Spectral Relaxation Research Articles

Unsteady mixed convection flow through a permeable stretching flat surface with partial slip effects through MHD nanofluid using spectral relaxation method

Abstract An unsteady, laminar, mixed convective stagnation point nanofluid flow through a permeable stretching flat surface using internal heat source or sink and partial slip is investigated. The effects of thermophoresis and Brownian motion parameters are revised on the traditional model of nanofluid for which nanofluid particle volume fraction is passively controlled on the boundary. Spectral relaxation method is applied here to solve the non-dimensional conservation equations. The results show the illustration of the impact of skin friction coefficient, different physical parameters, and the heat transfer rate. The nanofluid motion is enhanced with increase in the value of the internal heat sink or source. On the other hand, the rate of heat transfer on the stretching sheet and the skin friction coefficient are reduced by an increase in internal heat generation. This study further shows that the velocity slip increases with decrease in the rate of heat transfer. The outcome results are benchmarked with previously published results.

Spectral hole lifetimes and spin population relaxation dynamics in neodymium-doped yttrium orthosilicate

We present a detailed study of the lifetime of optical spectral holes due to population storage in Zeeman sublevels of Nd$^{3+}$:Y$_2$SiO$_5$. The lifetime is measured as a function of magnetic field strength and orientation, temperature and Nd$^{3+}$ doping concentration. At the lowest temperature of 3 K we find a general trend where the lifetime is short at low field strengths, then increases to a maximum lifetime at a few hundreds of mT, and then finally decays rapidly for high field strengths. This behaviour can be modelled with a relaxation rate dominated by Nd$^{3+}$-Nd$^{3+}$ cross relaxation at low fields and spin lattice relaxation at high magnetic fields. The maximum lifetime depends strongly on both the field strength and orientation, due to the competition between these processes and their different angular dependencies. The cross relaxation limits the maximum lifetime for concentrations as low as 30 ppm of Nd$^{3+}$ ions. By decreasing the concentration to less than 1 ppm we could completely eliminate the cross relaxation, reaching a lifetime of 3.8 s at 3~K. At higher temperatures the spectral hole lifetime is limited by the magnetic-field independent Raman and Orbach processes. In addition we show that the cross relaxation rate can be strongly reduced by creating spectrally large holes of the order of the optical inhomogeneous broadening. Our results are important for the development and design of new rare-earth-ion doped crystals for quantum information processing and narrow-band spectral filtering for biological tissue imaging.

A Note on Heat Transfer Unsteady Similar Boundary Layer Flow Over a Streatching Surface with Power Law Temperature

The aim of this paper is to investigate the effects of thermal radiation and viscous dissipation on unsteady two dimensional viscous and incompressible boundary layer flow and heat transfer from a stretching surface. The governing partial differential equations are transformed into a system of ordinary differential equations by using similarity transformation. The governing equations are solved through the use of Spectral relaxation method. The solution is found to be dependent on the governing parameters including the Prandtl number, unsteadiness parameter, thermal radiation parameter, Eckert number and power law temperature parameter. Flow profiles are presented graphically for various values of the problem parameters.

Distributed methods for synchronization of orthogonal matrices over graphs

This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as a least-squares optimization problem with nonlinear constraints. The synchronization problem appears as one of the key components in applications ranging from 3D-localization to image registration. The main contributions of this work can be summarized as the introduction of two novel algorithms; one for symmetric graphs and one for graphs that are possibly asymmetric. Under general conditions, the former has guaranteed convergence to the solution of a spectral relaxation to the synchronization problem. The latter is stable for small step sizes when the graph is quasi-strongly connected. The proposed methods are verified in numerical simulations.

Temperature and Phase Dependence of the Spectral and Molecular Relaxation Characteristics of (1 – x)RbNO3 + xAl2O3 Composites

Temperature and phase dependences of Raman spectra (RS) and molecular relaxation characteristics of nitrate-ion vibrations in (1 – x)RbNO3 + xAl2O3 composites with various concentrations of Al2O3 nanopowder were studied. It was shown that the ν 1(A) vibrational relaxation time with filler concentration x = 0.6 was essentially constant in high-temperature phase RbNO3-II as compared with RbNO3-III, which indicated that the cubic RbNO3-III phase was stabilized. The salt subsystem was highly disordered at high filler concentrations so that structurally distinct states were difficult to detect at the macro level.

