Surfaces that locally minimize area have been extensively used to model physical phenomena, including soap films, black holes, compound polymers, protein folding, etc. The mathematical field dates to the 1740s but has recently become an area of intense mathematical and scientific study, specifically in the areas of molecular engineering, materials science, and nanotechnology because of their ma...

In this paper, we use a deep mathematical result (namely, a minor modi cation of Kolmogorov's solution to Hilbert's 13th problem) to explain why fundamental physical equations are of second order. This same result explain why all these fundamental equations naturally lead to nonsmooth solutions like singularity. Formulation of the problem. Most physical phenomena are described in terms of parti...

String Quantum Gravity is motivated and introduced. Advances in the study of the classical and quantum string dynamics in curved spacetime are reported : In 1987, we started a programme [1] to study the string dynamics in curved spacetime and its associated physical phenomena. This study revealed new insights and new physical phenomena with respect to string propagation in flat spacetime (and w...

Standard model successfully described all the physical phenomena up to recent time. But recent discovery of oscillations of atmospheric neutrino shows that minimal Standard model has to be extended. The main trends are connected with determination of neutrino properties, including masses and mixing angles, search for double beta decay and a problem of hidden mass of Galaxy. Below the main resul...

Understanding the fundamental mechanisms governing fluctuating oscillations in large-scale cortical circuits is a crucial prelude to a proper knowledge of their role in both adaptive and pathological cortical processes. Neuroscience research in this area has much to gain from understanding the Kuramoto model, a mathematical model that speaks to the very nature of coupled oscillating processes, ...

We propose a spin model with quenched disorder which exhibits in slow driving two drastically different types of critical nonequilibrium steady states. One of them corresponds to classical criticality requiring fine-tuning of the disorder. The other is a self-organized criticality which is insensitive to disorder. The crossover between the two types of criticality is determined by the mode of d...

This paper provides an overview of the developing needs for sim10 ulation software technologies for the computational modelling of problems that involve combinations of interactions amongst varying physical phenomena over a variety of time and space scales. Computational modelling of such problems requires software technologies that enable the mathematical description of the interact15 ing phys...

When driven by an external thermodynamic gradient, nonbiological physical systems can exhibit a wide range of behaviours usually associated with living systems. Consequently, Artificial Life researchers should be open to the possibility that there is no hard-and-fast distinction between the biological and the physical. This suggests a novel field of research: the application of biologists’ meth...

The mathematical description of physical systems makes often use of the Hamiltonian formalism, which from its original application to derive the so-called Hamilton’s equations of motion in classical mechanics quickly spread on many other physical phenomena, ranging from statistical physics to quantum mechanics [1]. Although the Hamiltonian formulation of a problem of mathematical physics in gen...

An overarching mathematical framework is proposed to describe entire mineral particle precipitation processes including multiple polymorphic forms and ranges of temperatures. While existing models portray individual physical phenomena, the presented approach incorporates a diverse set of the physical phenomena simultaneously within a single mathematical description. The liquid and solid phase d...