Jian Liu - Department of Astronomy, University of Florida, Bryant Space Science Center, Gainesville, FL 32611-2055, USA

Jian Liu
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Name
Jian Liu
Affiliation
Department of Astronomy, University of Florida, Bryant Space Science Center, Gainesville, FL 32611-2055, USA
City
Gainesville
Country
United States

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Mathematics - Analysis of PDEs (15)
 
Physics - Plasma Physics (9)
 
Mathematical Physics (4)
 
Mathematics - Mathematical Physics (4)
 
Mathematics - Numerical Analysis (3)
 
Physics - Chemical Physics (3)
 
Physics - Materials Science (3)
 
Computer Science - Cryptography and Security (3)
 
Physics - Statistical Mechanics (3)
 
Physics - Atomic Physics (2)
 
Quantum Physics (2)
 
Physics - Strongly Correlated Electrons (2)
 
Nonlinear Sciences - Adaptation and Self-Organizing Systems (2)
 
Mathematics - Classical Analysis and ODEs (2)
 
Physics - Instrumentation and Detectors (2)
 
Computer Science - Logic in Computer Science (2)
 
Mathematics - Differential Geometry (2)
 
Physics - Atomic and Molecular Clusters (2)
 
Physics - Superconductivity (2)
 
Physics - Computational Physics (2)
 
Quantitative Biology - Tissues and Organs (1)
 
Computer Science - Software Engineering (1)
 
Mathematics - Symplectic Geometry (1)
 
Statistics - Machine Learning (1)
 
Computer Science - Learning (1)
 
Physics - Physics and Society (1)
 
Physics - Accelerator Physics (1)
 
Physics - Biological Physics (1)
 
Physics - Optics (1)
 
Mathematics - Probability (1)
 
Computer Science - Distributed; Parallel; and Cluster Computing (1)
 
Physics - Mesoscopic Systems and Quantum Hall Effect (1)
 
High Energy Physics - Theory (1)
 
Instrumentation and Methods for Astrophysics (1)
 
Solar and Stellar Astrophysics (1)
 
Earth and Planetary Astrophysics (1)

Publications Authored By Jian Liu

In this paper, we study the stochastic gradient descent method in analyzing nonconvex statistical optimization problems from a diffusion approximation point of view. Using the theory of large deviation of random dynamical system, we prove in the small stepsize regime and the presence of omnidirectional noise the following: starting from a local minimizer (resp.~saddle point) the SGD iteration escapes in a number of iteration that is exponentially (resp. Read More

In this work we consider $$ w_t=[(w_{hh}+c_0)^{-3}]_{hh},\qquad w(0)=w^0, $$ which is derived from a thin film equation for epitaxial growth on vicinal surface. We formulate the problem as the gradient flow of a suitably-defined convex functional in a non-reflexive space. Then by restricting it to a Hilbert space and proving the uniqueness of its sub-differential, we can apply the classical maximal monotone operator theory. Read More

In this paper, we study the modified Camassa-Holm (mCH) equation in Lagrangian coordinates. For some initial data $m_0$, we show that classical solutions to this equation blow up in finite time $T_{max}$. Before $T_{max}$, existence and uniqueness of classical solutions are established. Read More

To guarantee the availability and reliability of data source in Magnetic Confinement Fusion (MCF) devices, incorrect diagnostic data, which cannot reflect real physical properties of measured objects, should be sorted out before further analysis and study. Traditional data sorting cannot meet the growing demand of MCF research because of the low-efficiency, time-delay, and lack of objective criteria. In this paper, a Time-Domain Global Similarity (TDGS) method based on machine learning technologies is proposed for the automatic data cleaning of MCF devices. Read More

We study a continuum model for solid films that arises from the modeling of one-dimensional step flows on a vicinal surface in the attachment-detachment-limited regime. The resulting nonlinear partial differential equation, $u_t = -u^2(u^3+\alpha u)_{hhhh}$, gives the evolution for the surface slope $u$ as a function of the local height $h$ in a monotone step train. Subject to periodic boundary conditions and positive initial conditions, we prove the existence, uniqueness and positivity of global strong solutions to this PDE using two Lyapunov energy functions. Read More

