Well-posedness of the Fifth Order Kadomtsev-Petviashvili I Equation in Anisotropic Sobolev Spaces with Nonnegative Indices

In this paper we establish the local and global well-posedness of the real valued fifth order Kadomstev-Petviashvili I equation in the anisotropic Sobolev spaces with nonnegative indices. In particular, our local well-posedness improves Saut-Tzvetkov's one and our global well-posedness gives an affirmative answer to Saut-Tzvetkov's $L^2$-data conjecture.Comment: 17page

Synchronous control of dual-channel all-optical multi-state switching

We have experimentally observed optical multistabilities (OMs) simultaneously on both the signal and generated Stokes fields in an optical ring cavity with a coherently-prepared multilevel atomic medium. The two observed OMs, which are governed by different physical processes, are coupled via the multilevel atomic medium and exhibit similar threshold behaviors. By modulating the cavity input (signal) field with positive or negative pulses, dual-channel all-optical multi-state switching has been realized and synchronously controlled, which can be useful for increasing communication and computation capacities

On averaging block Kaczmarz methods for solving nonlinear systems of equations

A class of averaging block nonlinear Kaczmarz methods is developed for the solution of the nonlinear system of equations. The convergence theory of the proposed method is established under suitable assumptions and the upper bounds of the convergence rate for the proposed method with both constant stepsize and adaptive stepsize are derived. Numerical experiments are presented to verify the efficiency of the proposed method, which outperforms the existing nonlinear Kaczmarz methods in terms of the number of iteration steps and computational costs

On multi-step extended maximum residual Kaczmarz method for solving large inconsistent linear systems

A multi-step extended maximum residual Kaczmarz method is presented for the solution of the large inconsistent linear system of equations by using the multi-step iterations technique. Theoretical analysis proves the proposed method is convergent and gives an upper bound on its convergence rate. Numerical experiments show that the proposed method is effective and outperforms the existing extended Kaczmarz methods in terms of the number of iteration steps and the computational costs

The Stability at the Solid-Solid and Liquid-Solid Interfaces

In this thesis, we studied three small subjects in the realm of continuum mechanics: imbibition in fluid mechanics, beam and rod buckling in solid mechanics and shell buckling at the solid-liquid interface. In chapter 2, we examined the radial imbibition into a homogenous semi-infinite porous media from a point source with infinite liquid supply. We proved that in the absence of gravity (or in the regime while gravity is negligible compared to surface tension), the shape of the wet area is a hemisphere, and the radius of the wet area evolves as a function with respect to time. This new law with respect to time has been verified by Finite Element Method simulation in software COMSOL and a series of experiments using packed glass microsphere as the porous media. We also found that even though the imbibition slows down, the flow rate through the point source remains constant. This new result for three dimensional radial imbibition complements the classic Lucas-Washburn law in one dimension and two dimensional radial imbibition in one plane. In chapter 3, we studied the elastic beam/rod buckling under lateral constraints in two dimension as well as in three dimension. For the two dimensional case with unique boundary conditions at both ends, the buckled beam can be divided into segments with alternate curved section and straight section. The curved section can be solved by the Euler beam equation. The straight sections, however, are key to the transition between different buckling modes, and the redistributed length of straight sections sets the upper limit and lower limit for the transition. We compared our theoretical model of varying straight sections with Finite Element Method simulation in software ABAQUS, and good agreements are found. We then attempted to employ this model as an explanation with qualitative feasibility for the crawling snake in horizontal plane between parallel walls, which shows unique shape like square wave. For the three dimensional buckling beam/rod confined in cylindrical constraints, three stages are found for the buckling and post buckling processes: initial two dimensional shape, three dimensional spiral/helix shape and final foldup/alpha shape. We characterized the shape at each stage, and then we calculated the transition points between the three stages using geometrical arguments for energy arguments. The theoretical analysis for three dimensional beam/rod are also complemented with Finite Element Method simulations from ABAQUS. In chapter 4, we investigated the buckling shape of solid shell filled with liquid core in two dimension and three dimension. A material model for liquid is first described that can be readily incorporated in the framework of solid mechanics. We then applied this material model in two dimensional and three dimensional Finite Element Method simulation using software ABAQUS. For the two dimensional liquid core solid shell model, a linear analysis is first performed to identify that ellipse corresponds to lowest order of buckling with smallest elastic energy. Finite Element Method simulation is then performed to determine the nonlinear post-buckling process. We discovered that two dimensional liquid core solid shell structures converge to peanut shape eventually while the evolution process is determined by two dimensionless parameters Kτ/μ and ρR^2/μτ. Amorphous shape exists before final peanut shape for certain models with specific Kτ/μ and ρR^2/μτ. The two dimensional peanut shape is also verified with Lattice Boltzmann simulations. For the three dimensional liquid core solid shell model, the post buckling shape is studied from Finite Element Method simulations in ABAQUS. Depending on the strain loading rate, the deformations show distinctive patterns. Large loading rate induces herringbone pattern on the surface of solid shell which resembles solid core solid shell structure, while small loading rate induces major concave pattern which resemble empty solid shell structure. For both two dimensional and three dimensional liquid core system, small scale ordered deformation pattern can be generated by increasing the shear stress in liquid core. In the final chapter, we summarized the discoveries in the dissertation with highlights on the role that geometry plays in all of the three subjects. Recommendations for future studies are also discussed

Large Magnetoresistance over an Extended Temperature Regime in Monophosphides of Tantalum and Niobium

We report extremely large magnetoresistance (MR) in an extended temperature regime from 1.5 K to 300 K in non-magnetic binary compounds TaP and NbP. TaP exhibits linear MR around $1.8\times 10^4$ at 2 K in a magnetic field of 9 Tesla, which further follows its linearity up to $1.4\times 10^5$ in a magnetic field of 56 Tesla at 1.5 K. At room temperature the MR for TaP and NbP follows a power law of the exponent about $1.5$ with the values larger than $300\%$ in a magnetic field of 9 Tesla. Such large MR in a wide temperature regime is not likely only due to a resonance of the electron-hole balance, but indicates a complicated mechanism underneath.Comment: 13 pages, 4 figures; submitted in May 20, 2015; accepted for publicatio

MASTERKEY: Practical Backdoor Attack Against Speaker Verification Systems

Speaker Verification (SV) is widely deployed in mobile systems to authenticate legitimate users by using their voice traits. In this work, we propose a backdoor attack MASTERKEY, to compromise the SV models. Different from previous attacks, we focus on a real-world practical setting where the attacker possesses no knowledge of the intended victim. To design MASTERKEY, we investigate the limitation of existing poisoning attacks against unseen targets. Then, we optimize a universal backdoor that is capable of attacking arbitrary targets. Next, we embed the speaker's characteristics and semantics information into the backdoor, making it imperceptible. Finally, we estimate the channel distortion and integrate it into the backdoor. We validate our attack on 6 popular SV models. Specifically, we poison a total of 53 models and use our trigger to attack 16,430 enrolled speakers, composed of 310 target speakers enrolled in 53 poisoned models. Our attack achieves 100% attack success rate with a 15% poison rate. By decreasing the poison rate to 3%, the attack success rate remains around 50%. We validate our attack in 3 real-world scenarios and successfully demonstrate the attack through both over-the-air and over-the-telephony-line scenarios.Comment: Accepted by Mobicom 202