Search results for "Mathematical physics"

Phase separation of symmetrical polymer mixtures in thin-film geometry

1995

Monte Carlo simulations of the bond fluctuation model of symmetrical polymer blends confined between two “neutral” repulsive walls are presented for chain lengthNA=NB=32 and a wide range of film thicknessD (fromD=8 toD=48 in units of the lattice spacing). The critical temperaturesTc(D) of unmixing are located by finite-size scaling methods, and it is shown that\(T_c (\infty ) - T_c (D) \propto D^{ - {1 \mathord{\left/ {\vphantom {1 {v_3 }}} \right. \kern-\nulldelimiterspace} {v_3 }}} \), wherev3≈0.63 is the correlation length exponent of the three-dimensional Ising model universality class. Contrary to this result, it is argued that the critical behavior of the films is ruled by two-dimensi…

Splittings of Toric Ideals

2019

Let $I \subseteq R = \mathbb{K}[x_1,\ldots,x_n]$ be a toric ideal, i.e., a binomial prime ideal. We investigate when the ideal $I$ can be "split" into the sum of two smaller toric ideals. For a general toric ideal $I$, we give a sufficient condition for this splitting in terms of the integer matrix that defines $I$. When $I = I_G$ is the toric ideal of a finite simple graph $G$, we give additional splittings of $I_G$ related to subgraphs of $G$. When there exists a splitting $I = I_1+I_2$ of the toric ideal, we show that in some cases we can describe the (multi-)graded Betti numbers of $I$ in terms of the (multi-)graded Betti numbers of $I_1$ and $I_2$.

Entanglement dynamics in superconducting qubits affected by local bistable impurities

2012

We study the entanglement dynamics for two independent superconducting qubits each affected by a bistable impurity generating random telegraph noise (RTN) at pure dephasing. The relevant parameter is the ratio $g$ between qubit-RTN coupling strength and RTN switching rate, that captures the physics of the crossover between Markovian and non-Markovian features of the dynamics. For identical qubit-RTN subsystems, a threshold value $g_\mathrm{th}$ of the crossover parameter separates exponential decay and onset of revivals; different qualitative behaviors also show up by changing the initial conditions of the RTN. We moreover show that, for different qubit-RTN subsystems, when both qubits are …

Host–virus evolutionary dynamics with specialist and generalist infection strategies: Bifurcations, bistability, and chaos

2019

In this work, we have investigated the evolutionary dynamics of a generalist pathogen, e.g., a virus population, that evolves toward specialization in an environment with multiple host types. We have particularly explored under which conditions generalist viral strains may rise in frequency and coexist with specialist strains or even dominate the population. By means of a nonlinear mathematical model and bifurcation analysis, we have determined the theoretical conditions for stability of nine identified equilibria and provided biological interpretation in terms of the infection rates for the viral specialist and generalist strains. By means of a stability diagram, we identified stable fixed…

Non-supersymmetric Extremal Black Holes: First-Order Flows and Stabilisation Equations

2013

We review the results of [1, 2] on reducing the second-order equations of motion for stationary extremal black holes in four-dimensional \({\textit{N}}\,=\,2\) supergravity to first-order flow equations and further to non-differential stabilisation equations.

NONSINGULAR BLACK HOLES IN PALATINI EXTENSIONS OF GENERAL RELATIVITY

2015

An introduction to extended theories of gravity formulated in metric-affine (or Palatini) spaces is presented. Focusing on spherically symmetric configurations with electric fields, we will see that in these theories the central singularity present in General Relativity is generically replaced by a wormhole structure. The resulting space-time becomes geodesically complete and, therefore, can be regarded as non-singular. We illustrate these properties considering two different models, namely, a quadratic f(R) theory and a Born-Infeld like gravity theory.

General Relativistic Hydrodynamics and Magnetohydrodynamics: Hyperbolic Systems in Relativistic Astrophysics

2008

A double mean field equation related to a curvature prescription problem

2019

We study a double mean field-type PDE related to a prescribed curvature problem on compacts surfaces with boundary. We provide a general blow-up analysis, then a Moser-Trudinger inequality, which gives energy-minimizing solutions for some range of parameters. Finally, we provide existence of min-max solutions for a wider range of parameters, which is dense in the plane if $��$ is not simply connected.

Structure of Dioxygen Binding Xerogels Incorporating Cyclams Complexed with CuCl2 Salts

2005

X-ray absorption/emission spectroscopies were combined in order to elucidate how hybrid xerogels complexed with CuCl2 could bind reversibly O2. Difference EXAFS analyses at the Cu K-edge revealed the existence of binuclear structures with long Cu...Cu distances, i.e. RCu–Cu ≈ 3.98 A and 3.87 A for the oxygenated and oxygen-free xerogels. In oxygenated xerogels, dioxygen would bridge two Cu atoms in a μ-η1 : η1 peroxo-like conformation. The Cu-O signal found at short distance (RCu−O1 = 1.85 ± 0.01 A) is fully consistent with 40% of O2 molecules being chemisorbed per Cu site. In oxygen-free xerogels, Cl K-edge EXAFS revealed the presence of CuI sites with short Cl-Cu bond lengths (RCl−Cu = 2.…

Quantum criticality on a chiral ladder: An SU(2) infinite density matrix renormalization group study

2019

In this paper we study the ground-state properties of a ladder Hamiltonian with chiral $\text{SU}(2)$-invariant spin interactions, a possible first step toward the construction of truly two-dimensional nontrivial systems with chiral properties starting from quasi-one-dimensional ones. Our analysis uses a recent implementation by us of $\text{SU}(2)$ symmetry in tensor network algorithms, specifically for infinite density matrix renormalization group. After a preliminary analysis with Kadanoff coarse graining and exact diagonalization for a small-size system, we discuss its bosonization and recap the continuum limit of the model to show that it corresponds to a conformal field theory, in agr…