Competing interactions in two dimensional Coulomb systems: Surface charge heterogeneities in co-assembled cationic-anionic incompatible mixtures

A binary mixture of oppositely charged components confined to a plane such as cationic and anionic lipid bilayers may exhibit local segregation. The relative strength of the net short range interactions, which favors macroscopic segregation, and the long range electrostatic interactions, which favors mixing, determines the length scale of the finite size or microphase segregation. The free energy of the system can be examined analytically in two separate regimes, when considering small density fluctuations at high temperatures, and when considering the periodic ordering of the system at low temperatures (F. J. Solis and M. Olvera de la Cruz, J. Chem. Phys. 122, 054905 (2000)). A simple Molecular Dynamics simulation of oppositely charged monomers, interacting with a short range Lennard Jones potential and confined to a two dimensional plane, is examined at different strengths of short and long range interactions. The system exhibits well-defined domains that can be characterized by their periodic length-scale as well as the orientational ordering of their interfaces. By adding salt, the ordering of the domains disappears and the mixture macroscopically phase segregates in agreement with analytical predictions.Comment: 8 pages, 5 figures, accepted for publication in J. Chem. Phys, Figure 1 include

Analytical method for determining the stationary thermal fields in layered structures

Запропоновано метод розрахунку двовимірних стаціонарних, періодичних по просторовій координаті, теплових полів у багатошарових плитах. На верхній і нижній межах плити температура описується парними періодичними функціями з однаковими періодами. На спільних межах шарів виконується умова неперервності температурного поля і рівність теплових потоків. Шукані температури в кожному із шарів записано у вигляді тригонометричних рядів по косинусах. Для забезпечення виконання умов на спільних межах шарів пропонується модифікація методу матриць податливості. Сформульовано алгоритм розв’язання задачі та показано, що спосіб дає точний розв’язок задачі для будь-якої скінченої кількості шарів. Наведено приклади результатів числових досліджень для різних граничних умов. Проведено порівняльний аналіз і зроблено висновки.The method of two-dimensional thermal stationary fields’ calculation in multilayer plates is proposed. Thermal fields are considered periodical along spatial value. The temperature of the upper and lower limits is described by pair periodic functions with similar periods. Continuity condition of thermal field and thermal flow equality is realized within layer limits. Found temperatures of the layers are expressed in trigonometric series cosines. There are two free constants of differential equations solution about amplitude to every layer and harmonic. The method of compliance matrices is proposed for realizing conditions within layer limits. Two auxiliary sequences are introduced for every layer. These sequences are connected with temperature and thermal flow on the upper layer limit. They realize thermal field distribution within layer. The author proved that the elements of one of these sequences are expressed by the elements of another sequence in this layer, and appropriate coefficient of Fourier series of the lower plate limit. Recurrence relations are built for the coefficients of these dependences. These dependences allow calculating the coefficients in accordance with geometrical and physical properties of the plate’s layers, beginning with the lower one. Algorithm of task solution is stated. The author stresses that if the functions describing the upper and lower plate’s limits spread out into the complete Fourier series, then the proposed method provides accurate task solution for any complete quantity of layers. The main advantage of this method is that its labor coefficient rises slowly with layer growth. The results of numerical experiments show the influence of geometrical and physical parameters on the heat distribution in a two-layer plate. Just shows graphs constructed for different conditions at the external borders of the plate. Influence of heat conductivity factor changing in the middle layer of three-dimensional plate on heat distribution within plate is analyzed. Three-dimensional temperature graphs are built. The conclusion has been drawn

Analytical method for determining the stationary thermal fields in layered structures

