In memoriam: Dimitar Shishkov

Bulgarian and world computer science lost a prominent colleague: Dimitar Petrov Shishkov 22th January 1939, Varna – 8th March 2004, Sofia D. Shishkov graduated mathematics at Sofia University in 1962. In the last year of his studies he started a specialization as a programmer at the Joint Institute of Nuclear Research – Dubna which lasted three years. Then he worked at the Institute of Mathematics for two years. In 1966 D. Shishkov together with a group of experts transferred to the newly created Central Laboratory for Information Technologies. In 1976 he defended his PhD dissertation. He has been an associate professor in computer science at Sofia University since 1985 and a professor in computer science since 2000. His scientific interests and results were in the fields of computer architectures, computational linguistics, artificial intelligence, numerical methods, data structures, etc. He was remarkable with his teaching activities. D. Shishkov was the creator of high-quality software for the first Bulgarian electronic calculator “ELKA” – one of the first calculators in the world as well as for the series of next calculators and for specialized minicomputers. He was the initiator of the international project “Computerization of the natural languages”. He was a member of a range of international scientific organizations. Among his numerous activities was the organization of the I-st Programming competition in 1979. D. Shishkov was the initiator of sport dancing in Bulgaria (1967) and founder of the first sport-dancing high school education in the world. D. Shishkov was a highly accomplished person with a diversity of interests, with a developed social responsibility and accuracy in his work. In 1996 D. Shishkov was awarded with the International Prize ITHEA for outstanding achievements in the field of Information Theories and Applications. We are grateful to D. Shishkov for the chance to work together with him for establishment and development of IJ ITA.

Nonlinear Waves: An Introduction

This book deals with equations of mathematical physics as the different modifications of the KdV equation, the Camassa-Holm type equations, several modifications of Burger's equation, the Hunter-Saxton equation, conservation laws equations and others. The equations originate from physics but are proposed here for their investigation via purely mathematical methods in the frames of university courses. More precisely, we propose classification theorems for the traveling wave solutions for a sufficiently large class of third order nonlinear PDE when the corresponding profiles develop different kind of singularities (cusps, peaks), existence and uniqueness results, etc. The orbital stability of the periodic solutions of traveling type for mKdV equations are also studied. Of great interest too is the interaction of peakon type solutions of the Camassa-Holm equation and the solvability of the classical and generalized Cauchy problem for the Hunter-Saxton equation. The Riemann problem for special systems of conservation laws and the corresponding -shocks are also considered. As it concerns numerical methods we apply the CNN approach. The book is addressed to a broader audience including graduate students, Ph.D. students, mathematicians, physicist, engineers and specialists in the domain of PDE.

Елементи на обучение чрез синтаксис за студенти от професионално направление „Технически науки”

Доклад, поместен в сборника на Националната конференция "Образованието в информационното общество", Пловдив, май, 2011 г.

Computer-Assisted Proofs and Symbolic Computations

We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems fast finite precision arithmetic is used. The results are absolutely rigorous. To demonstrate the power of reliable symbolic-numeric computations we investigate in some details the verification of very long periodic orbits of chaotic dynamical systems. The verification is done directly in Maple, e.g. using the Maple Power Tool intpakX or, more efficiently, using the C++ class library C-XSC.

On a Hypersingular Equation of a Problem, for a Crack in Elastic Media

Mathematics Subject Classification 2010: 45DB05, 45E05, 78A45.

A Model of a Diagnostic Test for Controlling the Results of a Computer Based Education in Applied Mathematics at the University of Ruse

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2015

A Didactic Model of Computer Supported Education in Higher Mathematics

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2016

Immunological synapse: a mathematical model of the bond formation process:mathematical modelling of the immature synapse

