Time-dependent Space Research Articles

Kinetics of two wave mixing gain for moving grating technique in photorefractive BaTiO_3 crystal

We present analytic expressions for time-dependent space charge field and two wave mixing gain under the external applied field accompanying the grating translation. The variations of complex space charge field are analyzed in a complex plane, and the explicit expressions for the resonance and optimum frequencies (or moving grating velocities), which maximize the magnitude and imaginary part of space charge field, respectively, are also obtained. In addition, two wave mixing experiment was conducted with a grating translation technique without the external applied field in a BaTiO(3) crystal and the transient behaviors of measured gain look like damped harmonic oscillations, showing excellent agreement with the theory for the entire time range.

A THEORETICAL STUDY ON DUAL FLUORESCENCE OF 4-DIMETHYLAMINOPYRIDINE BY POLARIZABLE CONTINUUM MODEL

Dual fluorescence spectra of 4-dimethylaminopyridine (DMAP) is investigated using time-dependent density functional theory and complete active space self-consistent field methods. Electronic absorption and emission spectra of DMAP have been investigated in three solvents, that is, cyclohexane, chloroform, and acetonitrile. The present study reveals that the dual fluorescence phenomena of DMAP appear in the cases of acetonitrile and chloroform, but not in cyclohexane. The electronic structures of the ground state and the intramolecular charge transfer states are, therefore, studied in order to reveal the insight of dual fluorescence. Our theoretical results suggest that the twisting of dimethylamino moiety in DMAP is necessary for the intramolecular charge transfer. The mechanism of the dual fluorescence of DMAP is discussed based on the twisted intramolecular charge transfer model and the dual fluorescence phenomenon is explained theoretically.

Microclimate and transpiration of a greenhouse banana crop

The interactions between a greenhouse banana crop and the surrounding environment were investigated within a large-scale type of greenhouse. This investigation took place through a whole development cycle of a mature banana crop in the region of Rabat, Morocco. Two measurement series are presented: the first from 4 to 9 March 1998 is representative of the Spring and Autumn conditions; the second which extends from 6 to 26 July 1999 is representative of the Summer period. Space- and time-dependent air evolution (the evolution of air temperature in time (time course) and space (vertically at trees levels in the greenhouse)) leaf temperature and air humidity were analysed, and evidence was provided for the significant oasis effect generated by the crop in the greenhouse. In addition, leaf area and stomatal resistance measurements are analysed and discussed. With regard to the function of microclimate-dependent parameters, a model of leaf stomatal resistance was additionally defined and developed. The transpiration model of the banana crop under cover was validated with respect to the estimated rates of heat and mass transfer implied from indoor and outdoor climatic measurements.

A robust and flexible model of hierarchical self-organizing maps for non-stationary environments

In this paper we extend the hierarchical self-organizing maps model (HSOM) to address the problem of learning topological drift under non-stationary and noisy environments. The new model, called robust and flexible hierarchical self-organizing maps (RoFlex-HSOM), combines the capabilities of robustness against noise and the flexibility to adapt to the changing environment. The RoFlex-HSOM model consists of a hierarchical tree structure of growing self-organizing maps (SOMs) that adapts its architecture based on the data. The model preserves the topology mapping from the high-dimensional time-dependent input space onto a neuron position in a low-dimensional hierarchical output space grid. Furthermore, the RoFlex-HSOM algorithm has the plasticity to track and adapt to the topological drift, it gradually forgets (but no catastrophically) previous learned patterns and it is resistant to the presence of noise. We empirically show the capabilities of our model with experimental results using synthetic sequential data sets and the “El Niño” real world data.

Transient pressure response in an anisotropic formation

In this paper we study the evolution of pressure of a single-phase, slightly compressible fluid in a porous medium where a non-permeable wellbore is present. The flow is induced by a single probe on the side of an otherwise sealed wellbore which is drilled at an angle to the vertical into the anisotropic rock formation. The formulation is derived by giving a transient correction due to the presence of the wellbore to the time dependent free space source field solution (the probe). Using the divergence theorem and the zero flux condition on the wellbore surface, a boundary element formulation is derived and solved numerically in the Laplace and Fourier transformed domain before being inverse-transformed to give the real time behaviour.

