arXiv subjects

Yu-Chen Cheng

Publications and source records attributed to Yu-Chen Cheng.

17 recordsLinked to original sources

arXiv2026

A low-dissipation central scheme for ideal MHD

Central schemes for conservation laws are Riemann solver free methods which are simple and easy to implement. In recent work for Euler equations [Kurganov & Xin, J. Sci. Comput., 96:56, 2023] their accuracy has been enhanced in terms of better resolution of contact waves. In this paper, we extend this low dissipation central upwind method to the ideal MHD system in one- and two-dimensions. In the two-dimensional case, we separate the variables into two groups: hydrodynamic and magnetic, which are stored at cell centers and faces, respectively. For the the hydrodynamic variables, we apply the low dissipation central upwind scheme while for the magnetic variables, a constrained transport method is used which maintains the divergence-free property of the magnetic field. The time integration is performed with third order strong stability preserving Runge-Kutta scheme. To validate the proposed scheme, we apply this method to several challenging test cases. The results show that the LDCU correction term plays a useful role at the contact discontinuity and enhances the resolution of waves. We also observe experimental second-order accuracy for smooth solutions and the divergence-free condition is maintained to machine precision.

math.NA↗

arXiv2024

Enhancing Distractor Generation for Multiple-Choice Questions with Retrieval Augmented Pretraining and Knowledge Graph Integration

In this paper, we tackle the task of distractor generation (DG) for multiple-choice questions. Our study introduces two key designs. First, we propose \textit{retrieval augmented pretraining}, which involves refining the language model pretraining to align it more closely with the downstream task of DG. Second, we explore the integration of knowledge graphs to enhance the performance of DG. Through experiments with benchmarking datasets, we show that our models significantly outperform the state-of-the-art results. Our best-performing model advances the F1@3 score from 14.80 to 16.47 in MCQ dataset and from 15.92 to 16.50 in Sciq dataset.

cs.CL↗

arXiv2024

WENDY: Covariance Dynamics Based Gene Regulatory Network Inference

Determining gene regulatory network (GRN) structure is a central problem in biology, with a variety of inference methods available for different types of data. For a widely prevalent and challenging use case, namely single-cell gene expression data measured after intervention at multiple time points with unknown joint distributions, there is only one known specifically developed method, which does not fully utilize the rich information contained in this data type. We develop an inference method for the GRN in this case, netWork infErence by covariaNce DYnamics, dubbed WENDY. The core idea of WENDY is to model the dynamics of the covariance matrix, and solve this dynamics as an optimization problem to determine the regulatory relationships. To evaluate its effectiveness, we compare WENDY with other inference methods using synthetic data and experimental data. Our results demonstrate that WENDY performs well across different data sets.

q-bio.MN↗

arXiv2024

A Well-Balanced Method for an Unstaggered Central Scheme, the two-space Dimensional Case

We develop a second-order accurate central scheme for the two-dimensional hyperbolic system of in-homogeneous conservation laws. The main idea behind the scheme is that we combine the well-balanced deviation method with the Kurganov-Tadmor (KT) scheme. The approach satisfies the well-balanced property and retains the advantages of KT scheme: Riemann-solver-free and the avoidance of oversampling on the regions between Riemann-fans. The scheme is implemented and applied to a number of numerical experiments for the Euler equations with gravitational source term and the results are non-oscillatory. Based on the same idea, we construct a semi-discrete scheme where we combine the above two methods and illustrate the maximum principle.

math.NA↗

arXiv2024

A Well-Balanced Method for an Unstaggered Central Scheme, the one-space Dimensional Case

In this paper, we propose a new MUSCL scheme by combining the ideas of the Kurganov and Tadmor scheme and the so-called Deviation method which results in a well-balanced finite volume method for the hyperbolic balance laws, by evolving the difference between the exact solution and a given stationary solution. After that, we derive a semi-discrete scheme from this new scheme and it can be shown to be essentially TVD when applied to a scalar conservation law. In the end, we apply and validate the developed methods by numerical experiments and solve classical problems featuring Euler equations with gravitational source term.

