Time-dependent Formulation Research Articles

Time-dependent simplified spherical harmonics formulations for a nuclear reactor system

The steady-state simplified spherical harmonics equations (SPN equations) are a higher order approximation to the neutron transport equations than the neutron diffusion equation that also have reasonable computational demands. This work extends these results for the analysis of transients by comparing of two formulations of time-dependent SPN equations considering different treatments for the time derivatives of the field moments. The first is the full system of equations and the second is a diffusive approximation of these equations that neglects the time derivatives of the odd moments. The spatial discretization of these methodologies is made by using a high order finite element method. For the time discretization, a semi-implicit Euler method is used. Numerical results show that the diffusive formulation for the time-dependent simplified spherical harmonics equations does not present a relevant loss of accuracy while being more computationally efficient than the full system.

Short Iterative Lanczos Integration in Time-Dependent Equation-of-Motion Coupled-Cluster Theory.

A time-dependent (TD) formulation of equation-of-motion coupled-cluster (EOM-CC) theory can provide excited-state information over an arbitrarily wide energy window with a reduced memory footprint relative to conventional, frequency-domain EOM-CC theory. However, the floating-point costs of the time-integration required by TD-EOM-CC are generally far larger than those of the frequency-domain form of the approach. This work considers the potential of the short iterative Lanczos (SIL) integration scheme [J. Chem. Phys. 1986, 85, 5870-5876] to reduce the floating-point costs of TD-EOM-CC simulations. Low-energy and K-edge absorption features for small molecules are evaluated using TD-EOM-CC with single and double excitations, with the time-integrations carried out via SIL and fourth-order Runge-Kutta (RK4) schemes. Spectra derived from SIL- and RK4-driven simulations are nearly indistinguishable, and with an appropriately chosen subspace dimension, the SIL requires far fewer floating-point operations than are required by RK4. For K-edge spectra, SIL is the more efficient scheme by an average factor of 7.2.

On the quasi-stationary approach to solve the electron Boltzmann equation in pulsed plasmas

This work analyzes the temporal evolution of the electron kinetics in dry-air plasmas (80% N2: 20% O2), excited by electric-field pulses with typical rise-times of 10−9 and 10−6 s, applied to a stationary neutral gaseous background at pressures of 105, 133 Pa and temperature of 300 K. The study is based on the solution of the electron Boltzmann equation (EBE), adopting either (i) a time-dependent formulation that considers an intrinsic time evolution for the electron energy distribution function (EEDF), assuming the classical two-term expansion and a space-independent exponential temporal growth of the electron density; or (ii) a quasi-stationary approach, where the time-independent form of the EBE is solved for different values of the reduced electric-field over the duration of the pulse. The EBE was solved using the LisbOn KInetics Boltzmann solver (LoKI-B), whose original capabilities were extended to accept time-dependent non-oscillatory electric fields as input data. The role of electron–electron collisions, under specific conditions, is also reported and discussed. The simulations show that the quasi-stationary approach gives solutions similar to the time-dependent formulation for rise-times longer than the characteristic evolution time of the EEDF, i.e. 20 ns at 105 Pa and 20 μs at 133 Pa, meaning that a quasi-stationary description is possible in a high-collisionality situation and long rise-times (e.g. microsecond pulses at atmospheric pressure), failing for faster rise-times (e.g. nanosecond pulses for both pressures considered here).

Photophysical properties of methyl ketone based multi-responsive electrochromic materials: A theoretical investigation

The working mechanism of a series of multi-responsive molecular switches has been investigated at atomistic level by using density functional theory (DFT) and its time dependent formulation (TDDFT). The keto-enol tautomerization has been explored considering the base assisted process, which can easily occur with a low activation energy, and also evaluating the feasibility of the electrically generation of the colored enolate form proposed in literature. Our data show that the electrically induced mechanism, consisting of a reduction followed by a proton transfer, is thermodynamically unfavorable, while a concerted proton coupled electron transfer process (PCET) can be proposed as working mechanism, resulting exergonic and able to better combine theoretical and experimental evidences.

Origin of symmetry-forbidden high-order harmonic generation in the time-dependent Kohn-Sham formulation

We find, for two-electron closed-shell systems (${\mathrm{H}}_{2}$ molecule, $\mathrm{He}$ atom), symmetry-forbidden peaks in the high-order harmonic spectra obtained by the time-dependent Kohn-Sham equations, and clarify their origin. It turns out that fixation of the number of Kohn-Sham orbitals and their occupations gives rise to unphysical transition paths and, therefore, incorrect populations of the one-electron excited states, which leads to even-order harmonics in systems with inversion symmetry. We show that the time-dependent natural Kohn-Sham and time-dependent configuration interaction equations do not suffer from this shortcoming.

