Time-dependent Space Research Articles

Time-dependent orbital-optimized coupled-cluster methods families for fermion-mixtures dynamics.

Five time-dependent orbital optimized coupled-cluster methods, of which four can converge to the time-dependent complete active space self-consistent-field method, are presented for fermion-mixtures with arbitrary fermion kinds and numbers. Truncation schemes maintaining the intragroup orbital rotation invariance, as well as equations of motion of coupled-cluster (CC) amplitudes and orbitals, are derived. Present methods are compact CC-parameterization alternatives to the time-dependent multiconfiguration self-consistent-field method for systems consisting of arbitrarily different kinds and numbers of interacting fermions. Theoretical analysis of applications of present methods to various chemical systems is reported.

Simulating ultrafast transient absorption spectra from first principles using a time-dependent configuration interaction probe.

Transient absorption spectroscopy (TAS) is among the most common ultrafast photochemical experiments, but its interpretation remains challenging. In this work, we present an efficient and robust method for simulating TAS signals from first principles. Excited-state absorption and stimulated emission (SE) signals are computed using time-dependent complete active space configuration interaction (TD-CASCI) simulations, leveraging the robustness of time-domain simulation to minimize electronic structure failure. We demonstrate our approach by simulating the TAS signal of 1'-hydroxy-2'-acetonapthone (HAN) from ab initio multiple spawning nonadiabatic molecular dynamics simulations. Our results are compared to gas-phase TAS data recorded from both jet-cooled (T ∼ 40 K) and hot (∼403 K) molecules via cavity-enhanced TAS (CE-TAS). Decomposition of the computed spectrum allows us to assign a rise in the SEsignal to excited-state proton transfer and the ultimate decay of the signal to relaxation through a twisted conical intersection. The total cost of computing the observable signal (∼1700 graphics processing unit hours for ∼4ns of electron dynamics) was markedly less than that of performing the abinitio multiple spawning calculations used to compute the underlying nonadiabatic dynamics.

3D clustering of gene expression data from systemic autoinflammatory diseases using self-organizing maps (Clust3D)

Background and objectiveSystemic autoinflammatory diseases (SAIDs) are characterized by widespread inflammation, but for most of them there is a lack of specific biomarkers for accurate diagnosis. Although a number of machine learning algorithms have been used to analyze SAID datasets, aiding in the discovery of novel biomarkers, there is a growing recognition of the importance of SAID timeseries clustering, as it can capture the temporal dynamics of gene expression patterns. MethodologyThis paper proposes a novel clustering methodology to efficiently associate three-dimensional data. The algorithm utilizes competitive learning to create a self-organizing neural network and adjust neuron positions in time-dependent and high dimensional feature space in order to assign them as clustering centers. The quantitative evaluation of the clustering was based on well-known clustering indices. Furthermore, a differential expression analysis and classification pipeline was employed to assess the capability of the proposed methodology to extract more accurate pathway-specific genes from its clusters. For that, a comparative analysis was also conducted against a heuristic timeseries clustering method. ResultsThe proposed methodology achieved better overall clustering indices scores and classification metrics using genes derived from its clusters. Notable cases include a threefold increase in the Calinski-Harabasz clustering index, a twofold improvement in the Davies–Bouldin clustering index and a ∼60% increase in the classification specificity score. ConclusionA novel clustering methodology was developed and applied on several gene expression timeseries datasets from systemic autoinflammatory diseases, and its ability to efficiently produce well separated clusters compared to existing heuristic methods was demonstrated.

Consistent Treatment of Quantum Systems with a Time-Dependent Hilbert Space.

We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a time-independent Hilbert space. We show that in general the Hamiltonian operator does not represent an observable of the system even if it is a self-adjoint operator. This is related to a hidden geometric aspect of quantum mechanics arising from the presence of an operator-valued gauge potential. We also offer a careful treatment of quantum systems whose Hilbert space is obtained by endowing a time-independent vector space with a time-dependent inner product.

MICPL: Motion-Inspired Cross-Pattern Learning for Small-Object Detection in Satellite Videos.

