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Finite difference, spectral and Galerkin methods for the approximate solution of time dependent problems are surveyed. A unified discussion on their accuracy, stability and convergence is given. In particular, the dilemma of high accuracy versus stability is studied in some detail.
A numerical technique is introduced for the solution of the time-dependent equation for the solar modulation of galactic cosmic rays, in which transport in heliographic latitude is ignored. We illustrate this method with a model for the solar cycle variation in cosmic ray intensity. The variation is assumed to result from changes in the number of enhanced cosmic ray scattering regions, which are produced by flare-generated shock waves in the solar wind. The model can account for the observed solar cycle variation in intensity at different energies as well as the observed spatial gradients. This model also provides a natural explanation for the cosmic ray hysteresis effect.
We calculate the time dependence of the reflected entropy of two disconnected regions after a global quench in (1 + 1)-dimensional conformal field theories and in large temperature limit. For rational conformal field theories, we find that the time evolution of the reflected entropy is the same as that of the mutual information. We get the same result for holographic theories in the limit where the separation between disconnected regions is much smaller than their respective sizes. We discuss how this result is consistent with the quasi-particle picture of Calabrese and Cardy.
Carrier induced defect creation at the semiconductor-oxide interface has been known as the origin of electronic device degradation for a long time, but how exactly the interface lattice can be damaged by carriers (especially low-energy ones) remains unclear. Here we carry out real-time time-dependent density functional theory simulations on concrete Si/SiO 2 interfaces to study the interaction between excited electrons and interface bonds. We show that the normal interface Si-H bonds are generally resistant to electrons due to the delocalized nature and high energy level of the Si-H antibonding states, and due to the high-energy barrier to break the Si-H bond. However, if an additional hydrogen atom exists by attaching to a nearby oxygen atom (forming a “Si-H···H-O” complex), the Si-H bond will be greatly weakened, including the reduction of energy barrier for bond breaking, and the lowering of the antibonding state energy level which favors electron injection. Together with the multiple vibrational excitation process, the corresponding Si-H bond can be broken much more easily. Thus we propose that the Si-H···H-O complex will be the center for defect creation and device degradation. Finally, we also explain why such a center might be relatively easy to form during the hydrogen annealing process.
In this paper, we report the results of a 4-dimensional (3 spatial dimensions plus time) in-situ creep experiment on a milli-core shale plug from Barnett formation in Texas. An outstanding challenge in shale mechanics is connecting observable characteristics to predictable mechanical and hydraulic behavior. We employ novel imaging and analysis techniques to statistically link sample mineralogy and structure to observed deformation. In particular, we focus on mechanisms of porosity reduction during transient response to step changes in stress, analogous to the aseismic deformation that occurs after an episode of fracturing. Our main goal in this study is to take the first steps to visualize and capture the small-scale deformation mechanisms involved in creep of shales, using imaging techniques. To do so, we conducted a uniaxial creep experiment inside an Xradia Versa 520 micro-CT system for 12 h at room temperature under a constant uniaxial stress of 25 MPa. We employed a Digital Volume Correlation (DVC) method to measure micro-scale deforspmation of the sample by comparing the resulting volumetric images with a high-resolution scan of the sample obtained prior to the creep experiment. The results indicate that the time-dependent deformation in the compliant clay plus kerogen matrix constituents facilitates rigid grain rotation and compaction of intergranular porosity at the boundary between rigid grains and matrix.
Following life-cycle assessment (LCA) methodology, this study presents a state-level estimation of embodied carbon of wood products harvested in 2019 from California and subsequently processed, manufactured, transported, used, and disposed at the end-of-life (EoL). In a conventional static approach to LCA, all GHG emissions were aggregated and considered to occur at year 0 of the given time horizon (500 years in this study) and used a static characterization factor (CF). In dynamic LCA, GHG emissions occurring in different years were considered, and their global warming impact (GWI) was determined using a time-dependent CF over the selected time horizon of 500 years. Four scenarios were developed to examine the impact of EoL choices on GWI. It was found that dynamic GWI for all scenarios ranged from 0.27 to 0.93 million tonne CO₂e, which were 45–73 % lower than those estimated with static LCA approach, indicating that the static LCA approach could lead to an underestimation of the benefits of substituting wood for non-wood products, compared to those based on dynamic LCA approach. This analysis also demonstrated that the choice of EoL treatment option is a key factor affecting the estimated GWI as it directly determines the annual emission of GHGs released into atmosphere and subsequently their warming effect depending on the time harvested wood products (HWPs) spend in the horizon of assessment. Altogether, the dynamic LCA performed in this study enabled more robust interpretations of embodied carbon by including temporal boundaries associated with the HWPs life cycle.
A theoretical overview of the response coefficient method for heat conduction transients with time-dependent input forcing functions is presented with a number of illustrative applications. The method may be the most convenient and economical if the same problem is to be solved many times with different input-time histories or if the solution time is relatively long. The method is applicable to a wide variety of problems, including irregular geometries, position-dependent boundary conditions, position-dependent physical properties, and nonperiodic irregular input histories. Nonuniform internal energy generation rates within the structure can also be handled by the method. The area of interest is long-time solutions, in which initial condition is unimportant, and not the early transient period. The method can be applied to one dimensional problems in cartesian, cylindrical, and spherical coordinates as well as to two dimensional problems in cartesian and cylindrical coordinates.
