Higher-order properties and Bell-inequality violation for the three-mode enhanced squeezed state

By extending the usual two-mode squeezing operator $S_{2}=\exp [ i\lambda (Q_{1}P_{2}+Q_{2}P_{1}) ]$ to the three-mode squeezing operator $S_{3}=\exp {i\lambda [ Q_{1}(P_{2}+P_{3}) +Q_{2}(P_{1}+P_{3}) +Q_{3}(P_{1}+P_{2}) ]}$, we obtain the corresponding three-mode squeezed coherent state. The state's higher-order properties, such as higher-order squeezing and higher-order sub-Possonian photon statistics, are investigated. It is found that the new squeezed state not only can be squeezed to all even orders but also exhibits squeezing enhancement comparing with the usual cases. In addition, we examine the violation of Bell-inequality for the three-mode squeezed states by using the formalism of Wigner representation

The Method of Particular Solutions Using Trigonometric Basis Functions

In this paper, the method of particular solutions (MPS) using trigonometric functions as the basis functions is proposed to solve two-dimensional elliptic partial differential equations. The inhomogeneous term of the governing equation is approximated by Fourier series and the closed-form particular solutions of trigonometric functions are derived using the method of undetermined coefficients. Once the particular solutions for the trigonometric basis functions are derived, the standard MPS can be applied for solving partial differential equations. In comparing with the use of radial basis functions and polynomials in the MPS, our proposed approach provides another simple approach to effectively solving two-dimensional elliptic partial differential equations. Five numerical examples are provided in this paper to validate the merits of the proposed meshless method

Solidification behavior of intensively sheared hypoeutectic Al-Si alloy liquid

The official published version of this article can be found at the link below.The effect of the processing temperature on the microstructural and mechanical properties of Al-Si (hypoeutectic) alloy solidified from intensively sheared liquid metal has been investigated systematically. Intensive shearing gives a significant refinement in grain size and intermetallic particle size. It also is observed that the morphology of intermetallics, defect bands, and microscopic defects in high-pressure die cast components are affected by intensive shearing the liquid metal. We attempt to discuss the possible mechanism for these effects.Funded by the EPSRC

Genetic determinants of the molecular portraits of epithelial cancers

The ability to characterize and predict tumor phenotypes is crucial to precision medicine. In this study, we present an integrative computational approach using a genome-wide association analysis and an Elastic Net prediction method to analyze the relationship between DNA copy number alterations and an archive of gene expression signatures. Across breast cancers, we are able to quantitatively predict many gene signatures levels within individual tumors with high accuracy based upon DNA copy number features alone, including proliferation status and Estrogen-signaling pathway activity. We can also predict many other key phenotypes, including intrinsic molecular subtypes, estrogen receptor status, and TP53 mutation. This approach is also applied to TCGA Pan-Cancer, which identify repeatedly predictable signatures across tumor types including immune features in lung squamous and basal-like breast cancers. These Elastic Net DNA predictors could also be called from DNA-based gene panels, thus facilitating their use as biomarkers to guide therapeutic decision making

Influence of intensive melt shearing on the microstructure and mechanical properties of an Al-Mg alloy with high added impurity content

The official published version can be accessed from the link below - Copyright @ The Minerals, Metals & Materials Society and ASM International 2011We have investigated the influence of melt conditioning by intensive shearing on the mechanical behavior and microstructure of Al-Mg-Mn-Fe-Cu-Si alloy sheet produced from a small book mold ingot with high added impurity content. The melt conditioned ingot has fine grains throughout its cross section, whereas a conventionally cast ingot, without melt shearing, has coarser grains and shows a wider variation of grain size. Both needle-shaped and coarse Chinese script iron bearing intermetallic particles are found in the microstructure at the center of the conventionally processed ingot, but for the melt conditioned ingot, only fine Chinese script intermetallic particles are observed. In addition to the iron bearing intermetallics, Mg2Si particles are also observed. The ingots were rolled to thin sheet and solution heat treated (SHT). During rolling, the iron-based intermetallics and Mg2Si particles are broken and aligned along the rolling direction. Yield strength (YS), ultimate tensile strength (UTS), and elongation of the intensively melt sheared and processed sheet are all improved compared to the conventionally cast and processed sheet. Fractographic analysis of the tensile fracture surfaces shows that the clustered and coarse iron bearing intermetallic particles are responsible for the observed reduction in mechanical properties of the conventionally cast sheet. We have shown that by refining the initial microstructure of the ingot by intensive shear melt conditioning, it is possible to achieve improved mechanical properties at the final sheet gage of an AlMgMn alloy with a high content of impurities.This study is under the Technology Strategy Board funded REALCAR projec