Review and Recent Developments on the Perfectly Matched Layer (PML) Method for the Numerical Modeling and Simulation of Elastic Wave Propagation in Unbounded Domains

This review article revisits and outlines the perfectly matched layer (PML) method and its various formulations developed over the past 25 years for the numerical modeling and simulation of wave propagation in unbounded media. Based on the concept of complex coordinate stretching, an efficient mixed displacement-strain unsplit-field PML formulation for second-order (displacementbased) linear elastodynamic equations is then proposed for simulating the propagation and absorption of elastic waves in unbounded (infinite or semi-infinite) domains. Both time-harmonic (frequency-domain) and time-dependent (timedomain) PML formulations are derived for two-and three-dimensional linear elastodynamic problems. Through the introduction of only a few additional variables governed by low-order auxiliary differential equations, the resulting mixed timedomain PML formulation is second-order in time, thereby allowing the use of standard time integration schemes commonly employed in computational structural dynamics and thus facilitating the incorporation into existing displacementbased finite element codes. For computational efficiency, the proposed timedomain PML formulation is implemented using a hybrid approach that couples a mixed (displacement-strain) formulation for the PML region with a classical (displacement-based) formulation for the physical domain of interest, using a standard Galerkin finite element method (FEM) for spatial discretization and a Newmark time scheme coupled with a finite difference (Crank-Nicolson) time scheme for time sampling. Numerical experiments show the performances of the PML method in terms of accuracy, efficiency and stability for two-dimensional linear elastodynamic problems in single-and multi-layer isotropic homogeneous elastic media.

Relativistic time-dependent quantum dynamics across supercritical barriers for Klein-Gordon and Dirac particles

We investigate wave-packet dynamics across supercritical barriers for the Klein-Gordon and Dirac equations. Our treatment is based on a multiple scattering expansion (MSE). For spin-0 particles, the MSE diverges, rendering invalid the use of the usual connection formulas for the scattering basis functions. In a time-dependent formulation, the divergent character of the MSE naturally accounts for charge creation at the barrier boundaries. In the Dirac case, the MSE converges and no charge is created. We show that this time-dependent charge behavior dynamics can adequately explain the Klein paradox in a first-quantized setting. We further compare our semianalytical wave-packet approach to exact finite-difference solutions of the relativistic wave equations.

Topology optimization of shape memory polymer structures with programmable morphology

We present a novel optimization framework for optimal design of structures exhibiting memory characteristics by incorporating shape memory polymers (SMPs). SMPs are a class of memory materials capable of undergoing and recovering applied deformations. A finite-element analysis incorporating the additive decomposition of small strain is implemented to analyze and predict temperature-dependent memory characteristics of SMPs. The finite element method consists of a viscoelastic material modelling combined with a temperature-dependent strain storage mechanism, giving SMPs their characteristic property. The thermo-mechanical characteristics of SMPs are exploited to actuate structural deflection to enable morphing toward a target shape. A time-dependent adjoint sensitivity formulation implemented through a recursive algorithm is used to calculate the gradients required for the topology optimization algorithm. Multimaterial topology optimization combined with the thermo-mechanical programming cycle is used to optimally distribute the active and passive SMP materials within the design domain. This allows us to tailor the response of the structures to design them with specific target displacements, by exploiting the difference in the glass-transition temperatures of the two SMP materials. Forward analysis and sensitivity calculations are combined in a PETSc-based optimization framework to enable efficient multi-functional, multimaterial structural design with controlled deformations.

Influence of bird mass and impact height on the fan-blade of an aero-engine

The impact of birds on aircraft during flight is a significant threat to passenger safety and the components of aircraft. Windshields and engine blading are vulnerable to damage. Airworthiness standards requirement states that critical structural parts should be able to withstand bird strikes to a certain level of damage criteria. In order to fulfill these requirements, bird impact response of aircraft components is evaluated by means of intensive experimental and numerical technique. Numerical methods help to reduce certification and development costs and have been increasingly adopted to analyze bird impact. Numerical simulation also predicts results which are not considered in experimental tests and helps in evaluating effectiveness of design modifications. Forces generated due to bird impact on an Engine fan blade are highly non-linear and extremely dynamic in nature. In this work, the forces and other transient behavior are analyzed using FEM techniques which are established upon explicit time-dependent formulation. The critical impact height of the designated Fan-blade was identified, which can also pave way for future work.