The cell:cell bond between an immune cell and an antigen presenting cell is a necessary event in the activation of the adaptive immune response. At the juncture between the cells, cell surface molecules on the opposing cells form non-covalent bonds and a distinct patterning is observed that is termed the immunological synapse. An important binding molecule in the synapse is the T-cell receptor (TCR), that is responsible for antigen recognition through its binding with a major-histocompatibility complex with bound peptide (pMHC). This bond leads to intracellular signalling events that culminate in the activation of the T-cell, and ultimately leads to the expression of the immune eector function. The temporal analysis of the TCR bonds during the formation of the immunological synapse presents a problem to biologists, due to the spatio-temporal scales (nanometers and picoseconds) that compare with experimental uncertainty limits. In this study, a linear stochastic model, derived from a nonlinear model of the synapse, is used to analyse the temporal dynamics of the bond attachments for the TCR. Mathematical analysis and numerical methods are employed to analyse the qualitative dynamics of the nonequilibrium membrane dynamics, with the specic aim of calculating the average persistence time for the TCR:pMHC bond. A single-threshold method, that has been previously used to successfully calculate the TCR:pMHC contact path sizes in the synapse, is applied to produce results for the average contact times of the TCR:pMHC bonds. This method is extended through the development of a two-threshold method, that produces results suggesting the average time persistence for the TCR:pMHC bond is in the order of 2-4 seconds, values that agree with experimental evidence for TCR signalling. The study reveals two distinct scaling regimes in the time persistent survival probability density prole of these bonds, one dominated by thermal uctuations and the other associated with the TCR signalling. Analysis of the thermal fluctuation regime reveals a minimal contribution to the average time persistence calculation, that has an important biological implication when comparing the probabilistic models to experimental evidence. In cases where only a few statistics can be gathered from experimental conditions, the results are unlikely to match the probabilistic predictions. The results also identify a rescaling relationship between the thermal noise and the bond length, suggesting a recalibration of the experimental conditions, to adhere to this scaling relationship, will enable biologists to identify the start of the signalling regime for previously unobserved receptor:ligand bonds. Also, the regime associated with TCR signalling exhibits a universal decay rate for the persistence probability, that is independent of the bond length.

Development of a mathematical and computer model to assess water quality impacts of hazardous compounds from minor gasoline spills in the inter-tidal zone of the Miami River, Florida

The objective of this study was to develop a model to predict transport and fate of gasoline components of environmental concern in the Miami River by mathematically simulating the movement of dissolved benzene, toluene, xylene (BTX), and methyl-tertiary-butyl ether (MTBE) occurring from minor gasoline spills in the inter-tidal zone of the river. Computer codes were based on mathematical algorithms that acknowledge the role of advective and dispersive physical phenomena along the river and prevailing phase transformations of BTX and MTBE. Phase transformations included volatilization and settling. ^ The model used a finite-difference scheme of steady-state conditions, with a set of numerical equations that was solved by two numerical methods: Gauss-Seidel and Jacobi iterations. A numerical validation process was conducted by comparing the results from both methods with analytical and numerical reference solutions. Since similar trends were achieved after the numerical validation process, it was concluded that the computer codes algorithmically were correct. The Gauss-Seidel iteration yielded at a faster convergence rate than the Jacobi iteration. Hence, the mathematical code was selected to further develop the computer program and software. The model was then analyzed for its sensitivity. It was found that the model was very sensitive to wind speed but not to sediment settling velocity. ^ A computer software was developed with the model code embedded. The software was provided with two major user-friendly visualized forms, one to interface with the database files and the other to execute and present the graphical and tabulated results. For all predicted concentrations of BTX and MTBE, the maximum concentrations were over an order of magnitude lower than current drinking water standards. It should be pointed out, however, that smaller concentrations than the latter reported standards and values, although not harmful to humans, may be very harmful to organisms of the trophic levels of the Miami River ecosystem and associated waters. This computer model can be used for the rapid assessment and management of the effects of minor gasoline spills on inter-tidal riverine water quality. ^

Elastic modulus study of gold thin film for use as an actuated membrane in a superconductive radio frequency (RF) microelectromechanical (MEM) switch

The objective of this research was to find Young's elastic modulus for thin gold films at room and cryogenic temperatures based on the flexional model which has not been previously attempted. Electrical Sonnet simulations and numerical methods using Abacus for the mechanical responses were employed for this purpose. A RF MEM shunt switch was designed and a fabrication process developed in house. The switch is composed of a superconducting YBa2 Cu3O7 coplanar waveguide structure with an Au bridge membrane suspended above an area of the center conductor covered with BaTiO3 dielectric. The Au membrane is actuated by the electrostatic attractive force acting between the transmission line and the membrane when voltage is applied. The value of the actuation force will greatly depend on the switch pull-down voltage and on the geometry and mechanical properties of the bridge material. Results show that the elastic modulus for Au thin film can be 484 times higher at cryogenic temperature than it is at room temperature. ^