For small-object detection, vision patterns can only provide limited support to feature learning. Most prior schemes mainly depend on a single vision pattern to learn object features, seldom considering more latent motion patterns. In the real world, humans often efficiently perceive small objects through multipattern signals. Inspired by this observation, this article attempts to address small-object detection from a new prospective of latent pattern learning. To fulfill this purpose, it regards a real-world moving object as the spatiotemporal sequences of a static object to capture latent motion patterns. In view of this, we propose a motion-inspired cross-pattern learning (MICPL) scheme to capture the motion patterns for moving small-object scenarios. This scheme mainly consists of two crucial parts: motion pattern mining (MPM) and motion-vision adaption. The former is designed to effectively mine the motion pattern from time-dependent representation space. The latter is devised to correlate between motion patterns and vision semantics. In the meanwhile, we explore their cross-pattern interactions to guide MICPL to capture motion patterns effectively. Comparison experiments verify that, cooperated by motion pattern, even a simple detector could often refresh state-of-the-art (SOTA) results on moving small-object detection. Moreover, the experiments on two small-object-related tasks further prove the adaptivity and advantages of our cross-pattern feature learning scheme. Our source codes are available at https://github.com/ UESTC-nnLab/MICPL.

Long-time behavior of nonclassical diffusion equations with memory on time-dependent spaces

This paper aims to study the long-time behavior of nonclassical diffusion equation with memory and disturbance parameters on time-dependent space. By using the contractive process method on the family of time-dependent spaces and operator decomposition technique, the existence of pullback attractors is first proved. Then the upper semi-continuity of pullback attractors with respect to perturbation parameter ν in M t is obtained. It’s remarkable that the nonlinearity f satisfies the polynomial growth of arbitrary order.

Scattering of a wave packet by the Pöschl-Teller potential well

We investigate the scattering of a wave packet by the Pöschl-Teller potential in momentum representation. The scattering dynamics of the wave packet for a long-time evolution is feasible in this representation. With the wave function in momentum space, we can construct the time-dependent phase space Wigner function. The corresponding density function in coordinate space is then calculated through the Wigner function. The reflectionless wave packet for integer ν and partially reflected for non-integer ν are demonstrated by analyzing the Wigner function.

Attractors for a fluid-structure interaction problem in a time-dependent phase space

This paper is concerned with the long-time dynamics of a fluid-structure interaction problem describing a Poiseuille inflow through a 2D channel containing a rectangular obstacle. Physically, this models the interaction between the wind and the deck of a bridge in a wind tunnel experiment, as time goes to infinity. Due to this interaction, the fluid domain depends on time in an unknown fashion and the problem needs a delicate functional analytic setting. As a result, the solution operator associated to the system acts on a time-dependent phase space, and it cannot be described in terms of a semigroup nor of a process. Nonetheless, we are able to extend the notion of global attractor to this particular setting, and prove its existence and regularity. This provides a strong characterization of the asymptotic behavior of the problem. Moreover, when the inflow is sufficiently small, the attractor reduces to the unique stationary solution of the system, corresponding to a perfectly symmetric configuration.

Attractor for the Extensible Beam Equation with Nonlocal Weak Damping on Time–Dependent Space

Attractor for the Extensible Beam Equation with Nonlocal Weak Damping on Time–Dependent Space

Ultrafast internal conversion and photochromism in gas-phase salicylideneaniline.

Salicylideneaniline (SA) is an archetypal system for excited-state intramolecular proton transfer (ESIPT) in non-planar systems. Multiple channels for relaxation involving both the keto and enol forms have been proposed after excitation to S1 with near-UV light. Here, we present transient absorption measurements of hot gas-phase SA, jet-cooled SA, and SA in Ar clusters using cavity-enhanced transient absorption spectroscopy (CE-TAS). Assignment of the spectra is aided by simulated TAS spectra, computed by applying time-dependent complete active space configuration interaction (TD-CASCI) to structures drawn from nonadiabatic molecular dynamics simulations. We find prompt ESIPT in all conditions followed by the rapid generation of the trans keto metastable photochrome state and fluorescent keto state in parallel. Increasing the internal energy increases the photochrome yield and decreases the fluorescent yield and fluorescent state lifetime observed in TAS. In Ar clusters, internal conversion of SA is severely hindered, but the photochrome yield is unchanged. Taken together, these results are consistent with the photochrome being produced via the vibrationally excited keto population after ESIPT.

