Existence and concentration of solutions for a class of biharmonic equations

Some superlinear fourth order elliptic equations are considered. A family of solutions is proved to exist and to concentrate at a point in the limit. The proof relies on variational methods and makes use of a weak version of the Ambrosetti-Rabinowitz condition. The existence and concentration of solutions are related to a suitable truncated equation. (C) 2012 Elsevier Inc. All rights reserved.

Liquid–Vapor Interface of Formic Acid Solutions in Salt Water: A Comparison of Macroscopic Surface Tension and Microscopic in Situ X-ray Photoelectron Spectroscopy Measurements

The liquid–vapor interface is difficult to access experimentally but is of interest from a theoretical and applied point of view and has particular importance in atmospheric aerosol chemistry. Here we examine the liquid–vapor interface for mixtures of water, sodium chloride, and formic acid, an abundant chemical in the atmosphere. We compare the results of surface tension and X-ray photoelectron spectroscopy (XPS) measurements over a wide range of formic acid concentrations. Surface tension measurements provide a macroscopic characterization of solutions ranging from 0 to 3 M sodium chloride and from 0 to over 0.5 mole fraction formic acid. Sodium chloride was found to be a weak salting out agent for formic acid with surface excess depending only slightly on salt concentration. In situ XPS provides a complementary molecular level description about the liquid–vapor interface. XPS measurements over an experimental probe depth of 51 Å gave the C 1s to O 1s ratio for both total oxygen and oxygen from water. XPS also provides detailed electronic structure information that is inaccessible by surface tension. Density functional theory calculations were performed to understand the observed shift in C 1s binding energies to lower values with increasing formic acid concentration. Part of the experimental −0.2 eV shift can be assigned to the solution composition changing from predominantly monomers of formic acid to a combination of monomers and dimers; however, the lack of an appropriate reference to calibrate the absolute BE scale at high formic acid mole fraction complicates the interpretation. Our data are consistent with surface tension measurements yielding a significantly more surface sensitive measurement than XPS due to the relatively weak propensity of formic acid for the interface. A simple model allowed us to replicate the XPS results under the assumption that the surface excess was contained in the top four angstroms of solution.

Low-cost retrofitting solutions for RC frames using masonry infill panels

A large number of reinforced concrete (RC) frame structures built in earthquake-prone areas such as Haiti are vulnerable to strong ground motions. Structures in developing countries need low-cost seismic retrofit solutions to reduce their vulnerability. This paper investigates the feasibility of using masonry infill walls to reduce deformations and damage caused by strong ground motions in brittle and weak RC frames designed only for gravity loads. A numerical experiment was conducted in which several idealized prototypes representing RC frame structures of school buildings damaged during the Port-au-Prince earthquake (Haiti, 2010) were strengthened by adding elements representing masonry infill walls arranged in different configurations. Each configuration was characterized by the ratio Rm of the area of walls in the direction of the ground motion (in plan) installed in each story to the total floor area. The numerical representations of these idealized RC frame structures with different values of Rm were (hypothetically) subjected to three major earthquakes with peak ground accelerations of approximately 0.5g. The results of the non-linear dynamic response analyses were summarized in tentative relationships between Rm and four parameters commonly used to characterize the seismic response of structures: interstory drift, Park and Ang indexes of damage, and total amount of energy dissipated by the main frame. It was found that Rm=4% is a reasonable minimum design value for seismic retrofitting purposes in cases in which available resources are not sufficient to afford conventional retrofit measures.

