Time Scaling Research Articles

Multiparticle Quantum Walks and Fisher Information in One-Dimensional Lattices.

Recent experiments on quantum walks (QWs) demonstrated a full control over the statistics-dependent walks of single particles and two particles in one-dimensional lattices. However, little is known about the general characterization of QWs at the many-body level. Here, we rigorously study QWs, Bloch oscillations, and the quantum Fisher information for three indistinguishable bosons and fermions in one-dimensional lattices using a time-evolving block decimation algorithm and many-body perturbation theory. We show that such strongly correlated QWs not only give rise to statistics-and-interaction-dependent ballistic transports of scattering states and of two- and three-body bound states but also allow a quantum enhanced precision measurement of the gravitational force. In contrast to the QWs of the fermions, the QWs of three bosons exhibit strongly correlated Bloch oscillations, which present a surprising time scaling t^{3} of the Fisher information below a characteristic time t_{0} and saturate to the fundamental limit of t^{2} for t>t_{0}.

Quantum sampling algorithms, phase transitions, and computational complexity

Drawing independent samples from a probability distribution is an important computational problem with applications in Monte Carlo algorithms, machine learning, and statistical physics. The problem can in principle be solved on a quantum computer by preparing a quantum state that encodes the entire probability distribution followed by a projective measurement. We investigate the complexity of adiabatically preparing such quantum states for the Gibbs distributions of various classical models including the Ising chain, hard-sphere models on different graphs, and a model encoding the unstructured search problem. By constructing a parent Hamiltonian, whose ground state is the desired quantum state, we relate the asymptotic scaling of the state preparation time to the nature of transitions between distinct quantum phases. These insights enable us to identify adiabatic paths that achieve a quantum speedup over classical Markov chain algorithms. In addition, we show that parent Hamiltonians for the problem of sampling from independent sets on certain graphs can be naturally realized with neutral atoms interacting via highly excited Rydberg states.

Bi-Fo time scaling method in the numerical simulation of transient conjugate heat transfer

Reliable transient thermal analysis plays a very important role in the engine safety analysis. Transient conjugate heat transfer simulation is an important way of temperature analysis. But there exists a great disparity in the time scales between solid conduction and fluid convection. The calculation cost of transient conjugate heat transfer analysis is very huge because of the tiny time step of computational fluid dynamics. The Bi-Fo time scaling method is proposed to improve the computational efficiency of transient conjugate heat transfer. On the one hand, this method carries out a similar transformation on solid heat conduction, scaling the calculation time with the product of density and specific heat capacity to maintain the consistency of Fourier number. On the other hand, it takes very short time for the fluid domain to recover stability after a boundary disturbance. Based on the above characteristic, the flow time is directly compressed to the same as that of the solid domain. It is verified by Mark Ⅱ vane that increasing the solid thermal diffusivity can reduce the time scale of heat conduction. In the situation of rapidly stable flow field, scaling flow time does not affect the solid thermal boundary under corresponding dimensionless time. Within the application scope, the Bi-Fo time scaling method can greatly reduce the time cost of transient conjugate heat transfer simulation while maintaining the accuracy of transient temperature analysis.

A Computational Approach to Optimal Control Problems with Almost Smooth Controls

In this paper, we consider a class of optimal control problems involving continuous control and state inequality constraints where the control is almost smooth. We first employ the control parametrization technique via approximating the control signal by a piecewise linear function. Then, we develop a time scaling transformation procedure for transforming the approximate problem into an equivalent problem that can be solved readily using conventional methods. On this basis, a novel exact penalty function method is constructed by appending penalized constraint violations to the cost function. The gradient formulas and convergent properties ensure that the transformed unconstrained optimal parameter selection problems can be solved by existing optimization algorithms or software packages. Finally, an example is solved showing the effectiveness and applicability of the approach proposed.

Scaling of rise time of drive current on development of magneto-Rayleigh-Taylor instabilities for single-shell Z-pinches

In fast Z-pinches, rise time of drive current plays an important role in development of magneto-Rayleigh-Taylor(MRT) instabilities. It is essential for applications of Z-pinch dynamic hohlraum (ZPDH), which could be used for drivinginertial confinement fusion (ICF), to understand the scaling of rise time on MRTs. Therefore, a theoretical model for nonlinear development of MRTs is developed according to the numerical analysis. It is found from the model that the implosion distance L = r 0 – r mc determines the development of MRTs, where r 0 is the initial radius and r mc is the position of the accelerating shell. The current rise time τ would affect the MRT development because of its strong coupling with the r 0. The amplitude of MRTs would increase with the rise time linearly if an implosion velocity is specified. The effects of the rise time on MRT, in addition, are studied by numerical simulation. The results are consistent with those of the theoretical model very well. Finally, the scaling of the rise time on amplitude of MRTs is obtained for a specified implosion velocity by the theoretical model and numerical simulations.

