Time-dependent Version Research Articles

Improved switching condition for reachable set estimation of discrete-time switched delayed neural networks

This research delves into the reachable set estimation (RSE) problem for general switched delayed neural networks (SDNNs) in the discrete-time context. Note that existing relevant research on SDNNs predominantly relies on either time-dependent or state-dependent switching approaches. The time-dependent versions necessitate the stability of each subnetwork beforehand, whereas the state-dependent switching strategies solely depend on the current state, thus disregarding the historical information of the neuron states. For fully harnessing the historical information pertaining to neuron states, a delicate combined switching strategy (CSS) is formulated with the explicit goal of furnishing a relaxed and less conservative design framework tailored for discrete-time SDNNs, where all subnetworks can also be unstable. By resorting to the established time-dependent multiple Lyapunov–Krasovskii functional (TDMLF) technique, the improved criteria are subsequently presented, ensuring that the reachable set encompassing all potential states of SDNNs is confined to an anticipated bounded set. Ultimately, the practicality and superiority of the presented RSE approach are thoroughly validated by two illustrative simulation examples.

An ultra-weak space-time variational formulation for the Schrödinger equation

We present a well-posed ultra-weak space-time variational formulation for the time-dependent version of the linear Schrödinger equation with an instationary Hamiltonian. We prove optimal inf-sup stability and introduce a space-time Petrov-Galerkin discretization with optimal discrete inf-sup stability.We show norm-preservation of the ultra-weak formulation. The inf-sup optimal Petrov-Galerkin discretization is shown to be asymptotically norm-preserving, where the deviation is shown to be in the order of the discretization. In addition, we introduce a Galerkin discretization, which has suboptimal inf-sup stability but exact norm-preservation.Numerical experiments underline the performance of the ultra-weak space-time variational formulation, especially for non-smooth initial data.

A unified mixed finite element method for fourth-order time-dependent problems using biorthogonal systems

This article introduces a unified mixed finite element framework based on a saddle-point formulation that applies to time-dependent fourth order linear and nonlinear problems with clamped, simply supported, and Cahn-Hilliard type boundary conditions. The classical mixed formulations lead to large matrix systems that demand huge storage and computational time making the schemes expensive, especially for the time-dependent problems. The proposed scheme circumvents this by employing biorthogonal basis functions that lead to sparse and positive-definite systems. The article discusses a mixed finite element method for the biharmonic problem and the time-dependent linear and nonlinear versions of the extended Fisher-Kolmogorov equations equipped with the aforementioned boundary conditions. The wellposedness of the scheme is discussed and a priori error estimates are presented for the semi-discrete and fully discrete finite element schemes. The numerical experiments validate the theoretical estimates derived in the paper.

Molecular factors determining brightness in fluorescence-encoded infrared vibrational spectroscopy.

Fluorescence-encoded infrared (FEIR) spectroscopy is a recently developed technique for solution-phase vibrational spectroscopy with detection sensitivity at the single-molecule level. While its spectroscopic information content and important criteria for its practical experimental optimization have been identified, a general understanding of the electronic and nuclear properties required for highly sensitive detection, i.e., what makes a molecule a "good FEIR chromophore," is lacking. This work explores the molecular factors that determine FEIR vibrational activity and assesses computational approaches for its prediction. We employ density functional theory (DFT) and its time-dependent version (TD-DFT) to compute vibrational and electronic transition dipole moments, their relative orientation, and the Franck-Condon factors involved in FEIR activity. We apply these methods to compute the FEIR activities of normal modes of chromophores from the coumarin family and compare these predictions with experimental FEIR cross sections. We discuss the extent to which we can use computational models to predict the FEIR activity of individual vibrations in a candidate molecule. The results discussed in this work provide the groundwork for computational strategies for choosing FEIR vibrational probes or informing the structure of designer chromophores for single-molecule spectroscopic applications.

