Time-dependent Phase Research Articles

Mathematical and Physical Modelling of Transient Multi-Phase Flows in a Ladle Shroud during Start-Up

The Ladle Shroud has become an important part of secondary steelmaking, with its role in reducing liquid steel contamination and process improvements. Due to the inherent negative pressure at the lower nozzle–Ladle Shroud joint, it is well known that Ladle Shrouds, protecting steel flows between a Ladle and a tundish below, can suffer from inadvertent ingress of air. Therefore, there is a need to apply inert gas injection at the joint. In the present paper, 3D transient multi-phase simulations of flows occurring for a Reverse Tapered Ladle Shroud during start-up were studied using CFD software ANSYS Fluent 19.1. This allowed us to study the initial multi-phase flow developed during the start-up and potential steel reoxidation, based on a first principles approach. Time-dependent phase fields as well as attendant velocity and turbulence fields were obtained, resulting in the prediction of a turbulent multi-phase flow during start-up and filling. Additionally, some transient phenomena like steel splashing and air suction were observed mathematically. A full-scale water model of the Ladle Shroud was used to qualitatively validate the initial multi-phase turbulent flow inside the Ladle Shroud, in the absence of inert gas injection.

Population pharmacokinetics and exposure-safety of lipophilic conjugates prodrug DP-VPA in healthy Chinese subjects for dose regime exploring

Phospholipid-valproic acid (DP-VPA)is a prodrug for treating epilepsy. The present study explored the pharmacokinetics (PK) and exposure safety of DP-VPA to provide a basis for future studies exploring the safe dosage and therapeutic strategies for epilepsy. The study included a randomized placebo-controlled dose-escalation tolerance evaluation trial and a randomized triple crossover food-effect trial in healthy Chinese volunteers. A population pharmacokinetic (PopPK) model was established to analyze the PK of DP-VPA and active metabolite VPA. The exposure safety was assessed with the adverse drug reaction (ADR) in CNS. The PopPK of DP-VPA and metabolite VPA fitted a two-compartment model coupling one-compartment with Michaelis-Menten metabolite kinetics and first-order elimination. The absorption processes after single oral administration of DP-VPA tablet demonstrated nonlinear characteristics, including 0-order kinetic phase and time-dependent phase fitting Weibull distribution. The final model indicated that the DP-VPA PK was significantly affected by dosage and food. The exposure-safety relationship demonstrated a generalized linear regression; mild/moderate ADRs occurred in some subjects with 600 mg and all subjects with 1500 mg of DP-VPA, and no severe ADRs were reported up to 2400 mg. In conclusion, the study established a PopPK model describing the processing of DP-VPA and VPA in healthy Chinese subjects. DP-VPA showed good tolerance after a single dose of 600–2400 mg with nonlinear PK and was affected by dosage and food. Based on the association between neurological ADRs and higher exposure to DP-VPA by exposure-safety analysis, 900–1200 mg was recommended for subsequent study of safety and clinical effectiveness.

Characteristic Features of Gravitational Wave Lensing as Probe of Lens Mass Model

AbstractTo recognize gravitational wave lensing events and being able to differentiate between similar lens models will be of crucial importance once one will be observing several lensing events of gravitational waves per year. In this work, the lensing of gravitational waves is studied in the context of LISA sources and wave‐optics regime. While different papers before the studied microlensing effects enhanced by simultaneous strong lensing, the focus is on frequency (time) dependent phase effects produced by one lens that will be visible with only one lensed signal. It is shows how, in the interference regime (i.e., when interference patterns are present in the lensed image), one is able to i) distinguish a lensed waveform from an unlensed one, and ii) differentiate between different lens models. In pure wave‐optics, on the other hand, the feasibility of the study depends on the signal‐to‐noise ratio of the signal and/or the amplitude of the lensing effect. To achieve these goals, the phase of the amplification factor of the different lens models and its effect on the unlensed waveform is studied, and the signal‐to‐noise calculation to provide some quantitative examples is exploited.

Recovering density disturbance spectra from FLDI. Part 1.

