scholarly journals NON-POSITIVE SEMIGROUP DYNAMICS IN CONTINUOUS VARIABLE MODELS

2007 ◽  
Vol 05 (01n02) ◽  
pp. 189-198 ◽  
Author(s):  
F. BENATTI ◽  
R. FLOREANINI
Keyword(s):  
Time Evolution ◽  
Initial Conditions ◽  
External Environment ◽  
Continuous Variable ◽  
Positive Semigroup ◽  
Density Matrices ◽  
Initial State ◽  
Variable Model ◽  
Markovian Semigroups

Non-positive, Markovian semigroups are sometimes used to describe the time evolution of subsystems immersed in an external environment. A widely adopted prescription to avoid the appearance of negative probabilities is to eliminate from the admissible initial conditions those density matrices that would not remain positive by the action of the semigroup dynamics. Using a continuous variable model, we show that this procedure leads to physical inconsistencies when two subsystems are considered and their initial state is entangled.

scholarly journals Handling Initial Conditions in Vector Fitting for Real Time Modeling of Power System Dynamics

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2471
Author(s):  
Tommaso Bradde ◽  
Samuel Chevalier ◽  
Marco De Stefano ◽  
Stefano Grivet-Talocia ◽  
Luca Daniel
Keyword(s):  
Dynamical Systems ◽  
Power System ◽  
System Dynamics ◽  
Real Time ◽  
Initial Conditions ◽  
Test System ◽  
Initial State ◽  
Power System Dynamics ◽  
Vector Fitting ◽  
Time Modeling

This paper develops a predictive modeling algorithm, denoted as Real-Time Vector Fitting (RTVF), which is capable of approximating the real-time linearized dynamics of multi-input multi-output (MIMO) dynamical systems via rational transfer function matrices. Based on a generalization of the well-known Time-Domain Vector Fitting (TDVF) algorithm, RTVF is suitable for online modeling of dynamical systems which experience both initial-state decay contributions in the measured output signals and concurrently active input signals. These adaptations were specifically contrived to meet the needs currently present in the electrical power systems community, where real-time modeling of low frequency power system dynamics is becoming an increasingly coveted tool by power system operators. After introducing and validating the RTVF scheme on synthetic test cases, this paper presents a series of numerical tests on high-order closed-loop generator systems in the IEEE 39-bus test system.

scholarly journals Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 984
Author(s):  
Regina Finsterhölzl ◽  
Manuel Katzer ◽  
Andreas Knorr ◽  
Alexander Carmele
Keyword(s):  
Time Evolution ◽  
Nearest Neighbor ◽  
Matrix Product ◽  
Body System ◽  
Many Body ◽  
Initial State ◽  
Matrix Product States ◽  
Open Quantum ◽  
Many Body Systems ◽  
The Many

This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.

scholarly journals Study of the influence of initial-state fluctuations on hydrodynamic simulations

2020 ◽  
Vol 245 ◽  
pp. 06005
Author(s):  
Marcin Słodkowski ◽  
Patryk Gawryszewski ◽  
Dominik Setniewski
Keyword(s):  
Initial Conditions ◽  
Graphics Processing Unit ◽  
Heavy Ion ◽  
Processing Unit ◽  
Initial State ◽  
Final State ◽  
Hydrodynamic Simulation ◽  
Hydrodynamic Simulations ◽  
Cartesian Coordinate ◽  
Ion Collision

In this work, we are focusing on assessing the contribution of the initial-state fluctuations of heavy ion collision in the hydrodynamic simulations. We are trying to answer the question of whether the hydrodynamic simulation retains the same level of fluctuation in the final-state as for the initial stage. In another scenario, the hydrodynamic simulations of the fluctuation drowns in the final distribution of expanding matter. For this purpose, we prepared sufficient relativistic hydrodynamic program to study A+A interaction which allows analysing initial-state fluctuations in the bulk nuclear matter. For such an assumption, it is better to use high spatial resolution. Therefore, we applied the (3+1) dimensional Cartesian coordinate system. We implemented our program using parallel computing on graphics cards processors - Graphics Processing Unit (GPU). Simulations were carried out with various levels of fluctuation in initial conditions using the average method of events coming from UrQMD models. Energy density distributions were analysed and the contribution of fluctuations in initial conditions was assessed in the hydrodynamic simulation.

scholarly journals Effect of Spheroidization Annealing on Pearlite Banding

2019 ◽  
Vol 949 ◽  
pp. 40-47 ◽  
Author(s):  
Sergey Guk ◽  
Eva Augenstein ◽  
Maksim Zapara ◽  
Rudolf Kawalla ◽  
Ulrich Prahl
Keyword(s):  
Empirical Model ◽  
Initial Conditions ◽  
The Other ◽  
Experimental Investigations ◽  
Initial State ◽  
Ferritic Matrix ◽  
Other Hand ◽  
Initial States ◽  
Hot Rolled