Transient analysis of high-Z impurity screening by additional injection of low-Z impurity using integrated divertor code SONIC

The dynamics of the screening effect of Ar impurity by the injection of additional Ne has been studied through time-dependent analysis with the integrated divertor code SONIC. In the preceding study (Yamoto et al 2020 Plasma Phys. Control. Fusion 62 045006), the predictive simulation of JT-60SA plasma by SONIC has shown that the injection of additional Ne into Ar-seeded plasma results in lower Ar density and radiation power in the SOL and core edge than in the Ar-only seeded case. The results have demonstrated that the mixed impurity seeding of Ar and Ne may be advantageous for maintaining a high core plasma performance with a low divertor heat load. It was found that the friction force induced by the high D+ flow in the SOL towards the inner divertor (ID) region in the Ar + Ne seeded case pushes Ar impurities to the ID. However, the dynamics of D+ flow acceleration cannot be interpreted in the previous study because SONIC was a steady state code. In this study, we have developed the time-dependent version of SONIC and applied it to the transient analysis of the injection of additional Ne into Ar-seeded plasma in JT-60SA. When additional Ne is injected, Ne ions stay in the ID plasma near the X-point. As a result, the Ne radiation power increases near the X-point. The electron pressure then decreases due to the radiation cooling and the D+ flow is accelerated by the electron pressure gradient. The ion pressure also decreases due to the convection by the accelerated D+ flow by electron pressure gradient. The resulting ion pressure gradient further accelerates the D+ flow velocity towards the ID. The results suggest that both the high-performance core plasma and the low divertor heat load can be achieved by the Ar + Ne mixed impurity seeding.

Passivity Analysis for Switched Generalized Delayed Neural Networks

This brief concerns the passivity issue for a class of continuous-time switched generalized neural networks (CSGNNs) with time-varying delay. Note that the existing related results about switched delayed neural networks are based on the time-dependent or the state-dependent switching strategies, where the time-dependent versions require the stability of each subnetwork, while the state-dependent versions can not avoid the frequent switching, chattering and Zeno problems. For handling this situation, the combined switching strategy is introduced on the basis of the constructed time-dependent multiple Lyapunov-Krasovskii functional approach. A new passivity criterion with less conservativeness is formulated, under which the addressed neural networks are passive with a guaranteed switching frequency. Also, each individual subnetwork can be non-passive. Finally, the employed simulation example substantiates the accuracy and superiority of the derived results.

Spectroscopic investigation of interstellar hydrogenated carbon clusters

Context. The assignment of the mid-infrared (mid-IR) emission features and plateaus observed in C-rich and H-rich regions of the interstellar medium (ISM) is still debated. Such mid-IR assignments must also be related to their contribution to the extinction curve in our galaxy and to the ultraviolet (UV) bump. Aims. The aim of this work is to investigate the influence of hydrogenation rate on the mid-IR spectra of populations of carbon clusters in order to constraint the nH/nC ratios in regions of the ISM where carbon is an important component. Their potential contribution to the extinction curve and in particular to the UV bump is also investigated. Methods. The absorption IR and optical spectra of tens of thousands of C24Hn (n = 0, 6, 12, 18, 24) isomers classified into structural families – namely flakes, branched, pretzels, and cages – were computed using the density functional based tight binding electronic structure method and its time-dependent version, respectively. Final spectra were obtained by averaging the spectra of many individual isomers. Results. The shapes and the relative intensities of the bands centered at ~3.25 and 3.40 µm and assigned to the C–H stretch of sp2 and sp3 carbon atoms, respectively, present a clear dependence on the nH/nC ratio. From a comparison with the astronomical spectrum from the Orion bar H2S1, the most interesting emitting candidates would pertain to the flakes population; this is the most energetically favorable family of clusters, possessing a high content of five and six carbon rings and being mostly planar, with no sp1 carbon atoms and with a nH/nC ratio of lower than 0.5. The same conclusion is drawn when comparing the computed IR features in the [4–20 µm] region with the observed plateaus from some C-rich and H-rich planetary nebulae objects of the Small Magellanic Cloud. The contribution of the same family could be considered for the UV bump. When nH/nC increases, only a contribution to the high-energy part of the continuum due to σ → π✶ excitations can reasonably be considered. Conclusions. These results bring some constraints on the structural features and on the nH/nC ratio of the hydrogenated carbon populations emitting in the mid-IR domain in interstellar objects such as protoplanetary and reflection nebulae. The flakes population, with a low nH/nC ratio, is an interesting candidate for the carbon population emitting in these regions, but not for that absorbing in the diffuse ISM. None of the populations studied in the present work can account for the UV bump, but they would contribute to a broad extinction rise in this domain. The computed features reported in this article could be used to interpret future astronomical data provided by the James Webb Space Telescope.

