About the relaxed cocoercivity and the convergence of the proximal point algorithm
Directory of Open Access Journals (Sweden)
Abdellatif Moudafi
2013-10-01
Full Text Available The aim of this paper is to study the convergence of two proximal algorithms via the notion of (α,r-relaxed cocoercivity without Lipschitzian continuity. We will show that this notion is enough to obtain some interesting convergence theorems without any Lipschitz-continuity assumption. The relaxed cocoercivity case is also investigated.
Directory of Open Access Journals (Sweden)
Poom Kumam
2012-01-01
Full Text Available We introduce an iterative algorithm for finding a common element of the set of solutions of a system of mixed equilibrium problems, the set of solutions of a general system of variational inequalities for Lipschitz continuous and relaxed cocoercive mappings, the set of common fixed points for nonexpansive semigroups, and the set of common fixed points for an infinite family of strictly pseudocontractive mappings in Hilbert spaces. Furthermore, we prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm under some suitable conditions which solves some optimization problems. Our results extend and improve the recent results of Chang et al. (2010 and many others.
Nonlinear fractional relaxation
Indian Academy of Sciences (India)
A Tofighi
2012-04-01
We deﬁne a nonlinear model for fractional relaxation phenomena. We use -expansion method to analyse this model. By studying the fundamental solutions of this model we ﬁnd that when → 0 the model exhibits a fast decay rate and when → ∞ the model exhibits a power-law decay. By analysing the frequency response we ﬁnd a logarithmic enhancement for the relative ratio of susceptibility.
Nonlinear Model of non-Debye Relaxation
Zon, Boris A
2010-01-01
We present a simple nonlinear relaxation equation which contains the Debye equation as a particular case. The suggested relaxation equation results in power-law decay of fluctuations. This equation contains a parameter defining the frequency dependence of the dielectric permittivity similarly to the well-known one-parameter phenomenological equations of Cole-Cole, Davidson-Cole and Kohlrausch-Williams-Watts. Unlike these models, the obtained dielectric permittivity (i) obeys to the Kramers-Kronig relation; (ii) has proper behaviour at large frequency; (iii) its imaginary part, conductivity, shows a power-law frequency dependence \\sigma ~ \\omega^n where n1 is also observed in several experiments. The nonlinear equation proposed may be useful in various fields of relaxation theory.
Nonlinear nonequilibrium quasiparticle relaxation in Josephson junctions.
Krasnov, V M
2009-11-27
I solve numerically a full set of nonlinear kinetic balance equations for stacked Josephson junctions, which allows analysis of strongly nonequilibrium phenomena. It is shown that nonlinearity becomes significant already at very small disequilibrium. The following new, nonlinear effects are obtained: (i) At even-gap voltages V = 2nDelta/e (n = 2, 3, ...) nonequilibrium bosonic bands overlap. This leads to enhanced emission of Omega = 2Delta bosons and to the appearance of dips in tunnel conductance. (ii) A new type of radiative solution is found at strong disequilibrium. It is characterized by the fast stimulated relaxation of quasiparticles. A stack in this state behaves as a light emitting diode and directly converts electric power to boson emission, without utilization of the ac-Josephson effect. The phenomenon can be used for realization of a new type of superconducting cascade laser in the THz frequency range.
Noninteracting control of nonlinear systems based on relaxed control
Jayawardhana, B.