math.NA↗

arXiv2022

Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems

We describe a numerical algorithm for approximating the equilibrium-reduced density matrix and the effective (mean force) Hamiltonian for a set of system spins coupled strongly to a set of bath spins when the total system (system+bath) is held in canonical thermal equilibrium by weak coupling with a "super-bath". Our approach is a generalization of now standard typicality algorithms for computing the quantum expectation value of observables of bare quantum systems via trace estimators and Krylov subspace methods. In particular, our algorithm makes use of the fact that the reduced system density, when the bath is measured in a given random state, tends to concentrate about the corresponding thermodynamic averaged reduced system density. Theoretical error analysis and numerical experiments are given to validate the accuracy of our algorithm. Further numerical experiments demonstrate the potential of our approach for applications including the study of quantum phase transitions and entanglement entropy for long-range interaction systems.

quant-ph↗

arXiv2021

Generalized Boltzmann distributions for systems strongly coupled to large finite bath -- a microcanonical approach

The theory of probability shows that, as the fraction $X_n/Y\to 0$, the conditional probability for $X_n$, given $X_n+Y \in h_δ:=[h, h+δ]$, has a limit law $f_{X_n}(x)e^{-ψ_n(h_δ)x}$, where $ψ_n(h_δ) $ equals to $[\partial \ln P(Y \in y_δ)/\partial y]_{y=h}$ plus an additional term, contributed from the correlation between $X_n$ and bath $Y$. By applying this limit law to an isolated composite system consisting of two strongly coupled parts, a system of interest and a large but finite bath, we derive the generalized Boltzmann distribution law for the system of interest in the exponential form of a redefined Hamiltonian and corrected Boltzmann temperature that reflects the modification due to strong system-bath coupling and the large but finite bath.

math-ph↗

arXiv2021

Potentials of Continuous Markov Process and Random Perturbations

With a scalar potential and a bivector potential, the vector field associated with the drift of a diffusion is decomposed into a generalized gradient field, a field perpendicular to the gradient, and a divergence-free field. We give such decomposition a probabilistic interpretation by introducing cycle velocity from a bivectorial formalism of nonequilibrium thermodynamics. New understandings on the mean rates of thermodynamic quantities are presented. Deterministic dynamical system is further proven to admit a generalized gradient form with the emerged potential as the Lyapunov function by the method of random perturbations.

cond-mat.stat-mech↗

arXiv2020

Asymptotic Behavior of a Sequence of Conditional Probability Distributions and the Canonical Ensemble

The probability distribution of a function of a subsystem conditioned on the value of the function of the whole, in the limit when the ratio of their values goes to zero, has a limit law: It equals the unconditioned marginal probability distribution weighted by an exponential factor whose exponent is uniquely determined by the condition. We apply this theorem to explain the canonical equilibrium ensemble of a system in contact with a heat reservoir. Since the theorem only requires analysis at the level of the function of the subsystem and reservoir, it is applicable even without the knowledge of the composition of the reservoir itself, which extends the applicability of the canonical ensemble. Furthermore, we generalize our theorem to a model with strong interaction that contributes an additional term to the exponent, which is beyond the typical case of approximately additive functions. This result is new in both physics and mathematics, as a theory for the Gibbs conditioning principle for strongly correlated systems. A corollary provides a precise formulation of what a temperature bath is in probabilistic term

math-ph↗

arXiv2020

Stochastic limit-cycle oscillations of a nonlinear system under random perturbations

Dynamical systems with $ε$ small random perturbations appear in both continuous mechanical motions and discrete stochastic chemical kinetics. The present work provides a detailed analysis of the central limit theorem (CLT), with a time-inhomogeneous Gaussian process, near a deterministic limit cycle in $\mathbb{R}^n$. Based on the theory of random perturbations of dynamical systems and the WKB approximation respectively, results are developed in parallel from both standpoints of stochastic trajectories and transition probability density and their relations are elucidated. We show rigorously the correspondence between the local Gaussian fluctuations and the curvature of the large deviation rate function near its infimum, connecting the CLT and the large deviation principle of diffusion processes. We study uniform asymptotic behavior of stochastic limit cycles through the interchange of limits of time $t\to\infty$ and $ε\to 0$. Three further characterizations of stochastic limit cycle oscillators are obtained: (i) An approximation of the probability flux near the cycle; (ii) Two special features of the vector field for the cyclic motion; (iii) A local entropy balance equation along the cycle with clear physical meanings. Lastly and different from the standard treatment, the origin of the $ε$ in the theory is justified by a novel scaling hypothesis via constructing a sequence of stochastic differential equations.