Запропоновано метод розрахунку двовимірних стаціонарних, періодичних по просторовій координаті, теплових полів у багатошарових плитах. На верхній і нижній межах плити температура описується парними періодичними функціями з однаковими періодами. На спільних межах шарів виконується умова неперервності температурного поля і рівність теплових потоків. Шукані температури в кожному із шарів записано у вигляді тригонометричних рядів по косинусах. Для забезпечення виконання умов на спільних межах шарів пропонується модифікація методу матриць податливості. Сформульовано алгоритм розв’язання задачі та показано, що спосіб дає точний розв’язок задачі для будь-якої скінченої кількості шарів. Наведено приклади результатів числових досліджень для різних граничних умов. Проведено порівняльний аналіз і зроблено висновки.The method of two-dimensional thermal stationary fields’ calculation in multilayer plates is proposed. Thermal fields are considered periodical along spatial value. The temperature of the upper and lower limits is described by pair periodic functions with similar periods. Continuity condition of thermal field and thermal flow equality is realized within layer limits. Found temperatures of the layers are expressed in trigonometric series cosines. There are two free constants of differential equations solution about amplitude to every layer and harmonic. The method of compliance matrices is proposed for realizing conditions within layer limits. Two auxiliary sequences are introduced for every layer. These sequences are connected with temperature and thermal flow on the upper layer limit. They realize thermal field distribution within layer. The author proved that the elements of one of these sequences are expressed by the elements of another sequence in this layer, and appropriate coefficient of Fourier series of the lower plate limit. Recurrence relations are built for the coefficients of these dependences. These dependences allow calculating the coefficients in accordance with geometrical and physical properties of the plate’s layers, beginning with the lower one. Algorithm of task solution is stated. The author stresses that if the functions describing the upper and lower plate’s limits spread out into the complete Fourier series, then the proposed method provides accurate task solution for any complete quantity of layers. The main advantage of this method is that its labor coefficient rises slowly with layer growth. The results of numerical experiments show the influence of geometrical and physical parameters on the heat distribution in a two-layer plate. Just shows graphs constructed for different conditions at the external borders of the plate. Influence of heat conductivity factor changing in the middle layer of three-dimensional plate on heat distribution within plate is analyzed. Three-dimensional temperature graphs are built. The conclusion has been drawn

Ion condensation on charged patterned surfaces

We study ion condensation onto a patterned surface of alternating charges. The competition between self-energy and ion-surface interactions leads to the formation of ionic crystalline structures at low temperatures. We consider different arrangements of underlying ionic crystals, including single ion adsorption, as well as the formation of dipoles at the interface between charged domains. Molecular dynamic simulation illustrates existence of single and mixed phases. Our results contribute to understanding pattern recognition, and molecular separation and synthesis near patterned surfaces.Comment: 3 figure

Electrostatic attraction between cationic-anionic assemblies with surface compositional heterogeneities

Electrostatics plays a key role in biomolecular assembly. Oppositely charged biomolecules, for instance, can co-assembled into functional units, such as DNA and histone proteins into nucleosomes and actin-binding protein complexes into cytoskeleton components, at appropriate ionic conditions. These cationic-anionic co-assemblies often have surface charge heterogeneities that result from the delicate balance between electrostatics and packing constraints. Despite their importance, the precise role of surface charge heterogeneities in the organization of cationic-anionic co-assemblies is not well understood. We show here that co-assemblies with charge heterogeneities strongly interact through polarization of the domains. We find that this leads to symmetry breaking, which is important for functional capabilities, and structural changes, which is crucial in the organization of co-assemblies. We determine the range and strength of the attraction as a function of the competition between the steric and hydrophobic constraints and electrostatic interactions.Comment: JCP June/200

Cloud service for interactive simulation of production location

The paper deals with a problem of decision-making support for production location problem. The paper describes the mathematical model of production location. Minimization of total cost of delivery of raw materials to the place of production is used as a criterion of potential production location. The problem belongs to the class of binary mathematical programming problems with linear constraints but could be reduced to a set of linear programming problems solved by sequential or parallel computing. Based on the mathematical model а software tool is implemented as a cloud service on heterogeneous computing architecture. The software architecture includes the simulation module and modules for control and visualization. The ontology and declarative model for information exchange between the modules are designed with JSON format. This declarative model includes the objects considered in the mathematical model which are “products”, “areas” and “communications”. The simulation module is implemented on a high-performance server platform. Visualization module allows us to present graphically the original and the resulting matrix data and to modify the input parameters of the model interactively. The control and visualization modules are produced within IACPaaS cloud platform. Communication between the modules is established via asynchronous http-queries. The paper demonstrates the use of the software tool for the simulation of production location for the Russian Far East regions based on input data provided by open statistics sources

Correlation of Notions “Democracy”, “Modernization”, “Democratic Transit”

Correlation of notions “democracy”, “modernization” and “democratic transit” is under study. The author sets forth the fundamentals, compares different modern approaches and assessments of democratic transit theory. The grounds to use the theory of democratic transit in modern history studies are given

Unusual features in the nonlinear microwave surface impedance of Y-Ba-Cu-O thin films

Striking features have been found in the nonlinear microwave (8 GHz) surface impedance $Z_s=R_s + jX_s$ of high-quality YBaCuO thin films with comparable low power characteristics [$R_{res}\sim 35--60 \mu\Omega$ and $\lambda_L(15 K)\sim 130--260 nm$]. The surface resistance $R_s$ is found to increase, decrease, or remain independent of the microwave field $H_{rf}$ (up to 60 mT) at different temperatures and for different samples. However, the surface reactance $X_s$ always follows the same functional form. Mechanisms which may be responsible for the observed variations in $R_s$ and $X_s$ are briefly discussed.Comment: 4 pages, 4 figure