arXiv subjects

Hua Chen

Publications and source records attributed to Hua Chen.

At least 127 records · Page 7Linked to original sources

arXiv2021

Encirclement Guaranteed Cooperative Pursuit with Robust Model Predictive Control

This paper studies a novel encirclement guaranteed cooperative pursuit problem involving $N$ pursuers and a single evader in an unbounded two-dimensional game domain. Throughout the game, the pursuers are required to maintain encirclement of the evader, i.e., the evader should always stay inside the convex hull generated by all the pursuers, in addition to achieving the classical capture condition. To tackle this challenging cooperative pursuit problem, a robust model predictive control (RMPC) based formulation framework is first introduced, which simultaneously accounts for the encirclement and capture requirements under the assumption that the evader's action is unavailable to all pursuers. Despite the reformulation, the resulting RMPC problem involves a bilinear constraint due to the encirclement requirement. To further handle such a bilinear constraint, a novel encirclement guaranteed partitioning scheme is devised that simplifies the original bilinear RMPC problem to a number of linear tube MPC (TMPC) problems solvable in a decentralized manner. Simulation experiments demonstrate the effectiveness of the proposed solution framework. Furthermore, comparisons with existing approaches show that the explicit consideration of the encirclement condition significantly improves the chance of successful capture of the evader in various scenarios.

cs.MA↗

arXiv2021

Force-feedback based Whole-body Stabilizer for Position-Controlled Humanoid Robots

This paper studies stabilizer design for position-controlled humanoid robots. Stabilizers are an essential part for position-controlled humanoids, whose primary objective is to adjust the control input sent to the robot to assist the tracking controller to better follow the planned reference trajectory. To achieve this goal, this paper develops a novel force-feedback based whole-body stabilizer that fully exploits the six-dimensional force measurement information and the whole-body dynamics to improve tracking performance. Relying on rigorous analysis of whole-body dynamics of position-controlled humanoids under unknown contact, the developed stabilizer leverages quadratic-programming based technique that allows cooperative consideration of both the center-of-mass tracking and contact force tracking. The effectiveness of the proposed stabilizer is demonstrated on the UBTECH Walker robot in the MuJoCo simulator. Simulation validations show a significant improvement in various scenarios as compared to commonly adopted stabilizers based on the zero-moment-point feedback and the linear inverted pendulum model.

cs.RO↗

arXiv2021

Nonequilibrium thermal transport and photon squeezing in a quadratic qubit-resonator system

We investigate steady-state thermal transport and photon statistics in a nonequilibrium hybrid quantum system, in which a qubit is longitudinally and quadratically coupled to an optical resonator. Our calculations are conducted with the method of the quantum dressed master equation combined with full counting statistics. The effect of negative differential thermal conductance is unravelled at finite temperature bias, which stems from the suppression of cyclic heat transitions and large mismatch of two squeezed photon modes at weak and strong qubit-resonator hybridizations, respectively. The giant thermal rectification is also exhibited at large temperature bias. It is found that the intrinsically asymmetric structure of the hybrid system and negative differential thermal conductance show the cooperative contribution. Noise power and skewness, as typical current fluctuations, exhibit global maximum with strong hybridization at small and large temperature bias limits, respectively. Moreover, the effect of photon quadrature squeezing is discovered in the strong hybridization and low-temperature regime, which shows asymmetric response to two bath temperatures. These results would provide some insight to thermal functional design and photon manipulation in qubit-resonator hybrid quantum systems.

quant-ph↗

arXiv2021

Intertwined Space-Time Symmetry, Orbital Magnetism and Dynamical Berry Curvature in a Circularly Shaken Optical Lattice

We study the circular shaking of a two dimensional optical lattice, which is essentially a (2+1) dimensional space-time lattice exhibiting periodicities in both spatial and temporal dimensions. The near-resonant optical shaking considered here dynamically couples the low-lying $s$ band and the first excited $p$ bands by transferring a photon of shaking frequency. The intertwined space-time symmetries are further uncovered to elucidate the degeneracy in the spectrum solved with the generalized Bloch-Floquet theorem. Setting the chirality of circular shaking explicitly breaks time reversal symmetry and lifts the degeneracy of $p_\pm = p_x \pm ip_y$ orbitals, leading to the local circulation of orbital magnetism, i.e the imbalanced occupation in $p_\pm$ orbitals. Moreover, the dynamics of Berry connection is revealed by the time evolution of the Berry curvature and the polarization, which have physical observable effects in experiments. Interestingly, the dynamics is found characterized by a universal phase shift, governed by the time screw rotational symmetry involving a fractional translation of time. These findings suggest that the present lattice-shaking scheme provides a versatile platform for the investigation of the orbital physics and the symmetry-protected dynamics.

