Temporal Dynamics in Perturbation Theory

Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our attention on the stability conditions permitting to control the convergence of approximation sequences. We show that several types of mapping multipliers and Lyapunov exponents can be introduced and, respectively, several types of conditions controlling local stability can be formulated. The ideas are illustrated by calculating the energy levels of an anharmonic oscillator.Comment: 1 file, 21 pages, RevTex, 2 table

Spatio-temporal dynamics in graphene

Temporally and spectrally resolved dynamics of optically excited carriers in graphene has been intensively studied theoretically and experimentally, whereas carrier diffusion in space has attracted much less attention. Understanding the spatio-temporal carrier dynamics is of key importance for optoelectronic applications, where carrier transport phenomena play an important role. In this work, we provide a microscopic access to the time-, momentum-, and space-resolved dynamics of carriers in graphene. We determine the diffusion coefficient to be $D \approx 360$cm$^{2}$/s and reveal the impact of carrier-phonon and carrier-carrier scattering on the diffusion process. In particular, we show that phonon-induced scattering across the Dirac cone gives rise to back-diffusion counteracting the spatial broadening of the carrier distribution

Basic principles of temporal dynamics

All ecological disciplines consider temporal dynamics, although relevant concepts have been developed almost independently. We here introduce basic principles of temporal dynamics in ecology. We figured out essential features that describe temporal dynamics by finding similarities among about 60 ecological concepts and theories. We found that considering the hierarchically nested structure of complexity in temporal patterns (i.e. hierarchical complexity) can well describe the fundamental nature of temporal dynamics by expressing which patterns are observed at each scale. Across all ecological levels, driver–response relationships can be temporally variant and dependent on both short- and long-term past conditions. The framework can help with designing experiments, improving predictive power of statistics, and enhancing communications among ecological disciplines

Temporal dynamics of tunneling. Hydrodynamic approach

We use the hydrodynamic representation of the Gross -Pitaevskii/Nonlinear Schroedinger equation in order to analyze the dynamics of macroscopic tunneling process. We observe a tendency to a wave breaking and shock formation during the early stages of the tunneling process. A blip in the density distribution appears in the outskirts of the barrier and under proper conditions it may transform into a bright soliton. Our approach, based on the theory of shock formation in solutions of Burgers equation, allows us to find the parameters of the ejected blip (or soliton if formed) including the velocity of its propagation. The blip in the density is formed regardless of the value and sign of the nonlinearity parameter. However a soliton may be formed only if this parameter is negative (attraction) and large enough. A criterion is proposed. An ejection of a soliton is also observed numerically. We demonstrate, theoretically and numerically, controlled formation of soliton through tunneling. The mass of the ejected soliton is controlled by the initial state.Comment: 11 pages, 6 figures, expanded and more detailed verions of the previous submissio

Uncovering the Temporal Dynamics of Diffusion Networks

Time plays an essential role in the diffusion of information, influence and disease over networks. In many cases we only observe when a node copies information, makes a decision or becomes infected -- but the connectivity, transmission rates between nodes and transmission sources are unknown. Inferring the underlying dynamics is of outstanding interest since it enables forecasting, influencing and retarding infections, broadly construed. To this end, we model diffusion processes as discrete networks of continuous temporal processes occurring at different rates. Given cascade data -- observed infection times of nodes -- we infer the edges of the global diffusion network and estimate the transmission rates of each edge that best explain the observed data. The optimization problem is convex. The model naturally (without heuristics) imposes sparse solutions and requires no parameter tuning. The problem decouples into a collection of independent smaller problems, thus scaling easily to networks on the order of hundreds of thousands of nodes. Experiments on real and synthetic data show that our algorithm both recovers the edges of diffusion networks and accurately estimates their transmission rates from cascade data.Comment: To appear in the 28th International Conference on Machine Learning (ICML), 2011. Website: http://www.stanford.edu/~manuelgr/netrate

The temporal dynamics of calibration target reflectance

A field experiment investigated the hypothesis that the nadir reflectance of calibration surface substrates (asphalt and concrete) remains stable over a range of time-scales. Measurable differences in spectral reflectance factors were found over periods as short as 30 minutes. Surface reflectance factors measured using a dual-field-of-view GER1500 spectroradiometer system showed a relationship with the relative proportion of diffuse irradiance, over periods when solar zenith changes were minimal. Reflectance measurements were collected over precise points on the calibration surfaces using a novel mobile spectroradiometer device, and uncertainty in terms of absolute reflectance was calculated as being < 0.05% within the usable range of the instrument (400-1000nm). Multi-date reflectance factors were compared using one-way ANOVA and found to differ significantly (p = 0.001). These findings illustrate the anisotropic nature of calibration surfaces, and place emphasis on the need to minimise the temporal delay in collection of field spectral measurements for vicarious calibration or empirical atmospheric correction purposes

Family-Personalized Dietary Planning with Temporal Dynamics

Poor diet and nutrition in the United States has immense financial and health costs, and development of new tools for diet planning could help families better balance their financial and temporal constraints with the quality of their diet and meals. This paper formulates a novel model for dietary planning that incorporates two types of temporal constraints (i.e., dynamics on the perishability of raw ingredients over time, and constraints on the time required to prepare meals) by explicitly incorporating the relationship between raw ingredients and selected food recipes. Our formulation is a diet planning model with integer-valued decision variables, and so we study the problem of designing approximation algorithms (i.e, algorithms with polynomial-time computation and guarantees on the quality of the computed solution) for our dietary model. We develop a deterministic approximation algorithm that is based on a deterministic variant of randomized rounding, and then evaluate our deterministic approximation algorithm with numerical experiments of dietary planning using a database of about 2000 food recipes and 150 raw ingredients

Spatio-temporal dynamics of quantum-well excitons

We investigate the lateral transport of excitons in ZnSe quantum wells by using time-resolved micro-photoluminescence enhanced by the introduction of a solid immersion lens. The spatial and temporal resolutions are 200 nm and 5 ps, respectively. Strong deviation from classical diffusion is observed up to 400 ps. This feature is attributed to the hot-exciton effects, consistent with previous experiments under cw excitation. The coupled transport-relaxation process of hot excitons is modelled by Monte Carlo simulation. We prove that two basic assumptions typically accepted in photoluminescence investigations on excitonic transport, namely (i) the classical diffusion model as well as (ii) the equivalence between the temporal and spatial evolution of the exciton population and of the measured photoluminescence, are not valid for low-temperature experiments.Comment: 8 pages, 6 figure

Interface instability in shear banding flow

We report on the spatio-temporal dynamics of the interface in shear-banding flow of a wormlike micellar system (cetyltrimethylammonium bromide and sodium nitrate in water) during a start-up experiment. Using the scattering properties of the induced structures, we demonstrate the existence of an instability of the interface between bands along the vorticity direction. Different regimes of spatio-temporal dynamics of the interface are indentified along the stress plateau. We build a model based on the flow symetry which qualitatively describes the observed patterns

Spatio-temporal dynamics of wormlike micelles under shear

Velocity profiles in a wormlike micelle solution (CTAB in D2O) are recorded using ultrasound every 2 s after a step-like shear rate into the shear-banding regime. The stress relaxation occurs over more than six hours and corresponds to the very slow nucleation and growth of the high-shear band. Moreover, oscillations of the interface position with a period of about 50 s are observed during the growth process. Strong wall slip, metastable states and transient nucleation of three-band flows are also reported and discussed in light of previous experiments and theoretical models.Comment: 4 pages, 5 figures, submitted to Phys.Rev.Let