Time-dependent Situation Research Articles

Analysis method for the design of long submarine cables

The recent push for renewable electrical energy sources has resulted in a significant increase in the installation of the offshore wind farms. These farms become much bigger than their earlier counterparts and the generated power is much larger. This puts additional performance requirements on the export cables. Long submarine export cables are not only subjected to changing laying conditions along the route, including depth and seabed material variations, but also the loading patterns vary significantly over time. Additionally, applied reactive power compensation measures and the time-dependent grid situation change the distribution of the current along the route. These unique features of long submarine power cables necessitate a new type of approach to their design and construction optimization. This paper introduces a new approach for ampacity calculations of long submarine power cables. As the ampacity calculations form a basis for the design of a cable route, it is of paramount importance that they are performed as accurately as possible. The approach can be applied to general-purpose circuit solvers, and this paper describes how to implement it using the ATP-EMTP software, which is extended to the consideration of concurrent electrical and thermal effects. The approach permits considering all the important local and time-dependent parameters of the analysis simultaneously. In particular, the approach allows simultaneous analysis of the varying laying conditions along the route including changes in the depth of burial and thermal resistivity of the soil together with the temporal variations of the cable loading. Additionally, current characteristics in long AC cable conductors are strongly affected by the reactive power flow, which in turn depends on the location of the reactive power compensation, the reactive power demand for grid operation, and the wind farm voltage reactive power control strategy. Such analysis cannot be performed with any existing analytical tool. Also, numerical tools cannot handle such problems because a 3-dimensional time-dependent analysis of a cable route which is 100 km long would encounter convergence problems as the size of such model would be prohibitive. Hence, at present, the proposed approach is the only one available to solve this complex electro-thermal problem. Several numerical examples illustrate an application of the proposed methodology.

Role of thermophoresis on unsteady/steady mixed convective flow in a vertical channel having convective boundary conditions

A numerical as well as analytical investigation is performed to study time dependent/steady state mixed convection flow in a vertical channel in presence of thermophoresis having convective boundary conditions. The main objective of this paper is to present exact solutions for steady state mathematical model under relevant boundary conditions and numerical solutions for time dependent situation under relevant initial and boundary conditions. The impact of various controlling parameters such as dimensionless time t, Schmidt number Sc, Biot numbers Bi_{1} and Bi_{2}, buoyancy ratio b and thermophoretic coefficient k have on the flow patterns is discussed. Graphical results show that the effect of increasing two or more of the parameters simultaneously with high mixed convection parameter changes the flow from bi-directional to unidirectional. Also, the occurrence of a flow reversal depends on buoyancy and dimensional time. Furthermore, there exists a convergence of Sherwood number values at the cold plate when thermophoretic values are high.Article HighlightsWhen buoyancy dominates the flow, a decrease of reverse flow at the cold plate is observed as thermophoresis approaches its peak.If Schmidt number increases simultaneously with time, a wider region across the channel where concentration of particles is zero is observed.When thermophoretic values are low, an increment in time reduces Sherwood numbers. Sherwood number values are observed to converge at the cold plate when thermophoretic values are high. These findings have implications in the developments of thermophoretic cells used in biochemical and medical researches because Sherwood numbers imply negative concentration fluxes at boundaries.

Self-energy method for time-dependent spectral functions of the Anderson impurity model within the time-dependent numerical renormalization group approach

The self-energy method for quantum impurity models expresses the correlation part of the self-energy in terms of the ratio of two Green's functions and allows for a more accurate calculation of equilibrium spectral functions than is possible directly from the one-particle Green's function [Bulla et al., J. Phys.: Condens. Matter 10, 8365 (1998)], for example, within the numerical renormalization group method. In addition, the self-energy itself is a central quantity required in the dynamical mean field theory of strongly correlated lattice models. Here, we show how to generalize the self-energy method to the time-dependent situation for the prototype model of strong correlations, the Anderson impurity model. We use the equation of motion method to obtain closed expressions for the local Green's function in terms of a time-dependent correlation self-energy, with the latter being given as a ratio of a one-particle time-dependent Green's function and a higher-order correlation function. We benchmark this self-energy approach to time-dependent spectral functions against the direct approach within the time-dependent numerical renormalization group method. The self-energy approach improves the accuracy of time-dependent spectral function calculations, and the closed-form expressions for the Green's function allow for a clear picture of the time-evolution of spectral features at the different characteristic time-scales. The self-energy approach is of potential interest also for other quantum impurity solvers for real-time evolution, including time-dependent density matrix renormalization group and continuous-time quantum Monte Carlo techniques.

