Mathematical Modeling and Numerical Simulations
Currently, 9 scientists work in the Department: two Professors DSc, one Assoc. Professor DSc, two Assoc. Professors Dr, two Assistant Professors. Dr, two Assistants. In addition two associate members (Assoc. Professors Dr) of the IMech work in the Department.


AM  Associate member
In the period 20172019 the staff of the Department will work on the following science projects:
Project DN 02/8 (ДН 02/8) 20182019 with the National Science Fund of Bulgaria; Project leader Prof. DSc D. Danchev The current project aims to provide exact results for basic statisticalmechanical models, as well as to obtain numerical results for them. We will study the modifications in the phase diagrams of such systems due to their finite size, the behavior of the order parameters profiles and the response functions. Special attention will be paid to the fluctuation induced interactions, including the Casimir effect, in model fluid systems undergoing phase transitions near the respective critical points of the infinite (bulk) or the finite systems. This topic is very important and currently actively researched since the abovementioned forces bear a significant impact on the understanding of the behavior and manipulation of nanodevices. Currently, the Casimir effect and other similar phenomena are a research object in the quantum electrodynamics, the chromodynamics, the cosmology, the condensed matter physics, in some branches of biology, as well as in nanotechnologies. The interested reader is directed to the following important review papers in this field [1.11.5]. With respect to the current knowledge on the critical Casimir effect, whose properties are of main interest in the present project, to a certain degree the main results are summarized and discussed in the following review articles [1.6,1.7], some more specific aspects are discussed in [1.4,1.8,1.9]. As it is becoming clear, the study of the properties of Casimir effect in different fields, unavoidably needs and involves knowledge from mathematics as well as numerical methods, and computer systems.
[1.1] A. Rodriguez, P.C. Hui, D. Woolf, S. Johnson, M. Lončar and F. Capasso, Classical and fluctuationinduced electromagnetic interactions in micronscale systems: designer bonding, antibonding, and Casimir forces, Ann. Phys., 527(12), 4580, 2015. [1.2] G. Klimchitskaya and V. Mostepanenko, Casimir and van der Waals forces: Advances and problems, Proc. of Peter the Great St.Petersburg Polytechnic University, N1(517), 4165, 2015. [1.3] L. Woods, D. Dalvit, A. Tkatchenko, P. RodriguezLopez, A. Rodriguez and R. Podgornik, A materials perspective on Casimir and van der Waals interactions, ArXiv eprints, 2015. [1.4] O. Vasilyev, Monte Carlo Simulation of Critical Casimir Forces. Order, Disorder and Criticality, vol. 4, ch. 2, 55110, World Scientific, 2015. [1.5] R. Zhao, Y. Luo and J. Pendry, Transformation optics applied to van der Waals interactions, Sci. Bull., 61(1), 5967, 2016. [1.6] M. Krech, Casimir Effect in Critical Systems, World Scientific, Singapore, 1994. [1.7] J. Brankov, D. Dantchev and N. Tonchev, The Theory of Critical Phenomena in FiniteSize Systems – Scaling and Quantum Effects, World Scientific, Singapore, 2000. [1.8] A. Gambassi and S. Dietrich, Critical Casimir forces steered by patterned substrates, Soft Matter, 7, 12471253, 2011. [1.9] D. Dean, Nonequilibrium fluctuationinduced interactions, Phys. Scripta, 86(5), 058502, 2012.
B) Theoretical Investigation of nonequilibrium gas flows in micro / nano systems Project DN 02/7 (20162019) with the National Science Fund of Bulgaria Research area Mathematical Sciences and Informatics; Project leader: Prof. DSc Stefan Stefanov
The main driver for the development of micro and nano technologies is the basic research both experimental and theoretical, that generates the necessary new knowledge and ideas about the physical processes occurring in MicroElectroMechanical Systems (MEMS). It is known that the knowledge of classical continuum mechanics, and more generally, continuum physics is based entirely on the assumption of continuity of matter, allowing the use of mathematical models describing the relevant physical processes with systems of partial differential equations and appropriate boundary conditions providing continuity. However, shortly speaking, such knowledge and models fails to be valid and accurate for processes in micro / nanosized areas. In such systems, the processes can be highly nonequilibrium with presence of discontinuities caused by the discrete nature of molecular flow. To adequately describe the nonequilibrium processes and phenomena in MEMS it is necessary to use more or less new approaches, methods and knowledge of kinetic theory, statistical and quantum physics in order to investigate the relationship and transition between continuum and discrete environments, as well as emerging phenomena in intermediate states. This is a relatively new scientific field in which a large number of scientists from many countries are engaged. This type of research is adopted for important and topical at the institutional level and comes as a part of the scientific priorities of the European Commission. Accordingly, they are intended as various subareas in the Bulgarian national strategy for research. Routes to the efficient use of resources must be identified and implemented to provide more environmentally friendly and resourceoriented technologies in the near future. European roadmap process intensification identified several measures: miniaturization, improved heat transfer and recovery of lost heat. The main objective of the proposed project is the Bulgarian team to participate with qualitative contributions in the research of phenomena and processes in the world of micro / nano scale in the field of microfluidics, in which researchers from the Institute have achieved significant scientific results. The team of scientists from the Institute of Mechanics at BAS offering this project has internationally recognized achievements in theoretical and numerical studies of nonequilibrium gas flows and phenomena in MEMS. This is evident from the list of publications in prestigious scientific journals, presented for each participant.
C) Mechanomathematical modelling and numerical simulations of contemporary technological processes Project leader: Assoc. Prof. DSc S. Iliev (priority areas 1,2,3 and 4 of the National Science Strategy)
D) Theoretical Investigation of Rarefied Gas Dynamics of Monoatomic Gas, Gas Mixtures, and Chemically Reacting Gases and FluidStructure Interaction in micro/nano systems Project KP06N32/6, with the National Science Fund of Bulgaria, Rresearch area, of the project: Mathematical Sciences and Informatics, Physical Sciences, Chemical Sciences, Technical Sciences Project leader: Assic. Prof. Dr. Kiril Shterev. During the last decade, the development of microelectromechanical systems (MEMS) increased dramatically. The main driver for this development appears the fundamental research (experimental and theoretical) that generate necessary new knowledge and ideas about the physical processes occurring in MicroElectroMechanical Systems.


Public Archive: A pressure based, iterative finite volume method is developed for calculation of compressible, viscous, heat conductive gas flows at all speeds. For more information click here.
Dynamic Meniscus Profile Method for Detertmination of the Dynamic Contact Angle in the Wilhelmy Plate Geometry is developed and availablel for use here.

Modified date:04072023