Convergence rates in zero-relaxation limits for Euler-Maxwell and Euler-Poisson systems

It was proved that Euler-Maxwell systems converge globally-in-time to drift-diffusion systems in a slow time scaling, as the relaxation time goes to zero. The convergence was established to the Cauchy problem with smooth periodic initial data sufficiently close to constant equilibrium states. In this paper, we establish error estimates between smooth periodic solutions of Euler-Maxwell systems and those of drift-diffusion systems. Similar error estimates are also obtained for Euler-Poisson systems in place of Euler-Maxwell systems. The proof of these results uses stream function techniques together with energy estimates.

Improved neoclassical plasma confinement and turbulence suppression in a magnetic well in tokamak reactors

It has been known that the width of the trapped particles, i.e. bananas, is reduced or squeezed in a magnetic well in tokamaks. The magnetic squeezing factor S B depends on the energy and pitch angle of the particles. When ρ p/a ∼ 1, S B becomes appreciably larger than unity; it can be of the order of 2 for a parabolic well with B −1 d2 B/dr 2 ∼ 2a −2. Here, ρ p is the poloidal gyro-radius, B is the magnetic field strength, r is the local minor radius, and a is the minor radius. However, the real orbit width measured in terms of the poloidal magnetic flux is still less than a because of the magnetic squeezing; for S B = 2, it is a 30% reduction. The transport consequences of the squeezed bananas in a magnetic well are calculated by solving the drift kinetic equation utilizing the constants of motion in the large aspect ratio limit. Consequently, neoclassical ion heat conductivity χ h in the reactor relevant collisionality regime (i.e. banana regime) is reduced by a factor of ; for S B = 2, it is almost a factor of three reduction for the same temperature. The ion temperature scaling of χ h improves from the conventional, and weakly favorable scaling to the strongly favorable scaling for high temperature fusion grade tokamak plasmas; the scaling however does not take the temperature dependence of the magnetic well itself into account. Here, T i is the ion temperature. In addition, it is shown that plasma turbulence is suppressed in a magnetic well using the reduced decorrelation time argument and anomalous plasma confinement is improved. The combined improvements result in a favorable temperature scaling in the ion energy confinement time, and make burning aneutronic fuels feasible. The implications on a tokamak with a magnetic well as a fusion reactor are discussed.

Stationary distribution convergence of the offered waiting processes in heavy traffic under general patience time scaling

We study a sequence of single server queues with customer abandonment (\(GI/GI/1+GI\)) under heavy traffic. The patience time distributions vary with the sequence, which allows for a wider scope of applications. It is known Lee and Weerasinghe (Stochastic Process Appl 121(11):2507–2552, 2011) and Reed and Ward (Math Oper Res 33(3):606–644, 2008) that the sequence of scaled offered waiting time processes converges weakly to a reflecting diffusion process with nonlinear drift, as the traffic intensity approaches one. In this paper, we further show that the sequence of stationary distributions and moments of the offered waiting times, with diffusion scaling, converge to those of the limit diffusion process. This justifies the stationary performance of the diffusion limit as a valid approximation for the stationary performance of the \(GI/GI/1+GI\) queue. Consequently, we also derive the approximation for the abandonment probability for the \(GI/GI/1+GI\) queue in the stationary state.

Graphon-valued stochastic processes from population genetics

The goal of this paper is to construct a natural class of graphon-valued processes arising from population genetics. We consider finite populations where individuals carry one of finitely many genetic types and change type according to Fisher–Wright resampling. At any time, each pair of individuals is linked by an edge with a probability that is given by a type-connection matrix, whose entries depend on the current types of the two individuals and on the current empirical type distribution of the entire population via a fitness function. We show that, in the large-population-size limit and with an appropriate scaling of time, the evolution of the associated adjacency matrix converges to a random process in the space of graphons, driven by the type-connection matrix and the underlying Fisher–Wright diffusion on the multi-type simplex. In the limit as the number of types tends to infinity, the limiting process is driven by the type-connection kernel and the underlying Fleming–Viot diffusion.