Focused laser differential interferometry (FLDI) measures the phase shift corresponding to localized fluctuations in the refractive index of a medium. The sensitivity, bandwidth, and spatial filtering properties of FLDI make it particularly suited to applications in high-speed gas flows. Such applications often require the quantitative measurement of density fluctuations, which are related to changes in the refractive index. In a two-part paper, a method is presented for the recovery of a spectral representation of density disturbances from the measured time-dependent phase shift for a particular class of flows able to be modeled using sinusoidal plane waves. The approach is based on the ray-tracing model of FLDI due to Schmidt and Shepherd [Appl. Opt.54, 8459 (2015)APOPAI0003-693510.1364/AO.54.008459]. In this first part, the analytical results for FLDI response to single- and multiple-frequency plane waves are derived and validated against a numerical implementation of the instrument. A spectral inversion method is then developed and validated, including consideration for the frequency-shifting effects of any underlying convective flows. In the second part [Appl. Opt.62, 3054 (2023)APOPAI0003-693510.1364/AO.480354], results from the present model are compared with previous exact solutions temporally averaged over a wave cycle and with an approximate method.

Soliton solutions and their degenerations in the (2+1)-dimensional Hirota–Satsuma–Ito equations with time-dependent linear phase speed

Soliton solutions and their degenerations in the (2+1)-dimensional Hirota–Satsuma–Ito equations with time-dependent linear phase speed

Phenotypic and transcriptomic acclimation of the green microalga Raphidocelis subcapitata to high environmental levels of the herbicide diflufenican

Herbicide pollution poses a worldwide threat to plants and freshwater ecosystems. However, the understanding of how organisms develop tolerance to these chemicals and the associated trade-off expenses are largely unknown. This study aims to investigate the physiological and transcriptional mechanisms underlying the acclimation of the green microalgal model species Raphidocelis subcapitata (Selenastraceae) towards the herbicide diflufenican, and the fitness costs associated with tolerance development. Algae were exposed for 12 weeks (corresponding to 100 generations) to diflufenican at the two environmental concentrations 10 and 310 ng/L. The monitoring of growth, pigment composition, and photosynthetic performance throughout the experiment revealed an initial dose-dependent stress phase (week 1) with an EC50 of 397 ng/L, followed by a time-dependent recovery phase during weeks 2 to 4. After week 4, R. subcapitata was acclimated to diflufenican exposure with a similar growth rate, content of carotenoids, and photosynthetic performance as the unexposed control algae. This acclimation state of the algae was explored in terms of tolerance acquisition, changes in the fatty acids composition, diflufenican removal rate, cell size, and changes in mRNA gene expression profile, revealing potential fitness costs associated with acclimation, such as up-regulation of genes related to cell division, structure, morphology, and reduction of cell size. Overall, this study demonstrates that R. subcapitata can quickly acclimate to environmental but toxic levels of diflufenican; however, the acclimation is associated with trade-off expenses that result in smaller cell size.

Brillouin light scattering from quantized spin waves in nanowires with antisymmetric exchange interactions

Antisymmetric exchange interactions lead to non-reciprocal spin-wave propagation. As a result, spin waves confined in a nanostructure are not standing waves; they have a time-dependent phase, because counter-propagating waves of the same frequency have different wavelengths. We report on a Brillouin light scattering (BLS) study of confined spin waves in Co/Pt nanowires with strong Dzyaloshinskii-Moriya interactions (DMI). Spin-wave quantization in narrow ($\lesssim 200$ nm width) wires dramatically reduces the frequency shift between BLS Stokes and anti-Stokes lines associated with the scattering of light incident transverse to the nanowires. In contrast, the BLS frequency shift associated with the scattering of spin waves propagating along the nanowire length is independent of nanowire width. A model that considers the chiral nature of modes captures this physics and predicts a dramatic reduction in frequency shift of light scattered from higher energy spin waves in narrow wires, which is confirmed by our experiments.