Open boundaries for the nonlinear Schrödinger equation

We present a new algorithm, the time dependent phase space filter (TDPSF) which is used to solve time dependent nonlinear Schrödinger equations (NLS). The algorithm consists of solving the NLS on a box with periodic boundary conditions (by any algorithm). Periodically in time we decompose the solution into a family of coherent states. Coherent states which are outgoing are deleted, while those which are not are kept, reducing the problem of reflected (wrapped) waves. Numerical results are given, and rigorous error estimates are described. The TDPSF is compatible with spectral methods for solving the interior problem. The TDPSF also fails gracefully, in the sense that the algorithm notifies the user when the result is incorrect. We are aware of no other method with this capability.

DYNAMICAL CASIMIR EFFECT IN A KICKED BOX

We investigate the Dynamical Casimir Effect (DCE) in the case of a scalar field enclosed in a box which undergoes a phase of strong acceleration (a kick) during its motion. Following a general-relativistic approach, we describe the acceleration field as a time-dependent space–time metric in the frame of a comoving, noninertial observer. Assuming a nonrelativistic motion of the box, we perturbatively solve the Klein–Gordon equation for the matter field, evaluating the β-Bogolubov coefficients, related to the particle creation. We show that, after the kick, a (small) number of created quanta is found inside the box. The resulting spectrum carries, in principle, information about the details of the box acceleration phase. The present approach can serve to shed light on the close relationship between DCE and Unruh–Hawking effect.

Trans–cis Photoisomerization of the Styrylpyridine Ligand in [Re(CO)3(2,2′‐bipyridine)(t‐4‐styrylpyridine)]+: Role of the Metal‐to‐Ligand Charge‐Transfer Excited States

The trans-cis isomerization of the styrylpyridine carbon-carbon double bond induced by visible light irradiation in fac-[Re(CO)(3)(bpy)(stpy)](+) (bpy = 2,2'-bipyridine; stpy = t-4-styrylpyridine) has been investigated by means of quantum-chemical methods. The structures of the various cis and trans conformers of [Re(CO)(3)(bpy)(stpy)](+) have been optimized at the density functional theory (DFT) level. Three rotational conformers for the most stable trans isomer lie within 2.3 kJ mol(-1) each other. The energy difference between the cis and trans isomers is 27.0 kJ mol(-1). The electronic spectroscopy of the most stable conformers has been investigated by time-dependent DFT (TD-DFT) and complete active space self-consistent field/CAS second order perturbation theory (CASSCF/CASPT2) calculations. The lowest absorption bands are dominated by metal-to-ligand charge-transfer (MLCT, d(Re)-->pi*(bpy)) transitions calculated at about 25,000 cm(-1) and by a strong intraligand (1)IL (pi(stpy)-->pi*(stpy)) transition in the near UV region. On the basis of CASSCF potential energy curves (PECs) calculated as a function of the torsion angle of the C=C bond of the styrylpyridine ligand, it is shown that the role of the low-lying MLCT states is important in the photoisomerization mechanism. In contrast to the free organic ligand, in which the singlet mechanism is operational via the (1)IL (S(1)) and electronic ground (S(0)) states, coordination to the rhenium steers the isomerization to the triplet PEC corresponding to the (3)IL state. From the (3)IL(t) (t = trans) the system evolves to the perpendicular intermediate (3)IL(p) (p = perpendicular) following a 90 degrees rotation around the styrylpyridine C=C bond. The metal center acts as a photosensitizer because of the presence of photoactive MLCT states under visible irradiation. The position of the crossing between the (3)IL and electronic ground state PEC determines the quantum yield of the isomerization process.

Fluctuation theorems for quantum master equations

A quantum fluctuation theorem for a driven quantum subsystem interacting with its environment is derived based solely on the assumption that its reduced density matrix obeys a closed evolution equation--i.e., a quantum master equation (QME). Quantum trajectories and their associated entropy, heat, and work appear naturally by transforming the QME to a time-dependent Liouville space basis that diagonalizes the instantaneous reduced density matrix of the subsystem. A quantum integral fluctuation theorem, a steady-state fluctuation theorem, and the Jarzynski relation are derived in a similar way as for classical stochastic dynamics.

