Time-dependent Quantities Research Articles

Unsteady flow of nanofluid over a sheet of variable thickness with nonlinear kinematics

The transport of heat in an unsteady flow of nanofluid has been discussed in this paper. The flow is maintained over a non-flat, variably porous, and moving sheet in the present simulation. Moreover, the sheet has both constant temperature and nanoparticle concentration at its surface. Unsteadiness in all field variables (i.e. the flow, temperature, and nanoparticles concentration) has been produced by the time-dependent quantities, specified at the surface of the sheet (i.e. kinematics of sheet). The well-known Buongiorno model of nanofluid has been undertaken in the present studies. Furthermore, the simulation includes the particular cases of uniform and linear (polynomial & algebraic functions) stretching/shrinking and injection/suction velocities. Besides that observations of the same nature have been recorded for the non-flat sheet. The boundary layer form of the governing PDEs has been utilized to evaluate the exact status of field variables in the flow domain. Appropriate conditions are imposed by considering the geometry of the flow problem. The problem at hand is simplified by introducing a new set of functions for the field variables because of boundary inputs. After this treatment, the system of boundary value ODEs, which contains several dimensionless numbers (parameters), has appeared, and the problem is solved numerically for various values of parameters, involved in it. More precisely, effects of unsteadiness, wall roughness, surface deformation parameters, Prandtl, Schmidt, thermophoretic, and Brownian motion numbers have been seen on profiles of four field variables. Besides that, the numerical results are also obtained for the skin friction coefficient, Nusselt, and Sherwood numbers. The present modelled problem and its solution are compared with classical models of that particular nature and with their solutions.

Quantitative evaluation of acid flow behavior in fractures and optimization of design parameters based on acid wormhole filtration losses

The technique of matrix acidification or acid fracturing is commonly utilized to establish communication with natural fractures during reservoir reconstruction. However, this process often encounters limitations due to filtration, which restricts the expansion of the primary acid-etching fracture. To address this issue, a computational model has been developed to simulate the expansion of an acid-etching wormhole by considering various factors such as formation process, injection duration, pressure build-up, and time-varying acid percolation rate. By analyzing the pumping displacement of acid-etching wormholes, this model provides valuable insights into the time-dependent quantities of acid percolation. It has been revealed that the filtration rate of acid-etching wormholes is strongly influenced by pumping displacement, viscosity, and concentration of the acid fluid used in stimulation as well as physical properties of the reservoir itself. Notably, viscosity plays a significant role in determining the effectiveness of acid fracturing especially in low-viscosity conditions. Acid concentration within 15% to 20% exhibits maximum impact on successful acid fracturing while concentrations below 15% or above 20% show no obvious effect. Furthermore, it was found that pumping displacement has a major influence on effective fracturing. However, beyond a certain threshold (> 5.0 m3/min), increased pumping displacement leads to slower etching distance for acids used in construction purposes. The simulation also provides real-time distribution analysis for acidity levels within eroded fractures during matrix-acidification processes and quantifies extent of chemical reactions between acids and rocks within these fractures thereby facilitating optimization efforts for design parameters related to matrix-acidification.

Reduced-order methods for neutron transport kinetics problem based on proper orthogonal decomposition and dynamic mode decomposition

This work proposes two reduced-order methods to address the high computing resource consumption of neutron transport kinetics problems. The first method is based on proper orthogonal decomposition (POD), which integrates the POD basis with the governing equation. The second method is based on dynamic mode decomposition (DMD), which constructs an approximate linear relationship to predict the time-dependent physical quantities. Numerical results demonstrate that both two reduced-order methods can achieve high accuracy and efficient prediction. For the selected cases, POD can obtain a speed-up ratio of 105 – 429, while DMD can obtain a speed-up ratio of 2300 – 12500. For step transient situations, POD and DMD predict power errors do not exceed 0.42% and 0.05%. For ramp transient situations, POD and DMD predict power errors do not exceed 0.69% and 1.9%. This work can provide some useful suggestions for applications and further development in neutron transport kinetics reduced-order model.