Continuity of the attractors in time-dependent spaces and applications

In this paper, we investigate the continuity of the attractors in time-dependent phase spaces. (i) We establish two abstract criteria on the upper semicontinuity and the residual continuity of the pullback D-attractor with respect to the perturbations, and an equivalence criterion between their continuity and the pullback equi-attraction, which generalize the continuity theory of attractors developed recently in [27,28] to that in time-dependent spaces. (ii) We propose the notion of pullback D-exponential attractor, which includes the notion of time-dependent exponential attractor [33] as its spacial case, and establish its existence and Hölder continuity criterion via quasi-stability method introduced originally by Chueshov and Lasiecka [12,13]. (iii) We apply above-mentioned criteria to the semilinear damped wave equations with perturbed time-dependent speed of propagation: ϵρ(t)utt+αut−Δu+f(u)=g, with perturbation parameter ϵ∈(0,1], to realize above mentioned continuity of pullback D and D-exponential attractors in time-dependent phase spaces, and the method developed here allows to overcome the difficulty of the hyperbolicity of the model. These results deepen and extend recent theory of attractors in time-dependent spaces in literatures [15,20,29].

Numerical investigation of the melting process of gallium under inclination and partial heating

Systems based on PCM rely not only on the capacity of the system to absorb or release energy but also on the rate at which these processes are carried out. The design and optimization of thermal management systems require understanding the phase change process under different conditions. In this work, the time-dependent phase change process is studied numerically. Gallium, contained in a thin cell, is considered the working fluid. Numerical modeling is done by ANSYS Fluent in two dimensions. This model is validated against reported experimental results. Subsequently, two conditions are systematically investigated: (i) inclination, considering five angles (−45,−22.5,0,22.5, and 45°), and (ii) partial heating, considering four relative heater sizes (0.25,0.50,0.75 and 1.00). Both cases are studied for three aspect ratios (A=0.50,0.75, and 1.00). Results show that small aspect ratios and positive tilting angles could modify flow dynamics, which ultimately affects the melting process and the Nusselt number. Moreover, partial heating reduces up to 38% the melting time compared to the case in which the heat flux is distributed homogeneously along the entire length of the wall. These results could be used as guidelines to address the “rate problem” for practical applications.

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.

Time-dependent strain-tuned topological magnon phase transition

Collinear magnets in honeycomb lattices under the action of time-dependent strains are investigated. Given the limits of high-frequency periodically varying deformations, we derive an effective Floquet theory for spin systems that results in the emergence of a spin chirality. We find that the coupling between magnons and spin chirality depends on the details of the strain such as the spatial dependence and applied direction. Magnonic fluctuations about the ferromagnetic state are determined, and it is found that spatially homogeneous strains drive the magnon system into topologically protected phases. In particular, we show that certain uniform strain fields play the role of an out-of-plane nearest-neighbor Dzyaloshinskii-Moriya interaction. Furthermore, we explore the application of nonuniform strains, which lead to a confinement of magnon states that for uniaxial strains propagates along the direction that preserves translational symmetry. Our work demonstrates a direct way in which to manipulate the magnon spectrum based on time-dependent strain engineering that is relevant for exploring topological transitions in quantum magnonics.

Stochastic resetting in a networked multiparticle system with correlated transitions

The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the possibility of modeling a wide variety of realistic systems but also leads to interesting novel phenomenology not present in reset-free cases. However, most models where stochastic resetting is studied address the case of a finite number of uncorrelated variables, commonly a single one, such as the position of non-interacting random walkers. Here we overcome this limitation by framing the process of network growth with node deletion as a stochastic resetting problem where an arbitrarily large number of degrees of freedom are coupled and influence each other, both in the resetting and non-resetting (growth) events. We find the exact, full-time solution of the model, and several out-of-equilibrium properties are characterized as function of the growth and resetting rates, such as the emergence of a time-dependent percolation-like phase transition, and first-passage statistics. Coupled multiparticle systems subjected to resetting are a necessary generalization in the theory of stochastic resetting, and the model presented herein serves as an illustrative, natural and solvable example of such a generalization.