Xrd_simulator: 3D X-ray diffraction simulation software supporting 3D polycrystalline microstructure morphology descriptions.

An open source Python package named xrd_simulator, capable of simulating geometrical interactions between a monochromatic X-ray beam and a polycrystalline microstructure, is described and demonstrated. The software can simulate arbitrary intragranular lattice variations of single crystals embedded within a multiphase 3D aggregate by making use of a tetrahedral mesh representation where each element holds an independent lattice. By approximating the X-ray beam as an arbitrary convex polyhedral region in space and letting the sample be moved continuously through arbitrary rigid motions, data from standard and non-standard measurement sequences can be simulated. This implementation is made possible through analytical solutions to a modified, time-dependent version of the Laue equations. The software, which primarily targets three-dimensional X-ray diffraction microscopy (high-energy X-ray diffraction microscopy) type experiments, enables the numerical exploration of which sample quantities can and cannot be reconstructed for a given acquisition scheme. Similarly, xrd_simulator targets investigations of different measurement sequences in relation to optimizing both experimental run times and sampling.

Iterated Maximum Large Neighborhood Search for the Traveling Salesman Problem with Time Windows and its Time-dependent Version

This article introduces a new algorithm for finding feasible or makespan-optimal solutions of Traveling Salesman Problems with Time Windows (TSPTWs) and Time-Dependent TSPTWs (TDTSPTWs). The algorithm starts from a sequence of visits of the customers involved in the problem, uses destroy and repair operations to iteratively improve this sequence, and applies perturbations to diversify search. For the destroy phase, customers are removed from the current sequence of visits as long as a parameter called the insertion-width is not too high. For the repair phase, the customers removed are reinserted for the best based on a dynamic programming procedure whose complexity is only linear in the number of customers. For the perturbation phase, some customers are randomly shifted in the sequence of visits. The algorithm obtained is called Iterated Maximum Large Neighborhood Search (ImaxLNS). On seven standard TSPTW benchmarks, it returns the best-known solution for each instance in less than one second on average. On two TDTSPTW benchmarks related to urban logistics, it provides new feasible solutions and best solutions. On a TDTSPTW benchmark related to Earth observing satellites, it solves most of the instances in less than a second.

First-passage process in degree space for the time-dependent Erdős-Rényi and Watts-Strogatz models.

In this work, we investigate the temporal evolution of the degree of a given vertex in a network by mapping the dynamics into a random walk problem in degree space. We analyze when the degree approximates a preestablished value through a parallel with the first-passage problem of random walks. The method is illustrated on the time-dependent versions of the Erdős-Rényi and Watts-Strogatz models, which were originally formulated as static networks. We have succeeded in obtaining an analytic form for the first and the second moments of the first-passage time and showing how they depend on the size of the network. The dominant contribution for large networks with N vertices indicates that these quantities scale on the ratio N/p, where p is the linking probability.

A three-dimensional discrete model for approximating the deformation of a viral capsid subjected to lying over a flat surface in the static and time-dependent case

In this paper, we present a three-dimensional discrete model governing the deformation of a viral capsid, modelled as a regular icosahedron and subjected not to cross a given flat rigid surface on which it initially lies in correspondence of one vertex only. First, we set up the model in the form of a set of variational inequalities posed over a non-empty, closed and convex subset of a suitable space. Second, we show the existence and uniqueness of the solution for the proposed model. Third, we numerically test this model and we observe that the outputs of the numerical experiments comply with physics. Finally, we establish the existence of solutions for the corresponding time-dependent version of the obstacle problem under consideration.

Control of Quantum Noise: On the Role of Dilations

We show that every finite-dimensional quantum system with Markovian (i.e. GKLS-generated) time evolution has an autonomous unitary dilation which can be dynamically decoupled. Since there is also always an autonomous unitary dilation which cannot be dynamically decoupled, this highlights the role of dilations in the control of quantum noise. We construct our dilation via a time-dependent version of Stinespring in combination with Howland’s clock Hamiltonian and certain point-localised states, which may be regarded as a C*-algebraic analogue of improper bra-ket position eigenstates and which are hence of independent mathematical and physical interest.