Dynamic of the nonclassical diffusion equation with memory

In this paper, we consider the nonclassical diffusion equation with memory and the nonlinearity of the polynomial growth condition of arbitrary order in the time-dependent space. First, the well-posedness of the solution for the equation is obtained in the time-dependent space mathscr{U}_{t}. Then, we establish the existence and regularity of the time-dependent global attractor. Finally, we also conclude that the fractal dimension of the time-dependent attractor is finite.

A smoothing analysis for multigrid methods applied to tempered fractional problems

ABSTRACT We consider the numerical solution of time-dependent space tempered fractional diffusion equations. The use of Crank–Nicolson in time and of second-order accurate tempered weighted and shifted Grünwald difference in space leads to dense (multilevel) Toeplitz-like linear systems. By exploiting the related structure, we design an ad-hoc multigrid solver and multigrid-based preconditioners, all with weighted Jacobi as smoother. A new smoothing analysis is provided, which refines state-of-the-art results expanding the set of suitable Jacobi weights. Furthermore, under the assumption that a multigrid method is effective in the non-tempered case, we prove that the same multigrid method is effective also in the tempered one. The numerical results confirm the theoretical analysis, showing that the resulting multigrid-based solvers are computationally effective for tempered fractional diffusion equations.

Sulfur-Containing Radical Anions Formed by Photolysis of Thiosulfate: Quantum-Chemical Analysis.

The photochemistry of sodium thiosulfate (S2O32-) in aqueous solutions is rather complicated. Several sulfur-containing radical anions are formed upon photoexcitation. Any of them are rather common (SO3•-, SO2•-, and SO5•-); others are rare (S2O3•-, •S4O63-, and S•-) or never documented (S2O5•-). In order to support the identification of intermediate radical anions, quantum-chemical (QM─quantum mechanical) calculations of the geometric and electronic structures of S2O3•-, S2O5•-, and •S4O63- were performed. Two different approaches, time-dependent density functional theory and complete active space self-consistent field, were applied to identify the method optimal for the reproduction of the experimental electronic absorption spectra. Several of the most commonly used functionals were considered. The best agreement with the experimentally observed spectra of reference compounds (common sulfur-containing anions and radical anions) was achieved for the WB97X-D3 functional. Using this approach, satisfactory agreement between experimental and calculated spectra of S2O3•-, S2O5•-, and •S4O63- was achieved. It was shown that S2O5•- and •S4O63- can exist in two isomeric forms with different spectral properties. These isomers are S2O3O2•-; SO3SO2•- for the case of S2O5•- and (S2O3)2•3-; (S3O32-...SO3•-) for the case of •S4O63-.

Pullback exponential attractors for second-order lattice system with nonstandard growth condition

In this paper, we study the existence of pullback attractors and pullback exponential attractors for lattice dynamical system in time-dependent sequence space. First, we introduce a new sequence space with time-dependent variable exponents. Second, two abstract criteria (or sufficient conditions) about the existence of pullback attractors and pullback exponential attractors are established for infinite dimensional lattice dynamical systems on time-dependent spaces of infinite sequences. Finally, for making full use of the above-mentioned abstract criteria, we consider a second order lattice system with nonstandard growth nonlinearity, and then the existence of bi-space pullback attractors and pullback exponential attractors on a time-dependent Musielak–Orlicz space is obtained. In particular, we point out that these criteria and analytical skills can be utilized to deal with other lattice systems satisfying nonstandard growth conditions.

Non-linear Schrödinger equation with time-dependent balanced loss-gain and space–time modulated non-linear interaction

We consider a class of one dimensional vector Non-linear Schrödinger Equation (NLSE) in an external complex potential with Balanced Loss-Gain (BLG) and Linear Coupling (LC) among the components of the Schrödinger field. The solvability of the generic system is investigated for various combinations of time modulated LC and BLG terms, space–time dependent strength of the nonlinear interaction and complex potential. We use a non-unitary transformation followed by a reformulation of the differential equation in a new coordinate system to map the NLSE to solvable equations. Several physically motivated examples of exactly solvable systems are presented for various combinations of LC and BLG, external complex potential and nonlinear interaction. Exact localized nonlinear modes with spatially constant phase may be obtained for any real potential for which the corresponding linear Schrödinger equation is solvable. A method based on supersymmetric quantum mechanics is devised to construct exact localized nonlinear modes for a class of complex potentials. The real superpotential corresponding to any exactly solved linear Schrödinger equation may be used to find a complex-potential for which exact localized nonlinear modes for the NLSE can be obtained. The solutions with singular phases are obtained for a few complex potentials.