Acceleration from M theory and fine-tuning

The compactification of M theory with time-dependent hyperbolic internal space gives an effective scalar field with exponential potential which provides a transient acceleration in the Einstein frame in four dimensions. Ordinary matter and radiation are present in addition to the scalar field coming from compactification. We find that we have to fine-tune the initial conditions of the scalar field so that our universe experiences acceleration now. During the evolution of our universe, the volume of the internal space increases about 12 times. The time variation of the internal space results in a large time variation of the fine structure constant which violates the observational constraint on the variation of the fine structure constant. The large variation of the fine structure constant is a generic feature of transient acceleration models.

Space Charge Formation in Polyimide Film under DC Stress with Visible Light Irradiation

The pulsed electro-acoustic (PEA) method has been widely used to observe a space charge distribution in various solid dielectric materials. In this report we applied the method to an investigation of the space charge behavior under a high electric filed with a visible light irradiation. It is well known that a property of the conduction in dielectric materials is affected by the irradiation of light. To observe the effect of the light irradiation on the space charge distribution in polyimide, we measured the time dependent space charge distribution under the irradiation of the visible light using three kind of LED.

Right as Opposed to Wrong as Opposed to Left: The Spatial Location of ?Right Parties? on the Israeli Political Map

POLITICS IS A DYNAMIC PROCESS: constantly changing directions and emphases; adjusting and readjusting to altering circumstances. People directly involved in this process relentlessly engage in a never-ending process of defining and redefining objectives and interests, of justifying and rationalizing changing modes of behavior and decision processes as opportunities arise. William Riker labeled the outcomes of this fluctuating process as the disequilibrium of preferences.' Seen from this perspective, the definition of a Right political orientation (or party, bloc, ideology) as opposed to a Left political orientation (or party, bloc, ideology) may merely constitute a tentative, not to say random, positioning of individuals and parties within an ever-changing, contracting or expanding, multidimensional, and time-dependent ideological space. Israeli politics notwithstanding: the political blocs consisting of loose groupings of ideologically similar Right-wing or Left-wing parties follow this definitional rule (or rather one should say-non-rule). Subsequently, an attempt to clarify the question of which parties belong to which political bloc often adds analytical confusion regarding actual or perceived ideological differences between the competing political parties. The research enterprise, as well, by grouping together distinct political groups along an ideological spectrum, often fails to grasp the full garment of the political messages carried out by these groups. Moreover, concepts and labels used to describe the different orientations of competing parties in Western democratic polities, such as nationalist, socialist, market oriented, security-minded, doves, hawks, liberal, and conservative, carry substantively different meanings in Israel. Over time, Israeli political

GEOMETRIC ASPECTS OF TIME-DEPENDENT SINGULAR DIFFERENTIAL EQUATIONS

A geometric framework for describing and solving time-dependent implicit differential equations F(t,x,x′) = 0 is studied, paying special attention to the linearly singular case, where F is affine in the velocities: A(t,x)x′ = b(t,x). This framework is based on the jet bundle of a time-dependent configuration space, and is an extension of the geometric framework of the autonomous case. When A is a singular matrix, the solutions can be obtained by means of constraint algorithms, either directly or through an equivalent autonomous system that can be constructed using the vector hull functor of affine spaces. As applications, we consider the jet bundle description of time-dependent lagrangian systems and the Skinner–Rusk formulation of time-dependent mechanics.