2010-01-01
In this paper, we propose methodology to solve noninteracting control problem for general nonlinear systems based on the relaxed control technique proposed by Artstein. For a class of nonlinear systems which cannot be stabilized by smooth feedback, a state-feedback relaxed control can be designed to
Dispersion of Sound in Dilute Suspensions with Nonlinear Particle Relaxation
Kandula, Max
2010-01-01
The theory accounting for nonlinear particle relaxation (viscous and thermal) has been applied to the prediction of dispersion of sound in dilute suspensions. The results suggest that significant deviations exist for sound dispersion between the linear and nonlinear theories at large values of Omega(Tau)(sub d), where Omega is the circular frequency, and Tau(sub d) is the Stokesian particle relaxation time. It is revealed that the nonlinear effect on the dispersion coefficient due to viscous contribution is larger relative to that of thermal conduction
Relaxation Processes in Nonlinear Optical Polymer Films
Directory of Open Access Journals (Sweden)
S.N. Fedosov
2010-01-01
Full Text Available Dielectric properties of the guest-host polystyrene/DR1 system have been studied by the AC dielectric spectroscopy method at frequencies from 1 Hz to 0,5 MHz and by the thermally stimulated depolarization current (TSDC method from – 160 to 0 °C. The relaxation peaks at infra-low frequencies from 10 – 5to 10–2 Hz were also calculated using the Hamon’s approximation. Three relaxation processes, namely, α, β and δ ones were identified from the TSDC peaks, while the ε''(fdependence showed a non-Debye ρ-peak narrowing with temperature. The activation energy of the α-relaxation appeared to be 2,57 eV, while that of the γ-process was 0,52 eV. Temperature dependence of the relaxation time is agreed with the Williams-Landel-Ferry model. The ε''(fpeaks were fitted to Havriliak-Negami’s expression and the corresponding distribution parameters were obtained.
Mäkelä, J T A; Korhonen, R K
2016-06-14
Modern fibril-reinforced computational models of articular cartilage can include inhomogeneous tissue composition and structure, and nonlinear mechanical behavior of collagen, proteoglycans and fluid. These models can capture well experimental single step creep and stress-relaxation tests or measurements under small strains in unconfined and confined compression. Yet, it is known that in indentation, especially at high strain velocities, cartilage can express highly nonlinear response. Different fibril reinforced poroelastic and poroviscoelastic models were used to assess measured highly nonlinear stress-relaxation response of rabbit articular cartilage in indentation. Experimentally measured depth-dependent volume fractions of different tissue constituents and their mechanical nonlinearities were taken into account in the models. In particular, the collagen fibril network was modeled using eight separate models that implemented five different constitutive equations to describe the nonlinearity. These consisted of linear elastic, nonlinear viscoelastic and multiple nonlinear elastic representations. The model incorporating the most nonlinearly increasing Young׳s modulus of collagen fibrils as a function of strain captured best the experimental data. Relative difference between the model and experiment was ~3%. Surprisingly, the difference in the peak forces between the experiment and the model with viscoelastic collagen fibrils was almost 20%. Implementation of the measured volume fractions did not improve the ability of the model to capture the measured mechanical data. These results suggest that a highly nonlinear formulation for collagen fibrils is needed to replicate multi-step stress-relaxation response of rabbit articular cartilage in indentation with high strain rates.
Nonlinear relaxation field in charged systems under high electric fields
Energy Technology Data Exchange (ETDEWEB)
Morawetz, K
2000-07-01
The influence of an external electric field on the current in charged systems is investigated. The results from the classical hierarchy of density matrices are compared with the results from the quantum kinetic theory. The kinetic theory yields a systematic treatment of the nonlinear current beyond linear response. To this end the dynamically screened and field-dependent Lenard-Balescu equation is integrated analytically and the nonlinear relaxation field is calculated. The classical linear response result known as Debye - On-Sager relaxation effect is only obtained if asymmetric screening is assumed. Considering the kinetic equation of one specie the other species have to be screened dynamically while the screening with the same specie itself has to be performed statically. Different other approximations are discussed and compared. (author)
On the prediction of stress relaxation from known creep of nonlinear materials
Energy Technology Data Exchange (ETDEWEB)
Touati, D.; Cederbaum, G. [Ben-Gurion Univ. of the Negev, Beer Sheva (Israel)
1997-04-01
A method to predict the nonlinear relaxation behavior from creep experiments of nonlinear viscoelastic materials is presented. It is shown that for given nonlinear creep properties, and creep compliance represented by the Prony series, the Schapery creep model can be transformed into a set of first order nonlinear equations. The solution of these equations enables the obtaining of the nonlinear stress relaxation curves. The strain-dependent constitutive equation can then be constructed for a given nonlinear viscoelastic model, as needed for engineering applications. A comparison example of the calculated stress relaxation curves, with test data for polyurethane demonstrates the very good accuracy of the proposed method.