cond-mat.quant-gas↗

arXiv2021

Orbital order in a bosonic $p$-band triangular lattice

We present a detailed study of the Bose-Hubbard model in a $p$-band triangular lattice by focusing on the evolution of orbital order across the superfluid-Mott insulator transition. Two distinct phases are found in the superfluid regime. One of these phases adiabatically connects the weak interacting limit. This phase is characterized by the intertwining of axial $p_\pm=p_x \pm ip_y$ and in-plane $p_θ=\cosθp_x+\sinθp_y$ orbital orders, which break the time-reversal symmetry and lattice symmetries simultaneously. In addition, the calculated Bogoliubov excitation spectrum gaps the original Dirac points in the single-particle spectrum but exhibits emergent Dirac points. The other superfluid phase in close proximity to the Mott insulator with unit boson filling shows a detwined in-plane ferro-orbital order. Finally, an orbital exchange model is constructed for the Mott insulator phase. Its classical ground state has an emergent SO$(2)$ rotational symmetry in the in-plane orbital space and therefore enjoys an infinite degeneracy, which is ultimately lifted by the orbital fluctuation via the order by disorder mechanism. Our systematic analysis suggests that the in-plane ferro-orbital order in the Mott insulator phase agrees with and likely evolves from the latter superfluid phase.

cond-mat.str-el↗

arXiv2021

Instantaneous Capture Input for Balancing the Variable Height Inverted Pendulum

Balancing is a fundamental need for legged robots due to their unstable floating-base nature. Balance control has been thoroughly studied for simple models such as the linear inverted pendulum thanks to the concept of the instantaneous capture point (ICP), yet the constant center of mass height assumption limits the application. This paper explores balancing of the variable-height inverted pendulum (VHIP) model by introducing the \emph{instantaneous capture input} (ICI), an extension of the ICP based on its key properties. Namely, the ICI can be computed as a function of the state, and when this function is used as the control policy, the ICI is rendered stationary and the system will eventually come to a stop. This characterization induces an analytical region of capturable states for the VHIP, which can be used to conceptually guide where to step. To further address state and control constraints during recovery, we present and theoretically analyze an explicit ICI-based controller with online optimal feedback gains. Simulations demonstrate the validity of our controller for capturability maintenance compared to an approach based on the divergent component of motion.

cs.RO↗

arXiv2021

Large Anomalous Hall Effect in Topological Insulators Proximitized by Collinear Antiferromagnets

CrSb is an attractive material for room-temperature antiferromagnetic spintronic applications because of its high Néel temperature $\sim$700 K and semi-metallic character. We study the magnetic properties of CrSb bilayers on few-layer topological insulator thin films using \emph{ab initio} density functional theory. We find that the intrinsic parts of the total anomalous Hall conductivities of the thin films are non-zero, and approximately quantized. The Néel temperature of CrSb bilayers on few-layer topological insulator thin films is found to be approximately two times larger than that of an isolated CrSb thin film. Due to the low Fermi level density of states of CrSb, Hall quantization might be achievable by introducing disorder. CrSb bilayers on topological insulator surfaces are therefore attractive candidates for high-temperature quantum anomalous Hall effects.

cond-mat.mes-hall↗

arXiv2021

The spectral gap to torsion problem for some non-convex domains

In this paper we study the following torsion problem \begin{equation*} \begin{cases} -Δu=1~&\mbox{in}\ Ω,\\[1mm] u=0~&\mbox{on}\ \partialΩ. \end{cases} \end{equation*} Let $Ω\subset \mathbb{R}^2$ be a bounded, convex domain and $u_0(x)$ be the solution of above problem with its maximum $y_0\in Ω$. Steinerberger proved that there are universal constants $c_1, c_2>0$ satisfying \begin{equation*} λ_{\max}\left(D^2u_0(y_0)\right)\leq -c_1\mbox{exp}\left(-c_2\frac{\text{diam}(Ω)}{\mbox{inrad}(Ω)}\right). \end{equation*} And he proposed following open problem: "Does above result hold true on domains that are not convex but merely simply connected or perhaps only bounded? The proof uses convexity of the domain $Ω$ in a very essential way and it is not clear to us whether the statement remains valid in other settings." Here by some new idea involving the computations on Green's function, we compute the spectral gap $λ_{\max}D^2u(y_0)$ for some non-convex smooth bounded domains, which gives a negative answer to above open problem. Also some extensions are given.

