Search results for "Names"

A Hooke's law-based approach to protein folding rate

2014

Kinetics is a key aspect of the renowned protein folding problem. Here, we propose a comprehensive approach to folding kinetics where a polypeptide chain is assumed to behave as an elastic material described by the Hooke[U+05F3]s law. A novel parameter called elastic-folding constant results from our model and is suggested to distinguish between protein with two-state and multi-state folding pathways. A contact-free descriptor, named folding degree, is introduced as a suitable structural feature to study protein-folding kinetics. This approach generalizes the observed correlations between varieties of structural descriptors with the folding rate constant. Additionally several comparisons am…

The Concept of Duality and Applications to Markov Processes Arising in Neutral Population Genetics Models

1999

One possible and widely used definition of the duality of Markov processes employs functions H relating one process to another in a certain way. For given processes X and Y the space U of all such functions H, called the duality space of X and Y, is studied in this paper. The algebraic structure of U is closely related to the eigenvalues and eigenvectors of the transition matrices of X and Y. Often as for example in physics (interacting particle systems) and in biology (population genetics models) dual processes arise naturally by looking forwards and backwards in time. In particular, time-reversible Markov processes are self-dual. In this paper, results on the duality space are presented f…

Dynamics of the Selkov oscillator.

2018

A classical example of a mathematical model for oscillations in a biological system is the Selkov oscillator, which is a simple description of glycolysis. It is a system of two ordinary differential equations which, when expressed in dimensionless variables, depends on two parameters. Surprisingly it appears that no complete rigorous analysis of the dynamics of this model has ever been given. In this paper several properties of the dynamics of solutions of the model are established. With a view to studying unbounded solutions a thorough analysis of the Poincar\'e compactification of the system is given. It is proved that for any values of the parameters there are solutions which tend to inf…

Random walk approach to the analytic solution of random systems with multiplicative noise—The Anderson localization problem

2006

We discuss here in detail a new analytical random walk approach to calculating the phase-diagram for spatially extended systems with multiplicative noise. We use the Anderson localization problem as an example. The transition from delocalized to localized states is treated as a generalized diffusion with a noise-induced first-order phase transition. The generalized diffusion manifests itself in the divergence of averages of wavefunctions (correlators). This divergence is controlled by the Lyapunov exponent $\gamma$, which is the inverse of the localization length, $\xi=1/\gamma$. The appearance of the generalized diffusion arises due to the instability of a fundamental mode corresponding to…

First results on applying a non-linear effect formalism to alliances between political parties and buy and sell dynamics

2016

We discuss a non linear extension of a model of alliances in politics, recently proposed by one of us. The model is constructed in terms of operators, describing the \emph{interest} of three parties to form, or not, some political alliance with the other parties. The time evolution of what we call \emph{the decision functions} is deduced by introducing a suitable hamiltonian, which describes the main effects of the interactions of the parties amongst themselves and with their \emph{environments}, {which are }generated by their electors and by people who still have no clear {idea }for which party to vote (or even if to vote). The hamiltonian contains some non-linear effects, which takes into…

A dynamical approach to compatible and incompatible questions

2019

We propose a natural strategy to deal with compatible and incompatible binary questions, and with their time evolution. The strategy is based on the simplest, non-commutative, Hilbert space $\mathcal{H}=\mathbb{C}^2$, and on the (commuting or not) operators on it. As in ordinary Quantum Mechanics, the dynamics is driven by a suitable operator, the Hamiltonian of the system. We discuss a rather general situation, and analyse the resulting dynamics if the Hamiltonian is a simple Hermitian matrix.

Structure and dynamics of yukawa systems

1993

Abstract Results of molecular dynamics simulations modelling two component charge stabilized colloidal particles interacting via a Yukawa potential are presented. After cooling, the systems freeze into either substitutionally disordered imperfect crystals or into glasslike states. This freezing is characterized by the divergence of a suitable correlation time due to loss of ergodicity. Describing the structure by bond correlation functions, local orientational ordering is observed in the glassy states which is not present in the liquid. In the liquid the diffusion constant obeys an Arrhenius law. As can be deduced from the van Hove functions, in the crystal the particles only oscillate arou…

Self-consistent Euclidean-random-matrix theory

2019

Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from separation of variables

2014

28 pages; International audience; We solve the longstanding problem to define a functional characterization of the spectrum of the transfer matrix associated to the most general spin-1/2 representations of the 6-vertex reflection algebra for general inhomogeneous chains. The corresponding homogeneous limit reproduces the spectrum of the Hamiltonian of the spin-1/2 open XXZ and XXX quantum chains with the most general integrable boundaries. The spectrum is characterized by a second order finite difference functional equation of Baxter type with an inhomogeneous term which vanishes only for some special but yet interesting non-diagonal boundary conditions. This functional equation is shown to…

Spatial decoherence in QED

2006

We consider the dynamics of a charged free particle, initially described by a coherent wave packet, interacting with an electromagnetic field characterized by the temperature T, considered as the environment. We have used dipole approximation neglecting the potential vector quadratic term in the minimal coupling Hamiltonian. This leads to the loss of coherence in the momentum representation, described by the decay of the off diagonal elements of the particle reduced density matrix, while the populations remain constant. Here we extend the analysis to the coordinate representation. We compute the particle reduced density matrix in this basis, analyzing in particular the mixing of various ef…