Quaternionic Kähler Metrics Associated to Special Kähler Manifolds with Mutually Local Variations of BPS Structures

We construct a quaternionic Kähler manifold from a conical special Kähler manifold with a certain type of mutually local variation of BPS structures. We give global and local explicit formulas for the quaternionic Kähler metric and specify under which conditions it is positive-definite. Locally, the metric is a deformation of the 1-loop corrected Ferrara–Sabharwal metric obtained via the supergravity c-map. The type of quaternionic Kähler metrics we obtain is related to work in the physics literature by S. Alexandrov and S. Banerjee, where they discuss the hypermultiplet moduli space metric of type IIA string theory, with mutually local D-instanton corrections.

Phase transition in a stochastic geometry model with applications to statistical mechanics

We study the connected components of the stochastic geometry model on Poisson points which is obtained by connecting points with a probability that depends on their relative position. Equivalently, we investigate the random clusters of the ran- dom connection model defined on the points of a Poisson process in d-dimensional space where the links are added with a particular probability function. We use the thermodynamicrelationsbetweenfreeenergy,entropyandinternalenergytofindthe functions of the cluster size distribution in the statistical mechanics of extensive and non-extensive. By comparing these obtained functions with the probability function predicted by Penrose, we provide a suitable approximate probability function. More- over, we relate this stochastic geometry model to the physics literature by showing how the fluctuations of the thermodynamic quantities of this model correspond to other models when a phase transition (10.1002/mma.6965, 2020) occurs. Also, we obtain the critical point using a new analytical method.

Linear stability analysis of the homogeneous Couette flow in a 2D isentropic compressible fluid

In this paper, we study the linear stability properties of perturbations around the homogeneous Couette flow for a 2D isentropic compressible fluid in the domain $$\mathbb {T}\times \mathbb {R}$$ T × R . In the inviscid case there is a generic Lyapunov type instability for the density and the irrotational component of the velocity field. More precisely, we prove that their $$L^2$$ L 2 norm grows as $$t^{1/2}$$ t 1 / 2 and this confirms previous observations in the physics literature. On the contrary, the solenoidal component of the velocity field experiences inviscid damping, namely it decays to zero even in the absence of viscosity. For a viscous compressible fluid, we show that the perturbations may have a transient growth of order $$\nu ^{-1/6}$$ ν - 1 / 6 (with $$\nu ^{-1}$$ ν - 1 being proportional to the Reynolds number) on a time-scale $$\nu ^{-1/3}$$ ν - 1 / 3 , after which it decays exponentially fast. This phenomenon is also called enhanced dissipation and our result appears to be the first to detect this mechanism for a compressible flow, where an exponential decay for the density is not a priori trivial given the absence of dissipation in the continuity equation.

Physics Formalism Helmholtz Matrix to Coulomb Gage

Iyer Markoulakis Helmholtz Hamiltonian mechanics formalisms mathematically modeled physics with vortex rotational fields acting with gradient fields, typically in zero-point microblackhole general fields. Here, Helmholtz metrics have been gaged to Coulombic Hilbert metrics, representing Gilbertian and Amperian natures of electromagnetic fields out of the mechanical fields from Helmholtz Hamiltonian mechanics. This ansatz general gaging helps to properly isolate field effects – mechanical, electric, magnetic components within the analytical processes. Vacuum gravitational fields and the flavor Higgs-Boson matter inertial gravitational fields have been thus quantified extending to stringmetrics constructs matrix showing charge asymmetry gage metrics, having the power to analyze dark energy superluminal phase, dark matter luminal phase, and light matter subluminal phase. Interpreting particle physics gage matrix pointing to Dirac seas electrons, monopoles with positrons, electron-positron annihilation leading to energy production, relativistic energy generating matter, and both monopoles – vacuum and compressed out of vortex Helmholtz decomposition fields have been interpolated. Quantum ASTROPHYSICS gage metrix posits superluminal profile of signals velocity generating electron-positron chain like “curdling” action that is consistent with physics literature reporting nature electron photon observed oscillatory fields configurations. This helps proposing creation of neutrino antineutrino pair orthogonal to electron positron “curdling” planes, that may lead to formation of protonic hydrogen of stars or orthogonally muon. These aspects will explain receding or fast expanding universe with dark matter in terms of flavor metrics versus gage associating metrics flavor. Additional interpretations of virtual gravitational dipoles that have gravitational charge of opposite signs, reported per physics literature at Planck dimensions, that may originate at the center of supermassive blackhole. On the other hands, vacuum monopoles occur probably at infinity with cosmos extent.