Right as Opposed to Wrong as Opposed to Left: The Spatial Location of "Right Parties" on the Israeli Political Map

Right as Opposed to Wrong as Opposed to LeftThe Spatial Location of “Right Parties” on the Israeli Political Map Gideon Doron (bio) Introduction Politics is a dynamic process: constantly changing directions and emphases; adjusting and readjusting to altering circumstances. People directly involved in this process relentlessly engage in a never-ending process of defining and redefining objectives and interests, of justifying and rationalizing changing modes of behavior and decision processes as opportunities arise. William Riker labeled the outcomes of this fluctuating process as the "disequilibrium of preferences."1 Seen from this perspective, the definition of a "Right" political orientation (or party, bloc, ideology) as opposed to a "Left" political orientation (or party, bloc, ideology) may merely constitute a tentative, not to say random, positioning of individuals and parties within an ever-changing, contracting or expanding, multi-dimensional, and time-dependent ideological space. Israeli politics notwithstanding: the political blocs consisting of loose groupings of ideologically similar Right-wing or Left-wing parties follow this definitional rule (or rather one should say—non-rule). Subsequently, an attempt to clarify the question of which parties belong to which political bloc often adds analytical confusion regarding actual or perceived ideological differences between the competing political parties. The research enterprise, as well, by grouping together distinct political groups along an ideological spectrum, often fails to grasp the full garment of the political messages carried out by these groups. Moreover, concepts and labels used to describe the different orientations of competing parties in Western democratic polities, such as "nationalist," "socialist," "market oriented," "security-minded," "doves," "hawks," "liberal," and "conservative," carry substantively different meanings in Israel. Over time, Israeli political [End Page 29] parties have changed their spatial positions, assumed different interpretations of their identities, added new dimensions to their platforms that are not always consistent with their previous positions, and for purposes of self-preservation and/or the desire to increase their power, have appeared with new packages of 'self-defining' elements. The purpose of this article is to introduce some order, albeit temporary and time-dependent, into the evaluation of the spatial locations of the Israeli political parties on a hypothetical right-to-left distribution that has, over the years, defined the positions of so-called right-wing voters and right-wing parties in Israel. Within this context the Herut Party (later Gahal and the Likud) the largest and leading right-wing party, is given particular attention The first part of this article explains the reasons for the analytical confusion that often prevails when political agents are defined as holding "rightist" or "leftist" positions on the political map. The key to understanding this confusion, it is argued, lies in the multidimensionality of Israeli politics. Two examples illustrate this problem. The first involves the failure to conduct a one dimension Minimum Connecting Coalition (MCC) type of analysis.2 The second relates to voters' dilemmas during the 1988 and 1992 elections.3 The second part of this article is historical in essence. It explains why Herut is placed on the right side of the political map and why this party's principal rival—Mapai (later Ma'arach and Labor)—has been placed to the left of it. Starting the review at the pre-state period, a comparison of the spatial positions of the Labor and the Likud, the only parties that separately and jointly have dominated Israeli modern politics, is presented. The article concludes with a proposal for an empirically more relevant classification of these two competing parties. The classification offered relies on three elements. The first element stresses the institutional differences between governing and opposition parties. Whereas governing parties are perceived as preservers of the prevailing political status quo, opposition parties by definition seek to promote changes in it. The second element focuses on voters' behavior as an outcome of their preference distributions across a diversity of issues, and the third on the ideological rationalization of the above differences. [End Page 30] A. The Multidimensional Space of the Israeli Polity A political space usually consists of several dimensions. Each dimension, in turn, contains substantively related elements.4 For example, the security of communities and individuals constitutes a dimension which depicts people's preferences concerning the...

Dynamic properties of a classical anisotropic Heisenberg chain under external magnetic field

We investigate the dynamic properties of a classical anisotropic Heisenberg chain interacting with an external magnetic field at different temperatures. Properties such as time-dependent energy autocorrelation and space–time spin–spin correlation are obtained by solving the dynamic equation S ˙ i = S i × ∇ S i H . While the static spin–spin correlation length decreases as the system is heated up, it increases when an external magnetic field is present. The time-dependent spin–spin correlation decreases when the system is heated up, resulting in a decrease of the spin-diffusion speed. The presence of the magnetic field contributes to the order, and therefore produces an increase of the spin-diffusion speed. In contrast, the single-ion type anisotropy behaves dynamically as a local field, inducing disorder in the chain.