Thermal transport in graphene with defect and doping: Phonon modes analysis

The effects of defect and isotopic doping with different ratios on the thermal conductivity of graphene are investigated by using non-equilibrium molecular dynamics simulations and normal mode analysis method. In contrast to the persisted size dependent thermal conductivity in the pristine graphene, thermal conductivity of defected graphene quickly saturates when the size is greater than 100 nm. Similar to the pristine graphene, we find the thermal conductivity of defected and doped graphene follows ∼T−α behavior, and the power exponent α is sensitive to the defect and doping ratio. The spectral phonon relaxation time and normalized accumulation thermal conductivity with respect to the phonon mean free path (MFP) reveal that the long-MFP phonon modes are strongly suppressed in the defected and doped graphene, resulting in the suppressed size dependence and the weaker temperature dependence of the thermal conductivity compared to the pristine graphene. The phonon modal analysis in our work establishes a deep understanding of the defect and doping effects on the thermal transport in graphene, which would provide effective guidance to the graphene-based phonon engineering applications.

Fluorescence Dynamics of LicT Protein by Time-Resolved Spectroscopy

In this paper, the fluorescence dynamics of tryptophan residues in LicT protein is investigated by time-resolved fluorescence method combined with UV absorption and steady-state fluorescence spectroscopy. The local microenvironment and structural changes of LicT protein before and after activation are studied. The activated LicT protein AC 141 prevents the antitermination of gene transcription involved in carbohydrate utilization to accelerate the body's metabolism. The structural properties and microenvironment of activated protein AC 141 and wild-type protein Q 22 were determined by different fluorescence emissions and lifetimes of tryptophan residues. The interaction between tryptophan residues and solvent is elucidated by decay associated spectroscopy (DAS) and time-resolved emission spectra (TRES), indicating that upon activation, the structure of AC 141 is more compact than that of wild-type Q 22. In addition, TRES also showed that tryptophan residues in the protein had a continuous spectral relaxation process. Anisotropy results illustrated the conformational motions of residues and whole proteins, suggesting that tryptophan residues had independent local motions in the protein system, and that the motions were more intense in the activated protein.

Imaging Cellular Dynamics with Spectral Relaxation Imaging Microscopy: Distinct Spectral Dynamics in Golgi Membranes of Living Cells.

Spectral relaxation from fluorescent probes is a useful technique for determining the dynamics of condensed phases. To this end, we have developed a method based on wide-field spectral fluorescence lifetime imaging microscopy to extract spectral relaxation correlation times of fluorescent probes in living cells. We show that measurement of the phase and modulation of fluorescence from two wavelengths permit the identification and determination of excited state lifetimes and spectral relaxation correlation times at a single modulation frequency. For NBD fluorescence in glycerol/water mixtures, the spectral relaxation correlation time determined by our approach exhibited good agreement with published dielectric relaxation measurements. We applied this method to determine the spectral relaxation dynamics in membranes of living cells. Measurements of the Golgi-specific C6-NBD-ceramide probe in living HeLa cells revealed sub-nanosecond spectral dynamics in the intracellular Golgi membrane and slower nanosecond spectral dynamics in the extracellular plasma membrane. We interpret the distinct spectral dynamics as a result of structural plasticity of the Golgi membrane relative to more rigid plasma membranes. To the best of our knowledge, these results constitute one of the first measurements of Golgi rotational dynamics.

Cross-Diffusion Effects on Unsteady Bioconvective Flow Past a Stretching Sheet

This paper presents a mathematical analysis of bioconvection heat, mass, and motile microorganisms transfer over a stretching sheet in a medium filled with a fluid containing gyrotactic microorganisms. Cross-diffusion is taken into account in the medium. Using the boundary layer approximations, the set of unsteady partial differential equations governing the fluid flow is transformed into nonlinear PDEs form and then solved numerically using bivariate spectral relaxation method (BSRM) and bivariate spectral quasi-linearization method (BSQLM). A comparison between BSRM and BSQLM is made for the first time in this work. The accuracy and convergence analysis of the methods are also discussed. The methods are found to be convergent and give very accurate results with very few grid points in the numerical discretization procedure. A parametric study of the entire flow regime is carried out to illustrate the effects of various governing parameters on the fluid properties and flow characteristics. The results obtained show a significant effect of cross-diffusion on the fluid properties and flow characteristics. The Dufour number was found to increase the local Sherwood number and density number of motile microorganisms while decreasing the Nusselt number, and the reverse effect is true for the Soret number. Furthermore, the Nusselt number, Sherwood number, and density number of motile microorganisms are highly influenced by buoyancy and bioconvection parameters.