Lattice Boltzmann method for flow and heat transfer in microgeometries

Recent technological developments have made it possible to design various microdevices where fluid flow and heat transfer are involved. For the proper design of such systems, the governing physics needs to be investigated. Due to the difficulty to study complex geometries in micro scales using experimental techniques, computational tools are developed to analyze and simulate flow and heat transfer in microgeometries. However, conventional numerical methods using the Navier-Stokes equations fail to predict some aspects of microflows such as nonlinear pressure distribution, increase mass flow rate, slip flow and temperature jump at the solid boundaries. This necessitates the development of new computational methods which depend on the kinetic theory that are both accurate and computationally efficient. In this study, lattice Boltzmann method (LBM) was used to investigate the flow and heat transfer in micro sized geometries. The LBM depends on the Boltzmann equation which is valid in the whole rarefaction regime that can be observed in micro flows. Results were obtained for isothermal channel flows at Knudsen numbers higher than 0.01 at different pressure ratios. LBM solutions for micro-Couette and micro-Poiseuille flow were found to be in good agreement with the analytical solutions valid in the slip flow regime (0.01 < Kn < 0.1) and direct simulation Monte Carlo solutions that are valid in the transition regime (0.1 < Kn < 10) for pressure distribution and velocity field. The isothermal LBM was further extended to simulate flows including heat transfer. The method was first validated for continuum channel flows with and without constrictions by comparing the thermal LBM results against accurate solutions obtained from analytical equations and finite element method. Finally, the capability of thermal LBM was improved by adding the effect of rarefaction and the method was used to analyze the behavior of gas flow in microchannels. The major finding of this research is that, the newly developed particle-based method described here can be used as an alternative numerical tool in order to study non-continuum effects observed in micro-electro-mechanical-systems (MEMS).

Lattice Boltzmann Method for Flow and Heat Transfer in Microgeometries

Recent technological developments have made it possible to design various microdevices where fluid flow and heat transfer are involved. For the proper design of such systems, the governing physics needs to be investigated. Due to the difficulty to study complex geometries in micro scales using experimental techniques, computational tools are developed to analyze and simulate flow and heat transfer in microgeometries. However, conventional numerical methods using the Navier-Stokes equations fail to predict some aspects of microflows such as nonlinear pressure distribution, increase mass flow rate, slip flow and temperature jump at the solid boundaries. This necessitates the development of new computational methods which depend on the kinetic theory that are both accurate and computationally efficient. In this study, lattice Boltzmann method (LBM) was used to investigate the flow and heat transfer in micro sized geometries. The LBM depends on the Boltzmann equation which is valid in the whole rarefaction regime that can be observed in micro flows. Results were obtained for isothermal channel flows at Knudsen numbers higher than 0.01 at different pressure ratios. LBM solutions for micro-Couette and micro-Poiseuille flow were found to be in good agreement with the analytical solutions valid in the slip flow regime (0.01 < Kn < 0.1) and direct simulation Monte Carlo solutions that are valid in the transition regime (0.1 < Kn < 10) for pressure distribution and velocity field. The isothermal LBM was further extended to simulate flows including heat transfer. The method was first validated for continuum channel flows with and without constrictions by comparing the thermal LBM results against accurate solutions obtained from analytical equations and finite element method. Finally, the capability of thermal LBM was improved by adding the effect of rarefaction and the method was used to analyze the behavior of gas flow in microchannels. The major finding of this research is that, the newly developed particle-based method described here can be used as an alternative numerical tool in order to study non-continuum effects observed in micro-electro-mechanical-systems (MEMS).