Classical analogous quantum coherent superposition through the Hertz-type nonlinearity of elastic granules

The theory of quantum superposition of states is one of the fundamental concepts related to quantum information science and technology (QIST). Two or more pure quantum states can be superposed to get a distinct quantum state, and one of the examples is the quantum bit, or qubit, state. But decoherence makes it easy for the current qubits, the most critical part of QIST platforms, to lose their superposition of states. Therefore, we theoretically propose and experimentally realize a classical analogous to the coherent superposition of energy states through the Hertz-type nonlinearity of elastic granules driven externally. The granules’ nonlinear vibrations depend mutually through phase and form a coherent superposition when projected into linear modes of vibration. We demonstrate how the state vector components can emerge from the amplitudes of coherent states, spanning to the two-dimensional time-dependent parametric Hilbert space. These amplitudes represent an actual amplitude rather than a probability amplitude, which opens the possibility of exploring two-state quantum-like computations through the superposition of states without decoherence and wave function collapse. These characteristics make it possible to understand the material-based quantum analogous information technology through experimentation of elastic bit.

Attractor of the nonclassical diffusion equation with memory on time- dependent space

<abstract><p>We consider the dynamic behavior of solutions for a nonclassical diffusion equation with memory</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ u_{t}-\varepsilon(t) \triangle u_{t}- \triangle u-\int_{0}^{\infty}\kappa(s)\triangle u(t-s)ds+f(u) = g(x) $\end{document} </tex-math></disp-formula></p> <p>on time-dependent space for which the norm of the space depends on the time $ t $ explicitly, and the nonlinear term satisfies the critical growth condition. First, based on the classical Faedo-Galerkin method, we obtain the well-posedness of the solution for the equation. Then, by using the contractive function method and establishing some delicate estimates along the trajectory of the solutions on the time-dependent space, we prove the existence of the time-dependent global attractor for the problem. Due to very general assumptions on memory kernel $ \kappa $ and the effect of time-dependent coefficient $ \varepsilon(t) $, our result will include and generalize the existing results of such equations with constant coefficients. It is worth noting that the nonlinear term cannot be treated by the common decomposition techniques, and this paper overcomes the difficulty by dealing with it as a whole.</p></abstract>

Time-dependent asymptotic behavior of the solution for evolution equation with linear memory

<abstract><p>In this article, by using the operator decomposition technique, we discuss the existence of a time-dependent global attractor for a nonlinear evolution equation with linear memory within the theory of time-dependent space. Furthermore, the regularity and asymptotic structure of the time-dependent attractor are proved, which means that the time-dependent attractor of the evolution equation converges to the attractor of the limit wave equation when the coefficient $ \varepsilon(t)\rightarrow0 $ as $ t\rightarrow \infty $.</p></abstract>

Phase Space Reaction Dynamics Associated with an Index-2 Saddle Point for Time-Dependent Hamiltonian Systems

We analyze benchmark models for reaction dynamics associated with a time-dependent index-2 saddle point. The influence of index-2 saddle points on chemical reaction dynamics has received a great deal of attention in recent years and we extend this work in a new and important direction. Our model allows us to incorporate time dependence of a general form, subject to an exponential growth restriction. Under these conditions, we analytically compute the time-dependent normally hyperbolic invariant manifold and its time-dependent stable and unstable manifolds. These time-dependent phase space structures allow us to quantitatively determine the effect of the time dependence on reacting and nonreacting trajectories.

A Schwarz waveform relaxation method for time-dependent space fractional Schrödinger/heat equations

This paper is dedicated to the derivation and analysis of a Schwarz waveform relaxation domain decomposition method for solving time-dependent linear/nonlinear space fractional Schrödinger and heat equations. Along with the details of the derivation of the method and some mathematical properties, we also propose some illustrating numerical experiments and conjectures on the rate of convergence of the method.