Related papers: Equations of Motion that Recognize Biochemical Pat…
It is demonstrated that very general nonlinear dynamical systems covering all cases arising in practice can be brought down to rate equations of chemical kinetics
In this paper we introduce a formalism that allows to describe the response of a part of a biochemical system in terms of renewal equations. In particular, we examine under which conditions the interactions between the different parts of a…
Apparently, all partial differential equations that describe physical phenomena in space-time can be cast into a universal quasilinear, first-order form. In this paper, we do two things. First, we describe some broad features of systems of…
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
The theory of continuous phase transitions predicts the universal collective properties of a physical system near a critical point, which for instance manifest in characteristic power-law behaviours of physical observables. The…
Many examples of chemical and biological processes take place in large-scale environmental flows. Such flows generate filamental patterns which are often fractal due to the presence of chaos in the underlying advection dynamics. In such…
Chemically active mixtures exhibit complex patterns that emerge from the interplay of physical interactions and reactions among components. Individually, these two processes are well-understood: Physical interactions can give rise to phase…
Biological organisms are composed of numerous interconnected biochemical processes. Diseases occur when normal functionality of these processes is disrupted. Thus, understanding these biochemical processes and their interrelationships is a…
Hamilton's equations of motion are local differential equations and boundary conditions are required to determine the solution uniquely. Depending on the choice of boundary conditions, a Hamiltonian may thereby describe several different…
Equations of motion for single particle under two proper time model and three proper time model have been proposed and analyzed. The motions of particle are derived from pure classical method but they exhibit the same properties of quantum…
The article provides an overview of some advances in the mathematical understanding of the nature of the kinetic equations of quantum systems of many particles. The fundamental equations of modern mathematical physics are studied, in…
Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e.,…
The dynamical systems of identical particles admitting quadratic integrals of motion are classified. The relevant integrals are explicitly constructed and their relation to separation of variables in H-J equation is clarified.
Living systems are maintained out-of-equilibrium by external driving forces. At stationarity, they exhibit emergent selection phenomena that break equilibrium symmetries and originate from the expansion of the accessible chemical space due…
Measurement in biological systems became a subject of concern as a consequence of numerous reports on limited reproducibility of experimental results. To reveal origins of this inconsistency, we have examined general features of biological…
A review of the mechanisms of speciation is performed. The mechanisms of the evolution of species, taking into account the feedback of the state of the environment and mechanisms of the emergence of complexity, are considered. It is shown…
It is frequent for active or living entities to find themselves embedded in a surrounding medium. Resulting composite systems are usually classified as either active fluids or active solids. Yet, in reality, particularly in the biological…
The conditions under which, the continuity equation can be substituted by an ordinary non differential equation, will be discussed. Since continuity equation is a fundamental equation, this result will be applicable in a vast area of…
Active matter is not only indispensable to our understanding of diverse biological processes, but also provides a fertile ground for discovering novel physics. Many emergent properties impossible for equilibrium systems have been…
Reactions forming a pathway can be rewritten by making explicit the different molecular components involved in them. A molecular component represents a biological entity (e.g. a protein) in all its states (free, bound, degraded, etc.). In…