Holomorphic Sobolev spaces, Hermite and special Hermite semigroups and a Paley-Wiener theorem for the windowed Fourier transform

The images of Hermite and Laguerre-Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterized. These are used to characterize the image of Schwartz class of rapidly decreasing functions f on Rn and Cn under these semigroups. The image of the space of tempered distributions is also considered and a Paley-Wiener theorem for the windowed (short-time) Fourier transform is proved.     

Complete bounded trajectories and attractors for compressible barotropic self-gravitating fluid

In this paper, we consider the global behavior of weak solutions of the Navier-Stokes system of compressible barotropic self-gravitating fluids in time in a bounded three dimension domain-arbitrary forces. Under certain restrictions imposed on the adiabatic constant γ, we prove the existence of global compact attractors.     

Critical and multicritical behavior in the Ising–Heisenberg universality class

Critical behavior of three-dimensional classical frustrated antiferromagnets with a collinear spin ordering and with an additional twofold degeneracy of the ground state is studied. We consider two lattice models, whose continuous limit describes a single phase transition with a symmetry class differing from the class of non-frustrated magnets as well as from the classes of magnets with non-collinear spin ordering. A symmetry breaking is described by a pair of independent order parameters, which are similar to order parameters of the Ising and O(N) models correspondingly. Using the renormalization group method, it is shown that a transition is of first order for non-Ising spins. For Ising spins, a second order phase transition from the universality class of the O(2) model may be observed. The lattice models are considered by Monte Carlo simulations based on the Wang–Landau algorithm. The models are a ferromagnet on a body-centered cubic lattice with the additional antiferromagnetic exchange interaction between next-nearest-neighbor spins and an antiferromagnet on a simple cubic lattice with the additional interaction in layers. We consider the cases N = 1, 2, 3 and in all of them find a first-order transition. For the N = 1 case we exclude possibilities of the second order or pseudo-first order of a transition. An almost second order transition for large N is also discussed.     

Short Terahertz Pulse Generation from a Dispersion Compensated Modelocked Semiconductor Laser

Dispersion compensation is vital for the generation of ultrashort and single cycle pulses from modelocked lasers across the electromagnetic spectrum. It is typically based on addition of an extra dispersive element to the laser cavity that introduces a chromatic dispersion opposite to that of the gain medium. To date, however, no dispersion compensation schemes have been successfully applied to terahertz (THz) quantum cascade lasers for short and stable pulse generation in the THz range. In this work, a monolithic on‐chip compensation scheme is realized for a modelocked QCL, permitting THz pulses to be considerably shortened from 16ps to 4ps. This is based on the realization of a small coupled cavity resonator that acts as an ‘off resonance’ Gires‐Tournois interferometer (GTI), permitting large THz spectral bandwidths to be compensated. This novel application of a GTI opens up a direct and simple route to sub‐picosecond and single cycle pulses in the THz range from a compact semiconductor source.     

Study of Heat Transfer Control with Magnetic Field Using Higher Order Finite Difference Scheme

The control of convective heat transfer from a heated circular cylinder immersed in an electrically conducting fluid is achieved using an externally imposed magnetic field. A Higher Order Compact Scheme (HOCS) is used to solve the governing energy equation in cylindrical polar coordinates. The HOCS gives fourth order accurate results for the temperature field. The behavior of local Nusselt number, mean Nusselt number and temperature field due to variation in the aligned magnetic field is evaluated for the parameters 5≤$Re$≤40, 0≤$N$≤20 and 0.065≤$Pr$≤7. It is found that the convective heat transfer is suppressed by increasing the strength of the imposed magnetic field until a critical value of $N$, the interaction parameter, beyond which the heat transfer increases with further increase in $N$. The results are found to be in good agreement with recent experimental studies.     

Short electrospun composite nanofibers: Effects of nanoparticle concentration and surface charge on fiber length

Short composite nanofibers were fabricated by electrospinning polymer/TiO₂ nanoparticle solutions of 13 wt. % cellulose acetate as a polymer under a voltage of 5.5 kV and at a flow rate of 0.1 μL/min, and the nanoparticles could be added in concentrations as high as 50 wt. %. The length of the short composite nanofibers was significantly decreased from 112 to 70 μm by the addition of at least a 5 wt. % concentration of nanoparticles, and it gradually continued to decrease as the nanoparticle concentration was increased. The length of the short composite nanofibers with a low concentration of nanoparticles was affected by the surface charge of the nanoparticles, and negatively charged nanoparticles readily dispersed to the negatively charged polymers in solution, which resulted in an elongation of the fabricated short composite nanofibers.     

Maximizing MR signal for 2D UTE slice selection in the presence of rapid transverse relaxation

Ultrashort TE (UTE) sequences allow direct visualization of tissues with very short T2 relaxation times, such as tendons, ligaments, menisci, and cortical bone. In this work, theoretical calculations, simulations, and phantom studies, as well as in vivo imaging were performed to maximize signal-to-noise ratio (SNR) for slice selective RF excitation for 2D UTE sequences. The theoretical calculations and simulations were based on the Bloch equations, which lead to analytic expressions for the optimal RF pulse duration and amplitude to maximize magnetic resonance signal in the presence of rapid transverse relaxation. In steady state, it was found that the maximum signal amplitude was not obtained at the classical Ernst angle, but at an either lower or higher flip angle, depending on whether the RF pulse duration or amplitude was varied, respectively.     

In vivo quantitative 1H MRS of cerebellum and evaluation of quantitation reproducibility by simulation of different levels of noise and spectral resolution

A quantitative analysis of cerebellar metabolites in normal subjects has been performed by proton MR spectroscopy (MRS) with relaxation time correction. Quantitation was carried out in seven healthy human subjects with the well-established LCModel program. The prior knowledge utilized for quantitation was obtained from solutions containing the major brain metabolites and MRS investigated under the same experimental conditions. The tissue water signal was used as an internal standard for the in vivo studies. Both in vitro (for the prior knowledge template) and in vivo data were acquired separately at 1.5 T by PRESS sequence (TR, 1500 ms; TE, 30 ms). The absolute concentration of main cerebellar metabolites was corrected for relaxation time effects. Different noise and line broadening conditions were considered and simulated in the spectral processing in order to evaluate the effect of spectral quality on the concentration estimates.     

About the fastest growth of the Order Parameter in models of percolation

The growth of the average size 〈_smax〉$〈s_{max}〉$ of the largest component at the percolation threshold _pc(N)$p_c\left(N\right)$ on a graph of size N$N$ has been defined as 〈_smax(_pc(N),N)〉∼N^χ$〈s_{max}(p_c\left(N\right),N)〉\sim N^{\chi }$. Here we argue that the precise value of the ‘growth exponent’ χ$\chi$ indicates the nature of percolation transition; χ<1$\chi <1$ or χ=1$\chi =1$ determines if the transition is continuous or discontinuous. We show that a related exponent η=1−χ$\eta =1-\chi$ which describes how the average maximal jump sizes in the Order Parameter decays on increasing the system size, is the single exponent that describes the finite-size scaling of a number of distributions related to the fastest growth of the Order Parameter in these problems. Excellent quality scaling analysis are presented for the two single peak distributions corresponding to the Order Parameters at the two ends of the maximal jump, the bimodal distribution constructed by the weighted average of these distributions and for the distribution of the maximal jump in the Order Parameter.     

Order-convexity in order topologies

In this survey the role of order-convexity in topologies compatible with a preference (i.e a negatively transitive partial order) is considered. Two main issues are highlighted:the (topoiogical) subspaces of preference ordered topological spaces, and the orderability of a topological space