On the Thermodynamic and Kinetic Aspects of Immersion Ice Nucleation

Heterogeneous ice nucleation initiated by particles immersed within droplets is likely the main pathway of ice formation in the atmosphere. Theoretical models commonly used to describe this process assume that it mimics ice formation from the vapor, neglecting interactions unique to the liquid phase. This work introduces a new approach that accounts for such interactions by linking the ability of particles to promote ice formation to the modification of the properties of water near the particle-liquid interface. It is shown that the same mechanism that lowers the thermodynamic barrier for ice nucleation also tends to decrease the mobility of water molecules, hence the ice-liquid interfacial flux. Heterogeneous ice nucleation in the liquid phase is thus determined by the competition between thermodynamic and kinetic constraints to the formation and propagation of ice. At the limit, ice nucleation may be mediated by kinetic factors instead of the nucleation work. This new ice nucleation regime is termed spinodal ice nucleation. Comparison of predicted nucleation rates against published data suggests that some materials of atmospheric relevance may nucleate ice in this regime

Perfect Sampling of the Master Equation for Gene Regulatory Networks

We present a Perfect Sampling algorithm that can be applied to the Master Equation of Gene Regulatory Networks (GRNs). The method recasts Gillespie's Stochastic Simulation Algorithm (SSA) in the light of Markov Chain Monte Carlo methods and combines it with the Dominated Coupling From The Past (DCFTP) algorithm to provide guaranteed sampling from the stationary distribution. We show how the DCFTP-SSA can be generically applied to genetic networks with feedback formed by the interconnection of linear enzymatic reactions and nonlinear Monod- and Hill-type elements. We establish rigorous bounds on the error and convergence of the DCFTP-SSA, as compared to the standard SSA, through a set of increasingly complex examples. Once the building blocks for GRNs have been introduced, the algorithm is applied to study properly averaged dynamic properties of two experimentally relevant genetic networks: the toggle switch, a two-dimensional bistable system, and the repressilator, a six-dimensional genetic oscillator.Comment: Minor rewriting; final version to be published in Biophysical Journa

The problem of non-renewable energy resources in the production of physical capital

This paper studies the possibilities of technical progress to deal with the growth limit problem imposed by the usage of non-renewable energy resources, when physical capital production is relatively more energy-intensive than consumption. In particular, this work presents the conditions under which energy-saving technologies can sustain long-run growth, although energy is produced by means of non-renewable energy resources. The mechanism behind that is energy efficiency.nonrenewable resources, energy-saving technical progress, economic growth.

The problem of non-renewable energy resources in the production of physical capital

This paper studies the possibilities of technical progress to deal with the growth limit problem imposed by the usage of non-renewable energy resources, when physical capital production is relatively more energy-intensive than consumption. In particular, this work presents the conditions under which energy-saving technologies can sustain long-run growth, although energy is produced by means of non-renewable energy resources. The mechanism behind that is energy efficiency.Nonrenewable resources, Energy-saving technical progress, Economic growth

Pinned states in Josephson arrays: A general stability theorem

Using the lumped circuit equations, we derive a stability criterion for superconducting pinned states in two-dimensional arrays of Josephson junctions. The analysis neglects quantum, thermal, and inductive effects, but allows disordered junctions, arbitrary network connectivity, and arbitrary spatial patterns of applied magnetic flux and DC current injection. We prove that a pinned state is linearly stable if and only if its corresponding stiffness matrix is positive definite. This algebraic condition can be used to predict the critical current and frustration at which depinning occurs.Comment: To appear in Phys. Rev.

A linear programming approach to increasing the weight of all minimum spanning trees

Dans cet article nous étudions le problème qui consiste à augmenter au moindre coût le poids de tous les arbres couvrants de poids minimum. Nous considérons le cas où le coût d'augmenter le poids d'une arête du graphe est une fonction linéaire par morceaux, convexe et croissante. Nous formulons ce problème par un programme linéaire et nous donnons un algorithme polynomial pour sa résolution et la résolution du son problème dual.

On the p-media polytope of special class of graphs

Dans cet article nous étudions les inégalités de cycles impairs. Nous donnons un nouvel algorithme de séparation de ces inégalités, et nous montrons que lorsque nous ajoutons ces inégalités aux inégalités de la relaxation linéaire nous obtenons le polytope du p-médian dans la classe des graphes sans Y. Pour cela nous caractérisons d'abord les points extrêmesfractionnaires du système défini par la relaxation linéaire dans les graphes sans Y.

On the stability of the Kuramoto model of coupled nonlinear oscillators

We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for all-to-all networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary interconnection topology with uncertain natural frequencies. Using tools from spectral graph theory and control theory, we prove that for couplings above a critical value, the synchronized state is locally asymptotically stable, resulting in convergence of all phase differences to a constant value, both in the case of identical natural frequencies as well as uncertain ones. We further explain the behavior of the system as the number of oscillators grows to infinity.Comment: 8 Pages. An earlier version appeared in the proceedings of the American Control Conference, Boston, MA, June 200