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## Agent based models and opinion dynamics as Markov chains

Banisch, Sven; Lima, Ricardo; Araújo, Tanya
Fonte: ISEG - Departamento de Economia Publicador: ISEG - Departamento de Economia
Tipo: Outros
Relevância na Pesquisa
47.07345%
This paper introduces a Markov chain approach that allows a rigorous analysis of agent based opinion dynamics as well as other related agent based models (ABM). By viewing the ABM dynamics as a micro description of the process, we show how the corresponding macro description is obtained by a projection construction. Then, well known conditions for lumpability make it possible to establish the cases where the macro model is stillMarkov. In this case we obtain a complete picture of the dynamics including the transient stage, the most interesting phase in applications. For such a purpose a crucial role is played by the type of probability distribution used to implement the stochastic part of the model which defines the updating rule and governs the dynamics. In addition, we show how restrictions in communication leading to the co–existence of different opinions follow from the emergence of new absorbing states. We describe our analysis in detail with some specific models of opinion dynamics. Generalizations concerning different opinion representations as well as opinion models with other interaction mechanisms are also discussed. We find that our method may be an attractive alternative to mean–field approaches and that this approach provides new perspectives on the modeling of opinion exchange dynamics...

## Transient dynamics and food-web complexity in the Lotka-Volterra cascade model.

Chen, X.; Cohen, J. E.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.13096%
How does the long-term behaviour near equilibrium of model food webs correlate with their short-term transient dynamics? Here, simulations of the Lotka -Volterra cascade model of food webs provide the first evidence to answer this question. Transient behaviour is measured by resilience, reactivity, the maximum amplification of a perturbation and the time at which the maximum amplification occurs. Model food webs with a higher probability of local asymptotic stability may be less resilient and may have a larger transient growth of perturbations. Given a fixed connectance, the sizes and durations of transient responses to perturbations increase with the number of species. Given a fixed number of species, as connectance increases, the sizes and durations of transient responses to perturbations may increase or decrease depending on the type of link that is varied. Reactivity is more sensitive to changes in the number of donor-controlled links than to changes in the number of recipient-controlled links, while resilience is more sensitive to changes in the number of recipient-controlled links than to changes in the number of donor-controlled links. Transient behaviour is likely to be one of the important factors affecting the persistence of ecological communities.

## Transient Dynamics of Genetic Regulatory Networks

Bennett, Matthew R.; Volfson, Dmitri; Tsimring, Lev; Hasty, Jeff
Fonte: Biophysical Society Publicador: Biophysical Society
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
47.12562%
We present an approximation scheme for deriving reaction rate equations of genetic regulatory networks. This scheme predicts the timescales of transient dynamics of such networks more accurately than does standard quasi-steady state analysis by introducing prefactors to the ODEs that govern the dynamics of the protein concentrations. These prefactors render the ODE systems slower than their quasi-steady state approximation counterparts. We introduce the method by examining a positive feedback gene regulatory network, and show how the transient dynamics of this network are more accurately modeled when the prefactor is included. Next, we examine the repressilator, a genetic oscillator, and show that the period, amplitude, and bifurcation diagram defining the onset of the oscillations are better estimated by the prefactor method. Finally, we examine the consequences of the method to the dynamics of reduced models of the phage lambda switch, and show that the switching times between the two states is slowed by the presence of the prefactor that arises from protein multimerization and DNA binding.

## Transient dynamics of an elastic capsule in a microfluidic constriction

Park, Sun-Young; Dimitrakopoulos, P.
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
47.16919%
In this paper we investigate computationally the transient dynamics of an elastic capsule flowing in a square microchannel with a rectangular constriction, and compare it with that of a droplet. The confinement and expansion dynamics of the fluid flow results in a rich deformation behavior for the capsule, from an elongated shape at the constriction entrance, to a flattened parachute shape at its exit. Larger capsules are shown to take more time to pass the constriction and cause higher additional pressure difference, owing to higher flow blocking. Our work highlights the effects of two different mechanisms for non-tank-treading transient capsule dynamics. The capsule deformation results from the combined effects of the surrounding and inner fluids’ normal stresses on the soft particle’s interface, and thus when the capsule viscosity increases, its transient deformation decreases, as for droplets. However, the capsule deformation is not able to create a strong enough inner circulation (owing to restrictions imposed by the material membrane), and thus the viscosity ratio does not affect much the capsule velocity and the additional pressure difference. In addition, the weak inner circulation results in a positive additional pressure difference ΔP+ even for low-viscosity capsules...

