arXiv subjects

Min Li

Publications and source records attributed to Min Li.

At least 271 records · Page 15Linked to original sources

arXiv2018

On the Gravitational Instabilities of Protoplanetary Disks

The gravitational instabilities are important to the evolution of the disks and the planet formation in the disks. We calculate the evolution of the disks which form from the collapse of the molecular cloud cores. By changing the properties of the cloud cores and the hydrodynamical viscosity parameters, we explore their effects on the properties of the gravitational instabilities. We find that the disk is unstable when the angular velocity of the molecular cloud core is larger than a critical value. The time duration of the instability increases as the angular velocity of the core increases. The increase of the hydrodynamical viscosity parameter hardly affects the stability of the disk, but decreases the time duration of the critical state of the gravitational instability in the disk. The instability of the disks can happen at very early time of evolution of the disk, which is consistent with the observations.

astro-ph.EP↗

arXiv2018

Identifying multi-scale communities in networks by asymptotic surprise

Optimizing statistical measures for community structure is one of the most popular strategies for community detection, but many of them lack the flexibility of resolution and thus are incompatible with multi-scale communities of networks. Here, we further studied a statistical measure of interest for community detection, asymptotic surprise, an asymptotic approximation of surprise. We discussed the critical behaviors of asymptotic surprise in phase transition of community partition theoretically. Then, according to the theoretical analysis, a multi-resolution method based on asymptotic surprise was introduced, which provides an alternative approach to study multi-scale networks, and an improved Louvain algorithm was proposed to optimize the asymptotic surprise more effectively. By a series of experimental tests in various networks, we validated the critical behaviors of the asymptotic surprise further and the effectiveness of the improved Louvain algorithm, displayed its ability to solve the first-type resolution limit and stronger tolerance against the second-type resolution limit, and confirmed its effectiveness of revealing multi-scale community structures in multi-scale networks.

physics.soc-ph↗

arXiv2018

Projected Euler method for stochastic delay differential equation under a global monotonicity condition

This paper investigates projected Euler-Maruyama method for stochastic delay differential equations under a global monotonicity condition. This condition admits some equations with highly nonlinear drift and diffusion coefficients. We appropriately generalized the idea of C-stability and B-consistency given by Beyn et al. [J. Sci. Comput. 67 (2016), no. 3, 955-987] to the case with delay. Moreover, the method is proved to be convergent with order $\frac{1}{2}$ in a succinct way. Finally, some numerical examples are included to illustrate the obtained theoretical results.

math.NA↗

arXiv2018

Cooperative Multi-Sender Index Coding

In this paper, we propose a new coding scheme and establish new bounds on the capacity region for the multi-sender unicast index-coding problem. We revisit existing partitioned Distributed Composite Coding (DCC) proposed by Sadeghi et al. and identify its limitations in the implementation of multi-sender composite coding and in the strategy of sender partitioning. We then propose two new coding components to overcome these limitations and develop a multi-sender Cooperative Composite Coding (CCC). We show that CCC can strictly improve upon partitioned DCC, and is the key to achieve optimality for a number of index-coding instances. The usefulness of CCC and its special cases is illuminated via non-trivial examples, and the capacity region is established for each example. Comparisons between CCC and other non-cooperative schemes in recent works are also provided to further demonstrate the advantage of CCC.

cs.IT↗

arXiv2018

Experimental Observation of a Generalized Thouless Pump with a Single Spin

Adiabatic cyclic modulation of a one-dimensional periodic potential will result in quantized charge transport, which is termed the Thouless pump. In contrast to the original Thouless pump restricted by the topology of the energy band, here we experimentally observe a generalized Thouless pump that can be extensively and continuously controlled. The extraordinary features of the new pump originate from interband coherence in nonequilibrium initial states, and this fact indicates that a quantum superposition of different eigenstates individually undergoing quantum adiabatic following can also be an important ingredient unavailable in classical physics. The quantum simulation of this generalized Thouless pump in a two-band insulator is achieved by applying delicate control fields to a single spin in diamond. The experimental results demonstrate all principal characteristics of the generalized Thouless pump. Because the pumping in our system is most pronounced around a band-touching point, this work also suggests an alternative means to detect quantum or topological phase transitions.

quant-ph↗

arXiv2018

Corrections to di-Higgs boson production with light stops and modified Higgs couplings