The tissue transglutaminase: a potential target regulating MDR in breast cancer.

Multi-drug resistance (MDR) is the main obstacle influencing the anti-tumor effect in breast cancer. To date, no proper potential targets are found to overcome MDR. Here, tTG was explored to show whether it is a potential target to regulate MDR in breast cancer. tTG was silenced by small interfere siRNA. After that, the mRNA level of CD44, CD24, LRP, MRP and MDR1 were detected by RT-PCR. The Western blot analysis was used to detect the expression of LRP, P-gp and MRP. In addition, the impact of tTG on cell apoptosis, as well as cell proliferation were observed. Finally, to evaluate the role of tTG in BALB/c nude mice, the growth of tumor was performed, and the immunohistochemistry analysis was used to observe the expression of LRP, P-gp and MRP in vivo. In MCF-7/ADR, Compared to MCF-7, tTG expression was highly increased. After silencing tTG, the mRNA level and the protein level of P-gp, MRP, LRP were both differently decreased. The mRNA level of CD44 and CD24 was also down-regulated after silencing tTG. In addition, the cell proliferation was significantly inhibited in the ADR + tTG siRNA+Adriamycin group (p<0.05), and the tumor growth was prevented in a time-dependent situation. Cell apoptosis was significantly strengthened in the ADR+tTG siRNA+Adriamycin group (p<0.05). In vivo, the growth of tumors was reduced after silencing tTG, and the LRP, P-gp and MRP expression were significantly down-regulated in ADR + tTG SiRNA +adriamycin group (p<0.05). It is concluded that the tTG may be a potential target regulating the MDR by regulating LRP, P-gp and MRP expression as well as the expression of CD44CD24 to improve the MDR in breast cancer.

On Faraday's law in the presence of extended conductors

The use of Faraday's Law of induction for calculating the induced currents in an extended conducting body is discussed. In a general case with arbitrary geometry, the solution to the problem of a moving metal object in the presence of a magnetic field is difficult and implies solving Maxwell's equations in a time-dependent situation. In many cases, including cases with good conductors (but not superconductors) Ampère's Law can be neglected and a simpler solution based solely in Faraday's law can be obtained. The integral form of Faraday's Law along any loop in the conducting body is equivalent to a Kirkhhoff's voltage law of a circuit. Therefore, a numerical solution can be obtained by solving a linear system of equations corresponding to a discrete number of loops in the body.

Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems

The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the linear response of the expectation of a specified observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. We also consider the inhomogeneous or time-dependent situation where the governing dynamics is not stationary and one wishes to select a sequence of small perturbations so as to maximise the overall linear response at some terminal time. We develop the theory for finite-state Markov chains, provide explicit solutions for some illustrative examples, and numerically apply our theory to stochastically perturbed dynamical systems, where the Markov chain is replaced by a matrix representation of an approximate annealed transfer operator for the random dynamical system.

Spectral representation of the heat current in a driven Josephson junction

We discuss thermal transport through a Josephson junction in a time-dependent situation. We write the spectral representation of the heat current pumped by a generic drive. This enables separation of the dissipative and reactive contributions, of which the latter do not contribute to long-time averages. We discuss the physical interpretation, and note that the condensate heat current identified in [K. Maki and A. Griffin, Phys. Rev. Lett. 15, 921 (1965)] is purely reactive. The results enable a convenient description of heat exchanges in a Josephson system in the presence of an external drive, with possible applications for the implementation of new cooling devices.

Acceleration in a nonplanar time-dependent billiard.

We study the dynamical properties of a particle in a nonplanar square billiard. The plane of the billiard has a sinusoidal shape. We consider both the static and time-dependent plane. We study the affect of different parameters that control the geometry of the billiard in this model. We consider variations of different parameters of the model and describe how the particle trajectory is affected by these parameters. We also investigate the dynamical behavior of the system in the static condition using its reduced phase plot and show that the dynamics of the particle inside the billiard may be regular, mixed, or chaotic. Finally, the problem of the particle energy growth is studied in the billiard with the time-dependent plane. We show that when in the static case, the billiard is chaotic, then the particle energy in the time-dependent billiard grows for a small number of collisions, and then it starts to saturate. But when the dynamics of the static case is regular, then the particle average energy in the time-dependent situation stays constant.