Characterization of Water and a Model Lipophilic Compound in Human Stratum Corneum by NMR Spectroscopy and Equilibrium Sorption

The stratum corneum (SC) is the outermost skin layer in humans and other mammals and the primary barrier to water loss and environmental exposure to chemicals and microorganisms. It consists of flattened, keratin-filled corneocytes surrounded by well-organized lipid layers. Human SC at varying degrees of hydration with and without addition of a model lipophilic compound, 2-(trifluoromethyl) benzonitrile (TFMB), was studied using proton (1H) and fluorine (19F) nuclear magnetic resonance techniques. Proton spectral analyses revealed that water mainly occupies the corneocytes in agreement with prior studies. Observations from 19F spectral and spin-lattice relaxation time (T1) analyses showed that TFMB is primarily present in the lipids with small amounts in water, which is located within the corneocytes. This is consistent with TFMB sorption, which was measured in SC with and without lipid extraction. The presence of TFMB within the corneocytes supports the hypothesis that transcellular diffusion of a lipophilic compound like TFMB may contribute to SC permeation.

Bounds on skyline probability for databases with uncertain preferences

For determining skyline objects for an uncertain database with uncertain preferences, it is necessary to compute the skyline probability of a given object with respect to other objects. The problem boils down to computing the probability of the union of events from the probabilities of all possible joint probabilities. Linear Bonferroni bound is concerned with computing the bounds on the probability of the union of events with partial information. We use this technique to estimate the skyline probability of an object and propose a polynomial-time algorithm for computing sharp upper bound. We show that the use of partial information does not affect the quality of solution but helps in improving the efficiency. We formulate the problem as a Linear Programming Problem (LPP) and characterize a set of feasible points that is believed to contain all extreme points of the LPP. The maximization of the objective function over this set of points is equivalent to a bi-polar quadratic optimization problem. We use a spectral relaxation technique to solve the bi-polar quadratic optimization problem. The proposed algorithm is of O(n3) time complexity and is the first ever polynomial-time algorithm to determine skyline probability. We show that the bounds computed by our proposed algorithm determine almost the same set of skyline objects as that with the deterministic algorithm. Experimental results are presented to corroborate this claim.

Analysis of MHD Forced Convective Flow of Variable Fluid Properties over a Saturated Porous Medium with Thermal Radiation Effect

The present paper addresses the problem of MHD forced convective flow in a fluid saturated porous medium with Brinkman-Forchheimer model, which is an important physical phenomena in engineering applications. The paper extends the previous models to account for effects of variable fluid properties on the forced convective flow through a porous medium in the presence of radiative heat loss using bivariate spectral relaxation method (BSRM). The dynamic viscosity and thermal conductivity of the newtonian fluid are assumed to vary linearly respectively, with temperature whereas the contribution of thermal radiative heat loss is based on Rosseland diffussion approximation. The flow model is described and expressed in form of a highly coupled nonlinear system of partial differential equations. The method of solution BSRM as proposed by Motsa [25] seeks to decouple the original system of PDEs to form a sequence of equations that can be solved in a computationally efficient manner. BSRM is an approach that applies spectral collocation independently in all underlying independent variable is executed to obtain approximate solutions of the problem. The proposed algorithm is supposed to be a very accurate, convergent and very effective in generating numerical results. The results obtained show a significant effects of the flow control parameters on the fluid velocity and temperature respectively. Consequently, the wall shear stress and local heat transfer rate of the present paper are compared with the available results in literatures. Remarkable impacts and a good agreement are found.

Modulation of Symmetry-Breaking Intramolecular Charge-Transfer Dynamics Assisted by Pendant Side Chains in π-Linkers in Quadrupolar Diketopyrrolopyrrole Derivatives.

