Vassil M. Vassilev

Cylindrical equilibrium shapes of fluid membranes

Within the framework of the well-known curvature models, a fluid lipid bilayer membrane is regarded as a surface embedded in the three-dimensional Euclidean space whose equilibrium shapes are described in terms of its mean and Gaussian curvatures by the so-called membrane shape equation. In the present paper, all solutions to this equation determining cylindrical membrane shapes are found and presented, together with the expressions for the corresponding position vectors, in explicit analytic form. The necessary and sufficient conditions for such a surface to be closed are derived and several sufficient conditions for its directrix to be simple or self-intersecting are given.

An interactive procedure for multiple objective integer linear programming problems

Abstract There are many practical problems where the objective functions and the constraints can be represented by linear functions but the decision variables are restricted to only integer values. Our objective is to present an interactive procedure for the multiple objective integer linear programming problem that is fast, does not place too many demands on the decision maker and can be implemented without requiring any special software. We illustrate the proposed procedure with a numerical example and report some computational experience.

An approximate algorithm for nonlinear integer programming

Abstract This paper suggests an approximate algorithm, designed to solve nonlinear integer problems. This algorithm belongs to the class of component algorithms of feasible integer directions. The search for a feasible integer direction is done on the basis of a linear approximation of the objective function and the constraints at the integer points under consideration. Theoretical analysis is presented, as well as experimental investigation, using the algorithm for test examples taken from the literature.

Single- and Multi-Date Crop Identification Using PROBA-V 100 and 300 m S1 Products on Zlatia Test Site, Bulgaria

The monitoring of crops is of vital importance for food and environmental security in a global and European context. The main goal of this study was to assess the crop mapping performance provided by the 100 m spatial resolution of PROBA-V compared to coarser resolution data (e.g., PROBA-V at 300 m) for a 2250 km2 test site in Bulgaria. The focus was on winter and summer crop mapping with three to five classes. For classification, single- and multi-date spectral data were used as well as NDVI time series. Our results demonstrate that crop identification using 100 m PROBA-V data performed significantly better in all experiments compared to the PROBA-V 300 m data. PROBA-V multispectral imagery, acquired in spring (March) was the most appropriate for winter crop identification, while satellite data acquired in summer (July) was superior for summer crop identification. The classification accuracy from PROBA-V 100 m compared to PROBA-V 300 m was improved by 5.8% to 14.8% depending on crop type. Stacked multi-date satellite images with three to four images gave overall classification accuracies of 74%–77% (PROBA-V 100 m data) and 66%–70% (PROBA-V 300 m data) with four classes (wheat, rapeseed, maize, and sunflower). This demonstrates that three to four image acquisitions, well distributed over the growing season, capture most of the spectral and temporal variability in our test site. Regarding the PROBA-V NDVI time series, useful results were only obtained if crops were grouped into two broader crop type classes (summer and winter crops). Mapping accuracies decreased significantly when mapping more classes. Again, a positive impact of the increased spatial resolution was noted. Together, the findings demonstrate the positive effect of the 100 m resolution PROBA-V data compared to the 300 m for crop mapping. This has important implications for future data provision and strengthens the arguments for a second generation of this mission originally designed solely as a “gap-filler mission”.

Conservation laws and group-invariant solutions of the von Kármán equations

Abstract The present paper is concerned with the classical von Karman equations for large deflection of thin elastic plates both in 2 (space) and in 2 + 1 (space-time) dimensions. All infinitesimal divergence symmetries of two action functionals whose Euler-Lagrange equations coincide with the von Karman equations are established and the corresponding conservation laws obtainable through Noethers theorem are determined. Wave phenomena in infinite thin elastic plates are studied using group-invariant solutions to the time-dependent von Karman equations, the derived conservation laws being taken into consideration.

Traveling Wave Solutions of the Gardner Equation and Motion of Plane Curves Governed by the mKdV Flow

The Gardner equation is well‐known in the mathematical literature since the late sixties of 20th century. Initially, it appeared in the context of the construction of local conservation laws admitted by the KdV equation. Later on, the Gardner equation was generalized and found to be applicable in various branches of physics (solid‐state and plasma physics, fluid dynamics and quantum field theory). In this paper, we examine the travelling wave solutions of the Gardner equation and derive the full set of solutions to the corresponding reduced equation in terms of Weierstrass and Jacobi elliptic functions. Then, we use the travelling wave solutions of the focusing mKdV equation and obtain in explicit analytic form exact solutions of a special type of plane curve flow, known as the mKdV flow.

An algorithm of internal feasible directions for linear integer programming

Abstract An approximate algorithm for solving pure integer problems is examined. The algorithm belongs to the class of component algorithms using feasible integer directions. The basic characteristics of the algorithm are analyzed. Testing on an IBM/PC/AT personal computer is carried out. The proposed algorithm is compared with other well known approximate algorithms.

Exact results for the temperature-field behavior of the Ginzburg-Landau Ising type mean-field model

We investigate the dependence of the order parameter profile, local and total susceptibilities on both the temperature and external magnetic field within the mean-filed Ginzburg-Landau Ising type model. We study the case of a film geometry when the boundaries of the film exhibit strong adsorption to one of the phases (components) of the system. We do that using general scaling arguments and deriving exact analytical results for the corresponding scaling functions of these quantities. In addition, we examine their behavior in the capillary condensation regime. Based on the derived exact analytical expressions we obtained an unexpected result -- the existence of a region in the phase transitions line where the system jumps below its bulk critical temperature from a less dense gas to a more dense gas before switching on continuously into the usual jump from gas to liquid state in the middle of the system. It is also demonstrated that on the capillary condensation line one of the coexisting local susceptibility profiles is with one maximum, whereas the other one is with two local maxima centered, approximately, around the two gas-liquid interfaces in the system.

An Interactive Algorithm for Solving Multiple Objective Nonlinear Programming Problems

We propose an interactive algorithm to solve multiple objective nonlinear programming problems. The algorithm is based on the reference direction approach. The decision maker has to specify aspiration level for each objective. A number of solutions are generated along the projection of the reference direction onto the efficient surface. Each solution is an (weak) efficient solution. The algorithm is illustrated with an example.

Equilibrium Configurations of Lipid Bilayer Membranes and Carbon Nanostructures

The present article concerns the continuum modelling of the mechanical behaviour and equilibrium shapes of two types of nano-scale objects: fluid lipid bilayer membranes and carbon nanostructures. A unified continuum model is used to handle four different case studies. Two of them consist in representing in analytic form cylindrical and axisymmetric equilibrium configurations of single-wall carbon nanotubes and fluid lipid bilayer membranes subjected to uniform hydrostatic pressure. The third one is concerned with determination of possible shapes of junctions between a single-wall carbon nanotube and a flat graphene sheet or another single-wall carbon nanotube. The last one deals with the mechanical behaviour of closed fluid lipid bilayer membranes (vesicles) adhering onto a flat homogeneous rigid substrate subjected to micro-injection and uniform hydrostatic pressure.