Picosecond optical shutter for particle detection

Characteristics of an optical shutter utilizing Kerr effect induced by picosecond laser pulses in carbon disulfide are studied experimentally. The shutter has a gate time of 4.5 to 5 ps full width at half-maximum and a transmission of approximately 15 percent at a wavelength 0.53 $mu$m. Such an ultrafast shutter can be used as an optical signal gate in a sampling detection scheme that has picosecond time-resolution. The picosecond optical detection scheme is envisioned to have applications in experimental high-energy physics such as to time-resolve ultrashort Cherenkov or synchrotron radiation emitted by relativistic particles. Methods of synchronizing a laser-activated Kerr shutter with a particle accelerator or synchrotron are discussed. (auth

Picosecond optical shutter for particle detection

Characteristics of an optical shutter utilizing Kerr effect induced by picosecond laser pulses in carbon disulfide are studied experimentally. The shutter has a gate time of 4.5 to 5 ps full width at half-maximum and a transmission of approximately 15 percent at a wavelength 0.53 $mu$m. Such an ultrafast shutter can be used as an optical signal gate in a sampling detection scheme that has picosecond time-resolution. The picosecond optical detection scheme is envisioned to have applications in experimental high-energy physics such as to time-resolve ultrashort Cherenkov or synchrotron radiation emitted by relativistic particles. Methods of synchronizing a laser-activated Kerr shutter with a particle accelerator or synchrotron are discussed. (auth

Regular autodense languages

A regular component is either autodense or anti-autodense. Characterizations of a regular component being a pure autodense language and being a pure autodense code are obtained. A relationship between intercodes and anti-autodense languages is that for an intercode L of index m, L n is an anti-autodense language for every n > m

Continuous twin screw rheo-extrusion of an AZ91D magnesium alloy

© The Minerals, Metals & Materials Society and ASM International 2012The twin screw rheo-extrusion (TSRE) is designed to take advantage of the nondendritc microstructure and thixotropic characterization of semisolid-metal slurries and produce simple metal profiles directly from melts. The extrusion equipment consists of a rotor-stator high shear slurry maker, a twin screw extruder, and a die assembly. The process is continuous and has a potential for significantly saving energy, manufacturing cost, and enhancing efficiency. The present investigation was carried out to study the process performance for processing rods of an AZ91D magnesium alloy and the microstructure evolution during processing. The semisolid slurry prepared by the process was characterized by uniformly distributed nondendritic granular primary phase particles. AZ91D rods with uniform and fine microstructures and moderate mechanical properties were produced. For the given slurry making parameters, decreasing extrusion temperature was found to improve microstructures and properties. The mechanisms of particle granulation and refinement and the effect of processing parameters on process performance and thermal management are discussed. © 2012 The Minerals, Metals & Materials Society and ASM International.EPSRC (UK) and Rautomead Lt

On geometric problems related to Brown-York and Liu-Yau quasilocal mass

We discuss some geometric problems related to the definitions of quasilocal mass proposed by Brown-York \cite{BYmass1} \cite{BYmass2} and Liu-Yau \cite{LY1} \cite{LY2}. Our discussion consists of three parts. In the first part, we propose a new variational problem on compact manifolds with boundary, which is motivated by the study of Brown-York mass. We prove that critical points of this variation problem are exactly static metrics. In the second part, we derive a derivative formula for the Brown-York mass of a smooth family of closed 2 dimensional surfaces evolving in an ambient three dimensional manifold. As an interesting by-product, we are able to write the ADM mass \cite{ADM61} of an asymptotically flat 3-manifold as the sum of the Brown-York mass of a coordinate sphere $S_r$ and an integral of the scalar curvature plus a geometrically constructed function $\Phi(x)$ in the asymptotic region outside $S_r$. In the third part, we prove that for any closed, spacelike, 2-surface $\Sigma$ in the Minkowski space $\R^{3,1}$ for which the Liu-Yau mass is defined, if $\Sigma$ bounds a compact spacelike hypersurface in $\R^{3,1}$, then the Liu-Yau mass of $\Sigma$ is strictly positive unless $\Sigma$ lies on a hyperplane. We also show that the examples given by \'{O} Murchadha, Szabados and Tod \cite{MST} are special cases of this result.Comment: 28 page