A simple one-dimensional time-dependent diffusion-convection model for the modulation of cosmic rays is presented. This model predicts that the observed intensity at a given time is approximately equal to the intensity given by the time independent diffusion convection solution under interplanetary conditions which existed a time iota in the past, (U(t sub o) = U sub s(t sub o - tau)) where iota is the average time spent by a particle inside the modulating cavity. Delay times in excess of several hundred days are possible with reasonable modulation parameters. Interpretation of phase lags observed during the 1969 to 1970 solar maximum in terms of this model suggests that the modulating region is probably not less than 10 a.u. and maybe as much as 35 a.u. in extent.
The primary computational challenge when simulating nonadiabatic ab initio molecular dynamics is the unfavourable compute costs of electronic structure calculations with molecular size. Simple electronic structure theories, like time-dependent density functional theory within the Tamm–Dancoff approximation (TDDFT/TDA), alleviate this cost for moderately sized molecular systems simulated on realistic time scales. Although TDDFT/TDA does have some limitations in accuracy, an appealing feature is that, in addition to including electron correlation through the use of a density functional, the cost of calculating analytic nuclear gradients and nonadiabatic coupling vectors is often computationally feasible even for moderately sized basis sets. Here in this work, some of the benefits and limitations of TDDFT/TDA are discussed and analysed with regard to its applicability as a ‘back-end’ electronic structure method for the symmetric quasi-classical Meyer–Miller model (SQC/MM). In order to investigate the benefits and limitations of TDDFT/TDA, SQC/MM is employed to predict and analyse a prototypical example of excited-state hydrogen transfer in gas-phase malonaldehyde. Then, the ring-opening dynamics of selenophene are simulated, which highlight some of the deficiencies of TDDFT/TDA. Additionally, some new algorithms are proposed that speed up the calculation of analytic nuclear gradients and nonadiabatic coupling vectors for a set of excited electronic states.
This paper considers the problem of the stabilization and control of distributed systems with time-dependent spatial domains. The evolution of the spatial domains with time is described by a finite-dimensional system of ordinary differential equations, while the distributed systems are described by first-order or second-order linear evolution equations defined on appropriate Hilbert spaces. First, results pertaining to the existence and uniqueness of solutions of the system equations are presented. Then, various optimal control and stabilization problems are considered. The paper concludes with some examples which illustrate the application of the main results.
Frequency and time dependent gains of dye solution lasers for pumping by lasers and flashlamps
Numerical solution for one dimensional, time dependent problem of collisionless plasma impinging on flat conducting plate
Chapman-Ferraro two dimensional problem with neutral sheet, investigating magnetospheric flows and time dependence
The behavior of a weakly ionized plasma in slowly varying time-dependent magnetic fields is studied through an extension of Williamson's stochastic theory. In particular, attention is focused on the properties of electron diffusion in the plane perpendicular to the direction of the magnetic field, when the field strength is large. It is shown that, in the strong field limit, the classical 1/B-squared dependence of the perpendicular diffusion coefficient is obtained for two models in which the field B(t) is monotonic in t and for two models in which B(t) possesses at least one turning point.
The problem of generating local mesh refinements when solving time dependent partial differential equations was examined. The problem of creating an appropriate grid, given a mesh function h defined over the spatial domain is discussed. A data structure which permits efficient use of the resulting grid is described. A good choice for h is an estimate of the local truncation error, and several ways to estimate it are discussed. The efficiency and implementation problems of these error estimates were compared.
An expression is derived for the time dependent temperature distribution in a finite solid state laser rod for an end-pumped beam of arbitrary shape. The specific case of end pumping by circular (constant) or Gaussian beam is described. The temperature profile for a single pump pulse and for repetitive pulse operation is discussed. The particular case of the temperature distribution in a pulsed titanium:sapphire rod is considered.
The paper presents a three-dimensional time-dependent simulation of a solar-ejected diamagnetic plasmoid that retains its closed topology to and beyond earth. It is assumed in this case that, before entering the computational domain, the plasmoid already exists at or near the sun. A simulation is also presented for a plasmoid that is formed in the corona near the sun or in the interplanetary medium as a consequence of the reconnection of opposite-directed IMF lines. The plasma and magnetic properties of the expanding plasmoid as it moves toward an observer at 1 AU are described.
The computer program CARES/LIFE calculates the time-dependent reliability of monolithic ceramic components subjected to thermomechanical and/or proof test loading. This program is an extension of the CARES (Ceramics Analysis and Reliability Evaluation of Structures) computer program. CARES/LIFE accounts for the phenomenon of subcritical crack growth (SCG) by utilizing either the power or Paris law relations. The two-parameter Weibull cumulative distribution function is used to characterize the variation in component strength. The effects of multiaxial stresses are modeled using either the principle of independent action (PIA), the Weibull normal stress averaging method (NSA), or the Batdorf theory. Inert strength and fatigue parameters are estimated from rupture strength data of naturally flawed specimens loaded in static, dynamic, or cyclic fatigue. Two example problems demonstrating proof testing and fatigue parameter estimation are given.