Related papers: Exact results concerning multifield moduli of two-…
This is an English translation of the author's Ph.D. thesis, accumulating his results on a construction of Cohen-Macaulay modules over a polynomial ring that appeared in the study of Cauchy-Fueter equations. This construction is generalized…
Any moduli space of representations of a quiver (possibly with oriented cycles) has an embedding as a dense open subvariety into a moduli space of representations of a bipartite quiver having the same type of singularities. A connected…
Obtaining a rigorous and reliable method for linking computer simulations of polymer blends and composites at different length scales of interest is a highly desirable goal in soft matter physics. In this paper a multiscale modeling…
This paper presents a framework based on matrices of monoids for the study of coupled cell networks. We formally prove within the proposed framework, that the set of results about invariant synchrony patterns for unweighted networks also…
The central aim of this monograph is to provide decomposition results for quasi-coherent sheaves on the moduli stack of one-dimensional formal groups. These results will be based on the geometry of the stack itself, particularly the height…
We use Maxwell's equations to derive several models describing the interaction of the multi-mode fundamental field and its second harmonic in a ring microresonator with quadratic nonlinearity and quasi-phase-matching. We demonstrate how…
Chemically active mixtures exhibit complex patterns that emerge from the interplay of physical interactions and reactions among components. Individually, these two processes are well-understood: Physical interactions can give rise to phase…
By the reduced component in a moduli space of stable quasimaps to n-dimensional projective space we mean the closure of the locus in which the domain curves are smooth. As in the moduli space of stable maps, we prove the reduced component…
Let M be a closed 3-manifold and S(M) the skein module of M at some odd root of unity. Using the Frobenius morphism, we can see S(M) as the space of global sections of a coherent sheaf over the SL2 character scheme of M. We prove that when…
Two-phase composites with non-overlapping inclusions randomly embedded in matrix are investigated. A straight forward approach is applied to estimate the effective properties of random 2D composites. First, deterministic boundary value…
We examine metastable configurations of a two-dimensional system of interacting particles on a quenched random potential landscape and ask how the configurational pair correlation function is related to the particle interactions and the…
For time (t) dependent wave functions we derive rigorous conjugate relations between analytic decompositions (in the complex t-plane) of the phases and of the log moduli. We then show that reciprocity, taking the form of Kramers-Kronig…
Over a Cohen-Macaulay (CM) local ring, we characterize those modules that can be obtained as a direct limit of finitely generated maximal CM modules. We point out two consequences of this characterization: (1) Every balanced big CM module,…
We introduce three non-compact moduli stacks parametrizing noncommutative deformations of Hirzebruch surfaces; the first is the moduli stack of locally free sheaf bimodules of rank 2, which appears in the definition of noncommutative…
In this work, we study the adhesion of multi-component vesicle membrane to both flat and curved substrates, based on the conventional Helfrich bending energy for multi-component vesicles and adhesion potentials of different forms. A phase…
We investigate the effective properties (conductivity, diffusivity and elastic moduli) of model random composite media derived from Gaussian random fields and overlapping hollow spheres. The morphologies generated in the models exhibit low…
This note describes moduli spaces of complexes in the derived category of a Veronese double cone $Y$. Focusing on objects with the same class $\kappa_1$ as ideal sheaves of lines, we describe the moduli space of Gieseker stable sheaves and…
The Flory-Huggins theory is a well-established lattice model that is commonly used to study the mixing of distinct chemical species. It can successfully predict phase separation phenomena in blends of incompatible materials. However, it is…
As a continuation of the authors and Wakatsuki's previous paper [5], we study relations among Dirichlet series whose coefficients are class numbers of binary cubic forms. We show that for any integral models of the space of binary cubic…
It is shown that a general two-component feedback loop can be viewed as a deformed Hamiltonian system. Some of the implications of using ideas from theoretical physics to study biological processes are discussed.