math-ph↗

arXiv2020

A high-repetition rate attosecond light source for time-resolved coincidencespectroscopy

Attosecond pulses, produced through high-order harmonic generation in gases, have been successfully used for observing ultrafast, sub-femtosecond electron dynamics in atoms, molecules and solid state systems. Today's typical attosecond sources, however, are often impaired by their low repetition rate and the resulting insufficient statistics, especially when the number of detectable events per shot is limited. This is the case for experiments where several reaction products must be detected in coincidence, and for surface science applications where space-charge effects compromise spectral and spatial resolution. In this work, we present an attosecond light source operating at 200 kHz, which opens up the exploration of phenomena previously inaccessible to attosecond interferometric and spectroscopic techniques. Key to our approach is the combination of a high repetition rate, few-cycle laser source, a specially designed gas target for efficient high harmonic generation, a passively and actively stabilized pump-probe interferometer and an advanced 3D photoelectron/ion momentum detector. While most experiments in the field of attosecond science so far have been performed with either single attosecond pulses or long trains of pulses, we explore the hitherto mostly overlooked intermediate regime with short trains consisting of only a few attosecond pulses.e also present the first coincidence measurement of single-photon double ionization of helium with full angular resolution, using an attosecond source. This opens up for future studies of the dynamic evolution of strongly correlated electrons.

physics.atom-ph↗

arXiv2020

Kinematic Basis of Emergent Energetics of Complex Dynamics

Stochastic kinematic description of a complex dynamics is shown to dictate an energetic and thermodynamic structure. An energy function $φ(x)$ emerges as the limit of the generalized, nonequilibrium free energy of a Markovian dynamics with vanishing fluctuations. In terms of the $\nablaφ$ and its orthogonal field $γ(x)\perp\nablaφ$, a general vector field $b(x)$ can be decomposed into $-D(x)\nablaφ+γ$, where $\nabla\cdot\big(ω(x)γ(x)\big)=$ $-\nablaωD(x)\nablaφ$. The matrix $D(x)$ and scalar $ω(x)$, two additional characteristics to the $b(x)$ alone, represent the local geometry and density of states intrinsic to the statistical motion in the state space at $x$. $φ(x)$ and $ω(x)$ are interpreted as the emergent energy and degeneracy of the motion, with an energy balance equation $dφ(x(t))/dt=γD^{-1}γ-bD^{-1}b$, reflecting the geometrical $\|D\nablaφ\|^2+\|γ\|^2=\|b\|^2$. The partition function employed in statistical mechanics and J. W. Gibbs' method of ensemble change naturally arise; a fluctuation-dissipation theorem is established via the two leading-order asymptotics of entropy production as $ε\to 0$. The present theory provides a mathematical basis for P. W. Anderson's emergent behavior in the hierarchical structure of complexity science.

physics.gen-ph↗

arXiv2019

Controlling the Photoelectric Effect in the Time Domain

When an atom or molecule absorbs a high-energy photon, an electron is emitted with a well-defined energy and a highly-symmetric angular distribution, ruled by energy quantization and parity conservation. These rules seemingly break down when small quantum systems are exposed to short and intense light pulses, which raise the question of their universality for the simplest case of the photoelectric effect. Here we investigate the photoionization of helium by a sequence of attosecond pulses in the presence of a weak infrared dressing field. We continuously control the energy and introduce an asymmetry in the emission direction of the photoelectrons, thus contradicting well established quantum-mechanical predictions. This control is possible due to an extreme temporal confinement of the light-matter interaction. Our work extends time-domain coherent control schemes to one of the fastest processes in nature, the photoelectric effect.