Isotope effects on transport in LHD

Isotope effects are one of the most important issues for predicting future reactor operations. Large helical device (LHD) is the presently working largest stellarator/helical device using super conducting helical coils. In LHD, deuterium experiments started in 2017. Extensive studies regarding isotope effects on transport have been carried out. In this paper, the results of isotope effect studies in LHD are reported. The systematic studies were performed adjusting operational parameters and nondimensional parameters. In L mode like normal confinement plasma, where internal and edge transport barriers are not formed, the scaling of global energy confinement time (τ E) with operational parameters shows positive mass dependence (M 0.27; where M is effective ion mass) in electron cyclotron heating plasma and no mass dependence (M 0.0) in neutral beam injection heating plasma. The non-negative ion mass dependence is anti-gyro-Bohm scaling. The role of the turbulence in isotope effects was also found by turbulence measurements and gyrokinetic simulation. Better accessibility to electron and ion internal transport barrier (ITB) plasma is found in deuterium (D) plasma than in hydrogen (H). Gyro kinetic non-linear simulation shows reduced ion heat flux due to the larger generation of zonal flow in deuterium plasma. Peaked carbon density profile plays a prominent role in reducing ion energy transport in ITB plasma. This is evident only in plasma with deuterium ions. New findings on the mixing and non-mixing states of D and H particle transports are reported. In the mixing state, ion particle diffusivities are higher than electron particle diffusivities and D and H ion density profiles are almost identical. In the non-mixing state, ion particle diffusivity is much lower than electron diffusivity. Deuterium and hydrogen ion profiles are clearly different. Different turbulence structures were found in the mixing and non-mixing states suggesting different turbulence modes play a role.

A scheduling policy to save 10% of communication time in parallel fast Fourier transform

SummaryThe fast Fourier transform (FFT) has applications in almost every frequency related study, for example, in image and signal processing, and radio astronomy. It is also used as a Poisson operator inversion kernel in partial differential equations in fluid flows, in density functional theory, many‐body theory, and others. The three‐dimensional FFT has large time complexity . Hence, parallelization is used to compute such FFTs. Popular libraries perform slab division or pencil decomposition of data. None of the existing libraries achieve perfect inverse scaling of time with cores because FFT requires all‐to‐all communication and clusters hitherto do not have physical all‐to‐all connections. Dragonfly, one of the popular topologies for the interconnect, supports hierarchical connections among the components. We show that if we align the all‐to‐all communication of FFT with the physical connections of Dragonfly topology we will achieve a better scaling and reduce communication time.

Unsteady dynamics in the streamwise-oscillating cylinder wake for forcing frequencies below lock-on

Forcing a cylinder in the streamwise direction with a frequency much lower than the stationary shedding frequency significantly alters wake dynamics. During certain portions of the forcing cycle the wake resembles that of a stationary cylinder, while in others it exhibits strong unsteadiness. Although a range of flow phenomena are observed, it is shown that a novel time scaling framework can be used to relate the forced and unforced systems.

Experimental investigation of solute transport in variably saturated porous media using x-ray computed tomography

Solute transport through variably saturated porous media is ubiquitous in multiple subsurface flows, piquing the geoscience community's interest. This study adopts a novel experimental approach using microfocus x-ray computed tomography for real-time imaging of a three-dimensional NaI tracer plume in a partially saturated packing column. A stabilized two-phase flow field is achievable through continuous co-injection of two-phase fluids: NaCl solvent and pump oil. Thus, the critical role of the NaCl saturation Sw and Péclet number on dispersion can be fully studied by controlling the NaCl fractional flow rate and the total flow rate from the Buckley–Leverett theory. Furthermore, we study solute transport behavior based on statistical moments, the dispersion coefficient, the dilution index, and the mean scalar dissipation rate. Experimental results indicate that the solute transport is Fickian for high Sw ≥ 0.34. In contrast, anomalous transport behavior is found for Sw < 0.34, where the concentration distribution is initially left-tailed and leptokurtic before reaching a well-dispersed regime. The dispersion coefficient is 2–10 times larger for partially saturated cases compared with the fully saturated case and shows a non-monotonical dependency on Sw. Finally, the analysis of the dilution index indicates that the overall mixing strength increases when Sw decreases, whereas the mean scalar dissipation rate reveals that the time scaling of transverse mixing is the largest at an intermediate Sw. The results can be used to elucidate the solute transport behavior in a two-phase system.