The effect of the length of pendant side chains in centrosymmetric quadrupolar molecules on dynamics of their most perplexing photophysical phenomenon, i.e., symmetry-breaking intramolecular charge transfer, has been discovered. Unexpectedly, considerable influence of length of these pendant side chains in π-linkers arose as a structural factor enabling the control of the degree of fluorescence solvatochromism. The symmetry-breaking intramolecular charge-transfer dynamics has been described on quadrupolar diketopyrrolopyrrole derivatives possessing fluorene moieties as π-linkers and diarylamino groups as electron donors. On the basis of the evolution of transient fluorescence spectra obtained by a femtosecond broadband fluorescence up-conversion spectroscopy, it was found that the relative contribution of diffusive solvation and torsional relaxation in overall spectral relaxation can be modulated by the length of pendant side chain in π-linkers. Consequently, we demonstrated that this modulation plays a significant role in determining the photophysical properties of diketopyrrolopyrroles in a polar medium.

Effects of macromolecular crowding on a small lipid binding protein probed at the single-amino acid level

Macromolecular crowding is a distinctive feature of the cellular interior, influencing the behaviour of biomacromolecules. Despite significant advancements in the description of the effects of crowding on global protein properties, the influence of cellular components on local protein attributes has received limited attention. Here, we describe a residue-level systematic interrogation of the structural, dynamic, and binding properties of the liver fatty acid binding protein (LFABP) in crowded solutions.Two-dimensional NMR spectral fingerprints and relaxation data were collected on LFABP in the presence of polymeric and biomolecular crowders. Non-interacting crowders produced minimal site-specific spectral perturbations on ligand-free and lipid-bound LFABP. Conformational adaptations upon ligand binding reproduced those observed in dilute solution, but a perturbation of the free oleate state resulted in less favorable uptake. When LFABP engaged in direct interactions with background molecules, changes in local chemical environments were detected for residues of the internal binding pocket and of the external surface.Enhanced complexity was introduced by investigating LFABP in cell lysates, and in membrane-bounded compartments. LFABP was able to capture ligands from prokaryotic and eukaryotic cell lysates, and from artificial cells (water-in-oil emulsion droplets).The data suggest that promiscuous interactions are a major factor influencing protein function in the cell.

Unsteady Boundary Layer Flow over a Vertical Surface due to Impulsive and Buoyancy in the Presence of Thermal-Diffusion and Diffusion-Thermo using Bivariate Spectral Relaxation Method

In this article, unsteady boundary layer flow formed over a vertical surface due to impulsive motion and buoyancy is investigated. The mathematical model which properly accounts for space and temperature-dependent internal heat source in a flowing fluid is incorporated into the energy equation. This model is presented in this study as a term which accounts for two different forms of internal heat generation during the short time period and long time period. Due to the fluid flow under consideration, the influence of thermal-diffusion and diffusion-thermo are incorporated into the governing equation since it may not be realistic to assume that both effects are of smaller order of magnitude than the effects described by Fourier’s or Fick’s law. The corresponding effect of internal heat source on viscosity is considered; the viscosity is assumed to vary as a linear function of temperature. The flow model is described in terms of a highly coupled and nonlinear system of partial differential equations. The governing equations are non-dimensionalized by using suitable similarity transformation which unraveled the behavior of the fluid flow at short time and long time periods. The dimensionless system of non-linear coupled partial differential equations (PDEs) is solved using Bivariate Spectral Relaxation Method (BSRM). A parametric study of selected parameters is conducted and results of the surface shear stress, heat transfer and mass transfer at the wall are illustrated graphically and physical aspects of the problem are discussed.

On Couple Stress Effects on Unsteady Nanofluid Flow over Stretching Surfaces with Vanishing Nanoparticle Flux at the Wall

In this paper the problem of unsteady nanofluid flow over a stretching sheet subject to couple stress effects is presented. Most previous studies have assumed that the nanoparticle volume fraction at the boundary surface may be actively controlled. However, a realistic boundary condition for the nanoparticle volume fraction model is that the nanoparticle flux at the boundary be set to zero. This paper differs from previous studies in that we assume there is no active control of the nanoparticle volume fraction at boundary. The spectral relaxation method has been used to solve the governing equations, moreover the results were further confirmed by using the quasi-linearization method. The qualitative and quantitative effects of the dimensionless parameters in the problem such as the couple stress parameter, the Prandtl number, the Brownian motion parameter, the thermophoresis parameter, the Lewis number on the fluid behavior are determined.