physics.atom-ph↗

arXiv2019

Ternary Representation of Stochastic Change and the Origin of Entropy and Its Fluctuations

A change in a stochastic system has three representations: Probabilistic, statistical, and informational: (i) is based on random variable $u(ω)\to\tilde{u}(ω)$; this induces (ii) the probability distributions $F_u(x)\to F_{\tilde{u}}(x)$, $x\in\mathbb{R}^n$; and (iii) a change in the probability measure $\mathbb{P}\to\tilde{\mathbb{P}}$ under the same observable $u(ω)$. In the informational representation a change is quantified by the Radon-Nikodym derivative $\ln\left( \frac{ d \tilde{\mathbb{P}}}{ d\mathbb{P}}(ω)\right)=-\ln\left(\frac{ d F_u}{ d F_{\tilde{u}}}(x)\right)$ when $x=u(ω)$. Substituting a random variable into its own density function creates a fluctuating entropy whose expectation has been given by Shannon. Informational representation of a deterministic transformation on $\mathbb{R}^n$ reveals entropic and energetic terms, and the notions of configurational entropy of Boltzmann and Gibbs, and potential of mean force of Kirkwood. Mutual information arises for correlated $u(ω)$ and $\tilde{u}(ω)$; and a nonequilibrium thermodynamic entropy balance equation is identified.

cond-mat.stat-mech↗

arXiv2019

Spatial Control of Multiphoton Electron Excitations in InAs Nanowires by Varying Crystal Phase and Light Polarization

We demonstrate the control of multiphoton electron excitations in InAs nanowires (NWs) by altering the crystal structure and the light polarization. Using few-cycle, near-infrared laser pulses from an optical parametric chirped-pulse amplification system, we induce multiphoton electron excitations in InAs nanowires with controlled wurtzite (WZ) and zincblende (ZB) segments. With a photoemission electron microscope, we show that we can selectively induce multiphoton electron emission from WZ or ZB segments of the same wire by varying the light polarization. Developing \textit{ab-initio GW} calculations of 1st to 3rd order multiphoton excitations and using finite-difference time-domain simulations, we explain the experimental findings: While the electric-field enhancement due to the semiconductor/vacuum interface has a similar effect for all NW segments, the 2nd and 3rd order multiphoton transitions in the band structure of WZ InAs are highly anisotropic, in contrast to ZB InAs. As the crystal phase of NWs can be precisely and reliably tailored, our findings opens up for new semiconductor optoelectronics with controllable nanoscale emission of electrons through vacuum or dielectric barriers.

physics.optics↗

arXiv2019

Phase Control of Attosecond Pulses in a Train

Ultrafast processes in matter can be captured and even controlled by using sequences of few-cycle optical pulses, which need to be well characterized, both in amplitude and phase. The same degree of control has not yet been achieved for few-cycle extreme ultraviolet pulses generated by high-order harmonic generation in gases, with duration in the attosecond range. Here, we show that by varying the spectral phase and carrier-envelope phase (CEP) of a high-repetition rate laser, using dispersion in glass, we achieve a high degree of control of the relative phase and CEP between consecutive attosecond pulses. The experimental results are supported by a detailed theoretical analysis based upon the semiclassical three-step model for high-order harmonic generation.

physics.atom-ph↗

arXiv2019

Compact 200 kHz HHG source driven by a few-cycle OPCPA

We present efficient high-order harmonic generation (HHG) based on a high-repetition rate, few-cycle, near infrared (NIR), carrier-envelope phase stable, optical parametric chirped pulse amplifier (OPCPA), emitting 6fs pulses with 9μJ pulse energy at 200kHz repetition rate. In krypton, we reach conversion efficiencies from the NIR to the extreme ultraviolet (XUV) radiation pulse energy on the order of ~10^{-6} with less than 3μJ driving pulse energy. This is achieved by optimizing the OPCPA for a spatially and temporally clean pulse and by a specially designed high-pressure gas target. In the future, the high efficiency of the HHG source will be beneficial for high-repetition rate two-colour (NIR-XUV) pumpprobe experiments, where the available pulse energy from the laser has to be distributed economically between pump and probe pulses.

physics.atom-ph↗