## Bounds on transient instability for complex ecosystems

Caravelli, Francesco; Staniczenko, Phillip
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.27415%
Stability is a desirable property of complex ecosystems. If a community of interacting species is at a stable equilibrium point then it is able to withstand small perturbations without any adverse effect. In ecology, the Jacobian matrix evalufated at an equilibrium point is known as the community matrix, which represents the population dynamics of interacting species. The system's asymptotic short- and long-term behaviour can be determined from eigenvalues derived from the community matrix. Here we use results from the theory of pseudospectra to describe intermediate, transient dynamics. We show that the transition from stable to unstable dynamics includes a region of transient instability, where the effect of a small perturbation is amplified before ultimately decaying. The shift from stability to transient instability depends on the magnitude of a perturbation, and we show how to determine lower and upper bounds to the maximum amplitude of perturbations. Of five different types of community matrix, we find that amplification is least severe with predator-prey interactions. This analysis is relevant to other systems whose dynamics can be expressed in terms of the Jacobian matrix. Through understanding transient instability, we can learn under what conditions multiple perturbations - multiple external shocks - will irrecoverably break stability.; Comment: 6 pages...

## Photoassociation and coherent transient dynamics in the interaction of ultracold rubidium atoms with shaped femtosecond pulses - I. Experiment

Salzmann, Wenzel; Mullins, Terry; Götz, Simone; Albert, Magnus; Eng, Judith; Wester, Roland; Weidemüller, Matthias; Weise, Fabian; Merli, Andrea; Weber, Stefan M.; Sauer, Franziska; Wöste, Ludger; Lindinger, Albrecht
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
47.01425%
We experimentally investigate various processes present in the photoassociative interaction of an ultracold atomic sample with shaped femtosecond laser pulses. We demonstrate the photoassociation of pairs of rubidium atoms into electronically excited, bound molecular states using spectrally cut femtosecond laser pulses tuned below the rubidium D1 or D2 asymptote. Time-resolved pump-probe spectra reveal coherent oscillations of the molecular formation rate, which are due to coherent transient dynamics in the electronic excitation. The oscillation frequency corresponds to the detun-ing of the spectral cut position to the asymptotic transition frequency of the rubidium D1 or D2 lines, respectively. Measurements of the molecular photoassociation signal as a function of the pulse energy reveal a non-linear dependence and indicate a non-perturbative excitation process. Chirping the association laser pulse allowed us to change the phase of the coherent transients. Furthermore, a signature for molecules in the electronic ground state is found, which is attributed to molecule formation by femtosecond photoassociation followed by spontaneous decay. In a subsequent article [A. Merli et al., submitted] quantum mechanical calculations are presented...

## Floquet-Magnus Theory and Generic Transient Dynamics in Periodically Driven Many-Body Quantum Systems

Kuwahara, Tomotaka; Mori, Takashi; Saito, Keiji
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
47.080645%
This work explores a fundamental dynamical structure for a wide range of many-body quantum systems under periodic driving. Generically, in the thermodynamic limit, such systems are known to heat up to infinite temperature states after infinite-time evolution, irrespective of dynamical details. In the present study, instead of considering infinitely long-time scale, we aim to provide a framework to understand the long but finite time behavior, namely the transient dynamics. In the analysis, we focus on the Floquet-Magnus (FM) expansion that gives a formal expression of the effective Hamiltonian on the system. Although in general the full series expansion is not convergent in the thermodynamics limit, we give a clear relationship between the FM expansion and the transient dynamics. More precisely, we rigorously show that a truncated version of the FM expansion accurately describes the exact dynamics for a finite-time scale. Our result reveals a reliable time scale of the validity of the FM expansion, which can be comparable to the experimental time scale. Furthermore, we discuss several dynamical phenomena, such as the effect of small integrability breaking, efficient numerical simulation of periodically driven systems, dynamical localization and thermalization. Especially on thermalization...