Local and parallel efficient BDF2 and BDF3 rotational pressure-correction schemes for a coupled Stokes/Darcy system

In this paper, the local and parallel two- and three-step backward differentiation formula (BDF2/BDF3) rotational pressure-correction schemes are developed for a coupled Stokes/Darcy system. The central advantage of these schemes is a time-dependent version of domain decomposition by solving the Stokes problem and Darcy problems in their respective domain. By following a similar idea in Guermond et al. (2005), the Stokes problem is solved by a vector-valued elliptic equation and a scalar Poisson equation per time step. The whole system can be composed of three simple linear equations that consume almost the same computational time. Thus, the presented methods can be efficiently applied with less communication requirements and has good parallelism. In theorey, we prove the unconditional stability and long-time stability of the BDF2/BDF3 rotational pressure-correction schemes for the coupled Stokes/Darcy system. Furthermore, some numerical experiments are presented to show the accuracy and efficiency of these schemes in terms of numerical convergence rates and reservoir engineering.

Finite-time Response of Dynamo Mean-field Effects in Magnetorotational Turbulence

Abstract Accretion disk turbulence along with its effect on large-scale magnetic fields plays an important role in understanding disk evolution in general, and the launching of astrophysical jets in particular. Motivated by enabling a comprehensive subgrid description for global long-term simulations of accretions disks, we aim to further characterize the transport coefficients emerging in local simulations of magnetorotational disk turbulence. For the current investigation, we leverage a time-dependent version of the test-field method, which is sensitive to the turbulent electromotive force (EMF) generated as a response to a set of pulsating background fields. We obtain Fourier spectra of the transport coefficients as a function of oscillation frequency. These are well approximated by a simple response function, describing a finite-time buildup of the EMF as a result of a time-variable mean magnetic field. For intermediate timescales (i.e., slightly above the orbital frequency), we observe a significant phase lag of the EMF compared to the causing field. Augmented with our previous result on a nonlocal closure relation in space, and incorporated into a suitable mean-field description that we briefly sketch out here, the new framework will allow us to drop the restrictive assumption of scale separation.

Synthesis and optical properties of a fluorene-benzothiadiazole anthracene copolymer

A novel green-emitting terpolymer of Poly[2,7-(9,9-dihexylfluorene)-co-4,7-(2,1,3-benzothiadiazole)-co-9,10-(anthracene)] (PFABT), containing 9,9-dihexylfluorene and anthracene as electron-pushing unit and benzothiadiazole as electron-pulling unit, was synthesized via Suzuki coupling reaction. Poly[2,7-(9,9-dihexylfluorene)-co-9,10-(anthracene)] (PFA) and Poly[2,7-(9,9-dihexylfluorene)-co-4,7-(2,1,3-benzothiadiazole)] (PFBT) copolymers were also synthesized for comparative purposes. These copolymers were characterized by GPC, FTIR and 13C NMR and computational calculations were performed using density functional theory (DFT) and its time-dependent version (TDDFT) at CAM-B3LYP/6–311 +G(d,p) level. Natural transition orbitals (NTO) and vertical excitation energies were obtained from oligomer models that represent the PFA, PFBT and PFABT polymers. The NTO densities showed that the excitation of the anthracene moiety is responsible for the S1 state on both PFA and PFABT, and that the S2 state of PFBT and PFABT is a consequence of the excitation of the benzothiadiazole-anthracene moiety. We also studied polymer light-emitting diodes (PLEDs) of blends of poly(9-vinylcarbazole) (PVK) as a host matrix with PFA, PFBT or PFABT as guests. The concentrations of the copolymers in the PVK were varied at 5, 25 and 50 wt%. The PL spectra for all blends exhibited one band at 400 nm attributed to PVK and another centered at 535 nm assigned to the PFO derivatives emission. We observed an increase in energy transfer efficiency, E < FRET> , with an increase in the weight ratio of the copolymer (PFA, PFBT or PFABT) into the PVK matrix. All the PLEDs emitted a greenish color, and the concentration of the polymer guest impacted on the performance of the diode.