Update of [formula omitted]: Newly added functions and methods in versions 2 and 3

HΦ [aitch-phi] is an open-source software package of numerically exact and stochastic calculations for a wide range of quantum many-body systems. In this paper, we present the newly added functions and the implemented methods in vers. 2 and 3. In ver. 2, we implement spectrum calculations by the shifted Krylov method, and low-energy excited state calculations by the locally optimal block preconditioned conjugate gradient (LOBPCG) method. In ver. 3, we implement the full diagonalization method using ScaLAPACK and GPGPU computing via MAGMA. We also implement a real-time evolution method and the canonical thermal pure quantum (cTPQ) state method for finite-temperature calculations. The Wannier90 format for specifying the Hamiltonians is also implemented. Using the Wannier90 format, it is possible to perform the calculations for the abinitio low-energy effective Hamiltonians of solids obtained by the open-source software RESPACK. We also update Standard mode—simplified input format in HΦ—to use these functions and methods. We explain the basics of the implemented methods and how to use them. Program summaryProgram Title:HΦ [aitch-phi]CPC Library link to program files:https://doi.org/10.17632/vnfthtyctm.2Developer's repository link:https://github.com/issp-center-dev/HPhiLicensing provisions: GPLv3Programming language: C, FortranJournal reference of previous version: Comput. Phys. Commun. 217 (2017) 180–192Does the new version supersede the previous version?: Yes. The latest version has compatibility with the old versions. Although most functions are available in newer versions, some redundant/unnecessary functions were abolished in newer versions.Reasons for the new version: Implementation of new functions and methods, development of utilities, and bug fixes.Summary of revisions: We added new functions to obtain excited spectrum, low-energy excited states, and time-dependent physical quantities. We also implemented the full diagonalization method by using MAGMA on GPGPUs and finite-temperature simulations by using the canonical thermal pure quantum state method. In addition, we developed utilities for connection with RESPACK and a submodule for a generator of input files.Nature of problem: Physical properties in quantum lattice models with finite system sizesSolution method: In HΦ, we implemented several numerical methods such as the Lanczos method, the full diagonalization method, the locally optimal block preconditioned conjugate gradient (LOBPCG) method, the real-time evolution method based on the Taylor expansion, the shifted Krylov method, and the microcanonical/canonical thermal pure quantum state method.

CFD Uncertainty Quantification using PCE–HDMR: Exemplary Application to a Buoyancy-Driven Mixing Process

For the investigation of uncertainties in high dimensional spaces of computationally expensive engineering applications, reliable Uncertainty Quantification (UQ) methods are needed. These methods should provide accurate and efficient High-Dimensional Model Representations of stochastic results using a reasonable number of calculations. Therefore, the PCE–HDMR approach (Polynomial Chaos Expansion–High-Dimensional Model Representation) is utilized to qualify appropriate UQ methods for large-scale computations in the field of Computational Fluid Dynamics. This technique is a combination of Cut-HDMR, a hierarchical decomposition modeling approach, with PCE. To demonstrate its effectiveness, the PCE–HDMR methodology in conjunction with complementary modeling techniques is applied for the UQ analysis of a buoyancy-driven mixing process between two miscible fluids within the Differentially Heated Cavity of aspect ratio 4. The results include a thorough probabilistic representation of time-dependent response quantities that comprehensively describe the mixing process. The stochastic models are derived from Large Eddy Simulations using PCE–HDMR and the Sparse Grid Method, which serves as a reference for the results from PCE–HDMR. The results show that PCE–HDMR provides accurate statistics of the modeled time-dependent stochastic processes and shows good agreement with the reference results. Thus, PCE–HDMR indicates great potential for UQ of technical-scale computations due to its efficiency and flexibility in the construction of stochastic models.

