We solve analytically the model of gene expression induction which consists of three steps: gene activation, gene products synthesis, and product degradation. The solution is given as a time-dependent probability distribution for gene products. Following the distribution in time from the inactive state of the gene to the stationary state we observe binary or graded response depending solely on the ratio $r$ of the gene activation rate to the rate of the gene product degradation. If $r⪡1$ the response is binary and the continuous transition from binary to graded response occurs between $r=0.1$ and $r=1$. Therefore, if binary response is observed during relaxation to steady state, then the activation rate constant must be smaller than the degradation rate constant.

Recent works on evaporation and condensation demonstrate that even these sim-plest irreversible processes, studied for over 100 years, are not well understood. In the caseof a liquid evaporating into its vapor, the liquid temperature is constant during evaporationand the evaporation flux is governed by the heat transfer from the hotter vapor into the colderliquid. Whether liquid evaporates into its own vapor or into the vacuum, the irreversible path-way in the process goes through a number of steps which quickly lead to the steady-state con-ditions with mechanical equilibrium in most parts of the system—the fact overlooked in allprevious studies. Even less is known about general rules which govern systems far from equi-librium. Recently, it has been demonstrated that a work done in an irreversible process canbe related to the free energy difference between equilibrium states joined by the process.Finally, a real challenge in thermodynamics is a description of living systems since they donot have equilibrium states, are nonextensive, (i.e., they cannot be divided into subsystems),and cannot be isolated. Thus, their proper description requires new paradigms in thermo -dynamics.

We investigate the morphology of the spatial pattern resulting from the division of land into the parcels that is observed in the centers of the cities, by analyzing the distribution function of the parcel areas. A simple model based on a two-dimensional bond percolation is employed to mimic the process of the formation of the city. The model reproduces the empirical distribution of the parcel areas that is found to exhibit the power law with the exponent $\tau =2.0$. We argue that the city emerges from a collection of separated settlements in a process that can be described as a structural phase transition.

Pulling apart: The authors demonstrate experimentally that oscillating electric fields can be used to accelerate the rate of phase separation by up to three orders of magnitude (see picture), and to change the character of the phase‐separation process from a power to exponential evolution of the mean size of the domains.

We demonstrate using molecular dynamics simulations of the Lennard-Jones fluid that the evaporation process of nanodroplets at the nanoscale is limited by the heat transfer. The temperature is continuous at the liquid-vapor interface if the liquid/vapor density ratio is small (of the order of 10) and discontinuous otherwise. The temperature in the vapor has a scaling form $T(r,t)=T[r/R(t\left)\right]$, where $R\left(t\right)$ is the radius of an evaporating droplet at time $t$ and $r$ is the distance from its center. Mechanical equilibrium establishes very quickly, and the pressure difference obeys the Laplace law during evaporation.

Understanding a biological module involves recognition of its structure and the dynamics of its principal components. In this report we present an analysis of the dynamics of the repression module within the regulation of the trp operon in Escherichia coli. We combine biochemical data for reaction rate constants for the trp repressor binding to trp operator and in vivo data of a number of tryptophan repressors (TrpRs) that bind to the operator. The model of repression presented in this report greatly differs from previous mathematical models. One, two or three TrpRs can bind to the operator and repress the transcription. Moreover, reaction rates for detachment of TrpRs from the operator strongly depend on tryptophan (Trp) concentration, since Trp can also bind to the repressor–operator complex and stabilize it. From the mathematical modeling and analysis of reaction rates and equilibrium constants emerges a high-quality, accurate and effective module of trp repression. This genetic switch responds accurately to fast consumption of Trp from the interior of a cell. It switches with minimal dispersion when the concentration of Trp drops below a thousand molecules per cell.

Light membranes composed of single-walled carbon nanotubes (SWNTs) can serve as efficient nanoscale vessels for encapsulation of tetrafluoromethane at 300 K and operating external pressure of 1 bar. We use grand canonical Monte Carlo simulation for modeling of CF₄ encapsulation at 300 K and pressures up to 2 bar. We find that the amount of adsorbed CF₄ strongly depends on the pore size in nanotubes; at 1 bar the most efficient nanotubes for volumetric storage have size R = 0.68 nm. This size corresponds to the (10,10) armchair nanotubes produced nowadays in large quantities. For mass storage (i.e., weight %) the most efficient nanotubes have size R = 1.02 nm corresponding to (15,15) armchair nanotubes. They are better adsorbents than currently used activated carbons and zeolites, reaching ≈2.4 mol kg⁻¹ of CF₄, whereas, the best activated carbon Carbosieve G molecular sieve can adsorb 1.7 mol kg⁻¹ of CF₄ at 300 K and 1 bar. We demonstrate that the high enthalpy of adsorption cannot be used as an only measure of storage efficiency. The optimal balance between the binding energy (i.e., enthalpy of adsorption) and space available for the accommodation of molecules (i.e., presence of inaccessible pore volume) is a key for encapsulation of van der Walls molecules. Our systematic computational study gives the clear direction in the timely problem of control emission of CF₄ and other perfluorocarbons into atmosphere.