Unusual eigenvalue spectrum and relaxation in the Levy-Ornstein-Uhlenbeck process

We consider the rates of relaxation of a particle in a harmonic well, subject to Levy noise characterized by its Levy index mu. Using the propagator for this Levy-Ornstein-Uhlenbeck process (LOUP), we show that the eigenvalue spectrum of the associated Fokker-Planck operator has the form (n + m mu)nu where nu is the force constant characterizing the well, and n, m is an element of N. If mu is irrational, the eigenvalues are all nondegenerate, but rational mu can lead to degeneracy. The maximum degeneracy is shown to be 2. The left eigenfunctions of the fractional Fokker-Planck operator are very simple while the right eigenfunctions may be obtained from the lowest eigenfunction by a combination of two different step-up operators. Further, we find that the acceptable eigenfunctions should have the asymptotic behavior vertical bar x vertical bar(-n1-n2 mu) as vertical bar x vertical bar -> infinity, with n(1) and n(2) being positive integers, though this condition alone is not enough to identify them uniquely. We also assert that the rates of relaxation of LOUP are determined by the eigenvalues of the associated fractional Fokker-Planck operator and do not depend on the initial state if the moments of the initial distribution are all finite. If the initial distribution has fat tails, for which the higher moments diverge, one can have nonspectral relaxation, as pointed out by Toenjes et al. Phys. Rev. Lett. 110, 150602 (2013)].

Cross polarization in laser beams

Polarization properties of Gaussian laser beams are analyzed in a manner consistent with the Maxwell equations, and expressions are developed for all components of the electric and magnetic field vectors in the beam. It is shown that the transverse nature of the free electromagnetic field demands a nonzero transverse cross-polarization component in addition to the well-known component of the field vectors along the beam axis. The strength of these components in relation to the strength of the principal polarization component is established. It is further shown that the integrated strengths of these components over a transverse plane are invariants of the propagation process. It is suggested that cross- polarization measurement using a null detector can serve as a new method for accurate determination of the center of Gaussian laser beams.

Crystallization Kinetics and Electrical Relaxation of BaO-0.5Li(2)O-4.5B(2)O(3) Glasses

Transparent glasses in the composition BaO-0.5Li(2)O-4.5B(2)O(3) (BLBO) were fabricated via the conventional melt-quenching technique. X-ray powder diffraction combined with differential scanning calorimetric (DSC) studies carried out on the as-quenched samples confirmed their amorphous and glassy nature, respectively. The crystallization behavior of these glasses has been studied by isothermal and nonisothermal methods using DSC. Crystallization kinetic parameters were evaluated from the Johnson-Mehl-Avrami equation. The value of the Avrami exponent (n) was found to be 3.6 +/- 0.1, suggesting that the process involves three-dimensional bulk crystallization. The average value of activation energy associated with the crystallization of BLBO glasses was 317 +/- 10 kJ/mol. Transparent glass-ceramics were fabricated by controlled heat-treatment of the as-quenched glasses at 845 K/40 min. The dielectric constants for BLBO glasses and glass-ceramics in the 100 Hz-10 MHz frequency range were measured as a function of the temperature (300-925 K). The electrical relaxation and dc conductivity characteristics were rationalized using electric modulus formalism. The imaginary part of the electric modulus spectra was modeled using an approximate solution of the Kohlrausch-Williams-Watts relation. The temperature-dependent behavior of stretched exponent (beta) was discussed for the as-quenched and heat-treated BLBO glasses.

Influence of Cooling Rate on the Enthalpy Relaxation and Fragility of a Metallic Glass

Structural relaxation behavior of a rapidly quenched (RQ) and a slowly cooled Pd40Cu30Ni10P20 metallic glass was investigated and compared. Differential scanning calorimetry was employed to monitor the relaxation enthalpies at the glass transition temperature, T-g , and the Kolrausch-Williams-Watts (KWW) stretched exponential function was used to describe its variation with annealing time. It was found that the rate of enthalpy recovery is higher in the ribbon, implying that the bulk is more resistant to relaxation at low temperatures of annealing. This was attributed to the possibility of cooling rate affecting the locations where the glasses get trapped within the potential energy landscape. The RQ process traps a larger amount of free volume, resulting in higher fragility, and in turn relaxes at the slightest thermal excitation (annealing). The slowly cooled bulk metallic glass (BMG), on the other hand, entraps lower free volume and has more short-range ordering, hence requiring a large amount of perturbation to access lower energy basins.

Subquadratic wavenumber dependence of the structural relaxation of supercooled liquid in the crossover regime

As a liquid is progressively supercooled toward its glass transition temperature, an intriguing weakening of the wavenumber (q) dependence of the structural relaxation time tau(q) in the intermediate-to-large q limit is observed both in experiments and simulation studies. Neither continuous Brownian diffusive dynamics nor discontinuous activated events can alone explain the anomalous wavenumber dependence. Here we use our recently developed theory that unifies the mode coupling theory for continuous dynamics, with the random first order transition theory treatment of activated discontinuous motion as a nucleationlike instanton process to understand the wavenumber dependence of density relaxation. The predicted smooth change in mechanism of relaxation from diffusive to activated, in the crossover regime, is wavevector dependent and appears to be responsible for the observed subquadratic,nalmost linear, q dependence of the relaxation time.

