Lattice ϕ4\phi^4 theory of finite-size effects above the upper critical dimension

We present a perturbative calculation of finite-size effects near $T_c$ of the $\phi^4$ lattice model in a $d$-dimensional cubic geometry of size $L$ with periodic boundary conditions for $d > 4$. The structural differences between the $\phi^4$ lattice theory and the $\phi^4$ field theory found previously in the spherical limit are shown to exist also for a finite number of components of the order parameter. The two-variable finite-size scaling functions of the field theory are nonuniversal whereas those of the lattice theory are independent of the nonuniversal model parameters.One-loop results for finite-size scaling functions are derived. Their structure disagrees with the single-variable scaling form of the lowest-mode approximation for any finite $\xi/L$ where $\xi$ is the bulk correlation length. At $T_c$, the large-$L$ behavior becomes lowest-mode like for the lattice model but not for the field-theoretic model. Characteristic temperatures close to $T_c$ of the lattice model, such as $T_{max}(L)$ of the maximum of the susceptibility $\chi$, are found to scale asymptotically as $T_c - T_{max}(L) \sim L^{-d/2}$, in agreement with previous Monte Carlo (MC) data for the five-dimensional Ising model. We also predict $\chi_{max} \sim L^{d/2}$ asymptotically. On a quantitative level, the asymptotic amplitudes of this large -$L$ behavior close to $T_c$ have not been observed in previous MC simulations at $d = 5$ because of nonnegligible finite-size terms $\sim L^{(4-d)/2}$ caused by the inhomogeneous modes. These terms identify the possible origin of a significant discrepancy between the lowest-mode approximation and previous MC data. MC data of larger systems would be desirable for testing the magnitude of the $L^{(4-d)/2}$ and $L^{4-d}$ terms predicted by our theory.Comment: Accepted in Int. J. Mod. Phys.

Establishment of effective metamodels for seakeeping performance in multidisciplinary ship design optimation

Ship design is a complex multidisciplinary optimization process to determine configuration variables that satisfy a set of mission requirements. Unfortunately, high fidelity commercial software for the ship performance estimation such as Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA) are computationally expensive and time consuming to execute and deter the ship designer’s ability to explore larger range of optimization solutions. In this paper, the Latin Hypercube Design was used to select the sample data for covering the design space. A comprehensive seakeeping evaluation index, The percentage of downtime, a comprehensive seakeeping evaluation index, was also used to evaluate the seakeeping performance within the short-term and long-term wave distribution in the Multidisciplinary Design Optimization (MDO) process. The five motions of ship seakeeping performance contained roll, pitch, yaw, sway and heave. Particularly, a new effective approximation modelling technique—Single-Parameter Lagrangian support vector regression ?SPL-SVR? was investigated to construct ship seakeeping metamodels to facilitate the application of MDO. By considering the effects of two ship speeds, the established metamedels of ship seakeeping performance for the short-term percentage downtime are satisfactory for seakeeping predictions during the conceptual design stage; thus, the new approximation algorithm provides an optimal and cost-effective solution for constructing the metamodels using the MDO process

XPS and XMCD study of Fe3O4/GaAs interface

Ultrathin Fe oxide films of various thicknesses prepared by post-growth oxidation on GaAs(100) surface have been investigated with X-ray photoelectron spectroscopy (NPS), X-ray absorption spectroscopy (XAS), and X-ray magnetic circular dichroism (XMCD). The XPS confirms that the surfaces of the oxide are Fe3O4 rather than Fe2O3. XAS and XMCD measurements indicate the presence of nsulating Fe divalent oxide phases (FeO) beneath the surface Fe-3 O-4 layer with the sample thickness above 4 mn. This FeO might act as a barrier for the spin injection into the GaAs

Vacuum State of Lattice Gauge Theory with Fermions in 2+1 Dimensions

We investigate the vacuum state of the lattice gauge theory with fermions in 2+1 dimensions. The vacuum in the Hermite form for the fermion part is obtained; the vacuum in the unitary form has been proposed by Luo and Chen. It is shown that the Hermite vacuum has a lower energy than the unitary one through the variational method.Comment: 16 pages, 5 embedded PS figures, LaTeX with special styl

The cumulative effects of known susceptibility variants to predict primary biliary cirrhosis risk.

Multiple genetic variants influence the risk for development of primary biliary cirrhosis (PBC). To explore the cumulative effects of known susceptibility loci on risk, we utilized a weighted genetic risk score (wGRS) to evaluate whether genetic information can predict susceptibility. The wGRS was created using 26 known susceptibility loci and investigated in 1840 UK PBC and 5164 controls. Our data indicate that the wGRS was significantly different between PBC and controls (P=1.61E-142). Moreover, we assessed predictive performance of wGRS on disease status by calculating the area under the receiver operator characteristic curve. The area under curve for the purely genetic model was 0.72 and for gender plus genetic model was 0.82, with confidence limits substantially above random predictions. The risk of PBC using logistic regression was estimated after dividing individuals into quartiles. Individuals in the highest disclosed risk group demonstrated a substantially increased risk for PBC compared with the lowest risk group (odds ratio: 9.3, P=1.91E-084). Finally, we validated our findings in an analysis of an Italian PBC cohort. Our data suggested that the wGRS, utilizing genetic variants, was significantly associated with increased risk for PBC with consistent discriminant ability. Our study is a first step toward risk prediction for PBC

Dynamical Casimir Effect in Optically Modulated Cavities

Cavities with periodically oscillating mirrors have been predicted to excite photon pairs out of the quantum vacuum in a process known as the Dynamical Casimir effect. Here we propose and analyse an experimental layout that can provide an efficient modulation of the effective optical length of a cavity mode in the near-infrared spectral region. An analytical model of the dynamical Casimir emission is developed and compared to the predictions of a direct numerical solution of Maxwell's equations in real time. A sizeable intensity of dynamical Casimir emission is anticipated for realistic operating parameters. In the presence of an external coherent seed beam, we predict amplification of the seed beam and the appearance of an additional phase-conjugate beam as a consequence of stimulated dynamical Casimir processes.Comment: 6 pages, 5 figure