions**and separate the symmetry-preserving phases from the symmetry-breaking ones. Expand abstract.

**boundary**

**condition**. This is akin to gauging a discrete global symmetry at the

**boundary**of Dijkgraaf-Witten theory. We describe how to "ungauge" the fusion category symmetry in these

**boundary**

**conditions**and separate the symmetry-preserving phases from the symmetry-breaking ones. For Tambara-Yamagami categories and their generalizations, which are associated with Kramers-Wannier-like self-dualities under orbifolding, we develop gauge theoretic techniques which simplify the analysis. We include some examples of CFTs with fusion category symmetry derived from Kramers-Wannier-like dualities as an appetizer for the Part II companion paper.

5/10 relevant

arXiv

Existence of contacts for the motion of a rigid body into a viscous
incompressible fluid with the Tresca **boundary** **conditions**

**boundary**

**condition**s, that permit the fluid to slip tangentially on the boundary under some

**conditions**on the stress tensor. Expand abstract.

**boundary**of the fluid domain, we use the Tresca

**boundary**conditions, that permit the fluid to slip tangentially on the

**boundary**under some

**conditions**on the stress tensor. More precisely, there is a threshold determining if the fluid can slip or not and there is a friction force acting on the part where the fluid can slip. Our main result is the existence of contact in finite time between the ball and the exterior

**boundary**of the fluid for this system in the bidimensional case and in presence of gravity.

10/10 relevant

arXiv

Experimental **boundary** **conditions** of reinstatement induced return of fear in humans: Is reinstatement in humans what we think it is?

**boundary**

**condition**in experimentally-induced return of fear in humans and may challenge what we think we know about the reinstatement phenomenon in humans and call for a critical reconsideration of paradigms as well as mechanisms that may... Expand abstract.

**boundary**

**condition**that may explain divergent findings in the field. A sample of 173 participants is exposed to a fear acquisition training, immediate extinction training, and reinstatement test experiment. Three groups differing in the number of reinstatement US are employed: one (n = 57) or four (n = 55) in experimental groups and zero (n = 61) in the control group. We adopt Bayesian statistical approaches beyond classical null hypothesis significance testing to qualify evidence for or against this potential methodological

**boundary**

**condition**in reinstatement-induced return of fear. Both groups exposed to reinstatement USs (RI-USone and RI-USfour) showed increased startle potentiation to the reinstatement administration context as compared to the RI-USzero group, supporting the role of context conditioning in reinstatement. This did however not transfer to responding to conditioned stimuli during the return of fear-test, as no evidence for an effect of the number of reinstatement USs (zero, one, four) was observed in either behavioral or physiological measures. In sum, our results speak against the number of reinstatement USs as a potential

**boundary**

**condition**in experimentally-induced return of fear in humans and may challenge what we think we know about the reinstatement phenomenon in humans and call for a critical reconsideration of paradigms as well as mechanisms that may underlie some reinstatement effects in the literature.

10/10 relevant

PsyArXiv

Artificial **boundary** method for the solution of pricing European options
under the Heston model

**boundary**

**conditions**by Heston in the original paper (Heston, 1993). Expand abstract.

**boundary**method for solving the problem on a truncated domain, and derive several artificial

**boundary**

**conditions**(ABCs) on the artificial

**boundary**of the bounded computational domain. A typical finite difference scheme and quadrature rule are used for the numerical solution of the reduced problem. Numerical experiments show that the proposed ABCs are able to improve the accuracy of the results and have a significant advantage over the widely-used

**boundary**

**conditions**by Heston in the original paper (Heston, 1993).

4/10 relevant

arXiv

Extension and comparison of techniques to enforce **boundary** **conditions** in
Finite Volume POD-Galerkin reduced order models for fluid dynamic problems

**boundary**

**conditions**are controlled using two different boundary control strategies: the control function method, whose aim is to obtain homogeneous basis functions for the reduced basis space and... Expand abstract.

**boundary**

**conditions**are controlled using two different

**boundary**control strategies: the control function method, whose aim is to obtain homogeneous basis functions for the reduced basis space and the penalty method where the

**boundary**

**conditions**are enforced in the reduced order model using a penalty factor. The penalty method is improved by using an iterative solver for the determination of the penalty factor rather than tuning the factor with a sensitivity analysis or numerical experimentation. The

**boundary**control methods are compared and tested for two cases: the classical lid driven cavity benchmark problem and a Y-junction flow case with two inlet channels and one outlet channel. The results show that the boundaries of the reduced order model can be controlled with the

**boundary**control methods and the same order of accuracy is achieved for the velocity and pressure fields. Finally, the speedup ratio between the reduced order models and the full order model is of the order 1000 for the lid driven cavity case and of the order 100 for the Y-junction test case.