The Higgs pair production in gluon fusion is a sensitive probe of beyond-Standard Model (BSM) phenomena and its detection is a major goal for the LHC and higher energy hadron collider experiments. In this work we reanalyze the possible modifications of the Higgs pair production cross section within low energy supersymmetry models. We show that the supersymmetric contributions to the Higgs pair production cross section are strongly correlated with the ones of the single Higgs production in the gluon fusion channel. Motivated by the analysis of ATLAS and CMS Higgs production data, we show that the scalar superpartners' contributions may lead to significant modification of the di-Higgs production rate and invariant mass distribution with respect to the SM predictions. We also analyze the combined effects on the di-Higgs production rate of a modification of the Higgs trilinear and top-quark Yukawa couplings in the presence of light stops. In particular, we show that due to the destructive interference of the triangle and box amplitude contributions to the di-Higgs production cross section, even a small modification of the top-quark Yukawa coupling can lead to a significant increase of the di-Higgs production rate.

hep-ph↗

arXiv2017

Attosecond probing of nuclear dynamics with trajectory-resolved high-harmonic spectroscopy

We report attosecond-scale probing of the laser-induced dynamics in molecules. We apply the method of high-harmonic spectroscopy, where laser-driven recolliding electrons on various trajec- tories record the motion of their parent ion. Based on the transient phase-matching mechanism of high-order harmonic generation, short and long trajectories contributing to the same harmonic order are distinguishable in both the spatial and frequency domains, giving rise to a one-to-one map between time and photon energy for each trajectory. The short and long trajectories in H2 and D2 are used simultaneously to retrieve the nuclear dynamics on the attosecond and angstrom scale. Compared to using only short trajectories, this extends the temporal range of the measurement to one optical cycle. The experiment is also applied to methane and ammonia molecules.

physics.atom-ph↗

arXiv2017

Millimeter Wave Beam Alignment: Large Deviations Analysis and Design Insights

In millimeter wave cellular communication, fast and reliable beam alignment via beam training is crucial to harvest sufficient beamforming gain for the subsequent data transmission. In this paper, we establish fundamental limits in beam-alignment performance under both the exhaustive search and the hierarchical search that adopts multi-resolution beamforming codebooks, accounting for time-domain training overhead. Specifically, we derive lower and upper bounds on the probability of misalignment for an arbitrary level in the hierarchical search, based on a single-path channel model. Using the method of large deviations, we characterize the decay rate functions of both bounds and show that the bounds coincide as the training sequence length goes large. We go on to characterize the asymptotic misalignment probability of both the hierarchical and exhaustive search, and show that the latter asymptotically outperforms the former, subject to the same training overhead and codebook resolution. We show via numerical results that this relative performance behavior holds in the non-asymptotic regime. Moreover, the exhaustive search is shown to achieve significantly higher worst-case spectrum efficiency than the hierarchical search, when the pre-beamforming signal-to-noise ratio (SNR) is relatively low. This study hence implies that the exhaustive search is more effective for users situated further from base stations, as they tend to have low SNR.

cs.IT↗

arXiv2017

Extended ADMM and BCD for Nonseparable Convex Minimization Models with Quadratic Coupling Terms: Convergence Analysis and Insights

In this paper, we establish the convergence of the proximal alternating direction method of multipliers (ADMM) and block coordinate descent (BCD) for nonseparable minimization models with quadratic coupling terms. The novel convergence results presented in this paper answer several open questions that have been the subject of considerable discussion. We firstly extend the 2-block proximal ADMM to linearly constrained convex optimization with a coupled quadratic objective function, an area where theoretical understanding is currently lacking, and prove that the sequence generated by the proximal ADMM converges in point-wise manner to a primal-dual solution pair. Moreover, we apply randomly permuted ADMM (RPADMM) to nonseparable multi-block convex optimization, and prove its expected convergence for a class of nonseparable quadratic programming problems. When the linear constraint vanishes, the 2-block proximal ADMM and RPADMM reduce to the 2-block cyclic proximal BCD method and randomly permuted BCD (RPBCD). Our study provides the first iterate convergence result for 2-block cyclic proximal BCD without assuming the boundedness of the iterates. We also theoretically establish the expected iterate convergence result concerning multi-block RPBCD for convex quadratic optimization. In addition, we demonstrate that RPBCD may have a worse convergence rate than cyclic proximal BCD for 2-block convex quadratic minimization problems. Although the results on RPADMM and RPBCD are restricted to quadratic minimization models, they provide some interesting insights: 1) random permutation makes ADMM and BCD more robust for multi-block convex minimization problems; 2) cyclic BCD may outperform RPBCD for "nice" problems, and therefore RPBCD should be applied with caution when solving general convex optimization problems.

