Numerical search for a fundamental theory

We propose a numerical test of fundamental physics based on the complexity measure of a general set of functions, which is directly related to the Kolmogorov (or algorithmic) complexity studied in mathematics and computer science. The analysis can be carried out for any scientific experiment and might lead to a better understanding of the underlying theory. From a cosmological perspective, the anthropic description of fundamental constants can be explicitly tested by our procedure. We perform a simple numerical search by analyzing two fundamental constants: the weak coupling constant and the Weinberg angle, and find that their values are rather atypical.Comment: 6 pages, 3 figures, RevTeX, expansion and clarification, references adde

Evanescent character of the repulsive thermal Casimir force

The physical origin of the negative thermal correction to the Casimir force between metals is clarified. For this purpose the asymptotic behavior of the thermal Casimir force is analyzed at large and small distances in the real frequency representation. Contributions from propagating and evanescent waves are considered separately. At large distances they cancel each other in substantial degree so that only the attractive Lifshitz limit survives. At smaller separations the repulsive evanescent contribution of s-polarization dominates in the case of two metals or a metal and a high-permittivity dielectric. Common origin and order of magnitude of the repulsion in these two cases demonstrate naturalness of the controversial large thermal correction between metals.Comment: to be published in Phys. Rev.

Gravitoviscous protoplanetary disks with a dust component. I. The importance of the inner sub-au region

The central region of a circumstellar disk is difficult to resolve in global numerical simulations of collapsing cloud cores, but its effect on the evolution of the entire disk can be significant. We use numerical hydrodynamics simulations to model the long-term evolution of self-gravitating and viscous circumstellar disks in the thin-disk limit. Simulations start from the gravitational collapse of prestellar cores of 0.5--1.0~$M_\odot$ and both gaseous and dusty subsystems were considered, including a model for dust growth. The inner unresolved 1.0 au of the disk is replaced with a central "smart" cell (CSC) -- a simplified model that simulates physical processes that may occur in this region. We found that the mass transport rate through the CSC has an appreciable effect on the evolution of the entire disk. Models with slow mass transport form more massive and warmer disks and they are more susceptible to gravitational instability and fragmentation, including a newly identified episodic mode of disk fragmentation in the T Tauri phase of disk evolution. Models with slow mass transport through the CSC feature episodic accretion and luminosity bursts in the early evolution, while models with fast transport are characterized by a steadily declining accretion rate with low-amplitude flickering. Dust grows to a larger, decimeter size in the slow transport models and efficiently drifts in the CSC, where it accumulates reaching the limit when streaming instability becomes operational. We argue that gravitational instability, together with streaming instability likely operating in the inner disk regions, constitute two concurrent planet-forming mechanisms, which may explain the observed diversity of exoplanetary orbits (Abridged).Comment: Accepted for publication in Astronomy \& Astrophysic

The Limitations of Optimization from Samples

In this paper we consider the following question: can we optimize objective functions from the training data we use to learn them? We formalize this question through a novel framework we call optimization from samples (OPS). In OPS, we are given sampled values of a function drawn from some distribution and the objective is to optimize the function under some constraint. While there are interesting classes of functions that can be optimized from samples, our main result is an impossibility. We show that there are classes of functions which are statistically learnable and optimizable, but for which no reasonable approximation for optimization from samples is achievable. In particular, our main result shows that there is no constant factor approximation for maximizing coverage functions under a cardinality constraint using polynomially-many samples drawn from any distribution. We also show tight approximation guarantees for maximization under a cardinality constraint of several interesting classes of functions including unit-demand, additive, and general monotone submodular functions, as well as a constant factor approximation for monotone submodular functions with bounded curvature

Phonon-induced decay of the electron spin in quantum dots

We study spin relaxation and decoherence in a GaAs quantum dot due to spin-orbit interaction. We derive an effective Hamiltonian which couples the electron spin to phonons or any other fluctuation of the dot potential. We show that the spin decoherence time $T_2$ is as large as the spin relaxation time $T_1$, under realistic conditions. For the Dresselhaus and Rashba spin-orbit couplings, we find that, in leading order, the effective magnetic field can have only fluctuations transverse to the applied magnetic field. As a result, $T_2=2T_1$ for arbitrarily large Zeeman splittings, in contrast to the naively expected case $T_2\ll T_1$. We show that the spin decay is drastically suppressed for certain magnetic field directions and values of the Rashba coupling constant. Finally, for the spin coupling to acoustic phonons, we show that $T_2=2T_1$ for all spin-orbit mechanisms in leading order in the electron-phonon interaction.Comment: 5 pages, 1 figur