The present paper deals with the influence of the duration of isothermal spheroidization annealing on the evolution of pearlite bands in various initial states. In this study, two initial conditions of the steel 16MnCrS5 are considered: a) industrially hot-rolled pearlite structures in their ferritic matrix and b) a specifically adjusted microstructure in the lab condition. Based on the experimental investigations and quantitative microstructural analyses, an empirical model for the prediction of pearlite banding within a broad range of annealing durations could be derived. Both, experiment and model, agree that pronounced pearlite bands in the initial state almost disappear after 25 h of spheroidization annealing. On the other hand, a marginal degree of pearlite banding in the initial state increases slightly during annealing. This fact could be explained by inhomogeneous cementite formation inside and outside the primary segregation regions of manganese.

DISCRETE TIME QUANTUM WALK ON A LINE WITH TWO PARTICLES

2006 ◽  
Vol 04 (03) ◽  
pp. 573-583 ◽  
Author(s):  
L. SHERIDAN ◽  
N. PAUNKOVIĆ ◽  
Y. OMAR ◽  
S. BOSE
Keyword(s):  
Discrete Time ◽  
Relative Phase ◽  
Initial Conditions ◽  
Quantum Walk ◽  
Degree Of Freedom ◽  
Initial State ◽  
Time Quantum

We introduce the idea of a quantum walk with two particles and study it for the case of a discrete time walk on a line. We consider both separable and maximally entangled initial conditions, and show how the entanglement and the relative phase between the states describing the coin degree of freedom of each particle will influence the evolution of the quantum walk. In particular, these factors will have consequences for the distance between the particles and the probability of finding them at a given point, yielding results that cannot be obtained from a separable initial state, be it pure or mixed. Finally, we review briefly proposals for implementations.

scholarly journals NOISE INDUCED PHENOMENA IN LOTKA-VOLTERRA SYSTEMS

2003 ◽  
Vol 03 (02) ◽  
pp. L177-L185 ◽  
Author(s):  
B. SPAGNOLO ◽  
A. FIASCONARO ◽  
D. VALENTI
Keyword(s):  
Time Evolution ◽  
Stochastic Resonance ◽  
Spatial Patterns ◽  
Discrete Model ◽  
Initial Conditions ◽  
External Noise ◽  
Competing Species ◽  
Interacting Species ◽  
Volterra Systems

We study the time evolution of two ecosystems in the presence of external noise and climatic periodical forcing by a generalized Lotka-Volterra (LV) model. In the first ecosystem, composed by two competing species, we find noise induced phenomena such as: (i) quasi deterministic oscillations, (ii) stochastic resonance, (iii) noise delayed extinction and (iv) spatial patterns. In the second ecosystem, composed by three interacting species (one predator and two preys), using a discrete model of the LV equations we find that the time evolution of the spatial patterns is strongly dependent on the initial conditions of the three species.

scholarly journals About the Reliability of Manual Model PV Corrections to Improve Forecasts

2012 ◽  
Vol 27 (6) ◽  
pp. 1554-1567 ◽  
Author(s):  
Philippe Arbogast ◽  
Karine Maynard ◽  
Catherine Piriou
Keyword(s):  
Potential Vorticity ◽  
Initial Conditions ◽  
Primary Source ◽  
Weather Forecast ◽  
Initial State ◽  
Sea Level Pressure ◽  
Potential Vorticity Inversion ◽  
Human Modification ◽  
Balanced Distribution ◽  
Source Of Information

Abstract The National Weather Forecast Centre of Météo-France has developed a tool that corrects the state of the atmosphere within the Action de Recherche Petite Echelle Grande Echelle (ARPEGE) operational global model by adjusting the potential vorticity when the initial conditions and available observations disagree. Among observational datasets, geostationary satellite data are the primary source of information. Here, the representation of the coherent structures of the tropopause in the model is assessed with Meteosat ozone and water vapor images. Modifications to the initial conditions of the potential vorticity (PV) in areas where the model fails can be applied using a potential vorticity inversion, thus providing a new balanced distribution of the wind and temperature that will then be used as a new initial state. The purpose of the paper is to investigate the degrees of weakness of the present qualitative approach. To this end, PV modifications to the initial conditions are applied by different experts on the eve of the windstorm Klaus (24 January 2009) that hit southwestern France. The different initial PV fields and the subsequent forecasts show significant differences in terms of wind and mean sea level pressure, while sharing some common features. The human modification process is therefore partially reproducible and skillful since the forecast is improved most of the time.

