Dynamics of Ginzburg‐Landau Vortices

(Accepted August 19, 1996)     

Optimal investment strategies with a reallocation constraint

We study a Merton type optimization problem under a reallocation constraint. Under this restriction, the stock holdings can not be liquidated faster than a certain rate. This is a common restriction in certain type of investment firms. Our main objective is to study the large time optimal growth rate of the expected value of the utility from wealth. We also consider a discounted infinite horizon problem as a step towards understanding the first problem. A numerical study is done by solving the dynamic programming equations. Under the assumption of a power utility function, an appropriate dimension reduction argument is used to reduce the original problem to a two dimensional one in a bounded domain with convenient boundary conditions. Computation of the optimal growth rate introduces additional numerical difficulties as the straightforward approach is unstable. In this direction, new analytical results characterizing the growth rate as the limit of a sequence of finite horizon problems with continuously derived utility are proved.     

Kasner Cosmological Models with Two-Fluid Source in General Relativity

In this paper we present Bianchi type-I metric of the Kasner form describing two-fluid source of the universe in general relativity. In Kasner cosmological models one fluid is a radiation field modeling the cosmic microwave background, while the other is a matter field, modeling material content of the universe. The radiation and matter content of the universe are in interactive phase. We have also presented anisotropic, homogeneous nature of Kasner cosmological models with two-fluid. The behavior of fluid parameters and kinematical parameters of the models are also discussed.     

Effect of anthraquinone on brightness value and crystalline structure of pulp during soda processes

The dependence of crystalline structure and optical properties of pulp on anthraquinone (AQ) added to the soda process at different cooking times was determined in this study. Wheat (Triticum aestevum L.) straw was used as the raw material for pulp. Soda and soda-AQ processes were selected for pulping at 80 min and 120 min. The soda-AQ process improved the yield and viscosity of pulp delignification ratio for pulping in comparison with the soda process. Crystallinity of pulp samples decreased by adding anthraquinone to the soda process because of stabilized less ordered cellulose and amorphous hemicelluloses in pulp. It was determined that crystallinity of pulp samples decreased with longer cooking time, from 80 min to 120 min, in both soda and soda-AQ processes. Monoclinic structure was dominant in pulp samples; however, the triclinic structure ratio increased in both soda and soda-AQ processes compared to raw material. It was found that brightness and lightness values in pulp samples decreased when using anthraquinone depending on the changes of the crystalline structure.     

On a Model of Associative Memory with Huge Storage Capacity

In Krotov et al. (in: Lee (eds) Advances in Neural Information Processing Systems, Curran Associates, Inc., Red Hook, 2016) Krotov and Hopfield suggest a generalized version of the well-known Hopfield model of associative memory. In their version they consider a polynomial interaction function and claim that this increases the storage capacity of the model. We prove this claim and take the ”limit” as the degree of the polynomial becomes infinite, i.e. an exponential interaction function. With this interaction we prove that model has an exponential storage capacity in the number of neurons, yet the basins of attraction are almost as large as in the standard Hopfield model.     

Pattern Hit-and-Run for sampling efficiently on polytopes

Pattern Hit-and-Run (PHR) is a Markov chain Monte Carlo sampler for a target distribution that was originally designed for general sets embedded in a box. A specific set of interest to many applications is a polytope intersected with discrete or mixed continuous/discrete lattices. PHR requires an acceptance/rejection mechanism along a bidirectional walk to guarantee feasibility. We remove this inefficiency by utilizing the linearity of the constraints defining the polytope, so each iteration of PHR can be efficiently implemented even though the variables are allowed to be integer valued. Moreover, PHR converges to a uniform distribution in polynomial time for a class of discrete polytopes.     

Stochastic control for a class of random evolution models

We construct the explicit connection existing between a solvable model of the discrete velocities non-linear Boltzmann equation and the Hamilton-Bellman-Jacobi equation associated with a simple optimal control of a piecewise deterministic process. This study extends the known relation that exists between the Burgers equation and a simple controlled diffusion problem. In both cases the resulting partial differential equations can be linearized via a logarithmic transformation and hence offer the possibility to solve physically relevant non-linear field models in full generality.     

Design of optimum response surface experiments for the adsorption of acetic,butyric, and oxalic acids on Amberlyst A21

In this study the adsorption equilibria of acetic, butyric, and oxalic acids onto Amberlyst A21 were investigated experimentally at 25°C. The process was optimized using response surface methodology (RSM). The time to reach the equilibrium state, effects of adsorbent amount, and initial acid concentrations on adsorption efficiency were investigated. Freundlich, Langmuir, and Temkin isotherms were applied to experimental data. The Freundlich isotherm revealed better results than the others. In addition to the main aim of this research, a statistical/mathematical approach – RSM – was utilized to simulate and determine the optimum conditions of acetic, butyric, and oxalic acids removal by Amberlyst A21 using three selected parameters (adsorbent dose, initial dye concentration, and type of acids). The significance of independent variables and their interactions were tested by the analysis of variance (ANOVA). The optimum acid concentration, amount of adsorbent, type of acid, and removal of acid (%) were found by desirability function to be 0.199?mol/L, 1.999?g, butyric acid, and 84.537%, respectively.     

Laminar forced convection with viscous dissipation in a concentric annular ductConvection laminaire forcée avec dissipation visqueuse dans un conduit annulaire concentrique

Forced convection heat transfer in fully developed flows of viscous dissipating fluids in concentric annular ducts is analyzed analytically. Special attention has been paid to the effect of the viscous dissipation. Two different cases of the thermal boundary conditions are considered: uniform heat flux at the outer wall and adiabatic inner wall (Case A) and uniform heat flux at the inner wall and adiabatic outer wall (Case B). Solutions for the velocity and temperature distributions and the Nusselt number are obtained for different values of the aspect ratio and the Brinkman number. The present analytical results for the case without the viscous dissipation effect are compared with those available in the literature and an excellent agreement is observed. To cite this article: M. Avc?, O. Ayd?n, C. R. Mecanique 334 (2006).