Roughness correction to the Casimir force at short separations: Contact distance and extreme value statistics

So far there has been no reliable method to calculate the Casimir force at separations comparable to the root-mean-square of the height fluctuations of the surfaces. Statistical analysis of rough gold samples has revealed the presence of peaks considerably higher than the root-mean-square roughness. These peaks redefine the minimum separation distance between the bodies and can be described by extreme value statistics. Here we show that the contribution of the high peaks to the Casimir force can be calculated with a pairwise additive summation, while the contribution of asperities with normal height can be evaluated perturbatively. This method provides a reliable estimate of the Casimir force at short distances, and it solves the significant, so far unexplained discrepancy between measurements of the Casimir force between rough surfaces and the results of perturbation theory. Furthermore, we illustrate the importance of our results in a technologically relevant situation.Comment: 29 pages, 11 figures, to appear in Phys. Rev.

Low vorticity and small gas expansion in premixed flames

Different approaches to the nonlinear dynamics of premixed flames exist in the literature: equations based on developments in a gas ex- pansion parameter, weak nonlinearity approximation, potential model equation in a coordinate-free form. However the relation between these different equations is often unclear. Starting here with the low vor- ticity approximation proposed recently by one of the authors, we are able to recover from this formulation the dynamical equations usually obtained at the lowest orders in gas expansion for plane on average flames, as well as obtain a new second order coordinate-free equation extending the potential flow model known as the Frankel equation. It is also common to modify gas expansion theories into phenomelogical equations, which agree quantitatively better with numerical simula- tions. We discuss here what are the restrictions imposed by the gas expansion development results on this process

Bases cognitivas da fono-gramática em russo e árabe

This article discusses the relationship of the inflected changes with the thought processes in two inflected languages belonging to different languages families i.e. Russian (the Slavonic subgroup of the IndoEuropean language family) and Arabic (the Semitic subgroup of the Afro-asiatic language family) by analyzing semantic, phonetic, morphological, and syntactic bases of phono-grammar of cognition – the knowledge of the full progressive inflectional categorization of linguistic levels represented by sound changes. The article is aimed at disclosing a direct relationship of the quantitative sound change of consonant composition with thought processes by which the human brain recognizes language categorization, identification of the mechanism of phonemic structure, which is quantitatively modified to mark the word morphologically and syntactically. Disclosed are the rules of the relationship of phonetic changes with thought processes. It’s stated that cognitive bases of phono-grammar in the Arabic and Russian languages reflect the perceivable association of the sound with meaning.Este artículo discute la relación de los cambios inflexos con los procesos de pensamiento en dos idiomas inflexibles pertenecientes a familias de diferentes idiomas, es decir, ruso (el subgrupo eslavo de la familia de lengua indoeuropea) y árabe (el subgrupo semítico de la familia de lengua afroasiática) mediante el análisis de las bases semánticas, fonéticas, morfológicas y sintácticas de la fono gramática de la cognición: el conocimiento de la categorización flexiva progresiva completa de los niveles lingüísticos representados por los cambios de sonido. El artículo tiene como objetivo revelar una relación directa del cambio de sonido cuantitativo de la composición consonántica con los procesos de pensamiento mediante el cual el cerebro humano reconoce la categorización del lenguaje, identificación del mecanismo de la estructura fonémica, que se modifica cuantitativamente para marcar la palabra morfológica y sintácticamente. Se revelan las reglas de la relación de los cambios fonéticos con los procesos de pensamiento. Se afirma que las bases cognitivas de la fono gramática en los idiomas árabe y ruso reflejan la asociación perceptible del sonido con el significadoEste artigo discute a relação de mudanças flexionadas processos de pensamento em duas línguas inflexíveis pertencentes a famílias de diferentes línguas, ou seja, russo (eslava subgrupo da família de línguas indoeuropéias) e árabe (Família subgrupo semita Afroasiatic) linguagem através da análise semântica, fonética, bases de telefone gramática morfológicas e sintáticas de cognição: o conhecimento da categorização flexiva progressiva cheio de níveis lingüísticos representados por mudanças de som. O artigo destina-se a revelar uma relação directa de mudança de som quantitativa da composição em consonância com os processos de pensamento, através da qual o cérebro humano reconhece a categorização de identificação dos idiomas estrutura mecanismo de fonemas, que é modificado para marcar o quantitativamente palavra morfológica e sintaticamente. As regras da relação das mudanças fonéticas com os processos de pensamento são reveladas. Afirma-se que as bases cognitivas da fono gramática nas línguas árabe e russa refletem a associação perceptível do som com o significad