Time-, Frequency-, and Wavevector-Resolved X-Ray Diffraction from Single Molecules

Using a quantum electrodynamic framework, we calculate the off-resonant scattering of a broad-band X-ray pulse from a sample initially prepared in an arbitrary superposition of electronic states. The signal consists of single-particle (incoherent) and two-particle (coherent) contributions that carry different particle form factors that involve different material transitions. Single-molecule experiments involving incoherent scattering are more influenced by inelastic processes compared to bulk measurements. The conditions under which the technique directly measures charge densities (and can be considered as diffraction) as opposed to correlation functions of the charge-density are specified. The results are illustrated with time- and wavevector-resolved signals from a single amino acid molecule (cysteine) following an impulsive excitation by a stimulated X-ray Raman process resonant with the sulfur K-edge. Our theory and simulations can guide future experimental studies on the structures of nano-particles and proteins

Clustering of matter in waves and currents

The growth rate of small-scale density inhomogeneities (the entropy production rate) is given by the sum of the Lyapunov exponents in a random flow. We derive an analytic formula for the rate in a flow of weakly interacting waves and show that in most cases it is zero up to the fourth order in the wave amplitude. We then derive an analytic formula for the rate in a flow of potential waves and solenoidal currents. Estimates of the rate and the fractal dimension of the density distribution show that the interplay between waves and currents is a realistic mechanism for providing patchiness of pollutant distribution on the ocean surface.Comment: 4 pages, 1 figur

Power-law tail distributions and nonergodicity

We establish an explicit correspondence between ergodicity breaking in a system described by power-law tail distributions and the divergence of the moments of these distributions.Comment: 4 pages, 1 figure, corrected typo

Representations of hom-Lie algebras

In this paper, we study representations of hom-Lie algebras. In particular, the adjoint representation and the trivial representation of hom-Lie algebras are studied in detail. Derivations, deformations, central extensions and derivation extensions of hom-Lie algebras are also studied as an application.Comment: 16 pages, multiplicative and regular hom-Lie algebras are used, Algebra and Representation Theory, 15 (6) (2012), 1081-109

THEORY OF INTEGRAL INDIVIDUALITY BY V. S. MERLIN: HISTORY AND NOWADAYS

The study is devoted to overview and analysis of V. S. Merlin’ theory of integral individuality.The aim of the study is to reveal a system’s background of the theory of integral individuality; to designate its current issues and to put new tasks of its further advancement. Methodology and research methods. Problematic and comparative analyses are used. A systematization of the main assumptions of the theory by V. S. Merlin shows that it is based on a general systemic approach and current ideas about integration. Results. It is demonstrated that the system-based approach provides a multi-focus perspective to view the integral individuality. Mostly, the following system ideas are embedded in V. S. Merlin’s theory. They are the concepts of structural levels, teleology, and polymorphism. With respect to the theory of integral individuality, a human is shown as a big system. It consists of a hierarchical set not included in each other, but relatively autonomous operative multilevel subsystems. They link one to another in a polymorphic multi-valued (many-tomany) way. The main features of integral individuality are seen as the hierarchical arrangement and levels, integration and differentiation, teleology and causality, flexibility of polymorphic links (between levels) and rigidity of causal links (within levels). In spite of its maturity, this theory can be put in a further progress. This perspective has been elaborated based on three key ideas – multi-quality, commonality, and isomerism. Scientific novelty. The routes of the phenomenon of integral individuality are uncovered. Its main properties are described: a systemic version of integrity, hierarchy, and polymorphism. Some topical problems are highlighted within the theory of integral individuality. Next tasks can be set to further develop the theory of integral individuality. They focus on shift from the systemic viewpoint to a multi-systemic outline, to combine integrity and commonality, to provide an isomerism coming from the polymorphic framework.Practical significance. The materials and thesis stressed in this article can be useful for researchers studying holistic conceptions of human. The theory of integral individuality can guide investigations designated to test Merlin’s assumptions under various conditions.Статья посвящена анализу теории интегральной индивидуальности, разработанной видным деятелем отечественной психологической науки, основателем Пермской психологической школы В. С. Мерлином. Цель публикации – выявить фундаментальные системные идеи в теории интегральной индивидуальности, обозначить ее актуальные направления и поставить очередные задачи ее дальнейшего развития. Методология и методы исследования. Использовались проблемный анализ, систематизация основных положений разбираемой теории. Методологической базой изучения обсуждаемых проблем послужил системный подход и современные представления об интеграции. Результаты. Показано, что системный подход открывает многоаспектное видение явления и позволяет рассматривать его в нескольких системах координат. Учение об интегральной индивидуальности представляет собой вариант целостного подхода к человеку с позиций принципов общей теории систем. В теории Мерлина реализованы, прежде всего, следующие фундаментальные идеи: о структурных уровнях, телеологической детерминации и полиморфизме. Теория интегральной индивидуальности трактует человека как большую систему, которая складывается из иерархической совокупности не входящих друг в друга, относительно автономно сосуществующих разноуровневых подсистем, много-многозначно (полиморфно) связанных между собой. Иерархический способ организации и уровни, единство интеграции и дифференциации, телеологический и каузальный типы детерминации, гибкость много-многозначных (полиморфных) и жесткость однозначных связей – таковы главные особенности взгляда на человека в этой теории. Учение Мерлина имеет значительный потенциал для дальнейшего развития. Эту задачу можно решать, сосредоточившись на трех актуальных проблемах – многокачественности, общности и изомерии.Научная новизна. Вскрыта сущность феномена интегральной индивидуальности. Описаны его главные атрибуты – системный вариант целостности, иерархия и полиморфизм. Обозначены актуальные проблемы и намечены очередные задачи дальнейшего развития теории интегральной индивидуальности по линиям перехода от системного к полисистемному ее развитию, общности и изомерии. Практическая значимость. Материалы статьи могут быть полезны исследователям, занимающимся изучением целостных представлений о человеке, проводящим эмпирические исследования в русле теории интегральной индивидуальности В. С. Мерлина

