A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time

Consider a system of independent random walks in the discrete torus with creation-annihilation of particles and possible explosion of the total number of particles in finite time. Rescaling space and rates for diffusion/creation/annihilation of particles, we obtain a strong law of large numbers for the density of particles in the supremum norm. The limiting object is a classical solution to the semilinear heat equation ? _t u=? _xx u+f(u). If f(u)=u ^p , 1<p??3, we also obtain a law of large numbers for the explosion time.     

Strong Law of Large Numbers for Betti Numbers in the Thermodynamic Regime

Journal of Statistical Physics - We establish the strong law of large numbers for Betti numbers of random ?ech complexes built on $${\mathbb {R}}^N$$ -valued binomial point processes and...     

基本物理常量的最新数值——现代计量科学专题之四

现代量子计量基准的量值建立在基本物理常量的基础之上,因此达到了极高的稳定性和复现性。而基本物理常量数值的精确测定也依赖于现代计量技术。因此在20世纪后半叶,物理学和计量学建立了极为密切的关系。国际物理和化学常量委员会特别成立了一个由物理学家和计量学家联合组成的基本物理常量任务组,收集各国在最精密的基本物理常量测量工作方面的最新进展,并进行“基本物理常量的平差工作”,得到基本物理常量的最新数值。     

Large Numbers Generated by the Riemann Zeta Function

Journal of Experimental and Theoretical Physics - Anomalously large numbers generated of the Riemann zeta function are analyzed. A set of Mersenne primes is investigated. The equations connecting...     

The Search for Variation of Fundamental Constants with Clocks

In many theories beyond the Standard Model the quantities that we call “fundamental constants” become space‐time dependent, leading to corresponding variation of atomic and molecular spectra and clock frequencies. The extraordinary improvement of the atomic clock precision in the past fifteen years enabled testing the constancy of the fundamental constant at a very high level of precision. Herein, searches for the variation of fundamental constants with clocks are discussed, focusing on recent key results and future proposals, including highly charged ion, molecular, and nuclear clocks. The relevance of the recent searches for oscillatory and transient variation of fundamental constants to the major unexplained phenomena of our Universe, the nature of dark matter, is discussed.     

Comment on Sensitivity Coefficients to Variation of Fundamental Constants

Atoms and molecules can serve as sensitive probes of a possible variation of the fine structure constant α and electron‐to‐proton mass ratio μ. Two types of sensitivity coefficients are often used to quantify and compare the sensitivity of different species to the variation of fundamental constants. The dimensionless coefficients K are related to the fractional sensitivity, while dimensional factors q are related to the absolute sensitivity. Here, several common errors and misconceptions regarding these coefficients that frequently appear in the literature are discussed.     

On the Relationship Between Macroscopic and Microscopic Time Constants in gas Discharges

The complicated relationship between macroscopic and microscopic time constants in gas discharges was given on the basis of the theory of the positive column of glow discharges.     

Geometric Origin of Physical Constants in a Kaluza-Klein Tetrad Model

An important feature of Kaluza-Klein theories is their ability to relate fundamental physical constants to the radii of higher dimensions. In previous Kaluza-Klein theory, which unifies the electromagnetic field with gravity as dimensionless components of a Kaluza-Klein metric, i) all fields have the same physical dimensions, ii) the Lagrangian has no explicit dependence on any physical constants except mass, and hence iii) all physical constants in the field equations except for mass originate from geometry. While it seems natural in Kaluza-Klein theory to add fermion fields by defining higher-dimensional bispinor fields on the Kaluza-Klein manifold, these Kaluza-Klein theories do not satisfy conditions (i), (ii), and (iii). In this paper, we show how conditions (i), (ii), and (iii) can be satisfied by including bispinor fields in a tetrad formulation of the Kaluza-Klein model, as well as in an equivalent teleparallel model. This demonstrates an unexpected feature of Dirac's bispinor equation, since conditions (i), (ii), (iii) imply a special relation among the terms in the Kaluza-Klein or teleparallel Lagrangian that would not be satisfied in general.     

Virtual Structure Constants as Intersection Numbers of Moduli Space of Polynomial Maps with Two Marked Points

In this paper, we derive the virtual structure constants used in the mirror computation of the degree k hypersurface in CP ^N-1, by using a localization computation applied to moduli space of polynomial maps from CP ¹ to CP ^N-1 with two marked points. This moduli space corresponds to the GIT quotient of the standard moduli space of instantons of Gauged Linear Sigma Model by the standard torus action. We also apply this technique to the non-nef local geometry ${{\cal O}(1)\oplus {\cal O}(-3)\rightarrow CP^{1}}$ and realize the mirror computation without using Birkhoff factorization. Especially, we obtain a geometrical construction of the expansion coefficients of the mirror maps of these models.     

A Law of Large Numbers for the Zeroes of Heine–Stieltjes Polynomials

We determine the limiting density of the zeroes of Heine–Stieltjes polynomials (or of any set of points satisfying the conclusion of Heine–Stieltjes Theorem) in the thermodynamic limit and use this to prove a strong law of large numbers for the zeroes.     

Physical Dimensions/Units and Universal Constants: Their Invariance in Special and General Relativity

The theory of physical dimensions and units in physics is outlined. This includes a discussion of the universal applicability and superiority of quantity equations. The International System of Units (SI) is one example thereof. By analyzing mechanics and electrodynamics, it naturally leads one, besides the dimensions of length and time, to the fundamental units of action $\mathfrak{h}$, electric charge q, and magnetic flux ?. Also, $q\times ?=\text{action}$ and $q/?=1/\text{resistance}$ are known. These results of classical physics suggests to look into the corresponding quantum aspects of q and ? (and also of $\mathfrak{h}$): The electric charge occurs exclusively in elementary charges e, whereas the magnetic flux can have any value; in specific situations, however, in superconductors of type II at very low temperatures, ? appears quantized in the form of fluxons (Abrikosov vortices). And $\mathfrak{h}$ leads, of course, to the Planck quantum h. Thus, one is directed to superconductivity and, because of the resistance, to the quantum Hall effect. In this way, the Josephson and the quantum Hall effects come into focus quite naturally. One goal is to determine the behavior of the fundamental constants in special and in general relativity.     

10TeV宇宙线时间变化研究

利用羊八井ASγ二期阵列实验数据,分析研究了10TeV宇宙线时间变化,以10.4σ和9.6σ的显著性发现了10TeV宇宙线流强气象效应修正后的半太阳日和太阳日周期变化,没有发现有恒星日变化.同时发现10TeV宇宙线流强有7天左右周期变化的迹象.     

Relation between the Values of Prime Numbers and Their Numbers

Journal of Experimental and Theoretical Physics - The Euler equation gives a set of an infinite number of relations between the values of prime numbers and their numbers. These relations are...