Out-of-time-order correlations and quantum chaos

Quantum Chaos has originally emerged as the field which studies how the properties of classical chaotic systems arise in their quantum counterparts. The growing interest in quantum many-body systems, with no obvious classical meaning has led to consider time-dependent quantities that can help to characterize and redefine Quantum Chaos. This article reviews the prominent role that the out of time ordered correlator (OTOC) plays to achieve such goal.

The Application of Thermomechanical Dynamics (TMD) to the Analysis of Nonequilibrium Irreversible Motion and a Low-Temperature Stirling Engine

We applied the method of Thermomechanical Dynamics (TMD) to a low-temperature Stirling engine, and the dissipative equation of motion and time-evolving physical quantities are self-consistently calculated for the first time in this field. The thermomechanical states of the heat engine are in Nonequilibrium Irreversible States (NISs), and time-dependent thermodynamic work W(t), internal energy E(t), energy dissipation or entropy Qd(t), and temperature T(t), are precisely studied and computed in TMD. We also introduced the new formalism, Q(t)-picture of thermodynamic heat-energy flows, for consistent analyses of NISs. Thermal flows in a long-time uniform heat flow and in a short-time heat flow are numerically studied as examples. In addition to the analysis of time-dependent physical quantities, the TMD analysis suggests that the concept of force and acceleration in Newtonian mechanics should be modified. The acceleration is defined as a continuously differentiable function of Class C2 in Newtonian mechanics, but the thermomechanical dynamics demands piecewise continuity for acceleration and thermal force, required from physical reasons caused by frictional variations and thermal fluctuations. The acceleration has no direct physical meaning associated with force in TMD. The physical implications are fundamental for the concept of the macroscopic phenomena in NISs composed of systems in thermal and mechanical motion.

PREDICTION OF PARKING ACCUMULATION FOR DIFFERENT LAND USES IN ABU DHABI CITY FROM AN EXISTING SURVEY

Parking accumulation profiles are time-dependent quantities at car parks that need data from longitudinal observational surveys. Car parks can be grouped into clusters based on the similarity in the shape of their accumulation profiles. This study investigates factors affecting parking accumulation and attempts to devise a methodology to construct parking accumulation profiles for different land uses in Abu Dhabi city. The study uses data available from Dubai city, which has a similar land-use type and distribution pattern as Abu Dhabi. A snapshot survey was conducted to observe the portion of the sampled car parks to calibrate the predicted parking accumulation. The estimation of parking accumulation profiles based on different land uses in Abu Dhabi city was done using the planning of the survey conducted in Dubai. The results suggest that a preliminary parking survey can help determine the initial accumulation profile and predict a robust parking accumulation profile that is applicable across different land-use types in Abu Dhabi.

Time-correlation function and average energy of molecules in presence of Deng-Fan potential in a moving boundary

For the Deng-Fan potential within a moving boundary condition, the time-dependent Schrödinger equation is considered analytically. The eigenvalue equation is solved by using a combination of Pekeris and Greene-Aldrich approximations. Various time-dependent quantities including density distribution function, auto-correlation function, disequilibrium, average energy, quantum similarity, and quantum similarity index are obtained for selected eight diatomic molecules. The motion of the peak of the density function, with moving boundary condition is investigated for ground states of some diatomic molecules along with the corresponding peak values.