Fully nonlinear numerical investigations on the dynamics of fluid resonance between multiple bodies in close proximity

Two-dimensional wave-induced fluid oscillations in two narrow gaps are numerically investigated in the time domain. The arbitrary-Lagrangian–Eulerian finite element model for free-surface flow problems is implemented based on the fully nonlinear potential flow theory. The aim of this study is to study the dynamic evolutions of gap resonance problems with focusing on both the initial transient and the final quasi-steady states, especially for the piston-mode oscillations of fluid bulk in multiple gaps that generally involve multiple response components and the nonlinear dynamic interactions between them. The transient and quasi-steady responses are examined through amplitude and phase analyses. The radiation damping and the time-dependent period-averaged phase adjustment are demonstrated to play significant roles in establishing the dynamic equilibrium process from the transient state to the quasi-steady state. The characteristics of the intrinsic synchronization modes of the quasi-steady oscillations allow us to derive the simplified formulas to predict the resonant and anti-resonant frequencies of the two-gaps system (two degrees-of-freedom) based on a simplified model of one degree-of-freedom. The predictive formulas provide useful insights into the dependence of resonant/anti-resonant frequencies on the relevant geometries of floating bodies. Significant nonlinear hardening stiffness behaviors of fluid responses between multiple bodies in close proximity are further demonstrated by different incident wave amplitudes. The effects of incident wave amplitudes on the amplitudes of responses and higher order harmonics are found to be highly dependent on the frequency bands. The contributions of the higher-order harmonics on the overall responses are explained utilizing the Fourier transformations analysis.

On-chip generation and dynamic piezo-optomechanical rotation of single photons

Integrated photonic circuits are key components for photonic quantum technologies and for the implementation of chip-based quantum devices. Future applications demand flexible architectures to overcome common limitations of many current devices, for instance the lack of tuneabilty or built-in quantum light sources. Here, we report on a dynamically reconfigurable integrated photonic circuit comprising integrated quantum dots (QDs), a Mach-Zehnder interferometer (MZI) and surface acoustic wave (SAW) transducers directly fabricated on a monolithic semiconductor platform. We demonstrate on-chip single photon generation by the QD and its sub-nanosecond dynamic on-chip control. Two independently applied SAWs piezo-optomechanically rotate the single photon in the MZI or spectrally modulate the QD emission wavelength. In the MZI, SAWs imprint a time-dependent optical phase and modulate the qubit rotation to the output superposition state. This enables dynamic single photon routing with frequencies exceeding one gigahertz. Finally, the combination of the dynamic single photon control and spectral tuning of the QD realizes wavelength multiplexing of the input photon state and demultiplexing it at the output. Our approach is scalable to multi-component integrated quantum photonic circuits and is compatible with hybrid photonic architectures and other key components for instance photonic resonators or on-chip detectors.

Emergence and manipulation of non-equilibrium Yu-Shiba-Rusinov states

The experimental advances in the study of time-dependent phenomena has opened a new path to investigating the complex electronic structure of strongly correlated and topological materials. Yu-Shiba-Rusinov (YSR) states induced by magnetic impurities in s-wave superconductors provide an ideal candidate system to study the response of a system to time-dependent manipulations of the magnetic environment. Here, we show that by imposing a time-dependent change in the magnetic exchange coupling, by changing the relative alignment of magnetic moments in an impurity dimer, or through a periodic drive of the impurity moment, one can tune the system through a time-dependent quantum phase transition, in which the system undergoes a transition from a singlet to a doublet ground state. We show that the electronic response of the system to external perturbations can be imaged through the time-dependent differential conductance, dI(t)/dV, which, in analogy to the equilibrium case, is proportional to a non-equilibrium local density of states. Our results open the path to visualizing the response of complex quantum systems to time-dependent external perturbations.

An NMR Study on Hydration and Molecular Interaction of Phytantriol-Based Liquid Crystals.

Phytantriol-based lyotropic liquid crystals (LLCs) have emerged as a new nanodrug delivery system. However, the understanding of phytantriol-based LLCs is lacking. In this study, we use NMR technology to characterize LLC formation over two months. Three samples in different phases were prepared with different hydration states. NMR data, including 1D-1H, 13C-{1H}, 2D-HSQC, HMBC, COSY, NOESY, etc., were collected. A comprehensive analysis of these NMR data was performed on the three phases of phytantriol-based LLCs. The following results were achieved from the study. First, the 1H and 13C-{1H} spectra of phytantriol were assigned. Second, the change of NMR spectra during the formation of the phases was observed, and the change of hydration was calculated for the time-dependent phase formation. Third, the correlation peaks of 2D-NOESY were used to describe the spatial relationship of lipids-water interaction and lipid-lipid interaction.