Fractional dynamics with non-local scaling

Nonlinear fractional dynamics with scale invariance in continuous and discrete time approaches are described. We use non-integer-order integro-differential operators that can be interpreted as generalizations of scaling (dilation) differential operator for the case of non-locality. Nonlinear integro-differential equations with Hadamard type operators of non-integer orders with respect to time and periodic sequence of kicks are considered. Exact solutions of these equations are derived without using approximations. Using these solutions for discrete time points, we derive mappings with non-local scaling in time from proposed equations without approximation. Non-local mappings are obtained in general for arbitrary orders of the Hadamard type fractional operators. An example of these mappings with non-local scaling in time is given for arbitrary positive orders of integro-differential equations with kicks. The proposed mappings are independent of the period of kicks at zero initial conditions. The proposed approach can be used to describe the nonlinear fractional dynamics that is characterized by scale invariance.

Fast Convergence of Dynamical ADMM via Time Scaling of Damped Inertial Dynamics

In this paper, we propose in a Hilbertian setting a second-order time-continuous dynamic system with fast convergence guarantees to solve structured convex minimization problems with an affine constraint. The system is associated with the augmented Lagrangian formulation of the minimization problem. The corresponding dynamics brings into play three general time-varying parameters, each with specific properties, and which are, respectively, associated with viscous damping, extrapolation and temporal scaling. By appropriately adjusting these parameters, we develop a Lyapunov analysis which provides fast convergence properties of the values and of the feasibility gap. These results will naturally pave the way for developing corresponding accelerated ADMM algorithms, obtained by temporal discretization.

Impact of the activation rate of the hyperpolarization- activated current $$\hbox {I}_{\mathrm{h}}$$ on the neuronal membrane time constant and synaptic potential duration

The temporal dynamics of membrane voltage changes in neurons is controlled by ionic currents. These currents are characterized by two main properties: conductance and kinetics. The hyperpolarization-activated current ($I_{\rm h}$) strongly modulates subthreshold potential changes by shortening the excitatory postsynaptic potentials and decreasing their temporal summation. Whereas the shortening of the synaptic potentials caused by the $I_{\rm h}$ conductance is well understood, the role of the $I_{\rm h}$ kinetics remains unclear. Here, we use a model of the $I_{\rm h}$ current model with either fast or slow kinetics to determine its influence on the membrane time constant ($\tau_m$) of a CA1 pyramidal cell model. Our simulation results show that the $I_{\rm h}$ with fast kinetics decreases $\tau_m$ and attenuates and shortens the excitatory postsynaptic potentials more than the slow $I_{\rm h}$. We conclude that the $I_{\rm h}$ activation kinetics is able to modulate $\tau_m$ and the temporal properties of excitatory postsynaptic potentials (EPSPs) in CA1 pyramidal cells. In order to elucidate the mechanisms by which $I_{\rm h}$ kinetics controls $\tau_m$, we propose a new concept called "time scaling factor". Our main finding is that the $I_{\rm h}$ kinetics influences $\tau_m$ by modulating the contribution of the $I_{\rm h}$ derivative conductance to $\tau_m$.

356-P: Population Pharmacokinetic Modeling of Dasiglucagon in Subjects with Type 1 Diabetes Mellitus