Steady flow of a maxwell fluid in a porous cylindrical annulus with circular cross-section

When a fluid with memory is injected into any flow region some assumptions regarding the initial state of stress have to be made in order to determine the state of stress at any subsequent instant. For a Maxwell fluid, it is assumed that the fluid near the surface of injection is suddenly stressed and responds by starting flow in accordance with the mechanical model chosen. The flow of a Maxwell fluid with a single relaxation time has been determined under the above assumption in the following two cases: (i) annulus between two porous concentric circular cylinders, and (ii) space between two porous and infinitely extending parallel plates. The nature of flow in the present case is similar to that of the Reiner-Rivlin fluids obtained by Narasimhan2).

Cascaded Cross Flow DBD-Adsorbent Technique for NOX Abatement in Diesel Engine Exhaust

In this paper, a different type of cross flow dielectric barrier discharge (DBD) reactor was designed and tested. Here the gas flow is perpendicular to the barrier discharge electrode. Discharge plasma was utilized to oxidize NO contained in the exhaust gas to NO2 and subsequent NO2 removal can be improved using an adsorbent system. A detailed study of DeNO(X) in a stationary diesel engine exhaust was carried out using pulsed electrical discharges/adsorbent processes. Activated alumina (Al2O3) and MS-13x were used as adsorbents at room temperature. The main emphasis is laid on the removal of NOX from the filtered diesel engine exhaust. In filtered exhaust environment, the cross flow reactor along with adsorbent exhibits a superior performance with regard to NOX removal when compared to that with axial flow of gas. In this paper we bring out a relative comparison of discharge plasma and plasma-adsorbent process at various gas flow rates, ranging from 2 l/min to 25 l/min. The discharge plasma-adsorbent assisted barrier discharge reactor has shown promising results in NOX removal at high flow rates.

Semi-Supervised Classification Using Sparse Gaussian Process Regression

Gaussian Processes (GPs) are promising Bayesian methods for classification and regression problems. They have also been used for semi-supervised learning tasks. In this paper, we propose a new algorithm for solving semi-supervised binary classification problem using sparse GP regression (GPR) models. It is closely related to semi-supervised learning based on support vector regression (SVR) and maximum margin clustering. The proposed algorithm is simple and easy to implement. It gives a sparse solution directly unlike the SVR based algorithm. Also, the hyperparameters are estimated easily without resorting to expensive cross-validation technique. Use of sparse GPR model helps in making the proposed algorithm scalable. Preliminary results on synthetic and real-world data sets demonstrate the efficacy of the new algorithm.

Three-dimensional computational modeling of momentum, heat, and mass transfer in a laser surface alloying process

A three- dimensional, transient model is developed for studying heat transfer, fluid flow, and mass transfer for the case of a single- pass laser surface alloying process. The coupled momentum, energy, and species conservation equations are solved using a finite volume procedure. Phase change processes are modeled using a fixed-grid enthalpy-porosity technique, which is capable of predicting the continuously evolving solid- liquid interface. The three- dimensional model is able to predict the species concentration distribution inside the molten pool during alloying, as well as in the entire cross section of the solidified alloy. The model is simulated for different values of various significant processing parameters such as laser power, scanning speed, and powder feedrate in order to assess their influences on geometry and dynamics of the pool, cooling rates, as well as species concentration distribution inside the substrate. Effects of incorporating property variations in the numerical model are also discussed.

A deep‐level spectroscopic technique for determining capture cross‐section activation energy of Si‐related DX centers in AlxGa1-xAs

A deep‐level transient spectroscopy (DLTS) technique is reported for determining the capture cross‐section activation energy directly. Conventionally, the capture activation energy is obtained from the temperature dependence of the capture cross section. Capture cross‐section measurement is often very doubtful due to many intrinsic errors and is more critical for nonexponential capture kinetics. The essence of this technique is to use an emission pulse to allow the defects to emit electrons and the transient signal from capture process due to a large capture barrier was analyzed, in contrast with the emission signal in conventional DLTS. This technique has been applied for determining the capture barrier for silicon‐related DX centers in AlxGa1−xAs for different AlAs mole fractions.