We show a unified second-order scheme for constructing simple, robust and accurate algorithms for typical thermostats for configurational sampling for the canonical ensemble. When Langevin dynamics is used, the scheme leads to the BAOAB algorithm that has been recently investigated. We show that the scheme is also useful for other types of thermostat, such as the Andersen thermostat and Nos\'e-Hoover chain. Read More

We investigate the transient photoexcited lattice dynamics in a layered perovskite Mott insulator Sr2IrO4 by femtosecond X-ray diffraction using a laser plasma-based X-ray source. Ultrafast structural dynamics of Sr2IrO4 thin films are determined by observing the shift and broadening of the (0012) Bragg diffraction after excitation by 1.5 eV and 3. Read More

In this paper, we study traveling wave solutions and peakon weak solutions of the modified Camassa-Holm (mCH) equation with dispersive term $2ku_x$ for $k\in\mathbb{R}$. We study traveling wave solutions through a Hamiltonian system obtained from the mCH equation by using a nonlinear transformation. The typical traveling wave solutions given by this Hamiltonian system are unbounded or multi-valued. Read More

We prepared superconducting and non-superconducting FeSe films on SrTiO3(001) substrates (FeSe/STO) and investigated the superconducting transition induced by charge transfer between organic molecules and FeSe layers by low temperature scanning tunneling microscopy and spectroscopy. At low coverage, donor- and acceptor-type molecules adsorbed preferentially on the non-superconducting and superconducting FeSe layers, respectively. Superconductivity was induced by donor molecules on non-superconducting FeSe layer, while the superconductivity was suppressed near acceptor molecules. Read More

In this paper, we show the rigidity of isometric immersions for a Riemannian manifold of dimension $n-1$ into the light cone of $n+1$ dimensional Minkowski, de Sitter and anti-de Sitter spacetimes for $n\geq 3$. Read More

In the absence of external material deposition, crystal surfaces usually relax to become flat by decreasing their free energy. We study an asymmetry in the relaxation of macroscopic plateaus, facets, of a periodic surface corrugation in 1+1 dimensions via a continuum model below the roughening transition temperature. The model invokes a highly degenerate parabolic partial differential equation (PDE) for surface diffusion, which is related to the weighted-$H^{-1}$ (nonlinear) gradient flow of a convex, singular surface free energy in homoepitaxy. Read More

In this paper, we study 1D autonomous fractional ODEs $D_c^{\gamma}u=f(u), 0< \gamma <1$, where $u: [0,\infty)\mapsto\mathbb{R}$ is the unknown function and $D_c^{\gamma}$ is the generalized Caputo derivative introduced by Li and Liu ( arXiv:1612.05103). Based on the existence and uniqueness theorem and regularity results in previous work, we show the monotonicity of solutions to the autonomous fractional ODEs and several versions of comparison principles. Read More

The hybrid optical pumping spin exchange relaxation free (SERF) atomic magnetometers can realize ultrahigh sensitivity measurement of magnetic field and inertia. We have studied the $^{\text{85}}$Rb polarization of two types of hybrid optical pumping SERF magnetometers based on $^{\text{39}}$K-$^{\text{85}}$Rb-$^{\text{4}}$He and $^{\text{133}}$Cs-$^{\text{85}}$Rb-$^{\text{4}}$He respectively. Then we found that $^{\text{85}}$Rb polarization varies with the number density of buffer gas $^{\text{4}}$He and quench gas N$_{\text{2}}$, pumping rate of pump beam and cell temperature respectively, which will provide an experimental guide for the design of the magnetometer. Read More

In magnetic multilayers, spin accumulation manifests itself as an excess of electrons in one spin channel and an equal deficiency in the other under the quasi-neutrality condition. Here, taking a typical ferromagnet/nonmagnet (FM/NM) junction as an example, we model the two spin channels as the two plates of a capacitor. This enables us to introduce the spin-accumulation (SA) capacitance to measure the ability of a material to store spins. Read More

The output of an automated theorem prover is usually presented by using a text format, they are often too heavy to be understood. In model checking setting, it would be helpful if one can observe the structure of models and the verification procedures. A 3D visualization tool (\textsf{VMDV}) is proposed in this paper to address these problems. Read More

Planet searches using the radial velocity technique show a paucity of companions to solar-type stars within ~5 AU in the mass range of ~10 - 80 M$_{\text{Jup}}$. This deficit, known as the brown dwarf desert, currently has no conclusive explanation. New substellar companions in this region help asses the reality of the desert and provide insight to the formation and evolution of these objects. Read More