Modified particle swarm optimization in a time-dependent vehicle routing problem: minimizing fuel consumption

In this paper, a new mathematical model for a time-dependent vehicle routing problem (TDVRP) is introduced as one of the sub-problems in the green VRP field. The model results in reducing carbon emissions by minimizing travel times, while congested routes are avoided and customers are served at the time of the day with an optimized speed. Hence, this paper presents a new bi-objective mathematical model in such a way that the total travel times and total fuel consumption are minimized in a time-dependent situation by considering the air drag, roads’ physical condition, the physical features of each vehicle, and the weight and load of the vehicles. To solve such a hard problem, a new method based on the modified particle swarm optimization (PSO) algorithm is proposed and the results are compared with the standard PSO on well-known benchmark problems with constant travel speeds and time-dependent travel speeds. The results show the capability of the proposed optimization algorithm for handling this problem.

Observation of topologically protected bound states in photonic quantum walks

Topological phases exhibit some of the most striking phenomena in modern physics. Much of the rich behaviour of quantum Hall systems, topological insulators, and topological superconductors can be traced to the existence of robust bound states at interfaces between different topological phases. This robustness has applications in metrology and holds promise for future uses in quantum computing. Engineered quantum systems--notably in photonics, where wavefunctions can be observed directly--provide versatile platforms for creating and probing a variety of topological phases. Here we use photonic quantum walks to observe bound states between systems with different bulk topological properties and demonstrate their robustness to perturbations--a signature of topological protection. Although such bound states are usually discussed for static (time-independent) systems, here we demonstrate their existence in an explicitly time-dependent situation. Moreover, we discover a new phenomenon: a topologically protected pair of bound states unique to periodically driven systems.

Testing theoretical models of magnetic damping using an air track

Magnetic braking is a long-established application of Lenz's law. A rigorous analysis of the laws governing this problem involves solving Maxwell's equations in a time-dependent situation. Approximate models have been developed to describe different experimental results related to this phenomenon. In this paper we present a new method for the analysis of magnetic braking using a magnet fixed to the glider of an air track. The forces acting on the glider, a result of the eddy currents, can be easily observed and measured. As a consequence of the air track inclination, the glider accelerates at the beginning, although it asymptotically tends towards a uniform rectilinear movement characterized by a terminal speed. This speed depends on the interaction between the magnetic field and the conductivity properties of the air track. Compared with previous related approaches, in our experimental setup the magnet fixed to the glider produces a magnetic braking force which acts continuously, rather than over a short period of time. The experimental results satisfactorily concur with the theoretical models adapted to this configuration.

Persistence of instanton connections in chemical reactions with time-dependent rates

The evolution of a system of chemical reactions can be studied, in the eikonal approximation, by means of a Hamiltonian dynamical system. The fixed points of this dynamical system represent the different states in which the chemical system can be found, and the connections among them represent instantons or optimal paths linking these states. We study the relation between the phase portrait of the Hamiltonian system representing a set of chemical reactions with constant rates and the corresponding system when these rates vary in time. We show that the topology of the phase space is robust for small time-dependent perturbations in concrete examples and state general results when possible. This robustness allows us to apply some of the conclusions on the qualitative behavior of the autonomous system to the time-dependent situation.

Measurement error reduction using weighted average method for repeated measurements from heterogeneous instruments

AbstractConsidering a situation in which observations are made by several instruments over time, researchers are interested in estimating the true quantity at a particular time point. Assuming observations made by different instruments at the same time point have the same time‐dependent mean but different variances, one approach is to estimate the true quantity or the time‐dependent mean by simply averaging the observations at a time point. However, since the variability of each instrument may be very different, the unweighted average can be improved by a weighted average with weights estimated from the longitudinal measurements produced by those instruments. Such a weighted average estimator is studied in this article. It is shown to be unbiased for the true quantity. Its variance is asymptotically smaller than that of any observation and also achieves the minimum variance among all the weighted estimates with known weights. The proposed method is illustrated by a real data example. The method is not restricted to the time‐dependent situation. The general setting where this method can be applied is described at the end of the article. Copyright © 2001 John Wiley &amp; Sons, Ltd.

Cosmology in the Randall–Sundrum brane world scenario

The cosmology of the Randall–Sundrum scenario for a positive tension brane in a 5-D Universe with localized gravity has been studied extensively recently. Here we extend it to more general situations. We consider the time-dependent situation where the two sides of the brane are different AdS/Schwarzschild spaces. We show that the expansion rate in these models during inflation could be larger than in brane worlds with compactified extra dimensions of fixed size. The enhanced expansion rate could lead to the production of density perturbations of substantially larger amplitude.