Calculating the periods of radio signal transmission between two spacecrafts through the Venus atmosphere in the problem of studying its composition

2019 ◽  
Author(s):  
K.S. Fedyaev ◽  
V.V. Koryanov ◽  
S.A. Bober ◽  
V.A. Zubko ◽  
A.A. Belyaev
Keyword(s):  
Radio Signal ◽  
Initial Conditions ◽  
Libration Point ◽  
Signal Transmission ◽  
Energy Costs ◽  
The Sun ◽  
Initial State ◽  
Collinear Libration Point ◽  
Small Spacecraft ◽  
Atmosphere Of Venus

The paper considers calculating the periods of radio signal transmission through the atmosphere of Venus between a small spacecraft placed in a limited orbit in the vicinity of the collinear libration point of the Sun-Venus system and a Venus orbiter. The problem arises in the framework of the project under discussion to study the atmosphere of Venus. The possibility of transfers of these spacecrafts to the required orbits under various initial conditions is also studied. The impulses required for transferring to the specified orbits at the selected initial state vector, the most suitable for solving this problem are calculated. The duration and the number of transmission periods depending on the location of one of the spacecrafts in a limited orbit in the vicinity of the libration point L1 or L2 of the Sun-Venus system are analyzed. The influence of the shape of the orbiter near-Venusian orbit on the character and duration of the periods of transmission through the atmosphere of Venus is investigated. It is concluded that the location of a small spacecraft in a limited orbit in the vicinity of the L1 libration point of the Sun-Venus system is more advantageous compared to L2 both in terms of the duration and the number of the transmission periods as well as terms of the necessary energy costs.

Receptor-Based Models with Diffusion-Driven Instability for Pattern Formation in Hydra

2003 ◽  
Vol 11 (03) ◽  
pp. 293-324 ◽  
Author(s):  
Anna Marciniak-Czochra
Keyword(s):  
Pattern Formation ◽  
Feedback Loop ◽  
De Novo ◽  
Initial Conditions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Variable Model ◽  
Dissociated Cells ◽  
Cutting Experiments ◽  
Positional Value

The aim of this paper is to show under which conditions a receptor-based model can produce and regulate patterns. Such model is applied to the pattern formation and regulation in a fresh water polyp, hydra. The model is based on the idea that both head and foot formation could be controlled by receptor-ligand binding. Positional value is determined by the density of bound receptors. The model is defined in the form of reaction-diffusion equations coupled with ordinary differential equations. The objective is to check what minimal processes are sufficient to produce patterns in the framework of a diffusion-driven (Turing-type) instability. Three-variable (describing the dynamics of ligands, free and bound receptors) and four-variable models (including also an enzyme cleaving the ligand) are analyzed and compared. The minimal three-variable model takes into consideration the density of free receptors, bound receptors and ligands. In such model patterns can evolve only if self-enhancement of free receptors, i.e., a positive feedback loop between the production of new free receptors and their present density, is assumed. The final pattern strongly depends on initial conditions. In the four-variable model a diffusion-driven instability occurs without the assumption that free receptors stimulate their own synthesis. It is shown that gradient in the density of bound receptors occurs if there is also a second diffusible substance, an enzyme, which degrades ligands. Numerical simulations are done to illustrate the analysis. The four-variable model is able to capture some results from cutting experiments and reflects de novo pattern formation from dissociated cells.

scholarly journals Geostrophic adjustment in a closed basin with islands

2013 ◽  
Vol 738 ◽  
pp. 358-377 ◽  
Author(s):  
E. R. Johnson ◽  
R. H. J. Grimshaw
Keyword(s):  
Initial Conditions ◽  
Initial Density ◽  
Circular Domain ◽  
Kelvin Wave ◽  
Geostrophic Adjustment ◽  
Homogeneous Fluid ◽  
Initial State ◽  
Linearized Theory ◽  
Baroclinic Modes ◽  
Initial Density Distribution

AbstractWe consider the geostrophic adjustment of a density-stratified fluid in a basin of constant depth on an $f$-plane in the context of linearized theory. For a single vertical mode, the equations are equivalent to those for a linearized shallow-water theory for a homogeneous fluid. Associated with any initial state there is a unique steady geostrophically adjusted component of the flow compatible with the initial conditions. This steady component gives the time average of the flow and is analogous to the adjusted flow in an unbounded domain without islands. The remainder of the response consists of superinertial Poincaré and subinertial Kelvin wave modes and expressions for the energy partition between the modes in arbitrary basins again follow directly from the initial conditions. The solution for an arbitrary initial density distribution released from rest in a circular domain is found in closed form. When the Rossby radius is much smaller than the basin radius, appropriate for the baroclinic modes, the interior adjusted solution is close to that of the initial state, except for small-amplitude trapped Poincaré waves, while Kelvin waves propagate around the boundaries, carrying, without change of form, the deviation of the initial height field from its average.

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