Interaction between like-charged colloidal spheres in electrolyte solutions

How colloidal particles interact with each other is one of the key issues that determines our ability to interpret experimental results for phase transitions in colloidal dispersions and our ability to apply colloid science to various industrial processes. The long-accepted theories for answering this question have been challenged by results from recent experiments. Herein we show from Monte-Carlo simulations that there is a short-range attractive force between identical macroions in electrolyte solutions containing divalent counterions. Complementing some recent and related results by others, we present strong evidence of attraction between a pair of spherical macroions in the presence of added salt ions for the conditions where the interacting macroion pair is not affected by any other macroions that may be in the solution. This attractive force follows from the internal-energy contribution of counterion mediation. Contrary to conventional expectations, for charged macroions in an electrolyte solution, the entropic force is repulsive at most solution conditions because of localization of small ions in the vicinity of macroions. Both Derjaguin–Landau–Verwey–Overbeek theory and Sogami–Ise theory fail to describe the attractive interactions found in our simulations; the former predicts only repulsive interaction and the latter predicts a long-range attraction that is too weak and occurs at macroion separations that are too large. Our simulations provide fundamental “data” toward an improved theory for the potential of mean force as required for optimum design of new materials including those containing nanoparticles.

Protein interactions studied by SAXS:effect of ionic strength and protein concentration for BSA in aqueous solutions

We have studied a series of samples of bovine serum albumin (BSA) solutions with protein concentration, c, ranging from 2 to 500 mg/mL and ionic strength, I, from 0 to 2 M by small-angle X-ray scattering (SAXS). The scattering intensity distribution was compared to simulations using an oblate ellipsoid form factor with radii of 17 x 42 x 42 A, combined with either a screened Coulomb, repulsive structure factor, S-SC(q), or an attractive square-well structure factor, S-SW(q). At pH = 7, BSA is negatively charged. At low ionic strength, I <0.3 M, the total interaction exhibits a decrease of the repulsive interaction when compared to the salt-free solution, as the net surface charge is screened, and the data can be fitted by assuming an ellipsoid form factor and screened Coulomb interaction. At moderate ionic strength (0.3-0.5 M), the interaction is rather weak, and a hard-sphere structure factor has been used to simulate the data with a higher volume fraction. Upon further increase of the ionic strength (I >= 1.0 M), the overall interaction potential was dominated by an additional attractive potential, and the data could be successfully fitted by an ellipsoid form factor and a square-well potential model. The fit parameters, well depth and well width, indicate that the attractive potential caused by a high salt concentration is weak and long-ranged. Although the long-range, attractive potential dominated the protein interaction, no gelation or precipitation was observed in any of the samples. This is explained by the increase of a short-range, repulsive interaction between protein molecules by forming a hydration layer with increasing salt concentration. The competition between long-range, attractive and short-range, repulsive interactions accounted for the stability of concentrated BSA solution at high ionic strength.

Strong-weak Stackelberg Problems in Finite Dimensional Spaces

We are concerned with two-level optimization problems called strongweak Stackelberg problems, generalizing the class of Stackelberg problems in the strong and weak sense. In order to handle the fact that the considered two-level optimization problems may fail to have a solution under mild assumptions, we consider a regularization involving ε-approximate optimal solutions in the lower level problems. We prove the existence of optimal solutions for such regularized problems and present some approximation results when the parameter ǫ goes to zero. Finally, as an example, we consider an optimization problem associated to a best bound given in [2] for a system of nondifferentiable convex inequalities.

Explicit Solutions of Nonlocal Boundary Value Problems, Containing Bitsadze-Samarskii Constraints

MSC 2010: 44A35, 35L20, 35J05, 35J25

Exact Solutions of Nonlocal Boundary Value Problems for One- and Two-Dimensional Heat Equation

Иван Хр. Димовски, Юлиан Ц. Цанков - Предложен е метод за намиране на явни решения на клас двумерни уравнения на топлопроводността с нелокални условия по пространствените променливи. Методът е основан на директно тримерно операционно смятане. Класическата дюамелова конволюция е комбинирана с две некласически конволюции за операторите ∂xx и ∂yy в една тримерна конволюция. Съответното операционно смятане използва мултипликаторни частни. Мултипликаторните частни позволяват да се продължи принципът на Дюамел за пространствените променливи и да се намерят явни решения на разглежданите гранични задачи. Общите разглеждания са приложени в случая на гранични условия от типа на Йонкин. Намерени са експлицитни решения в затворен вид.