Topological phononic states, facilitating acoustic unique transports immunizing to defects and disorders, have significantly revolutionized our scientific cognition of acoustic wave systems. Up to now, the theoretical and experimental demonstrations of topologically protected one-way transports with pseudospin states in a phononic crystal beyond the graphene lattice with C6v symmetry are still unexploited. Furthermore, the tunable topological states, in form of robust reconfigurable acoustic pathways, have been evaded in the topological phononic insulators. Read More

Structure-preserving geometric algorithm for the Vlasov-Maxwell (VM) equations is currently an active research topic. We show that spatially-discretized Hamiltonian systems for the VM equations admit a local energy conservation law in space-time. This is accomplished by proving that for a general spatially-discretized system, a global conservation law always implies a discrete local conservation law in space-time when the algorithm is local. Read More

In this paper we are concerned with the existence of a weak solution to the initial boundary value problem for the equation $\partial_t u= \Delta(\Delta u)^{-3}$. This problem arises in the mathematical modeling of the evolution of a crystal surface. Existence of a weak solution $u$ with $\Delta u\geq 0$ is obtained via a suitable substitution. Read More

The surging interest in blockchain technology has revitalized the search for effective Byzantine consensus schemes. In particular, the blockchain community has been looking for ways to effectively integrate traditional Byzantine fault-tolerant (BFT) protocols into a blockchain consensus layer allowing various financial institutions to securely agree on the order of transactions. However, existing BFT protocols can only scale to tens of nodes due to their $O(n^2)$ message complexity. Read More

We consider in this work stochastic differential equation (SDE) model for particles in contact with a heat bath when the memory effects are non-negligible. As a result of the fluctuation-dissipation theorem, the differential equations driven by fractional Brownian noise to model memory effects should be paired with Caputo derivatives and based on this we consider fractional stochastic differential equations (FSDEs), which should be understood in an integral form. We establish the existence of strong solutions for such equations. Read More

In this paper we investigate regularity properties of weak solutions to a PDE system that arises in the study of biological transport networks. The system consists of a possibly singular elliptic equation for the scalar pressure of the underlying biological network coupled to a diffusion equation for the conductance vector of the network. There are several different types of nonlinearities in the system. Read More

We study a class of fourth order nonlinear parabolic equations which include the thin-film equation and the quantum drift-diffusion model as special cases. We investigate these equations by first developing functional inequalities of the type $$ \int_\Omega u^{2\gamma-\alpha-\beta}\Delta\ua\Delta\ub dx \geq c\int_\Omega|\Delta \ur |^2dx, $$ which seem to be of interest on their own right. Read More

In this paper, by analyzing the thermodynamic properties of charged AdS black hole and asymptotically flat space-time charged black hole in the vicinity of the critical point, we establish the correspondence between the thermodynamic parameters of asymptotically flat space-time and nonasymptotically flat space-time, based on the equality of black hole horizon area in the two different space-time. The relationship between the cavity radius (which is introduced in the study of asymptotically flat space-time charged black holes) and the cosmological constant (which is introduced in the study of nonasymptotically flat space-time) is determined. The establishment of the correspondence between the thermodynamics parameters in two different space-time is beneficial to the mutual promotion of different time-space black hole research, which is helpful to understand the thermodynamics and quantumproperties of black hole in space-time. Read More

Depleted CMOS active sensors (DMAPS) are being developed for high-energy particle physics experiments in high radiation environments, such as in the ATLAS High Luminosity Large Hadron Collider (HL-LHC). Since charge collection by drift is mandatory for harsh radiation environment, the application of high bias voltage to high resistive sensor material is needed. In this work, a prototype of a DMAPS was fabricated in a 150nm CMOS process on a substrate with a resistivity of >2 k{\Omega}cm that was thinned to 100 {\mu}m. Read More

We study convolution groups generated by completely monotone sequences and completely monotone functions. Using a convolution group, we define a fractional calculus for a certain class of distributions. When acting on causal functions, this definition agrees with the traditional Riemann-Liouville definition for $t>0$ but includes some singularities at $t=0$ so that the group property holds. Read More