To quantify the impact of subject covariates on pharmacokinetics (PK) of the novel, ready-to-use glucagon analog dasiglucagon, we developed a population PK model. Dasiglucagon pharmacokinetics was dose linear in the tested dose range (0.1 to 1.0 mg) and described by a 1-compartment model with first-order absorption and elimination, including an absorption lag time and standard allometric scaling by body weight. The final model included injection site, age as covariates on bioavailability, and MDRD eGFR and sex as covariates on apparent clearance and absorption rate constant, respectively. The model also accounted for reduced drug content at end of shelf-life storage. Based on visual predictive checks the model reliably predicted observed data. The effect of covariates on dasiglucagon exposure measured by area under the concentration time curve (AUC) are shown in the figure below (predicted [95% CI]). AUCs are relative to the AUC predicted for a typical subject aged ≥ 24 years, weighing 78 kg with normal kidney function (eGFR 95 mL/min/1.73m2) and receiving a 0.6 mg dose of dasiglucagon in the abdomen. The model-predicted effects of PK covariates on dasiglucagon AUC generally fell within the observed AUC from the analysis population receiving 0.6 mg dasiglucagon (red markers, median, and 5th-95th percentile interval, n = 321) and observed across the trials to result in reliable recovery from hypoglycemia.View largeDownload slideView largeDownload slide DisclosureC. B. Knudsen: Employee; Self; Zealand Pharma A/S, Employee; Spouse/Partner; Novo Nordisk A/S, Stock/Shareholder; Self; Zealand Pharma A/S, Stock/Shareholder; Spouse/Partner; Novo Nordisk A/S. A. H. Valeur: Employee; Self; Zealand Pharma A/S. S. Maarbjerg: Employee; Self; Zealand Pharma A/S, Employee; Spouse/Partner; Zealand Pharma A/S, Stock/Shareholder; Self; Novo Nordisk A/S, Stock/Shareholder; Spouse/Partner; Zealand Pharma A/S. R. Tehranchi: Employee; Self; Zealand Pharma A/S. P. Diderichsen: Consultant; Self; Boehringer Ingelheim International GmbH, Zealand Pharma A/S, Employee; Self; Certara Netherlands bv. H. Witjes: Employee; Self; Certara.

Wavelength scaling of electron collision time in plasma for strong field laser-matter interactions in solids

Although the dielectric constant of plasma depends on electron collision time as well as wavelength and plasma density, experimental studies on the electron collision time and its effects on laser-matter interactions are lacking. Here, we report an anomalous regime of laser-matter interactions generated by wavelength dependence (1.2–2.3 µm) of the electron collision time in plasma for laser filamentation in solids. Our experiments using time-resolved interferometry reveal that electron collision times are small (<1 femtosecond) and decrease as the driver wavelength increases, which creates a previously-unobserved regime of light defocusing in plasma: longer wavelengths have less plasma defocusing. This anomalous plasma defocusing is counterbalanced by light diffraction which is greater at longer wavelengths, resulting in almost constant plasma densities with wavelength. Our wavelength-scaled study suggests that both the plasma density and electron collision time should be systematically investigated for a better understanding of strong field laser-matter interactions in solids.

One and Two-Step In Vitro-In Vivo Correlations Based on USP IV Dynamic Dissolution Applied to Four Sodium Montelukast Products.

Montelukast is a weak acid drug characterized by its low solubility in the range of pH 1.2 to 4.5, which may lead to dissolution-limited absorption. The aim of this paper is to develop an in vivo predictive dissolution method for montelukast and to check its performance by establishing a level-A in vitro-in vivo correlation (IVIVC). During the development of a generic film-coated tablet formulation, two clinical trials were done with three different experimental formulations to achieve a similar formulation to the reference one. A dissolution test procedure with a flow-through cell (USP IV) was used to predict the in vivo absorption behavior. The method proposed is based on a flow rate of 5 mL/min and changes of pH mediums from 1.2 to 4.5 and then to 6.8 with standard pharmacopoeia buffers. In order to improve the dissolution of montelukast, sodium dodecyl sulfate was added to the 4.5 and 6.8 pH mediums. Dissolution profiles in from the new method were used to develop a level-A IVIVC. One-step level-A IVIVC was developed from dissolution profiles and fractions absorbed obtained by the Loo–Riegelman method. Time scaling with Levy’s plot was necessary to achieve a linear IVIVC. One-step differential equation-based IVIVC was also developed with a time-scaling function. The developed method showed similar results to a previously proposed biopredictive method for montelukast, and the added value showed the ability to discriminate among different release rates in vitro, matching the in vivo clinical bioequivalence results.

An Encryption Architecture Suitable for on Chip Integration With Sensors

This paper demonstrates a hardware encryption algorithm that can be integrated directly with sensors on the same chip. In contrast to using power-hungry microprocessors and software implementations, the encryption algorithm was based on a Lorenz chaotic system and was implemented as time scaling chaotic shift keying (TS-CSK). The coupled differential equations of TS-CSK were implemented using low power integrators, multiplexers, switches, and passive components. Both a single-ended and differential system was developed. The single-ended based system showed no oscillation, while the differential based system demonstrated oscillation. Experimental measurements of the differential system with an integrated temperature sensor demonstrated the ability to encrypt and decrypt the transmitted signal. The differential encryption/decryption system was implemented in 180 nm technology and operated with a 1.8 V power supply and 1.5 mW of power.