Topology and Rigidity of Silicate Melts and Glasses

Research Article| May 01, 2022 Topology and Rigidity of Silicate Melts and Glasses Matthieu Micoulaut; Matthieu Micoulaut Sorbonne Université, Laboratoire de Physique Théorique de la Matière Condensée, Boite 121, 4 place Jussieu, 75252 Paris cedex 05, France mmi@lptmc.jussieu.fr Search for other works by this author on: GSW Google Scholar Mathieu Bauchy Mathieu Bauchy Physics of Amorphous and Inorganic Solids Laboratory (PARISlab), Department of Civil and Environmental Engineering, University of California, Los Angeles, 420 Westwood Plaza, 5731, Los Angeles, CA 90095, USA bauchy@ucla.edu Search for other works by this author on: GSW Google Scholar Author and Article Information Matthieu Micoulaut Sorbonne Université, Laboratoire de Physique Théorique de la Matière Condensée, Boite 121, 4 place Jussieu, 75252 Paris cedex 05, France Mathieu Bauchy Physics of Amorphous and Inorganic Solids Laboratory (PARISlab), Department of Civil and Environmental Engineering, University of California, Los Angeles, 420 Westwood Plaza, 5731, Los Angeles, CA 90095, USA mmi@lptmc.jussieu.fr bauchy@ucla.edu Publisher: Mineralogical Society of America First Online: 01 May 2022 Copyright © 2022 by the Mineralogical Society of AmericaMineralogical Society of America Reviews in Mineralogy and Geochemistry (2022) 87 (1): 163–191. https://doi.org/10.2138/rmg.2022.87.04 Article history First Online: 01 May 2022 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation Matthieu Micoulaut, Mathieu Bauchy; Topology and Rigidity of Silicate Melts and Glasses. Reviews in Mineralogy and Geochemistry 2022;; 87 (1): 163–191. doi: https://doi.org/10.2138/rmg.2022.87.04 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyReviews in Mineralogy and Geochemistry Search Advanced Search From a fundamental viewpoint, glasses are out of equilibrium systems, so that concepts and techniques from statistical mechanics cannot be applied in a straightforward fashion given the presence of broken ergodicity, which results from an incomplete sampling of the phase space on reasonable time scales. The breakdown of the relationship between spontaneous fluctuations and dissipation leads to time dependent thermodynamic quantities that induce ageing phenomena typical of glasses, i.e., their properties can vary quite substantially with the thermal history of the melt and the waiting time before the experiment/measurement is performed. Given these intrinsic features of the glassy state, atomistic... You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Making optical excitations visible – An exciton wavefunction extension to the time-dependent configuration interaction method

We report the animation and analysis of laser-driven many-electron dynamics by means of time-dependent local densities and quantities derived from the one-particle transition density matrix, such as time-dependent natural transition orbital densities, particle and hole positions and exciton size. The time-dependent configuration interaction method was used to revisit studies on hydrogen molecule and lithium cyanide by Saalfrank and coworkers and our study shines new light on the optical transitions in these small molecules to benchmark the implemented time-dependent exciton properties. One focus of our simulations is the comparison of the local densities to the quantities of the two-body exciton wavefunction for resonant excitations leading either to state-to-state transitions or to the creation of a wave packet.

Neural echo state network using oscillations of gas bubbles in water.

In the framework of physical reservoir computing (RC), machine learning algorithms designed for digital computers are executed using analog computerlike nonlinear physical systems that can provide energy-efficient computational power for predicting time-dependent quantities that can be found using nonlinear differential equations. We suggest a bubble-based RC (BRC) system that combines the nonlinearity of an acoustic response of a cluster of oscillating gas bubbles in water with a standard echo state network (ESN) algorithm that is well suited to forecast chaotic time series. We confirm the plausibility of the BRC system by numerically demonstrating its ability to forecast certain chaotic time series similarly to or even more accurately than ESN.

Effect of Elastomeric Bearings in Bridge Piers

In this paper, the influence of elastomeric bearings is investigated in terms of seismic responses and presented under effects of severe ground motions. For this purpose, seismic performance of an isolated pier system is analytically studied by using time history analyses. The isolation system is assembled by elastomeric bearings composed of rubber layers and steel-shims. The bearings are located between pier-top ends and box-girder of the bridge deck. Seismic solutions are obtained for isolated system and non-isolated pier system known as rigid connection. Time-dependent response quantities are obtained in transverse direction for two strong quakes. Additionally, nonlinear static procedure is carried out to obtain lateral seismic capacity. Thus, the displacement and shear force capacity are determined for the considered pier systems. Seismic responses are comparatively presented in terms of superstructure and base response values. Thanks to the isolation system, the bearings have yielded lower peak displacements and base responses with seismic demand as well. On the other hand, higher seismic capacity has been obtained in case of isolation system and the results are presented by computed lateral capacity curves. The results show that the elastomeric bearing is an effective tool in lateral strength and modal behavior of the pier system as well.