math.AP↗

arXiv2020

Underactuated Motion Planning and Control for Jumping with Wheeled-Bipedal Robots

This paper studies jumping for wheeled-bipedal robots, a motion that takes full advantage of the benefits from the hybrid wheeled and legged design features. A comprehensive hierarchical scheme for motion planning and control of jumping with wheeled-bipedal robots is developed. Underactuation of the wheeled-bipedal dynamics is the main difficulty to be addressed, especially in the planning problem. To tackle this issue, a novel wheeled-spring-loaded inverted pendulum (W-SLIP) model is proposed to characterize the essential dynamics of wheeled-bipedal robots during jumping. Relying on a differential-flatness-like property of the W-SLIP model, a tractable quadratic programming based solution is devised for planning jumping motions for wheeled-bipedal robots. Combined with a kinematic planning scheme accounting for the flight phase motion, a complete planning scheme for the W-SLIP model is developed. To enable accurate tracking of the planned trajectories, a linear quadratic regulator based wheel controller and a task-space whole-body controller for the other joints are blended through disturbance observers. The overall planning and control scheme is validated using V-REP simulations of a prototype wheeled-bipedal robot.

cs.RO↗

arXiv2020

Simulating the Palmer-Chalker state in an orbital superfluid

We consider a bosonic $s$ and $p$ orbital system in a face-centered cubic (FCC) optical lattice, and predict a fluctuation-induced instability towards the orbital analogue of Palmer-Chalker state, which is originally proposed in an electronic spin system. For bosons loaded in the FCC optical lattice, the single-particle spectrum has four degenerate band minima with their crystal momenta forming a tetrahedron in Brillouin zone. In the weakly interacting regime, the ensuing many-particle ground state, at the classical level, underlies a four-sublattice tetrahedral supercell of spontaneously generated $p$-orbital angular momenta through the Bravias-Bloch duality between real and momentum space, and is macroscopically degenerate originating from the geometric frustration. The fluctuations on top of the classical ground state lift its degeneracy and select the Palmer-Chalker ordering of $p$-orbital angular momenta as the quantum ground state through order-by-disorder mechanism. These findings raise the exciting possibility of simulating the Palmer-Chalker state with its orbital counterpart in ultracold atomic gases.

cond-mat.quant-gas↗

arXiv2020

Block-structured Integer Programming: Can we Parameterize without the Largest Coefficient?

We consider 4-block $n$-fold integer programming, which can be written as $\max\{w\cdot x: H x=b, l\le x\le u, x\in \mathbb{Z}^{N} \}$ where the constraint matrix $H$ is composed of small submatrices $A,B,C,D$ such that the first row of $H$ is $(C,D,D,\cdots,D)$, the first column of $H$ is $(C,B,B,\cdots,B)$, the main diagonal of $H$ is $(C,A,A,\cdots,A)$, and all the other entries are $0$. The special case where $B=C=0$ is known as $n$-fold integer programming. Prior algorithmic results for 4-block $n$-fold integer programming and its special cases usually take $Δ$, the largest absolute value among entries of $H$ as part of the parameters. In this paper, we explore the possibility of getting rid of $Δ$ from parameters, i.e., we are looking for algorithms that runs polynomially in $\logΔ$. We show that, assuming $\text{P}\neq \text{NP}$, this is not possible even if $A=(1,1,Δ)$ and $B=C=0$. However, this becomes possible if $A=(1,1,\cdots,1)$ or $A\in \mathbb{Z}^{1\times 2}$, or more generally if $A\in\mathbb{Z}^{s_A\times t_A} $ where $t_A=s_A+1$ and the rank of matrix $A$ satisfies that $\text{rank}(A)=s_A$. More precisely, 1. If $A=(1,\ldots,1)\in \mathbb{Z}^{1\times t_A} $, then 4-block $n$-fold IP can be solved in $(t_A+t_B)^{O(t_A+t_B)}\cdot poly(n,\logΔ)$ time. 2. If $A\in\mathbb{Z}^{s_A\times t_A} $, $t_A=s_A+1$ and $\text{rank}(A)=s_A$, then 4-block $n$-fold IP can be solved in $(t_A+t_B)^{O(t_A+t_B)}\cdot n^{O(t_A)}\cdot poly(\logΔ)$ time; Specifically, if in addition we have $B=C=0$ (i.e., $n$-fold integer programming), then it can be solved in linear time $n\cdot poly(t_A,\log Δ)$.