Conformal Killing horizons

For time dependent black hole space–times the event horizon cannot be described by a Killing horizon. In the case when the space–time admits a timelike conformal Killing field, which becomes null on a boundary called the conformal stationary limit surface, one can locally describe the expanding event horizon by using this boundary, provided that it is a null geodesic hypersurface. In this case the boundary is called a conformal Killing horizon and is shown to be null and geodesic if and only if the twist of the conformal Killing trajectories on the hypersurface vanishes. Moreover if the space–time is conformally related to a stationary asymptotically flat black hole space–time, it is shown that this hypersurface is globally equivalent to the event horizon, provided that the conformal factor goes to a constant at null infinity. When the conformal stationary limit surface does not coincide with the conformal Killing horizon, a generalization of the weak rigidity theorem which establishes the conformal Killing property of the event horizon and the rigidity of its rotation is obtained. A physical definition of surface gravity for conformal Killing horizons is given, which is then used to formulate a generalized zeroth law of black hole physics.

Time-dependent Hilbert spaces, geometric phases, and general covariance in quantum mechanics

We investigate consequences of allowing the Hilbert space of a quantum system to have a time-dependent metric. For a given possibly nonstationary quantum system, we show that the requirement of having a unitary Schrödinger time-evolution identifies the metric with a positive-definite (Ermakov–Lewis) dynamical invariant of the system. Therefore the geometric phases are determined by the metric. We construct a unitary map relating a given time-independent Hilbert space to the time-dependent Hilbert space defined by a positive-definite dynamical invariant. This map defines a transformation that changes the metric of the Hilbert space but leaves the Hamiltonian of the system invariant. We propose to identify this phenomenon with a quantum mechanical analogue of the principle of general covariance of general relativity. We comment on the implications of this principle for geometrically equivalent quantum systems and investigate the underlying symmetry group.

Astrophysical significance of the anisotropic kinetic alpha effect

The generation of large scale flows by the anisotropic kinetic alpha (AKA) effect is investigated in simulations with a suitable time-dependent space- and time-periodic anisotropic forcing lacking parity invariance. The forcing pattern moves relative to the fluid, which leads to a breaking of the Galilean invariance as required for the AKA effect to exist. The AKA effect is found to produce a clear large scale flow pattern when the Reynolds number, R, is small as only a few modes are excited in linear theory. In this case the non-vanishing components of the AKA tensor are dynamically independent of the Reynolds number. For larger values of R, many more modes are excited and the components of the AKA tensor are found to decrease rapidly with increasing value of R. However, once there is a magnetic field (imposed and of sufficient strength, or dynamo-generated and saturated) the field begins to suppress the AKA effect, regardless of the value of R. It is argued that the AKA effect is unlikely to be astrophysically significant unless the magnetic field is weak and R is small.

Particle-in-Cell Simulation of Inertial Electrostatic Confinement Fusion Plasma

A particle-in-cell calculation code was made to simulate the operation of an inertial electrostatic confinement (IEC) fusion device. The computation includes the effects of ionization by electron impact. Several techniques to save computational time are introduced in this program code. One of them is time-dependent fine space meshes used in the regions where the particles concentrate. Several superparticles that have similar radial position as well as similar energy are merged, while one superparticle is divided into several particles with a somewhat different velocity when the total number of superparticles decreases. The methods enable more precise determination of the characteristics of an IEC device in a shorter time than by previous methods.

The effect of Coulomb interactions on transport processes in one-dimensional systems such as discotic liquid crystals

We evaluate the consequences of interactions between charge carriers on the transport dynamics or currents in normally insulating one-dimensional systems where excess charges have been injected electrically, chemically, or optically. The time-dependent currents and space charge distribution are calculated using a many body Monte Carlo method adapted to stochastic transport. The idea is to study collective interaction phenomena and to learn how to distinguish them from disorder effects. The latter can in principle be modeled to explain almost any experimental result, however, this is often done at the expense of having to use unphysical or inconsistent parameters. Interactions can we argue, give for example, rise to low frequency anomalies in ac conductivity, negative differential resistance, low field spin magnetoresistance, and critical nonlinear noise like oscillations in currents as a function of time.