Characterization of topological phase of superlattices in superconducting circuits

The recent experimental observation of topological magnon insulator states in a superconducting circuit chain marks a breakthrough for topological physics with qubits, in which a dimerized qubit chain has been realized. Here, we extend such a dimer lattice to superlattice with arbitrary number of qubits in each unit cell in superconducting circuits, which exhibits rich topological properties. Specifically, by considering a quadrimeric superlattice, we show that the topological invariant (winding number) can be effectively characterized by the dynamics of the single-excitation quantum state through time-dependent quantities. Moreover, we explore the appearance and detection of the topological protected edge states in such a multiband qubit system. Finally, we also demonstrate the stable Bloch-like-oscillation of multiple interface states induced by the interference of them. Our proposal can be readily realized in experiment and may pave the way towards the investigation of topological quantum phases and topologically protected quantum information processing.

Forecasting of cosmic rays intensities with HelMod Model

HelMod model allows one to describe how solar modulation affects the propagation of galactic cosmic rays (GCR) through the heliosphere with an accuracy of the level of actual experimental uncertainties. The GCRs mainly constitute the high energy population of the so-called space radiation environment. The model treats the physical processes involved in solar modulation, like diffusion, particle drift, convection and adiabatic energy losses, and it embeds a description of both the inner and outer heliosphere. To obtain the modulated intensities, the model requires the knowledge of a few time-dependent heliospheric quantities, i.e., sunspot number, tilt angle of the neutral current sheet, solar wind speed and density, and interplanetary magnetic field. Using historical records, we present a template-based procedure that allows one to predict the heliospheric parameters for coming years, and, in turn, the forecasted modulated spectra. The forecasting templates reconstruct the typical time variation along with solar cycles and may be tuned to the current solar cycle. We estimate that the uncertainty of the forecasted cosmic rays intensity is below 5% (±10% at 68% C.L.) on average for short time predictions (up to 4 years), and below 15% (±(20-25)% at 68% C.L.) for long time predictions (up to 11 years).

Uncertainty Quantification of Time-Dependent Quantities in a System With Adjustable Level of Smoothness

Abstract We summarize the results of a computational study involved with uncertainty quantification (UQ) in a benchmark turbulent burner flame simulation. UQ analysis of this simulation enables one to analyze the convergence performance of one of the most widely used uncertainty propagation techniques, polynomial chaos expansion (PCE) at varying levels of system smoothness. This is possible because in the burner flame simulations, the smoothness of the time-dependent temperature, which is the study's quantity of interest (QoI), is found to evolve with the flame development state. This analysis is deemed important as it is known that PCE cannot construct an accurate data-fitted surrogate model for nonsmooth QoIs, and thus, estimate statistically convergent QoIs of a model subject to uncertainties. While this restriction is known and gets accounted for, there is no understanding whether there is a quantifiable scaling relationship between the PCE's convergence metrics and the level of QoI's smoothness. It is found that the level of QoI's smoothness can be quantified by its standard deviation allowing to observe its effect on the PCE's convergence performance. It is found that for our flow scenario, there exists a power–law relationship between a comparative parameter, defined to measure the PCE's convergence performance relative to Monte Carlo sampling, and the QoI's standard deviation, which allows us to make a more weighted decision on the choice of the uncertainty propagation technique.