Effects of an impurity on the dissipation in a partially coherent flux-driven ring

We have studied a mesoscopic ring threaded by a magnetic flux that increases linearly with time. The ring is partially coherent, such that conduction electrons in the ring will encounter incoherent scatterings. In addition, the electrons encounter elastic scatterings due to the presence of an impurity in the ring. We have adopted a S-matrix model, as proposed by Büttiker [M.Büttiker, Phys. Rev. B 32 (1985) 1846; M.Büttiker, Phys. Rev. B 33 (1986) 3020], for the incoherent scatterings in this time-dependent situation. This allows us to treat the incoherent scatterings, the elastic scatterings and the coherent inelastic processes on the same footing. We have solved the problem exactly. Our results demonstrate that, in the case of a weak impurity, the lower the energies of the electrons that emanate out of incoherent scatterings, the greater will be their net contribution to the dc component Idc of the induced current. In the case of a strong impurity, however, Idc alternates between regions of zero and nonzero values as the chemical potential μ increases. The peak value of Idc in the nonzero region increases with μ. We find that these regions of zero, and nonzero, Idc correspond closely with the gaps, and the bands, respectively, of a one-dimensional energy band. All these characteristics arise from the fact that the electrons traversing the ring have their energies shifted gradually until their energies fall upon a forbidden region, where they suffer total reflection. This total reflection at the forbidden region does not occur in a ring that has a constant flux. Rather, it results from the nonadiabatic effect of the changing flux. The evolution of the nonadiabatic effects in the intermediate impurity regime has also been investigated.

Treatment of pionic modes at the nuclear surface for transport descriptions

Dispersion relations and amplitudes of collective pionic modes are derived in a π + NN −1 + ΔN −1 model for use in transport descriptions by means of a local density approximation. It is discussed how pionic modes can be converted to real particles when penetrating the nuclear surface and how earlier treatments can be improved. When the surface is stationary only free pions emerge. The time-dependent situation is also addressed, as is the conversion of non-physical (i.e. unperturbed ΔN −1) modes to real particles when the nuclear density vanishes. A simplified one-dimensional scenario is used to investigate the reflection and transmission of pionic modes at the nuclear surface. It is found that reflection of pionic modes is rather unlikely, but the process can be incorporated into transport descriptions by the use of approximate local transmission coefficients.

Popular Electronic Structure Principles in a Dynamical Context

To understand the implications of the electronegativity equalization principle, the maximum hardness principle, the minimum polarizability principle, and the maximum entropy principle in a time dependent situation, a charge transfer process from a Be atom to an α-particle is studied within a quantum fluid density functional framework. It is observed that in general a system tries to evolve to a state associated with maximum hardness, maximum entropy, and minimum polarizability values.

Double excitation of helium by ion impact. I. Theory

We study the double excitation of helium by ion impact above 100 keV amu-1. More precisely, we determine the Shore parameters of the resonance profile observed in the doubly differential ionization cross sections when resonance effects due to doubly excited states show up. We generalize the Fano theory for the present time-dependent situation which allows us to express the impact-parameter-dependent transition amplitude in terms of amplitudes that vary slowly in the vicinity of a resonance. Consequently, we can perform a close-coupling calculation using correlated two-electron states and a 'coarse-grain' discretization of the continuum. For the first time, agreement is obtained between the theoretical and experimental Shore parameters and for energies down to 100 keV for proton impact. We also show that the two-centre effect on the ionization cross section is accurately represented in our one-centre close-coupling calculations.

Do-not-resuscitate orders. Where are they in the prehospital setting?

Without a well-functioning, prehospital, do-not-resuscitate (DNR) system in place, emergency medical service (EMS) providers must resuscitate all patients who access the system, regardless of the patients' wishes and regardless of what makes ethical or economic sense. In lieu of valid documentation, it is not appropriate to withhold resuscitative measures in this critical, time-dependent situation. In order to help EMS systems implement functional prehospital DNR protocols, this paper reviews the state-of-the-art of prehospital DNR including the issues to consider when designing such a system and a discussion of the features of some of the existing systems. This review includes: 1) the basis and requirements of a DNR system; 2) legal and physical forms for DNR orders; 3) eligibility for DNR status; 4) reversal of DNR orders; and 5) inappropriate use of EMS systems for DNR patients. Finally, a more general discussion of overall resource utilization in prehospital resuscitations is presented to emphasize that implementing prehospital DNR systems is only one piece of a larger issue.

A new philosophy for stochastic equivalent linearization

An extension, to the time-dependent situation, of what is known in static structural reliability as the ‘normal tail approximation’ is presented. This is pursued within the classical stochastic equivalent linearization scheme. Duffing and hysteretic oscillators are studied in detail.