We use the qualitative insight of a planar neuronal phase portrait to detect an excitability switch in arbitrary conductance-based models from a simple mathematical condition. The condition expresses a balance between ion channels that provide a negative feedback at resting potential (restorative channels) and those that provide a positive feedback at resting potential (regenerative channels). ...

Many enzymatic reactions in biochemistry are far more complex than the celebrated Michaelis-Menten scheme, but the observed turnover rate often obeys the hyperbolic dependence on the substrate concentration, a relation established almost a century ago for the simple Michaelis-Menten mechanism. To resolve the longstanding puzzle, we apply the flux balance method to predict the functional form of...

| Stochastic (Monte Carlo) solutions of the general balance ordinary diierential equations for measures are considered. For this purpose a wide class of n-particle processes is studied from the viewpoint of the main terms of asymptotical (n ! 1) bias and variance for the corresponding estimates. Boltzmann-like and linear equations are considered as the particular cases of balance equations, sev...

This paper studies the transformation properties of the spatial balance of energy equation for a dissipative material, under the superposition of arbitrary spatial diffeomorphisms. The study reveals that for a dissipative material the transformed energy balance equation has some non-standard terms in it. These terms are related to a system of microforces with its own balance equation. These mic...

In this paper we use information-theoretic measures to provide a theory and tools to analyze the flow of information from a discrete, multivariate source of information X to a discrete, multivariate sink of information Y joined by a distribution PXY . The first contribution is a decomposition of the maximal potential entropy of (X,Y ) that we call a balance equation, that can also be split into...

The blow-up in finite time for the solutions to the initial-boundary value problem associated to the multi-dimensional quantum hydrodynamic model in a bounded domain is proved. The model consists on conservation of mass equation and a momentum balance equation equivalent to a compressible Euler equations corrected by a dispersion term of the third order in the momentum balance. The proof is bas...

The population balance equation is used to describe the dynamics of a continuous crystallizer. A simple condition to guarantee the stability of a mixed suspended mixed product removal crystallizer is derived based on the population balance. A novel discretization scheme solves the population balance and the resulting discretized population balance is shown to be equivalent to the original popul...

In this paper, we establish exact solutions for nonlinear evolution equations. The homogeneous balance method is used to construct exact travelling wave solutions of the CalogeroDegasperis (CD) and Potential Kadomstev-Petviashvili (PKP) equations, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation. Many new f...

The capability of high order methods to solve the population balance equation is studied in this work. The Least Square Method, the Nyström Method and a low order version of the Nyström method, called the Discrete Method, are applied to a general population balance equation containing breakage terms only. In order to perform a rigorous error analysis, analytical solutions are used. In general t...

A complete set of scaling criteria for gas hydrate reservoir of five-spot well system case is derived from the 3D governing equations, involving the mass balance equation, the energy balance equation, the kinetic model, the endothermic model and the phase equilibrium model. In the scaling criteria, the key parameters of the experiment are the water/gas production rates, the water injection rate...