Nonlinear optical studies of relaxation in semiconductor microstructures
Remillard, Jeffrey Thomas
1990-11-01
Exposing a semiconductor to optical radiation near the fundamental band gap results in the creation of populations or elementary excitations including electrons, holes, and excitons, and also results in the creation of a superposition state between the ground and excited state of the solid. The relaxation of optically generated excitons and carriers in semiconductor microstructures was studied using four wave mixing (FWM) spectroscopy. The systems studied include CdSSe microcrystallite doped glasses and GaA/AlGaAs multiple quantum well structures (MQWS). First, the nonlinear optical response of simple two level systems is examined in order to provide insight into the types of line shapes expected from semiconductors. It is shown that the line shape is strongly dependent on how the system is coupled to the reservoir and the consequences of coupling to a reservoir are examined in a FWM measurement made in atomic sodium. The first semiconductor system studied is CdSSe microcrystallite doped glass. This system is shown to have a very slow component to the nonlinear response which has an optical intensity dependence and temperature dependence which suggests that the FWM response in these materials is trap mediated. Room temperature FWM measurements in GaAs MQWS enables the measurement of the carrier recombination time and the ambipolar diffusion coefficient. Using the technique of correlated optical fields, a slow component to the nonlinear response was measured showing an interference profile which suggests a possible shift of the exciton resonance due to the optically generated carriers. At low temperatures, measurements of the exciton line shape and relaxation time were made and evidence for exciton spectral diffusion was found. The low temperature line shapes can be qualitatively reproduced using Modified Optical Bloch equations which include the effects of spectral diffusion.
Towards a Generic Constructive Nonlinear Control Design Tool using Relaxed Control
Jayawardhana, Bayu
2015-01-01
In this paper, we revisit a control design approach for general (non-affine) nonlinear systems using relaxed control. Using the notion of relaxed input, where the ordinary real-valued control input is replaced by a measure-valued control input, we are able to manipulate the original system such that
Molecular structure-property correlations from optical nonlinearity and thermal-relaxation dynamics.
Bhattacharyya, Indrajit; Priyadarshi, Shekhar; Goswami, Debabrata
2009-02-01
We apply ultrafast single beam Z-scan technique to measure saturation absorption coefficients and nonlinear-refraction coefficients of primary alcohols at 1560 nm. The nonlinear effects result from vibronic transitions and cubic nonlinear-refraction. To measure the pure total third-order nonlinear susceptibility, we removed thermal effects with a frequency optimized optical-chopper. Our measurements of thermal-relaxation dynamics of alcohols, from 1560 nm thermal lens pump and 780 nm probe experiments revealed faster and slower thermal-relaxation timescales, respectively, from conduction and convection. The faster timescale accurately predicts thermal-diffusivity, which decreases linearly with alcohol chain-lengths since thermal-relaxation is slower in heavier molecules. The relation between thermal-diffusivity and alcohol chain-length confirms structure-property relationship.
Improvement of nonlinear diffusion equation using relaxed geometric mean filter for low PSNR images
DEFF Research Database (Denmark)
Nadernejad, Ehsan
2013-01-01
A new method to improve the performance of low PSNR image denoising is presented. The proposed scheme estimates edge gradient from an image that is regularised with a relaxed geometric mean filter. The proposed method consists of two stages; the first stage consists of a second order nonlinear...... anisotropic diffusion equation with new neighboring structure and the second is a relaxed geometric mean filter, which processes the output of nonlinear anisotropic diffusion equation. The proposed algorithm enjoys the benefit of both nonlinear PDE and relaxed geometric mean filter. In addition, the algorithm...... will not introduce any artefacts, and preserves image details, sharp corners, curved structures and thin lines. Comparison of the results obtained by the proposed method, with those of other methods, shows that a noticeable improvement in the quality of the denoised images, that were evaluated subjectively...
