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Lattice discretizations of continuous manifolds are common tools used in a variety of physical contexts. Conventional discrete approximations, however, cannot capture all aspects of the original manifold, notably its topology. In this paper…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
We develop a discrete differential geometry for surfaces of non-constant negative curvature, which can be used to model various phenomena from the growth of flower petals to marine invertebrate swimming. Specifically, we derive and…
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…
The quantum metric encodes the geometric structure of Bloch wave functions and governs a wide range of physical responses. Its Brillouin-zone integral, the quantum weight, appears in the structure factor and provides lower bounds on…
Topological insulators [1-6] is a new quantum phase of matter with exotic properties such as dissipationless transport and protection against Anderson localization [7]. These new states of quantum matter could be one of the missing links…
Topological crystalline superconductors have attracted rapidly rising attention due to the possibility of higher-order phases, which support Majorana modes on boundaries in $d-2$ or lower dimensions. However, although the classification and…
Quantized responses are important tools for understanding and characterizing the universal features of topological phases of matter. In this work, we consider a class of topological crystalline insulators in $3$D with $C_n$ lattice rotation…
(This is a report for the Proceedings of ``Journees Relativistes 1993'' written in September 1993. Containes a short description of the results published elsewhere in the joint paper with A. Ashtekar) Integral calculus on the space of gauge…
Colloids dispersed in nematic liquid crystals form topological composites in which colloid-associated defects mediate interactions while adhering to fundamental topological constraints. Better realising the promise of such materials…
The work is devoted to the development and computational implementation of the homogenization method for modeling unsteady flows of a viscous incompressible fluid in periodic porous media taking into account memory effects. At the…
We present a framework for characterizing higher-order topological phases directly from the one-particle density matrix, without any reference to an underlying Hamiltonian. Our approach extends the mode-shell correspondence, originally…
This paper aims at reviewing nonlinear methods for model order reduction of structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear based…
In recent years there has been a great interest in topological materials and in their fascinating properties. Topological band theory was initially developed for condensed matter systems, but it can be readily applied to arbitrary wave…
In recent years, higher-order topological phases have attracted great interest in various fields of physics. These phases have protected boundary states at lower-dimensional boundaries than the conventional first-order topological phases…
We introduce a computational method to optimize target physical properties in the full configuration space regarding atomic composition, chemical stoichiometry, and crystal structure. The approach combines the universal potential of the…
We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that…
A graphical expansion formula for non-commutative matrix integrals with values in a finite-dimensional real or complex von Neumann algebra is obtained in terms of ribbon graphs and their non-orientable counterpart called Moebius graphs. The…
Noncommutative hypersurfaces, in particular, noncommutative quadric hypersurfaces are major objects of study in noncommutative algebraic geometry. In the commutative case, Kn\"orrer's periodicity theorem is a powerful tool to study…
Multiresolution analyses based upon interpolets, interpolating scaling functions introduced by Deslauriers and Dubuc, are particularly well-suited to physical applications because they allow exact recovery of the multiresolution…