Scaling and front dynamics in Ising quantum chains

We study the relaxation dynamics of a quantum Ising chain initially prepared in a product of canonical states corresponding each to an equilibrium state of part of the chain at a given temperature. We focus our attention on the transverse magnetization for which a general expression is given. Explicite results are given for the completely factorized initial state, corresponding to a situation where all the spins are thermalized independently, and for the two-temperatures initial state, where part of the chain called the system is thermalized at a temperature $T_s$ and the remaining part is at a temperature $T_b$.Comment: 7 pages, submitted to EPJ

Network Evolution Induced by the Dynamical Rules of Two Populations

We study the dynamical properties of a finite dynamical network composed of two interacting populations, namely; extrovert ($a$) and introvert ($b$). In our model, each group is characterized by its size ($N_a$ and $N_b$) and preferred degree ($\kappa_a$ and $\kappa_b\ll\kappa_a$). The network dynamics is governed by the competing microscopic rules of each population that consist of the creation and destruction of links. Starting from an unconnected network, we give a detailed analysis of the mean field approach which is compared to Monte Carlo simulation data. The time evolution of the restricted degrees \moyenne{k_{bb}} and \moyenne{k_{ab}} presents three time regimes and a non monotonic behavior well captured by our theory. Surprisingly, when the population size are equal $N_a=N_b$, the ratio of the restricted degree \theta_0=\moyenne{k_{ab}}/\moyenne{k_{bb}} appears to be an integer in the asymptotic limits of the three time regimes. For early times (defined by $t<t_1=\kappa_b$) the total number of links presents a linear evolution, where the two populations are indistinguishable and where $\theta_0=1$. Interestingly, in the intermediate time regime (defined for $t_1<t<t_2\propto\kappa_a$ and for which $\theta_0=5$), the system reaches a transient stationary state, where the number of contacts among introverts remains constant while the number of connections is increasing linearly in the extrovert population. Finally, due to the competing dynamics, the network presents a frustrated stationary state characterized by a ratio $\theta_0=3$.Comment: 21 pages, 6 figure

Relaxation in the XX quantum chain

We present the results obtained on the magnetisation relaxation properties of an XX quantum chain in a transverse magnetic field. We first consider an initial thermal kink-like state where half of the chain is initially thermalized at a very high temperature $T_b$ while the remaining half, called the system, is put at a lower temperature $T_s$. From this initial state, we derive analytically the Green function associated to the dynamical behaviour of the transverse magnetisation. Depending on the strength of the magnetic field and on the temperature of the system, different regimes are obtained for the magnetic relaxation. In particular, with an initial droplet-like state, that is a cold subsystem of finite size in contact at both ends with an infinite temperature environnement, we derive analytically the behaviour of the time-dependent system magnetisation

Fourier's law on a one-dimensional optical random lattice

We study the transport properties of a one-dimensional hard-core bosonic lattice gas coupled to two particle reservoirs at different chemical potentials which generate a current flow through the system. In particular, the influence of random fluctuations of the underlying lattice on the stationary-state properties is investigated. We show analytically that the steady-state density presents a linear profile. The local steady-state current obeys the Fourier law $j=-\kappa(\tau)\nabla n$ where $\tau$ is a typical timescale of the lattice fluctuations and $\nabla n$ the density gradient imposed by the reservoirs.Comment: 9 pages, 2 figure

Regulation by small RNAs via coupled degradation: mean-field and variational approaches

Regulatory genes called small RNAs (sRNAs) are known to play critical roles in cellular responses to changing environments. For several sRNAs, regulation is effected by coupled stoichiometric degradation with messenger RNAs (mRNAs). The nonlinearity inherent in this regulatory scheme indicates that exact analytical solutions for the corresponding stochastic models are intractable. Here, we present a variational approach to analyze a well-studied stochastic model for regulation by sRNAs via coupled degradation. The proposed approach is efficient and provides accurate estimates of mean mRNA levels as well as higher order terms. Results from the variational ansatz are in excellent agreement with data from stochastic simulations for a wide range of parameters, including regions of parameter space where mean-field approaches break down. The proposed approach can be applied to quantitatively model stochastic gene expression in complex regulatory networks.Comment: 4 pages, 3 figure

Analytical results for a stochastic model of gene expression with arbitrary partitioning of proteins

In biophysics, the search for analytical solutions of stochastic models of cellular processes is often a challenging task. In recent work on models of gene expression, it was shown that a mapping based on partitioning of Poisson arrivals (PPA-mapping) can lead to exact solutions for previously unsolved problems. While the approach can be used in general when the model involves Poisson processes corresponding to creation or degradation, current applications of the method and new results derived using it have been limited to date. In this paper, we present the exact solution of a variation of the two-stage model of gene expression (with time dependent transition rates) describing the arbitrary partitioning of proteins. The methodology proposed makes full use of the the PPA-mapping by transforming the original problem into a new process describing the evolution of three biological switches. Based on a succession of transformations, the method leads to a hierarchy of reduced models. We give an integral expression of the time dependent generating function as well as explicit results for the mean, variance, and correlation function. Finally, we discuss how results for time dependent parameters can be extended to the three-stage model and used to make inferences about models with parameter fluctuations induced by hidden stochastic variables.Comment: 15 pages, 6 figure

Dynamical phase transition of a 1D transport process including death

Motivated by biological aspects related to fungus growth, we consider the competition of growth and corrosion. We study a modification of the totally asymmetric exclusion process, including the probabilities of injection $\alpha$ and death of the last particle $\delta$. The system presents a phase transition at $\delta_c(\alpha)$, where the average position of the last particle $$ grows as $\sqrt{t}$. For $\delta>\delta_c$, a non equilibrium stationary state exists while for $\delta<\delta_c$ the asymptotic state presents a low density and max current phases. We discuss the scaling of the density and current profiles for parallel and sequential updates.Comment: 4 pages, 5 figure

PARENT'S ROLE PREVENTING EARLY MARRIAGE

Background: Early marriage has many negative impacts; therefore, parents needed an effort to prevent early marriage. Purpose: To describe the role of parents in preventing early marriage. Method: quantitative descriptive, Accidental sampling technique, with a sample size of 95. The study was conducted in May 2019. The research instrument was a questionnaire on the Role of Parents in Preventing Early Marriage, modified from Novianti (2017), contained 30 questions, with a validity score of 0.3785 and alpha cronbach 0.707. Data analysis using frequency distribution. This research had been registered to the ethics committee with the ethics number of 535/UN6.KEP/EC/2019. Result: 56 people (59%) parents done their role excellent in preventing early marriage. Of the five roles of parents, the role of parents was an educator 64 (67%), role models and friends 46 (48%), counselor 40 (53%), and 60 (63%) as a communicator. Conclusion: the role of parents in preventing early marriage was categorized as either the role of educator, communicator and counselor, while the role of parents as friends and role models was said to be wrong. Suggestion: education about early marriage to the community and adolescents to reduce or minimize early marriage incidence Keywords: Prevention, Early Marriage, Role of Parents