## Transient Dynamics of d-wave Superconductors after a Sudden Excitation

Peronaci, Francesco; Schirò, Marco; Capone, Massimo
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.93676%
Motivated by recent ultafast pump probe experiments on high-temperature superconductors, we discuss the transient dynamics of a d-wave BCS model after a quantum quench of the interaction parameter. We find that the existence of gap nodes, with the associated nodal quasiparticles, introduces a dissipation channel which makes the dynamics much faster than in the conventional s-wave model. For every value of the quench parameters, the superconducting gap rapidly converges to a stationary value smaller than the one at equilibrium. Using a sudden approximation for the gap dynamics, we find an analytical expression for the reduction of spectral weight close to the nodes, which is in qualitative agreement with recent experiments.; Comment: 5 pages, 2 figures plus Supplementary Materials. Accepted in Phys. Rev. Lett

## Transient dynamics of a colloidal particle driven through a viscoelastic fluid

Gomez-Solano, Juan Ruben; Bechinger, Clemens
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
47.05489%
We experimentally study the transient motion of a colloidal particle actively dragged by an optical trap through different viscoelastic fluids (wormlike micelles, polymer solutions, and entangled $\lambda$-phage DNA). We observe that, after sudden removal of the moving trap, the particle recoils due to the recovery of the deformed fluid microstructure. We find that the transient dynamics of the particle proceeds via a double exponential relaxation, whose relaxation times remain independent of the initial particle velocity whereas their amplitudes strongly depend on it. While the fastest relaxation mirrors the viscous damping of the particle by the solvent, the slow relaxation results from the recovery of the strained viscoelastic matrix. We show that this transient information, which has no counterpart in Newtonian fluids, can be exploited to investigate linear and nonlinear rheological properties of the embedding fluid, thus providing a novel method to perform transient rheology at the micron-scale.; Comment: 19 pages, 7 Figures, submitted to New Journal of Physics

## Recursive dynamic mode decomposition of a transient cylinder wake

Noack, B. R.; Stankiewicz, W.; Morzynski, M.; Schmid, P. J.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.906357%
A novel data-driven modal decomposition of fluid flow is proposed comprising key features of POD and DMD. The first mode is the normalized real or imaginary part of the DMD mode which minimizes the time-averaged residual. The N-th mode is defined recursively in an analogous manner based on the residual of an expansion using the first N-1 modes. The resulting recursive DMD (RDMD) modes are orthogonal by construction, retain pure frequency content and aim at low residual. RDMD is applied to transient cylinder wake data and is benchmarked against POD and optimized DMD (Chen et al. 2012) for the same snapshot sequence. Unlike POD modes, RDMD structures are shown to have pure frequency content while retaining a residual of comparable order as POD. In contrast to DMD with exponentially growing or decaying oscillatory amplitudes, RDMD clearly identifies initial, maximum and final fluctuation levels. Intriguingly, RDMD outperforms both POD and DMD in the limit cycle resolution from the same snaphots. RDMD is proposed as an attractive alternative to POD and DMD for empirical Galerkin models, with nonlinear transient dynamics as a niche application.; Comment: 18 pages, 10 figures, 1 table

## From Equilibrium to Steady State: The Transient Dynamics of Colloidal Liquids under Shear

Zausch, J.; Horbach, J.; Laurati, M; Egelhaaf, S. U.; Brader, J. M.; Voigtmann, Th.; Fuchs, M.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.01425%
We investigate stresses and particle motion during the start up of flow in a colloidal dispersion close to arrest into a glassy state. A combination of molecular dynamics simulation, mode coupling theory and confocal microscopy experiment is used to investigate the origins of the widely observed stress overshoot and (previously not reported) super-diffusive motion in the transient dynamics. A link between the macro-rheological stress versus strain curves and the microscopic particle motion is established. Negative correlations in the transient auto-correlation function of the potential stresses are found responsible for both phenomena, and arise even for homogeneous flows and almost Gaussian particle displacements.; Comment: 24 pages, 14 figures, J. Phys.: Condens. Matter, in press

## Transient dynamics of the Anderson impurity model out of equilibrium

Schmidt, T. L.; Werner, P.; Muehlbacher, L.; Komnik, A.
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.906357%
We discuss the transient effects in the Anderson impurity model that occur when two fermionic continua with finite bandwidths are instantaneously coupled to a central level. We present results for the analytically solvable noninteracting resonant level system first and then consistently extend them to the interacting case using the conventional perturbation theory and recently developed nonequilibrium Monte Carlo simulation schemes. The main goal is to gain an understanding of the full time-dependent nonlinear current-voltage characteristics and the population probability of the central level. We find that, contrary to the steady state, the transient dynamics of the system depends sensitively on the bandwidth of the electrode material.; Comment: 10 pages, 5 figures, submitted to PRB