Reconstruction of Epidemiological Data in Hungary Using Stochastic Model Predictive Control

In this paper, we propose a model-based method for the reconstruction of not directly measured epidemiological data. To solve this task, we developed a generic optimization-based approach to compute unknown time-dependent quantities (such as states, inputs, and parameters) of discrete-time stochastic nonlinear models using a sequence of output measurements. The problem was reformulated as a stochastic nonlinear model predictive control computation, where the unknown inputs and parameters were searched as functions of the uncertain states, such that the model output followed the observations. The unknown data were approximated by Gaussian distributions. The predictive control problem was solved over a relatively long time window in three steps. First, we approximated the expected trajectories of the unknown quantities through a nonlinear deterministic problem. In the next step, we fixed the expected trajectories and computed the corresponding variances using closed-form expressions. Finally, the obtained mean and variance values were used as an initial guess to solve the stochastic problem. To reduce the estimated uncertainty of the computed states, a closed-loop input policy was considered during the optimization, where the state-dependent gain values were determined heuristically. The applicability of the approach is illustrated through the estimation of the epidemiological data of the COVID-19 pandemic in Hungary. To describe the epidemic spread, we used a slightly modified version of a previously published and validated compartmental model, in which the vaccination process was taken into account. The mean and the variance of the unknown data (e.g., the number of susceptible, infected, or recovered people) were estimated using only the daily number of hospitalized patients. The problem was reformulated as a finite-horizon predictive control problem, where the unknown time-dependent parameter, the daily transmission rate of the disease, was computed such that the expected value of the computed number of hospitalized patients fit the truly observed data as much as possible.

Searching for dynamical black holes in various theories of gravity

We construct models of Einstein and $f(R)$ gravity with two scalar fields, which admit analytical solutions describing time-varying dynamical black holes. Their thermodynamics is investigated in the adiabatic approximation. In addition to the Misner-Sharp-Hernandez quasilocal mass, we provide time-dependent thermodynamical quantities, including the Hawking temperature, Helmholtz free energy, entropy, and thermodynamical energy. The latter does not always coincide with the Misner-Sharp-Hernandez mass at the horizon, although they coincide in the static limit. For Schwarzschild-type (i.e., ${g}_{tt}{g}_{rr}=\ensuremath{-}1$) black holes in Einstein gravity, one of the two scalars is always a ghost with negative kinetic energy. We show that this ghost can be avoided in $f(R)$ gravity.

Nonlinear Electrostatic “Hesitant” Oscillator

In search of nonlinear oscillations, we envision a 3D elliptic curva-ture-dependent nonuniform charge distribution to creating an electric field along the symmetry axis causing a massive point-like charged particle placed on the symmetry axis to oscillate in a delayed/hesitant nonlinear mode. The charge distribution is a 3D twisted line creating nontrivial electric field causing an unexpected oscillation that is non-orthodox defying the common sense. Calculation of this research flavored investigation is entirely based on utilities accompanied with Computer Algebra Systems (CAS) especially Mathematic [1]. The characteristics of the delayed oscillations in addition to embodying classic graphics displaying the time-dependent kinematic quantities are augmented including various phase diagrams signifying the nonlinear oscillations. The output of our investigation is compared to nonlinear non-delayed oscillations revealing fresh insight. For comprehensive understanding of the hesitant oscillator a simulation program is crafted clarifying visually the scenario on hand.

Critical phenomena in the presence of symmetric absorbing states: A microscopic spin model with tunable parameters.

The Langevin description of systems with two symmetric absorbing states yields a phase diagram with three different phases (disordered and active, ordered and active, absorbing) separated by critical lines belonging to three different universality classes (generalized voter, Ising, and directed percolation). In this paper we present a microscopic spin model with two symmetric absorbing states that has the property that the model parameters can be varied in a continuous way. Our results, obtained through extensive numerical simulations, indicate that all features of the Langevin description are encountered for our two-dimensional microscopic spin model. Thus the Ising and direction percolation lines merge into a generalized voter critical line at a point in parameter space that is not identical to the classical voter model. A vast range of different quantities are used to determine the universality classes of the order-disorder and absorbing phase transitions. The investigation of time-dependent quantities at a critical point belonging to the generalized voter universality class reveals a more complicated picture than previously discussed in the literature.