math.OC↗

arXiv2020

Finite-thickness effect and spin polarization of the even-denominator fractional quantum Hall states

The spin-polarized even-denominator fractional quantum Hall (FQH) states in the second Landau level (LL), i.e. 5/2 and 7/2, may possess novel quasi-particle excitations obeying non-Abelian statistics. However, the spin polarization of the 7/2 FQH state has not been investigated experimentally and the spin polarization of the 5/2 FQH state from tilted field experiments remains controversial. Using a piezo-driven sample rotator with the lowest electron temperature down to 25 mK, we studied the energy gap of the even-denominator FQH states in the second LL by precise control of the tilted angles with a resolution less than 0.1°. We observed two different energy gap dependences on the in-plane magnetic field for 5/2, 7/2, other FQH states (7/3 and 8/3) in the second LL and reentrant integer quantum Hall (RIQH) states in the third LL. Though the transition fields vary from states, their corresponding in-plane magnetic lengths are comparable to the quantum well thickness of the sample, which may result from the influence of the finite-thickness effect. At low in-plane magnetic fields, before the conjectured finite-thickness effect starts to dominate, the energy gaps of both 5/2 and 7/2 states show a non-decreasing behavior, supporting spin-polarized ground states. Our results also suggest that the 7/3, 8/3 FQH states, and the RIQH states in the third LL are spin-polarized or partially spin-polarized.

cond-mat.mes-hall↗

arXiv2020

Realization of the kagome spin ice state in a frustrated intermetallic compound

Spin ices are exotic phases of matter characterized by frustrated spins obeying local ice rules, in analogy with the electric dipoles in water ice. In two dimensions, one can similarly define ice rules for in-plane Ising-like spins arranged on a kagome lattice. These ice rules require each triangle plaquette to have a single monopole, and can lead to various unique orders and excitations. Using experimental and theoretical approaches including magnetometry, thermodynamic measurements, neutron scattering and Monte Carlo simulations, we establish HoAgGe as a crystalline (i.e. non-artificial) system that realizes the kagome spin ice state. The system features a variety of partially and fully ordered states and a sequence of field-induced phases at low temperatures, all consistent with the kagome ice rule.

cond-mat.str-el↗

arXiv2020

Linear magnetoresistance induced by intra-scattering semiclassics of Bloch electrons

The weak field magnetoresistance has seen a revived interest due to the distinct role played by the momentum-space Berry curvature of Bloch electrons. While most previous studies in this regard focus on the inter-scattering motion of semiclassical Bloch electrons in electromagnetic fields, the intra-scattering effects of the semiclassical dynamics augmented by the Berry curvature, magnetic moment and shift vector on the magnetoresistance have been largely overlooked. Here we uncover that these intra-scattering effects, which are neglected in the field-independent relaxation time approximation to the Boltzmann collision integral, can be as important as the inter-scattering ones. Concrete calculations on the two dimensional gapped Dirac model show that the sign of the negative linear magnetoresistance given by the Berry curvature alone is reversed when one considers the magnetic moment and shift vector.