Interaction between superconductors and weak gravitational field

We consider the interaction between the Earth gravitational field and a superconductor in the fluctuation regime. Exploiting the weak field expansion formalism and using time dependent Ginzburg-Landau formulation, we show a possible short-time alteration of the gravitational field in the vicinity of the superconductor.

Mesalazine allergy and an attempt at desensitization therapy in patients with inflammatory bowel disease

Mesalazine is a key drug used for remission induction and maintenance therapy in inflammatory bowel disease (IBD). We sometimes encounter patients who develop allergic reactions to the drug and inevitably discontinue treatment. Of 692 patients who received mesalazine for IBD between 2014 and March 2020, 33 diagnosed with mesalazine allergy (43 episodes) were included, and their clinical manifestations were evaluated. For ten patients undergoing desensitization therapy, therapeutic outcomes were evaluated. The incidence of mesalazine allergy was 4.8%. The time from the start of oral medication to allergy onset was 10 ± 5 days for the first allergic attack and 2 ± 1 days for the second and subsequent allergic attacks. The observed clinical symptoms included fever (93%), diarrhea (26%), abdominal pain (23%), and bloody stool (12%). Drug-induced lymphocyte stimulation test was performed in 85% of the patients (28/33), and the sensitivity was 51%. Desensitization therapy with a time-dependent mesalazine granule formulation was successful in nine of the ten patients (90%), allowing them to receive 2000 mg or more of the drug. Fever was a common allergic symptom, and its presence appeared to be useful for distinguishing mesalazine allergy from exacerbation of the primary disease. Desensitization therapy was useful in patients with mesalazine allergy.

A general automatic method for optimal construction of matrix product operators using bipartite graph theory.

Constructing matrix product operators (MPOs) is at the core of the modern density matrix renormalization group (DMRG) and its time dependent formulation. For the DMRG to be conveniently used in different problems described by different Hamiltonians, in this work, we propose a new generic algorithm to construct the MPO of an arbitrary operator with a sum-of-products form based on the bipartite graph theory. We show that the method has the following advantages: (i) it is automatic in that only the definition of the operator is required; (ii) it is symbolic thus free of any numerical error; (iii) the complementary operator technique can be fully employed so that the resulting MPO is globally optimal for any given order of degrees of freedom; and (iv) the symmetry of the system could be fully employed to reduce the dimension of MPO. To demonstrate the effectiveness of the new algorithm, the MPOs of Hamiltonians ranging from the prototypical spin-boson model and the Holstein model to the more complicated ab initio electronic Hamiltonian and the anharmonic vibrational Hamiltonian with the sextic force field are constructed. It is found that for the former three cases, our automatic algorithm can reproduce exactly the same MPOs as the optimally hand-crafted ones already known in the literature.

Photonic band gap phenomenon in a metal–dielectric periodic structure

We study the photonic band structure of a metal–dielectric periodic structure. The metallic component is described by the Drude model; therefore, the electric permittivity is frequency dependent, i.e., dispersive. Rather than solving a nonlinear eigenvalue problem for the band structure of the material, we follow a time-dependent formulation described in Raman and Fan (Phys Rev Lett 104:087401, 2010) which leads to a linear eigenvalue problem. At issue is the question of completeness of the eigenfunctions, which is claimed but not proven in Raman and Fan (2010). We establish completeness in one dimension. We further describe the existence of accumulation points in the spectrum that lead to an infinite family of ‘zero group velocity’ waves. Numerical calculations illustrate some of the main ideas of this work.

On the role of thermal boundary conditions in typical problems of buoyancy convection: A combined experimental-numerical analysis

Buoyancy flows of thermal origin and related heat transfer problems are central in a variety of disciplines and technological applications. In the present study the classical case of a cavity heated from one side and cooled from the other (internal size 4 cm, filled with water) is tackled both experimentally and numerically for different circumstances (horizontal and inclined temperature gradients). The main objective is to fill a gap, namely, the surprising lack of knowledge relating to the role played by the effective heat loss taking place through the walls delimiting the fluid domain from above and from below and along the spanwise direction in influencing the instabilities of these flows and their progression towards chaos. We explore the response of such systems with respect to several parameters, including the inclination of the cavity with respect to gravity, the average temperature of the fluid, the applied temperature difference, the dependence of fluid properties on temperature and the intensity of heat transfer to the ambient. Experiments are supported by dedicated numerical simulations based on the Navier-Stokes and energy equations in their time-dependent and non-linear formulation (solved by means of the PISO method with a collocated-grid approach). It is shown that a kaleidoscope of states is possible depending on the considered conditions. The results reveal the counter-intuitive triadic relationship among heat loss through non-thermally active walls, the hierarchy of bifurcations displayed by the system and the prevailing two-dimensional or three-dimensional nature of the flow.

