We have 20years+ quantitative simulations expertise...we therefore develop theoretical models to describe physical systems, and seek physical systems that are described by our mathematical models...
what this means:
a) We have solved the Lotka-Volterra equations with generalized noise, and with specialized nonextensive noise...for certain cases..we have also developed computational solvers for these...L-K models describe bistable and nstable systems and or branching processes in genetics and or predator-prey models in epidemiology where for example pathogenic predators prey on a healthy human population as are studied in the field of epidemiology (think enfluenza)...L-K modeling describes also phase transitions in physics systems e.x. Ferromagnetism, and describes financial markets..last but certainly not least L-K describes pattern formation. We are currently active in almost all of these areas of research....see our cited papers and references therein in the first few web pages of our website.
b) We have recently proposed one possible solution to the Boltzmann Equation..this equation describes fluid flow, electronic flow, and much more, as a phase space equation.. We have provided both the molecular chaos approximation solution and its generalized nonextensive or history following solution.
c) We have recently proposed one possible solution of the Navier-Stokes Equation of hydrodynamics...these equations describe fluid and gas flow, for example weather modeling and prediction and forecasting, those trajectories of a Hurricane you see on television, are calculated by computers solving the Navier-Stokes equations...preprint is available upon request.
d) We have recently proposed that nth order nonlinear PDEs partial differential equations are solvable...by transforming recursively functionally to 2nd order Fokker-Planck standard form which has several solution methods. Applications to 3rd order Soliton equations ubiquitous in engineering and physics and biology are immediate.
e) We have recently produced a theory of biological mammalian neural networks, and the emergence of the observed power-spectrum of 'alpha waves' and so forth that are Q-cavity -like...we connect the theory to capacitance models, to random oscillator Wiener models...we discuss therefore artificial neural networks, network theory and design and creation of self-assembled networks. We furthermore recently proposed following research at UChicago to model sleepand awake cycles of n-neurons and to determine where this two-state distinction blurs or disappears and by modeling C. Elegans worm neural networks. Other connexions are to vision research, cognition and memory.
f) We have recently produced a continuous variables theory of Quantum Computing ensembles...following Tadd Hogg and Hubermann, we are able to show that portfolios of Qbits are more efficient, and have derived the statistics of such a quantum computation...further applications are to distributed classical computing and algorithms, clouds, vague nebula, etc..