cond-mat.mtrl-sci↗

arXiv2020

Big Bang Nucleosynthesis Hunts Chameleon Dark Matter

We study the chameleon field dark matter, dubbed \textit{scalaron}, in $F(R)$ gravity in the Big Bang Nucleosynthesis (BBN) epoch. With an $R^{2}$-correction term required to solve the singularity problem for $F(R)$ gravity, we first find that the scalaron dynamics is governed by the $R^{2}$ term and the chameleon mechanism in the early universe, which makes the scalaron physics model-independent regarding the low-energy scale modification. In viable $F(R)$ dark energy models including the $R^{2}$ correction, our analysis suggests the scalaron universally evolves in a way with a bouncing oscillation irrespective of the low-energy modification for the late-time cosmic acceleration. Consequently, we find a universal bound on the scalaron mass in the BBN epoch, to be reflected on the constraint for the coupling strength of the $R^2$ term, which turns out to be more stringent than the one coming from the fifth force experiments. It is then shown that the scalaron naturally develops a small enough fluctuation in the BBN epoch, hence can avoid the current BBN constraint placed by the latest Planck 2018 data, and can also have a large enough sensitivity to be hunted by the BBN, with more accurate measurements for light element abundances as well as the baryon number density fraction.

hep-ph↗

arXiv2019

Optimal Control of a Differentially Flat 2D Spring-Loaded Inverted Pendulum Model

This paper considers the optimal control problem of an extended spring-loaded inverted pendulum (SLIP) model with two additional actuators for active leg length and hip torque modulation. These additional features arise naturally in practice, allowing for consideration of swing leg kinematics during flight and active control over stance dynamics. On the other hand, nonlinearity and the hybrid nature of the overall SLIP dynamics introduce challenges in the analysis and control of the model. In this paper, we first show that the stance dynamics of the considered SLIP model are differentially flat, which has a strong implication regarding controllability of the stance dynamics. Leveraging this powerful property, a tractable optimal control strategy is developed. This strategy enables online solution while also treating the hybrid nature of the SLIP dynamics. Together with the optimal control strategy, the extended SLIP model grants active disturbance rejection capability at any point during the gait. Performance of the proposed control strategy is demonstrated via numerical tests and shows significant advantage over existing methods.

cs.RO↗

arXiv2019

Emergent flat band lattices in spatially periodic magnetic fields

Motivated by the recent discovery of Mott insulating phase and unconventional superconductivity due to the flat bands in twisted bilayer graphene, we propose more generic ways of getting two-dimensional (2D) emergent flat band lattices using either 2D Dirac materials or ordinary electron gas (2DEG) subject to moderate periodic orbital magnetic fields with zero spatial average. Employing both momentum-space and real-space numerical methods to solve the eigenvalue problems, we find stark contrast between Schrödinger and Dirac electrons, i.e., the former show recurring "magic" values of the magnetic field when the lowest band becomes flat, while for the latter the zero-energy bands are asymptotically flat without magicness. By examining the Wannier functions localized by the smooth periodic magnetic fields, we are able to explain these nontrivial behaviors using minimal tight-binding models on a square lattice. The two cases can be interpolated by varying the $g$-factor or effective mass of a 2DEG and by taking into account the Zeeman coupling, which also leads to flat bands with nonzero Chern numbers for each spin. Our work provides flexible platforms for exploring interaction-driven phases in 2D systems with on-demand superlattice symmetries.

cond-mat.mes-hall↗

arXiv2019

Estimates of Dirichlet Eigenvalues for a Class of Sub-elliptic Operators

Let $Ω$ be a bounded connected open subset in $\mathbb{R}^n$ with smooth boundary $\partialΩ$. Suppose that we have a system of real smooth vector fields $X=(X_{1},X_{2},$ $\cdots,X_{m})$ defined on a neighborhood of $\overlineΩ$ that satisfies the Hörmander's condition. Suppose further that $\partialΩ$ is non-characteristic with respect to $X$. For a self-adjoint sub-elliptic operator $\triangle_{X}= -\sum_{i=1}^{m}X_{i}^{*} X_i$ on $Ω$, we denote its $k^{th}$ Dirichlet eigenvalue by $λ_k$. We will provide an uniform upper bound for the sub-elliptic Dirichlet heat kernel. We will also give an explicit sharp lower bound estimate for $λ_{k}$, which has a polynomially growth in $k$ of the order related to the generalized Métivier index. We will establish an explicit asymptotic formula of $λ_{k}$ that generalizes the Métivier's results in 1976. Our asymptotic formula shows that under a certain condition, our lower bound estimate for $λ_{k}$ is optimal in terms of the growth of $k$. Moreover, the upper bound estimate of the Dirichlet eigenvalues for general sub-elliptic operators will also be given, which, in a certain sense, has the optimal growth order.

math.AP↗