Bounds on gravitational brane couplings and tomography in AdS3 black hole microstates

We study information theoretic properties of planar black hole microstates in 2 + 1 dimensional asymptotically anti-de Sitter spacetime, modeled by black holes with an end-of-the-world brane behind the horizon. The von Neumann entropy of sufficiently large subregions in the dual CFT exhibits a time-dependent phase, which from a doubly-holographic perspective corresponds to the appearance of quantum extremal islands in the brane description. Considering the case where dilaton gravity is added to the brane, we show that tuning the associated couplings affects the propagation of information in the dual CFT state. By requiring that information theoretic bounds on the growth of entanglement entropy are satisfied in the dual CFT, we can place bounds on the allowed values of the couplings on the brane. Furthermore, we initiate the study of brane tomography, by showing how subleading corrections to the entanglement velocity can be used to learn about the properties of the brane as well as any gravitational dynamics localized on it.

Operator complexity for quantum scalar fields and cosmological perturbations

We calculate the operator complexity for the displacement, squeeze and rotation operators of a quantum harmonic oscillator, assuming equal computational cost for the corresponding fundamental gates. The complexity of the time-dependent displacement operator is constant, equal to the magnitude of the coherent state parameter, while the complexity of unitary evolution by a generic quadratic Hamiltonian is proportional to the amount of squeezing and is sensitive to the time-dependent phase of the unitary operator. We apply these results to study the complexity of a free massive scalar field, finding that the complexity has a period of rapid linear growth followed by a saturation determined by the UV cutoff and the number of spatial dimensions. We also study the complexity of the unitary evolution of quantum cosmological perturbations in de Sitter space, which can be written as time-dependent squeezing and rotation operators on individual Fourier mode pairs. The complexity of a single mode pair at late times grows linearly with the number of $e$-folds, while the complexity at early times oscillates rapidly due to the sensitivity of operator complexity to the phase of unitary time evolution. Integrating over all modes, the total complexity of cosmological perturbations scales as the square root of the (exponentially) growing volume of de Sitter space, suggesting that inflation leads to an explosive growth in complexity of the Universe.

Backflow-assisted time-resolved phase modulation in nematic liquid crystal Pi-Cells

By monitoring the time-dependent phase modulation behavior, we demonstrate the benefits of backflow on the phase modulation depth of nematic liquid crystal (LC) pi-cells in comparison to the phase modulation observed for other nematic LC device configurations. Specifically, results are presented for the time-resolved phase modulation of three different nematic LC device configurations under a range of electric field conditions: pi-cell (parallel-rubbed alignment layers), Fréedericksz cell (anti-parallel rubbed alignment layers), and a hybrid aligned nematic (HAN) device. The time-dependent behavior is obtained experimentally with a Michelson interferometer with a piezoelectric scanning mirror in the reference arm, which provides a continuous phase ramp in the reference signal. By recording the interference signal intensity, it is then possible to extract the change in optical phase as a function of time. It is shown that both the pi-cell and Fréedericksz cell exhibit a modulation that is greater than π radians for a double-pass configuration (2π radians for a four-pass configuration), with the lowest voltage amplitude corresponding to π phase modulation being observed for the pi-cell. Through the time-resolved response, it is shown that the presence of backflow hinders the dynamic phase response of the Fréedericksz device but does not negatively impact the behavior of the pi-cell. These results are found to be in good agreement with simulations of the phase modulation for the three nematic devices when backflow is taken into consideration.

Parrondo’s Paradox for Discrete-Time Quantum Walks in Momentum Space

We investigate the possibility of implementing a sequence of quantum walks whose probability distributions give an overall positive winning probability, while it is negative for the single walks (Parrondo’s paradox). In particular, we have in mind an experimental realization with a Bose–Einstein condensate in which the walker’s space is momentum space. Experimental problems in the precise implementation of the coin operations for our discrete-time quantum walks are analyzed in detail. We study time-dependent phase fluctuations of the coins as well as perturbations arising from the finite momentum width of the condensate. We confirm the visibility of Parrondo’s paradox for experimentally available time scales of up to a few hundred steps of the walk.