10/10 relevant

arXiv

Lp-strong solution to fluid-rigid body interaction system with Navier
slip **boundary** **condition**

7/10 relevant

arXiv

Sufficient Stability **Conditions** for Time-varying Networks of
Telegrapher's Equations or Difference Delay Equations

**condition**for exponential stability of a network of lossless telegrapher's equations, coupled by linear time-varying

**boundary**

**conditions**. The sufficient

**conditions**is in terms of dissipativity of the couplings, which is natural for instance in the context of microwave circuits. Exponential stability is with respect to any $L^p$-norm, $1\leq p\leq\infty$. This also yields a sufficient

**condition**for exponential stability to a special class of linear time-varying difference delay systems which is quite explicit and tractable. One ingredient of the proof is that $L^p$ exponential stability for such difference delay systems is independent of $p$, thereby reproving in a simpler way some results from [3].

4/10 relevant

arXiv

Global existence, smooth and stabilization in a three-dimensional Keller-Segel-Navier-Stokes system with rotational flux

**boundary**

**conditions**in a bounded domain $\Omega\subseteq \mathbb{R}^{3}$ with smooth boundary, where $\phi\in W^{2,\infty} (\Omega)$ and $\kappa\in \mathbb{R}$ represent the prescribed gravitational potential and the strength of nonlinear fluid convection, respectively. Here the matrix-valued function $S(x,n,c)\in C^2(\bar{\Omega}\times[0,\infty)^2 ;\mathbb{R}^{3\times 3})$ denotes the rotational effect which satisfies $|S(x,n,c)|\leq C_S(1 + n)^{-\alpha}$ with some $C_S > 0$ and $\alpha\geq 0$. In this paper, by seeking some new functionals and using the bootstrap arguments on system $(*)$, we establish the existence of global weak solutions to system $(*)$ for arbitrarily large initial data under the assumption $\alpha\geq1$. Moreover, under an explicit

**condition**on the size of $C_S$ relative to $C_N$, we can secondly prove that in fact any such {\bf weak} solution $(n,c,u)$ becomes smooth ultimately, and that it approaches the unique spatially homogeneous steady state $(\bar{n}_0,\bar{n}_0,0)$, where $\bar{n}_0=\frac{1}{|\Omega|}\int_{\Omega}n_0$ and $C_N$ is the best Poincar\'{e} constant. To the best of our knowledge, there are the first results on asymptotic behavior of the system.

4/10 relevant

arXiv

Absorbing **Boundary** **Condition** as Limiting Case of Imaginary Potentials

**boundary**$\partial \Omega$ of $\Omega$ in the same way as by a Dirichlet

**boundary**

**condition**on $\partial \Omega$. This phenomenon, a cousin of the "quantum Zeno effect," might suggest that a hard detector is mathematically impossible. Nevertheless, a mathematical description of a hard detector has recently been put forward in the form of the "absorbing

**boundary**rule" involving an absorbing

**boundary**

**condition**on the detecting surface $\partial \Omega$. We show here that in a suitable (non-obvious) limit, the imaginary potential $V$ yields a non-trivial distribution of detection time and place in agreement with the absorbing

**boundary**rule. That is, a hard detector can be obtained as a limit, but it is a different limit than Allcock considered.

8/10 relevant

arXiv

Diffusion Maps for Embedded Manifolds with **Boundary** with Applications to
PDEs

**boundary**

**conditions**for some common PDEs based on the Laplacian. Expand abstract.

**boundary**

**conditions**. Notice that the construction of triangulations on unknown manifolds can be both difficult and expensive, both in terms of computational and data requirements, our goal is to solve these problems without such constructions. Instead, we rely only on using the sample points to define quadrature formulas on the unknown manifold. Our main tool is the diffusion maps algorithm. We re-analyze this well-known method in a weak (variational) sense. The latter reduces the smoothness requirements on the underlying functions which is crucial to approximating weak solutions to PDEs. As a by-product, we also provide a rigorous justification of the well-known relationship between diffusion maps and the Neumann eigenvalue problems. We then use a recently developed method of estimating the distance to

**boundary**function (notice that the

**boundary**location is assumed to be unknown and must be estimated from data) in order to correct the

**boundary**error term in the diffusion maps construction. Finally, using this estimated distance, we illustrate how to impose Dirichlet, Neumann, and mixed

**boundary**

**conditions**for some common PDEs based on the Laplacian. Several numerical examples confirm our theoretical findings.

5/10 relevant

arXiv