math.OC↗

arXiv2017

Diffractive molecular orbital tomography

High harmonic generation in the interaction of femtosecond lasers with atoms and molecules opens the path to molecular orbital tomography and to probe the electronic dynamics with attosecond-Ångström resolutions. Molecular orbital tomography requires both the amplitude and phase of the high harmonics. Yet the measurement of phases requires sophisticated techniques and represents formidable challenges at present. Here we report a novel scheme, called diffractive molecular orbital tomography, to retrieve the molecular orbital solely from the amplitude of high harmonics without measuring any phase information. We have applied this method to image the molecular orbitals of N$_2$, CO$_2$ and C$_2$H$_2$. The retrieved orbital is further improved by taking account the correction of Coulomb potential. The diffractive molecular orbital tomography scheme, removing the roadblock of phase measurement, significantly simplifies the molecular orbital tomography procedure and paves an efficient and robust way to the imaging of more complex molecules.

physics.optics↗

arXiv2017

Precoding for the Sparsely Spread MC-CDMA Downlink with Discrete-Alphabet Inputs

Sparse signatures have been proposed for the CDMA uplink to reduce multi-user detection complexity, but they have not yet been fully exploited for its downlink counterpart. In this work, we propose a Multi-Carrier CDMA (MC-CDMA) downlink communication, where regular sparse signatures are deployed in the frequency domain. Taking the symbol detection point of view, we formulate a problem appropriate for the downlink with discrete alphabets as inputs. The solution to the problem provides a power-efficient precoding algorithm for the base station, subject to minimum symbol error probability (SEP) requirements at the mobile stations. In the algorithm, signature sparsity is shown to be crucial for reducing precoding complexity. Numerical results confirm system-load-dependent power reduction gain from the proposed precoding over the zero-forcing precoding and the regularized zero-forcing precoding with optimized regularization parameter under the same SEP targets. For a fixed system load, it is also demonstrated that sparse MC-CDMA with a proper choice of sparsity level attains almost the same power efficiency and link throughput as that of dense MC-CDMA yet with reduced precoding complexity, thanks to the sparse signatures.

cs.IT↗

arXiv2016

Rational Solitons in the Parity-Time-Symmetric Nonlocal Nonlinear Schrödinger Model

In this paper, via the generalized Darboux transformation, rational soliton solutions are derived for the parity-time-symmetric nonlocal nonlinear Schrödinger (NLS) model with the defocusing-type nonlinearity. We find that the first-order solution can exhibit the elastic interactions of rational antidark-antidark, dark-antidark, and antidark-dark soliton pairs on a continuous wave background, but there is no phase shift for the interacting solitons. Also, we discuss the degenerate case in which only one rational dark or antidark soliton survives. Moreover, we reveal that the second-order rational solution displays the interactions between two solitons with combined-peak-valley structures in the near-field regions, but each interacting soliton vanishes or evolves into a rational dark or antidark soliton as $|z|\ra \infty$. In addition, we numerically examine the stability of the first- and second-order rational soliton solutions.

nlin.SI↗

arXiv2016

Darboux transformation and analytic solutions of the discrete \PT-symmetric nonlocal nonlinear Schrodinger equation

In this letter, for the discrete parity-time-symmetric nonlocal nonlinear Schrödinger equation, we construct the Darboux transformation, which provides an algebraic iterative algorithm to obtain a series of analytic solutions from a known one. To illustrate, the breathing-soliton solutions, periodic-wave solutions and localized rational soliton solutions are derived with the zero and plane-wave solutions as the seeds. The properties of those solutions are also discussed, and particularly the asymptotic analysis reveals all possible cases of the interaction between the discrete rational dark and antidark solitons.

nlin.SI↗

arXiv2016

Design and Analysis of Transmit Beamforming for Millimetre Wave Base Station Discovery

In this paper, we develop an analytical framework for the initial access (a.k.a. Base Station (BS) discovery) in a millimeter-wave (mm-wave) communication system and propose an effective strategy for transmitting the Reference Signals (RSs) used for BS discovery. Specifically, by formulating the problem of BS discovery at User Equipments (UEs) as hypothesis tests, we derive a detector based on the Generalised Likelihood Ratio Test (GLRT) and characterise the statistical behaviour of the detector. The theoretical results obtained allow analysis of the impact of key system parameters on the performance of BS discovery, and show that RS transmission with narrow beams may not be helpful in improving the overall BS discovery performance due to the cost of spatial scanning. Using the method of large deviations, we identify the desirable beam pattern that minimises the average miss-discovery probability of UEs within a targeted detectable region. We then propose to transmit the RS with sequential scanning, using a pre-designed codebook with narrow and/or wide beams to approximate the desirable patterns. The proposed design allows flexible choices of the codebook sizes and the associated beam widths to better approximate the desirable patterns. Numerical results demonstrate the effectiveness of the proposed method.