Interferometric gravitational wave detectors operate with high optical power in their arms in order to achieve high shot-noise limited strain sensitivity. A significant limitation to increasing the optical power is the phenomenon of three-mode parametric instabilities, in which the laser field in the arm cavities is scattered into higher order optical modes by acoustic modes of the cavity mirrors. The optical modes can further drive the acoustic modes via radiation pressure, potentially producing an exponential buildup. Read More

An infinite dimensional canonical symplectic structure and structure-preserving geometric algorithms are developed for the photon-matter interactions described by the Schr\"odinger-Maxwell equations. The algorithms preserve the symplectic structure of the system and the unitary nature of the wavefunctions, and bound the energy error of the simulation for all time-steps. This new numerical capability enables us to carry out first-principle based simulation study of important photon-matter interactions, such as the high harmonic generation and stabilization of ionization, with long-term accuracy and fidelity. Read More

We propose a new unified theoretical framework to construct equivalent representations of the multi-state Hamiltonian operator and present several approaches for the mapping onto the Cartesian phase space. After mapping an F-dimensional Hamiltonian onto an F+1- dimensional space, creation and annihilation operators are defined such that the F+1 dimensional space is complete for any combined excitations. Commutation and anti-commutation relations are then naturally derived, which show that the underlying degrees of freedom are neither bosons nor fermions. Read More

We introduce the isomorphism between the multi-state Hamiltonian and the second-quantized many-electron Hamiltonian (with only 1-electron interactions). This suggests that all methods developed for the former can be employed for the latter, and vice versa. The resonant level (Landauer) model for nonequilibrium quantum transport is used as a proof-of-concept example. Read More

We introduce a novel simple algorithm for thermostatting path integral molecular dynamics (PIMD) with the Langevin equation. The staging transformation of path integral beads is employed for demonstration. The optimum friction coefficients for the staging modes in the free particle limit are used for all systems. Read More

Fusion energy will be the ultimate clean energy source for mankind. One of the most visible concerns of the future fusion device is the threat of deleterious runaway electrons (REs) produced during unexpected disruptions of the fusion plasma. Both efficient long-term algorithms and super-large scale computing power are necessary to reveal the complex dynamics of REs in a realistic fusion reactor. Read More

Android Framework is a layer of software that exists in every Android system managing resources of all Android apps. A vulnerability in Android Framework can lead to severe hacks, such as destroying user data and leaking private information. With tens of millions of Android devices unpatched due to Android fragmentation, vulnerabilities in Android Framework certainly attract attackers to exploit them. Read More

Purpose: Rupture of an intracranial aneurysm is the most common cause of subarachnoid haemorrhage (SAH), which is a life-threatening acute cerebrovascular event that typically affects working-age people. This study aims to investigate the aneurysmal SAH incidence rate in elderly population than in middle aged population in China. Materials and methods: Aneurysmal SAH cases were collected retrospectively from the archives of 21 hospitals in Mainland China. Read More

A manifestly covariant, or geometric, field theory for relativistic classical particle-field system is developed. The connection between space-time symmetry and energy-momentum conservation laws for the system is established geometrically without splitting the space and time coordinates, i.e. Read More

Relativistic dynamics of a charged particle in time-dependent electromagnetic fields has theoretical significance and a wide range of applications. It is often multi-scale and requires accurate long-term numerical simulations using symplectic integrators. For modern large-scale particle simulations in complex, time-dependent electromagnetic field, explicit symplectic algorithms are much more preferable. Read More

We propose a semi-discrete scheme for 2D Keller-Segel equations based on a symmetrization reformation, which is equivalent to the convex splitting method and is free of any nonlinear solver. We show that, this new scheme is unconditionally stable as long as the initial condition does not exceed certain threshold, and it asymptotically preserves the quasi-static limit in the transient regime. Furthermore, we prove that the fully discrete scheme is conservative and positivity preserving, which makes it ideal for simulations. Read More

In this paper, we investigate numerical approximations of the scalar conservation law with the Caputo derivative, which introduces the memory effect. We construct the first order and the second order explicit upwind schemes for such equations, which are shown to be conditionally $\ell^1$ contracting and TVD. However, the Caputo derivative leads to the modified CFL-type stability condition, $ (\Delta t)^{\alpha} = O(\Delta x)$, where $\alpha \in (0,1]$ is the fractional exponent in the derivative. Read More