Structural Heterogeneity in the Localized Excited States of Poly(3-hexylthiophene).

Transient hole-burning and resonantly enhanced Raman spectroscopies are used to probe heterogeneities among localized singlet excitons of poly(3-hexylthiophene) in solution. Transient hole-burning spectroscopy facilitated by population dumping through wavelength-selective stimulated emission exposes inhomogeneous broadening of the exciton absorption band in the near-infrared, as reflected by correlations between stimulated emission and excited-state absorption transition energies. Dump-induced spectral diffusion of the exciton absorption band reflects structural fluctuations in the locally excited polymer. This diffusion is observed to occur slightly faster or slower than the nonequilibrium relaxation that follows direct excitation of the polymer (8-9 ps), with the time scale for diffusion varying with subpopulation: dumping across small vs large band gaps results in diffusion over 5 vs 35 ps, respectively. Furthermore, incomplete spectral relaxation of transient holes reflects that subsets of locally excited structural motifs prepared through photoexcitation cannot interchange through structural fluctuations that occur over the singlet-exciton lifetime. Raman spectra of the C═C/C-C stretching region collected in resonance at energies across the exciton absorption band exhibit frequency and intensity trends (Raman "dispersion") ascribed to variation in the local effective conjugation length. Together, results explicitly reveal heterogeneities among excitonic states associated with variations and fluctuations in local conformational order.

Influence of thermal radiation on free convective heat and mass transfer past an isothermal vertical oscillating porous plate in the presence of chemical reaction and heat generation-absorption

An approximate analysis of the problem of the transient free convective transfer flow of a Newtonian non-gray optically thin fluid past an isothermal vertical oscillating porous plate in the presence of chemical reaction and heat generation/absorption is studied. The dimensionless governing coupled linear partial differential equations are solved using a spectral relaxation method. The essence of the method of the solution-spectral relaxation method SRM is to linearize and decouple the original system of PDEs to form a sequence of independent linear equations that can be solved iteratively. The SRM approach applies the spectral collocation method and a finite different method independently in all underlying independent variables to obtain approximate solutions of the problem. Detailed computations on the influence of the chemical reaction parameter $A_{2}$ , the thermal radiation parameter R, the number Sc, the heat absorption/generation parameter $Q_{1}$ , and the Prandtl number on the flow velocity, temperature, and concentration distributions are illustrated graphically and in table format. It is observed that the flow velocity increases with the increase in either thermal radiation or thermal Grashof number. The temperature profile increases with the increase in either the thermal radiation parameter or the heat absorption/generation parameter. The rate of heat transfer decreases with the increase in the thermal radiation parameter, whereas it increases with increasing value of the heat generation/absorption parameter.

Nonspectral modes and how to find them in the Ornstein-Uhlenbeck process with white μ-stable noise.

We consider the Ornstein-Uhlenbeck process with a broad initial probability distribution (Lévy distribution), which exhibits so-called nonspectral modes. The relaxation rate of such modes differs from those determined from the parameters of the corresponding Fokker-Plank equation. The first nonspectral mode is shown to govern the relaxation process and allows for estimation of the initial distribution's Lévy index. A method based on continuous wavelet transformation is proposed to extract both (spectral and nonspectral) relaxation rates from a stochastic data sample.

On a bivariate spectral relaxation method for unsteady magneto-hydrodynamic flow in porous media.

The paper presents a significant improvement to the implementation of the spectral relaxation method (SRM) for solving nonlinear partial differential equations that arise in the modelling of fluid flow problems. Previously the SRM utilized the spectral method to discretize derivatives in space and finite differences to discretize in time. In this work we seek to improve the performance of the SRM by applying the spectral method to discretize derivatives in both space and time variables. The new approach combines the relaxation scheme of the SRM, bivariate Lagrange interpolation as well as the Chebyshev spectral collocation method. The technique is tested on a system of four nonlinear partial differential equations that model unsteady three-dimensional magneto-hydrodynamic flow and mass transfer in a porous medium. Computed solutions are compared with previously published results obtained using the SRM, the spectral quasilinearization method and the Keller-box method. There is clear evidence that the new approach produces results that as good as, if not better than published results determined using the other methods. The main advantage of the new approach is that it offers better accuracy on coarser grids which significantly improves the computational speed of the method. The technique also leads to faster convergence to the required solution.