Cross-Guided Clustering: Transfer of Relevant Supervision across Tasks

Lack of supervision in clustering algorithms often leads to clusters that are not useful or interesting to human reviewers. We investigate if supervision can be automatically transferred for clustering a target task, by providing a relevant supervised partitioning of a dataset from a different source task. The target clustering is made more meaningful for the human user by trading-off intrinsic clustering goodness on the target task for alignment with relevant supervised partitions in the source task, wherever possible. We propose a cross-guided clustering algorithm that builds on traditional k-means by aligning the target clusters with source partitions. The alignment process makes use of a cross-task similarity measure that discovers hidden relationships across tasks. When the source and target tasks correspond to different domains with potentially different vocabularies, we propose a projection approach using pivot vocabularies for the cross-domain similarity measure. Using multiple real-world and synthetic datasets, we show that our approach improves clustering accuracy significantly over traditional k-means and state-of-the-art semi-supervised clustering baselines, over a wide range of data characteristics and parameter settings.

NMR Analysis of Cross Strand Aromatic Interactions in an 8 Residue Hairpin and a 14 Residue Three Stranded beta-Sheet Peptide

Cross strand aromatic interactions between a facing pair of phenylalanine residues in antiparallel beta-sheet structures have been probed using two structurally defined model peptides. The octapeptide Boc-(LFVPPLFV)-P-D-P-L-OMe (peptide 1) favors the beta-hairpin conformation nucleated by the type II' beta-turn formed by the (D)Pro-(L)Pro segment, placing Phe2 and Phe7 side chains in proximity. Two centrally positioned (D)Pro-(L)Pro segments facilitate the three stranded beta-sheet formation in the 14 residue peptide Boc-LFV(D)P(L)PLFVA(D)P(L)PLFV-OMe (peptide 2) in which the Phe2/Phe7 orientations are similar to that in the octapeptide. The anticipated folded conformations of peptides 1 and 2 are established by the delineation of intramolecularly hydrogen bonded NH groups and by the observation of specific cross strand NOEs. The observation of ring current shifted aromatic protons is a diagnostic of close approach of the Phe2 and Phe7 side chains. Specific assignment of aromatic proton resonances using HSQC and HSQC-TOCSY methods allow an analysis of interproton NOEs between the spatially proximate aromatic rings. This approach facilitates specific assignments in systems containing multiple aromatic rings in spectra at natural abundance. Evidence is presented for a dynamic process which invokes a correlated conformational change about the C-alpha-C-beta(chi(1)) bond for the pair of interacting Phe residues. NMR results suggest that aromatic ring orientations observed in crystals are maintained in solution. Anomalous temperature dependence of ring current induced proton chemical shifts suggests that solvophobic effects may facilitate aromatic ring clustering in apolar solvents.

Formulation development and evaluation of lamivudine controlled release tablets using cross-linked sago starch

Objectives: Modified starches based polymeric substances find utmost applicability in pharmaceutical formulation development. Cross-linked starches showed very promising results in drug delivery application. The present investigation concerns with the development of controlled release tablets of lamivudine using cross-linked sago starch. Methods: The cross-linked derivative was synthesized with phosphorous oxychloride and native sago starch in basic pH medium. The cross-linked sago starch was tested for acute toxicity and drug-excipient compatibility study. The formulated tablets were evaluated for various physical characteristics, in vitro dissolution release study and in vivo pharmacokinetic study in rabbit model. Results: In vitro release study showed that the optimized formulation exhibited highest correlation (R) in case of zero order kinetic model and the release mechanism followed a combination of diffusion and erosion process. There was a significant difference in the pharmacokinetic parameters (T-max, C-max, AUC, V-d, T-1/2, and MDT) of the optimized formulation as compared to the marketed conventional tablet Lamivir (R). Conclusion: The cross-linked starch showed promising results in terms of controlling the release behavior of the active drug from the matrix. The hydrophilic matrix synthesized by cross-linking could be used with a variety of active pharmaceutical ingredients for making their controlled/sustained release formulations.

A practical approach for cross-functional vehicle body weight optimization

The goal of optimization in vehicle design is often blurred by the myriads of requirements belonging to attributes that may not be quite related. If solutions are sought by optimizing attribute performance-related objectives separately starting with a common baseline design configuration as in a traditional design environment, it becomes an arduous task to integrate the potentially conflicting solutions into one satisfactory design. It may be thus more desirable to carry out a combined multi-disciplinary design optimization (MDO) with vehicle weight as an objective function and cross-functional attribute performance targets as constraints. For the particular case of vehicle body structure design, the initial design is likely to be arrived at taking into account styling, packaging and market-driven requirements. The problem with performing a combined cross-functional optimization is the time associated with running such CAE algorithms that can provide a single optimal solution for heterogeneous areas such as NVH and crash safety. In the present paper, a practical MDO methodology is suggested that can be applied to weight optimization of automotive body structures by specifying constraints on frequency and crash performance. Because of the reduced number of cases to be analyzed for crash safety in comparison with other MDO approaches, the present methodology can generate a single size-optimized solution without having to take recourse to empirical techniques such as response surface-based prediction of crash performance and associated successive response surface updating for convergence. An example of weight optimization of spaceframe-based BIW of an aluminum-intensive vehicle is given to illustrate the steps involved in the current optimization process.