In the period 2017 - 2019 the staff of the Department will be working on тхе фолловинг basic projects:
А) Exact and numerical results for the behavior of finite-dimensional inhomogeneous
statistical-mechanical systems exhibiting phase transitions
This is project DN 02/8 with Bulgarian NSF 2016-2019
The project aims to provide exact results for basic statistical-mechanical 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 behaviour of the order parameters profiles and the response functions. A 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 is a very hot topic in the current front of research after it became clear that these forces influence essentially the nano-devices. Currently the Casimir, and Casimir-like effects are object of studies in quantum electrodynamics, chromodynamics, cosmology, condensed matter physics, biology and some elements of it, as well as in nano-technology. The interested reader can consult the existing impressive number of reviews on the subject some of which include Refs. [1.1-1.5]. So far the critical Casimir effect has enjoyed only two general reviews [1.6,1.7] and few concerning specific aspects of it [1.4,1.8,1.9]. Obviously the study in so different fields involve all of the knowledge available from the nowadays mathematics as well as the most advanced numerical methods and powerful computers.
[1.1] A. Rodriguez, P.-C. Hui, D. Woolf, S. Johnson, M. Lončar and F. Capasso, Classical and fluctuation-induced electromagnetic interactions in micron-scale systems: designer bonding, antibonding, and Casimir forces, Ann. Phys., 527(1-2), 45-80, 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 Univercity, N1(517), 41-65, 2015.
[1.3] L. Woods, D. Dalvit, A. Tkatchenko, P. Rodriguez-Lopez, A. Rodriguez and R. Podgornik, A materials perspective on Casimir and van der Waals interactions, ArXiv e-prints, 2015.
[1.4] O. Vasilyev, Monte Carlo Simulation of Critical Casimir Forces. Order, Disorder and Criticality, vol. 4, ch. 2, 55-110, World Scientific, 2015.
[1.5] R. Zhao, Y. Luo and J. Pendry, Transformation optics applied to van der Waals interactions, Sci. Bull., 61(1), 59-67, 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 Finite-Size 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, 1247-1253, 2011.
[1.9] D. Dean, Non-equilibrium fluctuation-induced interactions, Phys. Scripta, 86(5), 058502, 2012.
B)Mathematical modeling and numerical simulations of multi-scale processes and phenomena in micro- and nano-fluidic systems
The basic accent of the research carried on in the Department will be on the development of models, algorithms, numerical methods and software products for:
1. Mathematical modeling of the interactions, the properties and the behavior of low-dimensional fluidic systems, including their study as a part of micro and nano-systems and devices.
2. Modeling of processes in micro-fluidics and the emerging pioneering field of nano-fluidics.
3. Numerical algorithms and specific realizations for application of Monte Carlo methods for the study of:
- Rarefied gas-flows in micro-channels and gaseous MEMS
- Transport process and biological systems
- Phenomena, based on self-organized criticality: avalanches, earthquakes etc.
4. Modeling of the processes of wetting and spreading of liquid on chemically heterogeneous and rough surfaces. Modleing of interfaces - properties and interaction of micro and nano-objects with them.
5. Development of effective parallel algorithms for the specific software applications
6. Taking into account that the Institute of Mechanics is in the research field "Information and Communication Technologies" of BAS, mathematical models of information and communication processes, based on the complex system methodology will be developed in the department MM MCS.. The last includes using the experience in modeling of non-equilibrium thermodynamical systems, self-organized criticality, dissipative processes, which are also a subject of research in above formulated problems 1-4.