Related papers: Capacitance between Two Points in an Infinite Grid
Here, we propose a scheme to generate a controllable Ising interaction between superconducting flux qubits. Existing schemes rely on inducting couplings to realize Ising interactions between flux qubits, and the interaction strength is…
We have developed an efficient algorithm for steady axisymmetrical 2D fluid equations. The algorithm employs multigrid method as well as standard implicit discretization schemes for systems of partial differential equations. Linearity of…
In this paper two types of multgrid methods, i.e., the Rayleigh quotient iteration and the inverse iteration with fixed shift, are developed for solving the Maxwell eigenvalue problem with discontinuous relative magnetic permeability and…
We present a new approach to solve a Schr\"odinger Equation autonomous at infinity, by identifying the relation between the arrangement of the spectrum of the concerned operator and the behavior of the nonlinearity at zero and at infinity.…
A unified framework to derive optimized compact schemes for a uniform grid is presented. The optimal scheme coefficients are determined analytically by solving an optimization problem to minimize the spectral error subject to equality…
We study the equilibrium states of energy functions involving a large set of real variables, defined on the links of sparsely connected networks, and interacting at the network nodes, using the cavity and replica methods. When applied to…
The development of algorithms for enhancing the resilience and efficiency of the power grid requires performance evaluation with real topologies of power transmission networks. However, due to security reasons, such topologies and…
This paper deals with the solving of variational inequality problem where the constrained set is given as the intersection of a number of fixed-point sets. To this end, we present an extrapolated sequential constraint method. At each…
A large amount of research activity in power systems areas has focused on developing computational methods to solve load flow equations where a key question is the maximum number of isolated solutions.Though several concrete upper bounds…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
We present two different approaches to model power grids as interconnected networks of networks. Both models are derived from a model for spatially embedded mono-layer networks and are generalised to handle an arbitrary number of network…
We show that the spectral gap problem is undecidable. Specifically, we construct families of translationally-invariant, nearest-neighbour Hamiltonians on a 2D square lattice of d-level quantum systems (d constant), for which determining…
A methodology for handling block-to-block coupling of nonconforming, multiblock summation-by-parts finite difference methods is proposed. The coupling is based on the construction of projection operators that move a finite difference grid…
We consider a microgrid where different prosumers exchange energy altogether by the edges of a given network. Each prosumer is located to a node of the network and encompasses energy consumption, energy production and storage capacities…
Determination of the symmetry property of superconducting gaps has been a central issue in studies to understand the mechanisms of unconventional superconductivity. Although it is often difficult to completely achieve the aforementioned…
Supersymmetric Quantum Mechanics may be used to construct reflectionless potentials and phase-equivalent potentials. The exactly solvable case of the $\lambda sech^2$ potential is used to show that for certain values of the strength…
We prove that there are stationary solutions to the 2D incompressible free boundary Euler equations with two fluids, possibly with a small gravity constant, that feature a splash singularity. More precisely, in the solutions we construct…
The corner points of the capacity region of the two-user Gaussian interference channel under strong or weak interference are determined using the notions of almost Gaussian random vectors, almost lossless addition of random vectors, and…
We consider the interface problem between two incompressible and inviscid fluids in the presence of surface tension. Following the geometric approach of [Shatah,J.;Zeng,C. A priori estimates for Fluid Interface Problems. CPAM, vol.16, no.6,…
For each integer $m \geq 2$, a network is constructed which is solvable over an alphabet of size $m$ but is not solvable over any smaller alphabets. If $m$ is composite, then the network has no vector linear solution over any $R$-module…