## Time-dependent Landauer-B\"uttiker formula: application to transient dynamics in graphene nanoribbons

Tuovinen, Riku; Perfetto, Enrico; Stefanucci, Gianluca; van Leeuwen, Robert
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
47.1028%
In this work we develop a time-dependent extension of the Landauer-B\"uttiker approach to study transient dynamics in time-dependent quantum transport through molecular junctions. A key feature of the approach is that it provides a closed integral expression for the time-dependence of the density matrix of the molecular junction after switch-on of a bias or gate potential which can be evaluated without the necessity of propagating individual single-particle orbitals. This allows for the study of time-dependent transport in large molecular systems coupled to wide band leads. As an application of the formalism we study the transient dynamics of zigzag and armchair graphene nanoribbons of different symmetries. We find that the transient times can exceed several hundreds of femtoseconds while displaying a long time oscillatory motion related to multiple reflections of the density wave in the nanoribbons at the ribbon--lead interface. This temporal profile has a shape that scales with the length of the ribbons and is modulated by fast oscillations described by intra-ribbon and ribbon--lead transitions. Especially in the armchair nanoribbons there exists a sequence of quasi-stationary states related to reflections at the edge state located at the ribbon--lead interface. In the case of zigzag nanoribbons there is a predominant oscillation frequency associated with virtual transitions between the edge states and the Fermi levels of the electrode. We further study the local bond currents in the nanoribbons and find that the parity of the edges strongly affects the path of the electrons in the nanoribbons. We finally study the behavior of the transients for various added gate potentials.; Comment: 14 pages...

## A study of transient dynamics of perturbations in Keplerian discs using a variational approach

Zhuravlev, V. V.; Razdoburdin, D. N.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
57.1028%
We study linear transient dynamics in a thin Keplerian disc employing a method based on variational formulation of optimisation problem. It is shown that in a shearing sheet approximation due to a prominent excitation of density waves by vortices the most rapidly growing shearing harmonic has azimuthal wavelength, $\lambda_y$, of order of the disc thickness, $H$, and its initial shape is always nearly identical to a vortex having the same potential vorticity. Also, in the limit $\lambda_y\gg H$ the optimal growth $G\propto (\Omega/\kappa)^4$, where $\Omega$ and $\kappa$ stand for local rotational and epicyclic frequencies, respectively, what suggests that transient growth of large scale vortices can be much stronger in areas with non-Keplerian rotation, e.g. in the inner parts of relativistic discs around the black holes. We estimate that if disc is already in a turbulent state with effective viscosity given by the Shakura parameter $\alpha<1$, the considered large scale vortices with wavelengths $H/\alpha>\lambda_y>H$ have the most favourable conditions to be transiently amplified before they are damped. At the same time, turbulence is a natural source of the potential vorticity for this transient activity. We extend our study to a global spatial scale showing that global perturbations with azimuthal wavelengths more than an order of magnitude greater than the disc thickness still are able to attain the growth of dozens of times in a few Keplerian periods at the inner boundary of disc.; Comment: 21 pages...

## Transient dynamics for sequence processing neural networks

Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.16919%
An exact solution of the transient dynamics for a sequential associative memory model is discussed through both the path-integral method and the statistical neurodynamics. Although the path-integral method has the ability to give an exact solution of the transient dynamics, only stationary properties have been discussed for the sequential associative memory. We have succeeded in deriving an exact macroscopic description of the transient dynamics by analyzing the correlation of crosstalk noise. Surprisingly, the order parameter equations of this exact solution are completely equivalent to those of the statistical neurodynamics, which is an approximation theory that assumes crosstalk noise to obey the Gaussian distribution. In order to examine our theoretical findings, we numerically obtain cumulants of the crosstalk noise. We verify that the third- and fourth-order cumulants are equal to zero, and that the crosstalk noise is normally distributed even in the non-retrieval case. We show that the results obtained by our theory agree with those obtained by computer simulations. We have also found that the macroscopic unstable state completely coincides with the separatrix.; Comment: 21 pages, 4 figures