Energy Technology Data Exchange (ETDEWEB)
Jin Chen
2009-12-07
Efficient and robust Variable Relaxation Solver, based on pseudo-transient continuation, is developed to solve nonlinear anisotropic thermal conduction arising from fusion plasma simulations. By adding first and/or second order artificial time derivatives to the system, this type of method advances the resulting time-dependent nonlinear PDEs to steady state, which is the solution to be sought. In this process, only the stiffness matrix itself is involved so that the numerical complexity and errors can be greatly reduced. In fact, this work is an extension of integrating efficient linear elliptic solvers for fusion simulation on Cray XIE. Two schemes are derived in this work, first and second order Variable Relaxations. Four factors are observed to be critical for efficiency and preservation of solution's symmetric structure arising from periodic boundary condition: refining meshes in different coordinate directions, initializing nonlinear process, varying time steps in both temporal and spatial directions, and accurately generating nonlinear stiffness matrix. First finer mesh scale should be taken in strong transport direction; Next the system is carefully initialized by the solution with linear conductivity; Third, time step and relaxation factor are vertex-based varied and optimized at each time step; Finally, the nonlinear stiffness matrix is updated by just scaling corresponding linear one with the vector generated from nonlinear thermal conductivity.
Relaxation and decomposition methods for mixed integer nonlinear programming
Nowak, Ivo; Bank, RE
2005-01-01
This book presents a comprehensive description of efficient methods for solving nonconvex mixed integer nonlinear programs, including several numerical and theoretical results, which are presented here for the first time. It contains many illustrations and an up-to-date bibliography. Because on the emphasis on practical methods, as well as the introduction into the basic theory, the book is accessible to a wide audience. It can be used both as a research and as a graduate text.
Strain-enhanced stress relaxation impacts nonlinear elasticity in collagen gels.
Nam, Sungmin; Hu, Kenneth H; Butte, Manish J; Chaudhuri, Ovijit
2016-05-17
The extracellular matrix (ECM) is a complex assembly of structural proteins that provides physical support and biochemical signaling to cells in tissues. The mechanical properties of the ECM have been found to play a key role in regulating cell behaviors such as differentiation and malignancy. Gels formed from ECM protein biopolymers such as collagen or fibrin are commonly used for 3D cell culture models of tissue. One of the most striking features of these gels is that they exhibit nonlinear elasticity, undergoing strain stiffening. However, these gels are also viscoelastic and exhibit stress relaxation, with the resistance of the gel to a deformation relaxing over time. Recent studies have suggested that cells sense and respond to both nonlinear elasticity and viscoelasticity of ECM, yet little is known about the connection between nonlinear elasticity and viscoelasticity. Here, we report that, as strain is increased, not only do biopolymer gels stiffen but they also exhibit faster stress relaxation, reducing the timescale over which elastic energy is dissipated. This effect is not universal to all biological gels and is mediated through weak cross-links. Mechanistically, computational modeling and atomic force microscopy (AFM) indicate that strain-enhanced stress relaxation of collagen gels arises from force-dependent unbinding of weak bonds between collagen fibers. The broader effect of strain-enhanced stress relaxation is to rapidly diminish strain stiffening over time. These results reveal the interplay between nonlinear elasticity and viscoelasticity in collagen gels, and highlight the complexity of the ECM mechanics that are likely sensed through cellular mechanotransduction.
Lima, R. P. A.; Gléria, Iram; Cícero, C. H.; Lyra, M. L.; de Moura, F. A. B. F.
2017-03-01
The discrete nonlinear Schrodinger equation (DNSE) describes wave phenomena in several physical contexts, ranging from electronic transport in crystalline chains to light propagation in nonlinear media and Bose-Einstein condensates. Here, we study the influence of the nonlinear response time on the temporal evolution of a wavepacket initially localized in a single site of a finite closed chain. Distinct long-time wavepacket distributions are identified as a function of the nonlinear strength χ and the characteristic relaxation time τ. Besides the more standard delocalized and self-trapped regimes, we report the occurrence of intermediate phases. In one of them the wavepacket self-focus in the opposite chain site. A phase with asymptotically fragmented wavepackets also develops. A crossover regime on which the ultimate wavepacket distribution is strongly dependent on the precise set of model parameters is also identified. We provide the full phase diagram related to the long-time wavepacket distribution in the (χ, τ) space.