Iodine substituted phosphorus corrole complexes as possible photosensitizers in photodynamic therapy: Insights from theory.

The search for new dyes to be used as photosensitizers in photodynamic therapy (PDT) is a field of great interest from both experimental and theoretical viewpoints. In this study, the main photophysical properties (excitation energies, singlet-triplet energy gap, and spin orbit coupling matrix elements) of some unsubstituted and iodine substituted phosphorus corrole complexes have been determined by using density functional theory and its time-dependent formulation. Results show that these compounds can be proposed as photosensitizers in PDT. The heavy atom effects have been rationalized on the basis of El-Sayed rules.

The density matrix renormalization group in chemistry and molecular physics: Recent developments and new challenges

In the past two decades, the density matrix renormalization group (DMRG) has emerged as an innovative new method in quantum chemistry relying on a theoretical framework very different from that of traditional electronic structure approaches. The development of the quantum chemical DMRG has been remarkably fast: it has already become one of the reference approaches for large-scale multiconfigurational calculations. This perspective discusses the major features of DMRG, highlighting its strengths and weaknesses also in comparison with other novel approaches. The method is presented following its historical development, starting from its original formulation up to its most recent applications. Possible routes to recover dynamical correlation are discussed in detail. Emerging new fields of applications of DMRG are explored, such as its time-dependent formulation and the application to vibrational spectroscopy.

Posterior contraction rates for non-parametric state and drift estimation

<p style='text-indent:20px;'>We consider a combined state and drift estimation problem for the linear stochastic heat equation. The infinite-dimensional Bayesian inference problem is formulated in terms of the Kalman–Bucy filter over an extended state space, and its long-time asymptotic properties are studied. Asymptotic posterior contraction rates in the unknown drift function are the main contribution of this paper. Such rates have been studied before for stationary non-parametric Bayesian inverse problems, and here we demonstrate the consistency of our time-dependent formulation with these previous results building upon scale separation and a slow manifold approximation.

Stochastic many-body perturbation theory for electron correlation energies.

Treating electron correlation more accurately and efficiently is at the heart of the development of electronic structure methods. In the present work, we explore the use of stochastic approaches to evaluate high-order electron correlation energies, whose conventional computational scaling is unpleasantly steep, being O(Nn+3) with respect to the system size N and the perturbation order n for the Møller-Plesset (MP) series. To this end, starting from Goldstone's time-dependent formulation of ab initio many-body perturbation theory (MBPT), we present a reformulation of MBPT, which naturally leads to a Monte Carlo scheme with O(nN2 + n2N + f(n)) scaling at each step, where f(n) is a function of n depending on the specific numerical scheme. Proof-of-concept calculations demonstrate that the proposed quantum Monte Carlo algorithm successfully extends the previous Monte Carlo approaches for MP2 and MP3 to higher orders by overcoming the factorial scaling problem. For the first time, Goldstone's time-dependent formulation is made useful numerically for electron correlation energies, not only being purely as a theoretical tool.

A general time-domain formulation of equation-of-motion coupled-cluster theory for linear spectroscopy.

A time-dependent (TD) formulation of equation-of-motion (EOM) coupled-cluster (CC) theory is developed, which, unlike other similar TD-EOM-CC approaches [D. R. Nascimento and A. E. DePrince III, J. Chem. Theory Comput. 12, 5834-5840 (2016)], can be applied to any type of linear electronic spectroscopy. The TD-EOM-CC method is formally equivalent to the standard frequency-domain formulation of EOM-CC theory, with a potential computational advantage of a comparatively low memory footprint. This general TD-EOM-CC framework is applied to the linear absorption and electric circular dichroism spectra of several small oxirane derivatives.

Holonomic gates in pseudo-Hermitian quantum systems

The time-dependent pseudo-Hermitian formulation of quantum mechanics allows to study open system dynamics in analogy to Hermitian quantum systems. In this setting, we show that the notion of holonomic quantum computation can equally be formulated for pseudo-Hermitian systems. Starting from a degenerate pseudo-Hermitian Hamiltonian we show that, in the adiabatic limit, a non-Abelian geometric phase emerges which realizes a pseudounitary quantum gate. We illustrate our findings by studying a pseudo-Hermitian gain/loss system which can be written in the form of a tripod Hamiltonian by using the biorthogonal representation. It is shown that this system allows for arbitrary pseudo-$\mathrm{U}(2)$ transformations acting on the dark subspace of the system.