Related papers: Local Energy Optimality of Periodic Sets

In this paper, a local-global model reduction method is presented to solve stochastic optimal control problems governed by partial differential equations (PDEs). If the optimal control problems involve uncertainty, we need to use a few…

The ultimate precision of any measurement of the temperature of a quantum system is the inverse of the local quantum thermal susceptibility [De Pasquale et al., Nature Communications 7, 12782 (2016)] of the subsystem with whom the…

In this article, we study the small sphere limit of the Wang-Yau quasi-local energy defined in [18,19]. Given a point $p$ in a spacetime $N$, we consider a canonical family of surfaces approaching $p$ along its future null cone and evaluate…

This is the first in a series of papers on projective positive energy representations of gauge groups. Let $\Xi \rightarrow M$ be a principal fiber bundle, and let $\Gamma_{c}(M,\mathrm{Ad}(\Xi))$ be the group of compactly supported (local)…

Tobasco et al. [Physics Letters A, 382:382-386, 2018; see https://doi.org/10.1016/j.physleta.2017.12.023] recently suggested that trajectories of ODE systems that optimize the infinite-time average of a certain observable can be localized…

There are several concepts and definitions that characterize and give optimality conditions for solutions of a vector optimization problem. One of the most important is the first-order necessary optimality condition that generalizes the…

We perform the energy minimization of the paired composite fermion (CF) wave functions, proposed by M\"oller and Simon (MS) [PRB 77, 075319 (2008)] and extended by Yutushui and Mross (YM) [PRB 102, 195153 (2020)], where the energy is…

Let $f_n$ be a random polynomial of degree $n$ with i.i.d. mean-zero and finite variance random coefficients. It is well known that the roots of $f_n$ cluster uniformly around the unit circle as $n$ grows large. We give a simple and…

We consider the issue of strict, fully discrete \emph{local} energy conservation for a whole class of fully implicit local-charge- and global-energy-conserving particle-in-cell (PIC) algorithms. Earlier studies demonstrated these algorithms…

Number partitioning is a classical problem from combinatorial optimisation. In physical terms it corresponds to a long range anti-ferromagnetic Ising spin glass. It has been rigorously proven that the low lying energies of number…

Fix an odd prime $p$. If $r$ is a positive integer and $f$ a polynomial with coefficients in $\mathbb{F}_{p^r}$, let $P_{p,r}(f)$ be the proportion of $\mathbb{P}^1(\mathbb{F}_{p^r})$ that is periodic with respect to $f$. We show that as…

The energy minimization involved in density functional calculations of electronic systems can be carried out using an exponential transformation that preserves the orthonormality of the orbitals. The energy of the system is then represented…

In this note, we show that the Local Molecular Field theory of Weeks et. al. can be re-derived as an extremum problem for an approximate Helmholtz free energy. Using the resulting free energy as a classical, fluid density functional yields…

Consider the power map $x\mapsto x^L$ for a prime $L\neq 2$ such that $L|q-1$ where $q$ is a power of a prime. We determine the periodic points under this map for $\operatorname{M}_n(q)$, the algebra of $n\times n $ matrices over a finite…

We present a simple, robust and efficient method for varying the parameters in a many-body wave function to optimize the expectation value of the energy. The effectiveness of the method is demonstrated by optimizing the parameters in…

We enumerate and classify all stationary logarithmic configurations of d+2 points on the unit (d-1)-sphere in d-dimensions. In particular, we show that the logarithmic energy attains its relative minima at configurations that consist of two…

Within the two-center shell model parameterization we have defined the optimal shape which fissioning nuclei attain just before the scission and calculated the total deformation energy (liquid drop part plus the shell correction) as…

We develop efficient and high-order accurate finite difference methods for elliptic partial differential equations in complex geometry in the Difference Potentials framework. The main novelty of the developed schemes is the use of local…

We study the pointwise regularity of energy densities associated with harmonic functions on the $N$-dimensional Sierpinski gasket $(N\ge 2)$ with respect to the Kusuoka measure. For any nonconstant harmonic function, we prove that every…

We study point configurations on the torus $\mathbb T^d$ that minimize interaction energies with tensor product structure which arise naturally in the context of discrepancy theory and quasi-Monte Carlo integration. Permutation sets on…