A Preliminary Case for Wave Function Realism

This chapter explains the use of wave functions in quantum mechanics in order to develop a preliminary argument for wave function realism, one that is commonly found in the physics and philosophy of physics literature. It distinguishes ontological questions about the status of the wave function from the more discussed measurement problem for quantum mechanics, and explains how wave function realism is an approach to ontology that is compatible with several rival solutions to the measurement problem. The chapter then presents an initial, but not ultimately decisive, argument for wave function realism based on the ubiquity of wave function representations in quantum physics.

Symmetry, Antisymmetry, and Chirality: Use and Misuse of Terminology

We outline the need for rigorous and consensual definitions in the field of symmetry, in particular about chirality. We provide examples of confusing use of such terminology in the mathematical literature and in the physics literature. In particular, we prove that an antisymmetric function is symmetric for a wide class of metrics. It may be either direct-symmetric or achiral or both direct-symmetric and achiral.

Near-critical 2D percolation with heavy-tailed impurities, forest fires and frozen percolation

We introduce a new percolation model on planar lattices. First, impurities (“holes”) are removed independently from the lattice. On the remaining part, we then consider site percolation with some parameter p close to the critical value $$p_c$$ p c . The mentioned impurities are not only microscopic, but allowed to be mesoscopic (“heavy-tailed”, in some sense). For technical reasons (the proofs of our results use quite precise bounds on critical exponents in Bernoulli percolation), our study focuses on the triangular lattice. We determine explicitly the range of parameters in the distribution of impurities for which the connectivity properties of percolation remain of the same order as without impurities, for distances below a certain characteristic length. This generalizes a celebrated result by Kesten for classical near-critical percolation (which can be viewed as critical percolation with single-site impurities). New challenges arise from the potentially large impurities. This generalization, which is also of independent interest, turns out to be crucial to study models of forest fires (or epidemics). In these models, all vertices are initially vacant, and then become occupied at rate 1. If an occupied vertex is hit by lightning, which occurs at a very small rate $$\zeta $$ ζ , its entire occupied cluster burns immediately, so that all its vertices become vacant. Our results for percolation with impurities are instrumental in analyzing the behavior of these forest fire models near and beyond the critical time (i.e. the time after which, in a forest without fires, an infinite cluster of trees emerges). In particular, we prove (so far, for the case when burnt trees do not recover) the existence of a sequence of “exceptional scales” (functions of $$\zeta $$ ζ ). For forests on boxes with such side lengths, the impact of fires does not vanish in the limit as $$\zeta \searrow 0$$ ζ ↘ 0 . This surprising behavior, related to the non-monotonicity of these processes, was not predicted in the physics literature.

Speech tested for Zipfian fit using rigorous statistical techniques

Zipf’s law describes the relationship between the frequencies of words in a corpus and their rank. Its most basic form is a simple series, indicating that the frequency of a word is inverselyproportional to its rank:1/2, 1/3, 1/4,...The past two decades have seen the emergence of usage-based and cognitive approaches to language study. A key observation of these approaches, along with the importance of frequency, is that speech differs in substantial and structural ways from writing. Yet, except for a few older analyses performed on very small corpora, most studies of Zipf’s law have been done on written corpora. Further, a judgement of Zifianness in much of this work is based on loose and informal criteria. In fact, sophisticated statistical techniques have been developed for curve fitting in recent years in the mathematics and physics literature. These include the use of the Kolmogorov-Smirnov statistic, along with maximum likelihood estimation to generate p-values and the use of the complementary error function for normal distributions. The latter helps determine if a corpus, failing a Zipfian fit, might be better described by another distribution. In this paper, we will:Show that three corpora of recorded speech follow a power law distribution using rigorous statis- tical techniques: Buckeye, Santa Barbara, MiCaseDescribe preliminary results showing that the techniques outlined in this paper may be useful in the diagnoses of those conditions that can include disordered speech.Explain how to do the analyses described in this paper.Explain how to download and use the R/Python code we have written and packaged as the Zipf Tool Kit

Some Remarks on Replicated Simulated Annealing

Recently authors have introduced the idea of training discrete weights neural networks using a mix between classical simulated annealing and a replica ansatz known from the statistical physics literature. Among other points, they claim their method is able to find robust configurations. In this paper, we analyze this so called “replicated simulated annealing” algorithm. In particular, we give criteria to guarantee its convergence, and study when it successfully samples from configurations. We also perform experiments using synthetic and real data bases.