## Doubly Transient Chaos: The Generic Form of Chaos in Autonomous Dissipative Systems

Motter, Adilson E.; Gruiz, Marton; Karolyi, Gyorgy; Tel, Tamas
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.9949%
Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final state sensitivity observed in connection with fractal basin boundaries in conservative scattering systems and driven dissipative systems. Here we focus on the most prevalent case of undriven dissipative systems, whose transient dynamics fall outside the scope of previous studies since no time-dependent solutions can exist for asymptotically long times. We show that such systems can exhibit positive finite-time Lyapunov exponents and fractal-like basin boundaries which nevertheless have codimension one. In sharp contrast with its driven and conservative counterparts, the settling rate to the (fixed-point) attractors grows exponentially in time, meaning that the fraction of trajectories away from the attractors decays super-exponentially. While no invariant chaotic sets exist in such cases, the irregular behavior is governed by transient interactions with transient chaotic saddles, which act as effective, time-varying chaotic sets.; Comment: To appear in Physical Review Letters

## Transient dynamics of an adiabatic NEMS

Biggio, M.; Cavaliere, F.; Storace, M.; Sassetti, M.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.229175%
This paper is focused on the transient dynamics of an adiabatic nano-electromechanical system (NEMS), consisting of a nano-mechanical oscillator coupled to a quantum dot. By numerically solving the nonlinear stochastic differential equation governing the oscillator, the time evolution of the oscillator position, of the dot occupation number and of the current are studied. Different parameter settings are studied where the system exhibits bi-stable, tri-stable or mono-stable behavior on a finite-time horizon. It is shown that, after a typically long transient, the system under investigation exhibits no hysteretic behavior and that a unique steady state is reached, independently of the initial conditions. The transient dynamics is marked out by one or two well separated characteristic times, depending on the considered case (i.e., mono- or multi-stable). We evaluate these times for a dot on-resonance or off-resonance. It turns out that the characteristic time scales are long in comparison to the period of the uncoupled oscillator, particularly at low bias, suggesting that the predicted transient dynamics may be observed in state-of-the-art experimental setups.; Comment: 14 pages, 10 color figures

## Transient Dynamics of Elastic Hele-Shaw Cell Due to External Forces with Application to Impulse Mitigation

Tulchinsky, Arie; Gat, Amir D.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.87036%
We study the transient dynamics of a viscous liquid contained in a narrow gap between a rigid surface and a parallel elastic plate. The elastic plate is deformed due to an externally applied time-varying pressure-field. We model the flow-field via the lubrication approximation, and the plate deformation by the Kirchhoff-Love plate theory. We obtain a self-similarity solution for the case of an external point force acting on the elastic plate. The pressure and deformation field during and after the application of the external force are derived and presented by closed form expressions. We examine a uniform external pressure acting on the elastic plate over a finite region and during a finite time period, similar to the viscous-elastic interaction time-scale. The interaction between elasticity and viscosity is shown to reduce by order of magnitude the pressure within the Hele-Shaw cell compared with the externally applied pressure, thus suggesting such configurations may be used for impact mitigation.

## On the Diversity of Non-Linear Transient Dynamics in Several Types of Complex Networks

Costa, Luciano da Fontoura
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.906357%
Dynamic systems characterized by diversified evolutions are not only more flexible, but also more resilient to attacks, failures and changing conditions. This article addresses the quantification of the diversity of non-linear transient dynamics obtained in undirected and unweighted complex networks as a consequence of self-avoiding random walks. The diversity of walks starting at a specific node $i$ is quantified in terms of a signature composed by the entropies of the node visit probabilities along each of the initial steps. Six theoretical models of complex networks are considered: Erd\H{o}s-R\'enyi, Barab\'asi-Albert, Watts-Strogatz, a geographical model, as well as two recently introduced knitted networks formed by paths. The random walk diversity is explored at the level of network categories and of individual nodes. Because the diversity at successive steps of the walks tends to be correlated, principal component analysis is systematically applied in order to identify the more relevant linear combinations of the diversity entropies and to obtain optimal dimensionality reduction. Several interesting results are reported, including the facts that the transient diversity tends to increase with the average degree for all considered network models and that the Watts and Strogatz and geographical models tend to yield diversity entropies which increase more gradually with the number of steps...

## Transient dynamics and structure of optimal excitations in thermocapillary spreading: Precursor film model

Davis, Jeffrey M.; Kataoka, Dawn E.; Troian, Sandra M.
Fonte: Instituto de Tecnologia da Califórnia Publicador: Instituto de Tecnologia da Califórnia
Tipo: Article; PeerReviewed Formato: application/pdf