cs.IT↗

arXiv2016

Quenching effect in below-threshold high harmonic generation

We theoretically demonstrate the quenching effect in below-threshold high harmonic generation (HHG) by using the time-dependent density-functional theory (TDDFT) and solving the time-dependent Schrödinger equation (TDSE). It is shown that the HHG is substantially suppressed in particular harmonic orders in the below-threshold region when multi-electron interaction comes into play. The position of the suppression is determined by the energy gap between the highest occupied orbital and the higher-lying orbital of the target. We show that the quenching effect is due to a new class of multi-electron dynamics involving electron-electron energy transfer, which is analog to the fluorescence quenching owing to the energy transfer between molecules in fluorescent material. This work reveals the important role of the multi-electron interaction on HHG especially in the below-threshold region.

physics.atom-ph↗

arXiv2016

Quasineutral limit for the quantum Navier-Stokes-Poisson equation

In this paper, we study the quasineutral limit and asymptotic behaviors for the quantum Navier-Stokes-Possion equation. We apply a formal expansion according to Debye length and derive the neutral incompressible Navier-Stokes equation. To establish this limit mathematically rigorously, we derive uniform (in Debye length) estimates for the remainders, for well-prepared initial data. It is demonstrated that the quantum effect do play important roles in the estimates and the norm introduced depends on the Planck constant $\hbar>0$.

math-ph↗

arXiv2016

Breather transition dynamics, Peregrine combs/walls and modulation instability in a variable-coefficient nonlinear Schrödinger equation with higher-order effects

We study a variable-coefficient nonlinear Schrödinger (vc-NLS) equation with higher-order effects. We show that the breather solution can be converted into four types of nonlinear waves on constant backgrounds including the multi-peak solitons, antidark soliton, periodic wave and W-shaped soliton. The transition condition requiring the group velocity dispersion (GVD) and third-order dispersion (TOD) to scale linearly is obtained analytically. We display several kinds of elastic interactions between the transformed nonlinear waves. We discuss the dispersion management of multi-peak soliton, which indicates that the GVD coefficient controls the number of peaks of the wave while the TOD coefficient has compression effect. The gain or loss has influence on the amplitudes of the multi-peak soliton. We further derive the breather multiple births by using multiple compression points of Akhmediev breathers in optical fiber systems with periodic dispersion. The number of ABs depends on the amplitude of the modulation but not on its wavelength, which affects their separation distance. In the limiting case, the breather multiple births reduce to the Peregrine combs. We discuss the effects of TOD coefficient on the spatiotemporal characteristics of Peregrine combs. When the amplitude of the modulation is equal to 1, the Peregrine comb is converted into a Peregrine wall that can be seen as intermediate state between rogue wave and W-shaped soliton. We finally find that the modulational stability regions with zero growth rate coincide with the transition condition using rogue wave eigenvalues. Our results could be useful for the experimental control and manipulation of the formation of generalized Peregrine rogue waves in diverse physical systems modeled by vc-NLS equation with higher-order effects.

nlin.PS↗

arXiv2016

Stationary nonlinear waves, superposition modes and modulational instability characteristics in the AB system

We study the AB system describing marginally unstable baroclinic wave packets in geophysical fluids and also ultra-short pulses in nonlinear optics. We show that the breather can be converted into different types of stationary nonlinear waves on constant backgrounds, including the multi-peak soliton, M-shaped soliton, W-shaped soliton and periodic wave. We also investigate the nonlinear interactions between these waves, which display some novel patterns due to the non-propagating characteristics of the solitons: (1) Two antidark solitons can produce a W-shaped soliton instead of a higher-order antidark one, (2) The interaction between an antidark soliton and a W-shaped soliton can not only generate a higher-order antidark soliton, but also form a W-shaped solion pair, (3) The interactions between an oscillation W-shaped soliton and an oscillation M-shaped soliton show the multipeak structures. We find that the transition occurs at a modulational stability region in a low perturbation frequency region.

nlin.PS↗