A thermodynamic framework for modelling membrane transporters

Membrane transporters contribute to the regulation of the internal environment of cells by translocating substrates across cell membranes. Like all physical systems, the behaviour of membrane transporters is constrained by the laws of thermodynamics. However, many mathematical models of transporters, especially those incorporated into whole-cell models, are not thermodynamically consistent, leading to unrealistic behaviour. In this paper we use a physics-based modelling framework, in which the transfer of energy is explicitly accounted for, to develop thermodynamically consistent models of transporters. We then apply this methodology to model two specific transporters: the cardiac sarcoplasmic/endoplasmic Ca$^{2+}$ ATPase (SERCA) and the cardiac Na$^+$/K$^+$ ATPase

Anomalous roughness with system size dependent local roughness exponent

We note that in a system far from equilibrium the interface roughening may depend on the system size which plays the role of control parameter. To detect the size effect on the interface roughness, we study the scaling properties of rough interfaces formed in paper combustion experiments. Using paper sheets of different width \lambda L, we found that the turbulent flame fronts display anomalous multi-scaling characterized by non universal global roughness exponent \alpha and the system size dependent spectrum of local roughness exponents,\xi_q, whereas the burning fronts possess conventional multi-affine scaling. The structure factor of turbulent flame fronts also exhibit unconventional scaling dependence on \lambda These results are expected to apply to a broad range of far from equilibrium systems, when the kinetic energy fluctuations exceed a certain critical value.Comment: 33 pages, 16 figure

THE MACROKINETICS PARAMETERS OF THE HYDROCARBONS COMBUSTION IN THE NUMERICAL CALCULATION OF ACCIDENTAL EXPLOSIONS IN MINES

Purpose. Obtaining effective parameters of the macrokinetics of combustion of hydrocarbons in the deflagration and detonation regime for the numerical calculation of emergency explosions in mine workings. Methodology. Mathematical modeling, numerical experiment, kinetics analysis of explosive combustion reaction, analysis and synthesis. Findings. The paper analyzes the parameters of the kinetic equation against experimental data. Obtaining such data in a physical experiment for explosive chemical reactions meets serious difficulties. This is due to the size of the reaction zone not exceeding fractions of a millimeter, the lack of time resolution of experimental techniques and other factors leading to errors in direct measurements and the emergence of multiple solutions. This possibility contributes to obtaining a simultaneous numerical solution of the equations of gas dynamics and chemical kinetics. In the numerical experiment, a direct relationship between the macrokinetic characteristics of the chemical reaction and the parameters of the discontinuous flow of the reacting gas stream is established: velocity, pressure in the front and behind the front of the detonation and deflagration wave. Based on this, Arrhenius characteristics of the reaction – preexponential and effective activation energy for the hydrocarbons under consideration are obtained. Originality. Macrokinetic parameters are established for simulating one-stage ignition and burning of the most probable hydrocarbons of the mine atmosphere in the deflagration and detonation regime. Modeling of explosive combustion of premixed hydrocarbons in stoichiometric concentrations is performed. It is shown that the values of the effective activation energy in explosive combustion reactions are of less importance in contrast to steady-state combustion reactions because of the effect of the gas-dynamical effects of the shock wave on the reaction rate. The Arrhenius characteristics of the reaction – the pre-exponential and the effective activation energy – have been agreed upon, according to the gas dynamic and kinetic parameters of the course of the explosive combustion reaction. Practical value. The obtained parameters of the macrokinetics of the explosive combustion reaction make it possible to apply simple kinetic mechanisms in practical calculations of the processes of deflagration and detonation combustion, and to predict the parameters of emergency explosions in conditions of mine workings with sufficient accuracy. This also makes it possible to solve the problem of accounting for the presence of heavy hydrocarbons in themine atmosphere as products of coal pyrolysis in underground fires as factors of increasing the risk of emergency explosions

Analysis of General Power Counting Rules in Effective Field Theory

We derive the general counting rules for a quantum effective field theory (EFT) in $\mathsf{d}$ dimensions. The rules are valid for strongly and weakly coupled theories, and predict that all kinetic energy terms are canonically normalized. They determine the energy dependence of scattering cross sections in the range of validity of the EFT expansion. We show that the size of cross sections is controlled by the $\Lambda$ power counting of EFT, not by chiral counting, even for chiral perturbation theory ($\chi$PT). The relation between $\Lambda$ and $f$ is generalized to $\mathsf{d}$ dimensions. We show that the naive dimensional analysis $4\pi$ counting is related to $\hbar$ counting. The EFT counting rules are applied to $\chi$PT, low-energy weak interactions, Standard Model EFT and the non-trivial case of Higgs EFT.Comment: V2: more details and examples added; version published in journal. 17 pages, 4 figures, 2 table

Stochastic magnetohydrodynamic turbulence in space dimensions d≥2d\ge 2

Interplay of kinematic and magnetic forcing in a model of a conducting fluid with randomly driven magnetohydrodynamic equations has been studied in space dimensions $d\ge 2$ by means of the renormalization group. A perturbative expansion scheme, parameters of which are the deviation of the spatial dimension from two and the deviation of the exponent of the powerlike correlation function of random forcing from its critical value, has been used in one-loop approximation. Additional divergences have been taken into account which arise at two dimensions and have been inconsistently treated in earlier investigations of the model. It is shown that in spite of the additional divergences the kinetic fixed point associated with the Kolmogorov scaling regime remains stable for all space dimensions $d\ge 2$ for rapidly enough falling off correlations of the magnetic forcing. A scaling regime driven by thermal fluctuations of the velocity field has been identified and analyzed. The absence of a scaling regime near two dimensions driven by the fluctuations of the magnetic field has been confirmed. A new renormalization scheme has been put forward and numerically investigated to interpolate between the $\epsilon$ expansion and the double expansion.Comment: 12 pages, 4 figure

Hydrodynamic fluctuations and the minimum shear viscosity of the dilute Fermi gas at unitarity

We study hydrodynamic fluctuations in a non-relativistic fluid. We show that in three dimensions fluctuations lead to a minimum in the shear viscosity to entropy density ratio $\eta/s$ as a function of the temperature. The minimum provides a bound on $\eta/s$ which is independent of the conjectured bound in string theory, $\eta/s \geq \hbar/(4\pi k_B)$, where $s$ is the entropy density. For the dilute Fermi gas at unitarity we find \eta/s\gsim 0.2\hbar. This bound is not universal -- it depends on thermodynamic properties of the unitary Fermi gas, and on empirical information about the range of validity of hydrodynamics. We also find that the viscous relaxation time of a hydrodynamic mode with frequency $\omega$ diverges as $1/\sqrt{\omega}$, and that the shear viscosity in two dimensions diverges as $\log(1/ \omega)$.Comment: 26 pages, 5 figures; final version to appear in Phys Rev