The Accurate Particle Tracer (APT) code is designed for large-scale particle simulations on dynamical systems. Based on a large variety of advanced geometric algorithms, APT possesses long-term numerical accuracy and stability, which are critical for solving multi-scale and non-linear problems. Under the well-designed integrated and modularized framework, APT serves as a universal platform for researchers from different fields, such as plasma physics, accelerator physics, space science, fusion energy research, computational mathematics, software engineering, and high-performance computation. Read More

Motivated by the great success and adoption of Bitcoin, a number of cryptocurrencies such as Litecoin, Dogecoin, and Ethereum are becoming increasingly popular. Although existing blockchain-based cryptocurrency schemes can ensure reasonable security for transactions, they do not consider any notion of fairness. Fair exchange allows two players to exchange digital "items", such as digital signatures, over insecure networks fairly, so that either each player gets the other's item, or neither player does. Read More

In this paper, the Lorentz covariance of algorithms is introduced. Under Lorentz transformation, both the form and performance of a Lorentz covariant algorithm are invariant. To acquire the advantages of symplectic algorithms and Lorentz covariance, a general procedure for constructing Lorentz covariant canonical symplectic algorithms (LCCSA) is provided, based on which an explicit LCCSA for dynamics of relativistic charged particles is built. Read More

We study in this work a continuum model derived from 1D attachment-detachment-limited (ADL) type step flow on vicinal surface, $ u_t=-u^2(u^3)_{hhhh}$, where $u$, considered as a function of step height $h$, is the step slope of the surface. We formulate a notion of weak solution to this continuum model and prove the existence of a global weak solution, which is positive almost everywhere. We also study the long time behavior of weak solution and prove it converges to a constant solution as time goes to infinity. Read More

Strong Coulomb repulsion and spin-orbit coupling are known to give rise to exotic physical phenomena in transition metal oxides. Initial attempts to investigate systems where both of these fundamental interactions are comparably strong, such as 3d and 5d complex oxide superlattices, have revealed properties that only slightly differ from the bulk ones of the constituent materials. Here, we observe that the interfacial coupling between the 3d antiferromagnetic insulator SrMnO3 and the 5d paramagnetic metal SrIrO3 is enormously strong, yielding an anomalous Hall response as the result of charge transfer driven interfacial ferromagnetism. Read More

The superconductor-to-insulator transition (SIT) induced by means such as external magnetic fields, disorder or spatial confinement is a vivid illustration of a quantum phase transition dramatically affecting the superconducting order parameter. In pursuit of a new realization of the SIT by interfacial charge transfer, we developed extremely thin superlattices composed of high $T_c$ superconductor YBa$_2$Cu$_3$O$_7$ (YBCO) and colossal magnetoresistance ferromagnet La$_{0.67}$Ca$_{0. Read More

Exact eigen modes with orbital angular momentum (OAM) in the complex media of unmagnetized homogeneous plasma are studied. Three exact eigen modes with OAM are discovered, i.e. Read More

We investigate the long-time dynamics of an opinion formation model inspired by a work by Borghesi, Bouchaud and Jensen. Firstly, we derive a Fokker-Planck type equation under the assumption that interactions between individuals produce little consensus of opinion (grazing collision approximation). Secondly, we study conditions under which the Fokker-Planck equation has non-trivial equilibria and derive the macroscopic limit (corresponding to the long-time dynamics and spatially localized interactions) for the evolution of the mean opinion. Read More

Model checking and automated theorem proving are two pillars of formal methods. This paper investigates model checking from an automated theorem proving perspective, aiming at combining the expressiveness of automated theorem proving and the complete automaticity of model checking. The focus of this paper is on the verification of the temporal logic properties of Kripke models. Read More

In this paper, we study the quasi-local energy (QLE) and the surface geometry for Kerr spacetime in the Boyer-Lindquist coordinate without taking the slow rotation approximation. We also consider in the region $r<2m$, which is inside the ergosphere. For a certain region, $r>r_{k}(a)$, the Gaussian curvature is positive of the surface with constant $t,r$, and for $r>\sqrt{3}a$ the critical value of the QLE is positive. Read More

This work considers the rigorous derivation of continuum models of step motion starting from a mesoscopic Burton-Cabrera-Frank (BCF) type model following the work [Xiang, SIAM J. Appl. Math. Read More