Engineering Analysis in Imprecise Geometric Models

Engineering analysis in geometric models has been the main if not the only credible/reasonable tool used by engineers and scientists to resolve physical boundaries problems. New high speed computers have facilitated the accuracy and validation of the expected results. In practice, an engineering analysis is composed of two parts; the design of the model and the analysis of the geometry with the boundary conditions and constraints imposed on it. Numerical methods are used to resolve a large number of physical boundary problems independent of the model geometry. The time expended due to the computational process are related to the imposed boundary conditions and the well conformed geometry. Any geometric model that contains gaps or open lines is considered an imperfect geometry model and major commercial solver packages are incapable of handling such inputs. Others packages apply different kinds of methods to resolve this problems like patching or zippering; but the final resolved geometry may be different from the original geometry, and the changes may be unacceptable. The study proposed in this dissertation is based on a new technique to process models with geometrical imperfection without the necessity to repair or change the original geometry. An algorithm is presented that is able to analyze the imperfect geometric model with the imposed boundary conditions using a meshfree method and a distance field approximation to the boundaries. Experiments are proposed to analyze the convergence of the algorithm in imperfect models geometries and will be compared with the same models but with perfect geometries. Plotting results will be presented for further analysis and conclusions of the algorithm convergence

Elastic modulus study of gold thin film for use as an actuated membrane in a superconductive radio frequency (RF) MicroElectroMechanical (MEM) switch

The objective of this research was to find Young's elastic modulus for thin gold films at room and cryogenic temperatures based on the flexional model which has not been previously attempted. Electrical Sonnet simulations and numerical methods using Abacus for the mechanical responses were employed for this purpose. A RF MEM shunt switch was designed and a fabrication process developed in house. The switch is composed of a superconducting YBa2Cu3O7 coplanar waveguide structure with an Au bridge membrane suspended above an area of the center conductor covered with BaTiO3 dielectric. The Au membrane is actuated by the electrostatic attractive force acting between the transmission line and the membrane when voltage is applied. The value of the actuation force will greatly depend on the switch pull-down voltage and on the geometry and mechanical properties of the bridge material. Results show that the elastic modulus for Au thin film can be 484 times higher at cryogenic temperature than it is at room temperature.

Avaliação do desempenho da paligorsquita modificada e do carvão da pirólise do lodo de esgoto no processo de degradação fotocatalítica do fenol

The uncontrolled disposal of wastewaters containing phenolic compounds by the industry has caused irreversible damage to the environment. Because of this, it is now mandatory to develop new methods to treat these effluents before they are disposed of. One of the most promising and low cost approaches is the degradation of phenolic compounds via photocatalysis. This work, in particular, has as the main goal, the customization of a bench scale photoreactor and the preparation of catalysts via utilization of char originated from the fast pyrolysis of sewage sludge. The experiments were carried out at constant temperature (50°C) under oxygen (410, 515, 650 and 750 ml min-1). The reaction took place in the liquid phase (3.4 liters), where the catalyst concentration was 1g L-1 and the initial concentration of phenol was 500 mg L-1 and the reaction time was set to 3 hours. A 400 W lamp was adapted to the reactor. The flow of oxygen was optimized to 650 ml min-1. The pH of the liquid and the nature of the catalyst (acidified and calcined palygorskite, palygorskite impregnated with 3.8% Fe and the pyrolysis char) were investigated. The catalytic materials were characterized by XRD, XRF, and BET. In the process of photocatalytic degradation of phenol, the results showed that the pH has a significant influence on the phenol conversion, with best results for pH equal to 5.5. The phenol conversion ranged from 51.78% for the char sewage sludge to 58.02% (for palygorskite acidified calcined). Liquid samples analyzed by liquid chromatography and the following compounds were identified: hydroquinone, catechol and maleic acid. A mechanism of the reaction was proposed, whereas the phenol is transformed into the homogeneous phase and the others react on the catalyst surface. For the latter, the Langmuir-Hinshelwood model was applied, whose mass balances led to a system of differential equations and these were solved using numerical methods in order to get estimates for the kinetic and adsorption parameters. The model was adjusted satisfactorily to the experimental results. From the proposed mechanism and the operating conditions used in this study, the most favored step, regardless of the catalyst, was the acid group (originated from quinone compounds), being transformed into CO2 and water, whose rate constant k4 presented value of 0.578 mol L-1 min-1 for acidified calcined palygorskite, 0.472 mol L-1 min-1 for Fe2O3/palygorskite and 1.276 mol L-1 min-1 for the sludge to char, the latter being the best catalyst for mineralization of acid to CO2 and water. The quinones were adsorbed to the acidic sites of the calcined palygorskite and Fe2O3/palygorskite whose adsorption constants were similar (~ 4.45 L mol-1) and higher than that of the sewage sludge char (3.77 L mol-1).