Rational Approximate Symmetries of KdV Equation

We construct one-parameter deformation of the Dorfman Hamiltonian operator for the Riemann hierarchy using the quasi-Miura transformation from topological field theory. In this way, one can get the approximately rational symmetries of KdV equation and then investigate its bi-Hamiltonian structure.Comment: 14 pages, no figure

Applications of Temperley-Lieb algebras to Lorentz lattice gases

Motived by the study of motion in a random environment we introduce and investigate a variant of the Temperley-Lieb algebra. This algebra is very rich, providing us three classes of solutions of the Yang-Baxter equation. This allows us to establish a theoretical framework to study the diffusive behaviour of a Lorentz Lattice gas. Exact results for the geometrical scaling behaviour of closed paths are also presented.Comment: 10 pages, latex file, one figure(by request

Minimal Stochastic Model for Fermi's Acceleration

We introduce a simple stochastic system able to generate anomalous diffusion both for position and velocity. The model represents a viable description of the Fermi's acceleration mechanism and it is amenable to analytical treatment through a linear Boltzmann equation. The asymptotic probability distribution functions (PDF) for velocity and position are explicitly derived. The diffusion process is highly non-Gaussian and the time growth of moments is characterized by only two exponents $\nu_x$ and $\nu_v$. The diffusion process is anomalous (non Gaussian) but with a defined scaling properties i.e. $P(|{\bf x}|,t) = 1/t^{\nu_x}F_x(|{\bf x}|/t^{\nu_x})$ and similarly for velocity.Comment: RevTeX4, 4 pages, 2 eps-figures (minor revision

Crystallization of the ordered vortex phase in high temperature superconductors

The Landau-Khalatnikov time-dependent equation is applied to describe the crystallization process of the ordered vortex lattice in high temperature superconductors after a sudden application of a magnetic field. Dynamic coexistence of a stable ordered phase and an unstable disordered phase, with a sharp interface between them, is demonstrated. The transformation to the equilibrium ordered state proceeds by movement of this interface from the sample center toward its edge. The theoretical analysis dictates specific conditions for the creation of a propagating interface, and provides the time scale for this process.Comment: 8 pages and 3 figures; to be published in Phys. Rev. B (Rapid Communications section