On a conformal Schwarzschild-de Sitter spacetime

On the basis of the C-metric, we investigate the conformal Schwarzschild - deSitter spacetime and compute the source stress tensor and study its properties, including the energy conditions. Then we analyze its extremal version (\(b^{2} = 27m^{2}\), where b is the deS radius and m is the source mass), when the metric is nonstatic. The weak-field version is investigated in several frames, and the metric becomes flat with the special choice \(b = 1/a\), a being the constant acceleration of the Schwarzschild-like mass or black hole. This form is Rindler’s geometry in disguise and is also conformal to a de Sitter metric where the acceleration plays the role of the Hubble constant. In its time dependent version, one finds that the proper acceleration of a static observer is constant everywhere, in contrast with the standard Rindler case. The timelike geodesics along the z-direction are calculated and proves to be hyperbolae.

Joint Modeling of Longitudinal Markers and Time-to-Event Outcomes: An Application and Tutorial in Patients After Surgical Repair of Transposition of the Great Arteries.

Most patients with congenital heart disease survive into adulthood; however, residual abnormalities remain and management of the patients is life-long and personalized. Patients with surgical repair of transposition of the great arteries, for example, face the risk to develop neoaortic valve regurgitation. Cardiologists update the prognosis of the patient intuitively with updated information of the cardiovascular status of the patient, for instance from echocardiographic imaging. Usually a time-dependent version of the Cox model is used to analyze repeated measurements with a time-to-event outcome. New statistical methods have been developed with multiple advantages, of which the most prominent one being the joint model for longitudinal and time-to-event outcome. In this tutorial, the joint modeling framework is introduced and applied to patients with transposition of the great arteries after surgery with a long-term follow-up, where repeated echocardiographic values of the neoaortic root are evaluated against the risk of neoaortic valve regurgitation. The data are analyzed with the time-dependent Cox model as benchmark method, and the results are compared with a joint model, leading to different conclusions. The flexibility of the joint model is shown by adding the growth rate of the neoaortic root to the model and adding repeated values of body surface area to obtain a multimarker model. Lastly, it is demonstrated how the joint model can be used to obtain personalized dynamic predictions of the event. The joint model for longitudinal and time-to-event data is an attractive method to analyze data in follow-up studies with repeated measurements. Benefits of the method include using the estimated natural trajectory of the longitudinal outcome, great flexibility through multiple extensions, and dynamic individualized predictions.

Nonsteady fracture of transient networks: The case of vitrimer

We have discovered a peculiar form of fracture that occurs in polymer network formed by covalent adaptable bonds. Due to the dynamic feature of the bonds, fracture of this network is rate dependent, and the crack propagates in a highly nonsteady manner. These phenomena cannot be explained by the existing fracture theories, most of which are based on steady-state assumption. To explain these peculiar characteristics, we first revisit the fundamental difference between the transient network and the covalent network in which we highlighted the transient feature of the cracks. We extend the current fracture criterion for crack initiation to a time-evolution scheme that allows one to track the nonsteady propagation of a crack. Through a combined experimental modeling effort, we show that fracture in transient networks is governed by two parameters: the Weissenberg number [Formula: see text] that defines the history path of crack-driving force and an extension parameter Z that tells how far a crack can grow. We further use our understanding to explain the peculiar experimental observation. To further leverage on this understanding, we show that one can "program" a specimen's crack extension dynamics by tuning the loading history.

On path ranking in time-dependent graphs

In this paper we study a property of time-dependent graphs, dubbed “path ranking invariance”. Broadly speaking, a time-dependent graph is “path ranking invariant” if the ordering of its paths (w.r.t. travel time) is independent of the start time. In this paper we show that, if a graph is path ranking invariant, the solution of a large class of time-dependent vehicle routing problems can be obtained by solving suitably defined (and simpler) time-independent routing problems. We also show how this property can be checked by solving a linear program. If the check fails, the solution of the linear program can be used to determine a tight lower bound. In order to assess the value of these insights, the lower bounds have been embedded into an enumerative scheme. Computational results on the time-dependent versions of the Travelling Salesman Problem and the Rural Postman Problem show that the new findings enable to outperform state-of-the-art algorithms.

Elliptic Solutions of Dynamical Lucas Sequences.

We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution for this system is given by elliptic numbers. The second type involves a non-commutative version of Lucas sequences which defines the non-commutative (or abstract) Fibonacci polynomials introduced by Johann Cigler. If the non-commuting variables are specialized to be elliptic-commuting variables the abstract Fibonacci polynomials become non-commutative elliptic Fibonacci polynomials. Some properties we derive for these include their explicit expansion in terms of normalized monomials and a non-commutative elliptic Euler–Cassini identity.