Solvation dynamics in methanol: Experimental and molecular dynamics simulation studies

We have investigated the ultrafast dynamics of methanol by time dependent fluorescent shift experiments and molecular dynamic simulations. The experiments were performed with two different probe molecules, 1-aminonaphthalene and coumarin 153. The molecular dynamic simulations employed these probes as well as small atomic and diatomic solutes. We find a previously unobserved fast decay component in the solvation response of methanol. The molecular dynamics results are in good agreement with this experimental result. The origin of this fast response and the linearity of the solvent response are discussed.     

A formula for the number of Latin squares

We establish an explicit formula for the number of Latin squares of order n:

, where B_n is the set of n×n(0,1) matrices, σ₀(A is the number of zero elements of the matrix A and per A is the permanent of the matrix A.     

Experimental study of the time-dependent rate of K → πππ

The time-dependence of the decay rate of initially pure K⁰ into the final state (π⁺π⁻π⁰) has been studied in search for the decay k_S⁰→π⁺π⁻π⁰. No evidence is found in a sample of 384 observed events. The ratio of the CP -violating K_S⁰ amplitude and the K_L⁰ amplitude is η₊₋₀ = (0.13_−0.20^+0.17) + i(0.17_−0.26^+0.27); the ratio of the CP-conserving K_S⁰ amplitude and the K_L⁰ amplitude is < 0.4. The energy dependence of the K⁰→π⁺π⁻π⁰ matrix element is found to be a₊₋₀ = −0.31 ± 0.03.     

Distortion of alpha-uranium structure in praseodymium metal to 311 GPA

It is generally observed that the rare earth metals adapt an orthorhombic alpha-uranium (α-U) structure at high pressures following the delocalization of 4f shell under compression. We examine the stability of the α-U structure in praseodymium metal at ultrahigh pressures of 313 GPa (volume compression V/V ₀?=?0.343) in a diamond anvil cell at room temperature. X-ray diffraction data show a transformation from the α-U structure to a primitive orthorhombic P2₁2₁2₁ phase at 147±5 GPa, which is characterized by the anisotropic compressibility of various crystallographic axes. This anisotropic compressibility leads to an interesting situation when the b-axis and the c-axis of the orthorhombic phase become nearly equal above 260 GPa and the structure can be regarded as a pseudo-tetragonal phase. Our present study shows that the 4f band metal Pr does not adapt a body centred tetragonal phase as predicted by theory, but instead novel crystallographic phases are observed at extreme compressions. The present results have a broader impact on the stability of the α-U phase in a variety of f-band systems at high pressures.     

Determination of the spacetime from local time measurements

We consider an inverse problem for a Lorentzian spacetime (M, g), and show that time measurements, that is, the knowledge of the Lorentzian time separation function on a submanifold \(\Sigma \subset M\) determine the \(C^\infty \)-jet of the metric in the Fermi coordinates associated to \(\Sigma \). We use this result to study the global determination of the spacetime (M, g) when it has a real-analytic structure or is stationary and satisfies the Einstein-scalar field equations. In addition to this, we require that (M, g) is geodesically complete modulo scalar curvature singularities. The results are Lorentzian counterparts of extensively studied inverse problems in Riemannian geometry—the determination of the jet of the metric and the boundary rigidity problem. We give also counterexamples in cases when the assumptions are not valid, and discuss inverse problems in general relativity.     

d- Dimensional Dual Hyperovals in PG(d + n, 2) for d + 1 ≤ n ≤ 3d − 7

Assume that d ≥  4. Then there exists a d -dimensional dual hyperoval in PG(d +  n, 2) for d +  1  ≤  n ≤  3 d −  7.     

Particle Interactions Mediated by Dynamical Networks: Assessment of Macroscopic Descriptions

We provide a numerical study of the macroscopic model of Barré et al. (Multiscale Model Simul, 2017, to appear) derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodeling process is very fast, the macroscopic model takes the form of a single aggregation–diffusion equation for the density of particles. The theoretical study of the macroscopic model gives precise criteria for the phase transitions of the steady states, and in the one-dimensional case, we show numerically that the stationary solutions of the microscopic model undergo the same phase transitions and bifurcation types as the macroscopic model. In the two-dimensional case, we show that the numerical simulations of the macroscopic model are in excellent agreement with the predicted theoretical values. This study provides a partial validation of the formal derivation of the macroscopic model from a microscopic formulation and shows that the former is a consistent approximation of an underlying particle dynamics, making it a powerful tool for the modeling of dynamical networks at a large scale.     

Breakdown of a 2D Heteroclinic Connection in the Hopf-Zero Singularity (II): The Generic Case

In this paper, we prove the breakdown of the two-dimensional stable and unstable manifolds associated to two saddle-focus points which appear in the unfoldings of the Hopf-zero singularity. The method consists in obtaining an asymptotic formula for the difference between these manifolds which turns to be exponentially small respect to the unfolding parameter. The formula obtained is explicit but depends on the so-called Stokes constants, which arise in the study of the original vector field and which corresponds to the so-called inner equation in singular perturbation theory.     

Division Algebras with Left Algebraic Commutators

Let D be a division algebra with center F and K a (not necessarily central) subfield of D. An element a ∈ D is called left algebraic (resp. right algebraic) over K, if there exists a non-zero left polynomial a ₀ + a ₁ x + ? + a _n x ⁿ (resp. right polynomial a ₀ + x a ₁ + ? + x ⁿ a _n ) over K such that a ₀ + a ₁ a + ? + a _n a ⁿ = 0 (resp. a ₀ + a a ₁ + ? + a ⁿ a _n ). Bell et al. proved that every division algebra whose elements are left (right) algebraic of bounded degree over a (not necessarily central) subfield must be centrally finite. In this paper we generalize this result and prove that every division algebra whose all multiplicative commutators are left (right) algebraic of bounded degree over a (not necessarily central) subfield must be centrally finite provided that the center of division algebra is infinite. Also, we show that every division algebra whose multiplicative group of commutators is left (right) algebraic of bounded degree over a (not necessarily central) subfield must be centrally finite. Among other results we present similar result regarding additive commutators under certain conditions.