Nonlinear approximation method in Lagrangian relaxation-based algorithms for hydrothermal scheduling
Energy Technology Data Exchange (ETDEWEB)
Guan, X. [Pacific Gas and Electric, San Francisco, CA (United States); Luh, P.B.; Zhang, L. [Univ. of Connecticut, Storrs, CT (United States). Dept. of Electrical and Systems Engineering
1995-05-01
When the Lagrangian relaxation technique is used to solve hydrothermal scheduling problems, many subproblems have linear stage-wise cost functions. A well recognized difficulty is that the solutions to these subproblems may oscillate between maximum and minimum generations with slight changes of the multipliers. Furthermore, the subproblem solutions may become singular, i.e., they are un-determined when the linear coefficients become zero. This may result in large differences between subproblem solutions and the optimal primal schedule. In this paper, a nonlinear approximation method is presented which utilizes nonlinear functions, quadratic in this case, to approximate relevant linear cost functions. The analysis shows that the difficulty associated with solution oscillation is reduced, and singularity is avoided. Extensive testing based on Northeast Utilities data indicates that the method consistently generates better schedules than the standard Lagrangian relaxation method.
Relaxation of charge in monolayer graphene: Fast nonlinear diffusion versus Coulomb effects
Kolomeisky, Eugene B.; Straley, Joseph P.
2017-01-01
Pristine monolayer graphene exhibits very poor screening because the density of states vanishes at the Dirac point. As a result, charge relaxation is controlled by the effects of zero-point motion (rather than by the Coulomb interaction) over a wide range of parameters. Combined with the fact that graphene possesses finite intrinsic conductivity, this leads to a regime of relaxation described by a nonlinear diffusion equation with a diffusion coefficient that diverges at zero charge density. Some consequences of this fast diffusion are self-similar superdiffusive regimes of relaxation, the development of a charge depleted region at the interface between electron- and hole-rich regions, and finite extinction times for periodic charge profiles.
A nonlinear constitutive model for stress relaxation in ligaments and tendons.
Davis, Frances M; De Vita, Raffaella
2012-12-01
A novel constitutive model that describes stress relaxation in transversely isotropic soft collagenous tissues such as ligaments and tendons is presented. The model is formulated within the nonlinear integral representation framework proposed by Pipkin and Rogers (J. Mech. Phys. Solids. 16:59-72, 1968). It represents a departure from existing models in biomechanics since it describes not only the strain dependent stress relaxation behavior of collagenous tissues but also their finite strains and transverse isotropy. Axial stress-stretch data and stress relaxation data at different axial stretches are collected on rat tail tendon fascicles in order to compute the model parameters. Toward this end, the rat tail tendon fascicles are assumed to be incompressible and undergo an isochoric axisymmetric deformation. A comparison with the experimental data proves that, unlike the quasi-linear viscoelastic model (Fung, Biomechanics: Mechanics of Living Tissues. Springer, New York, 1993) the constitutive law can capture the observed nonlinearities in the stress relaxation response of rat tail tendon fascicles.
Nonlinear propagation and decay of intense regular and random waves in relaxing media
Gurbatov, S. N.; Rudenko, O. V.; Demin, I. Yu.
2015-10-01
An integro-differential equation is written down that contains terms responsible for nonlinear absorption, visco-heat-conducting dissipation, and relaxation processes in a medium. A general integral expression is obtained for calculating energy losses of the wave with arbitrary characteristics—intensity, profile (frequency spectrum), and kernel describing the internal dynamics of the medium. Profiles of stationary solutions are constructed both for an exponential relaxation kernel and for other types of kernels. Energy losses at the front of week shock waves are calculated. General integral formulas are obtained for energy losses of intense noise, which are determined by the form of the kernel, the structure of the noise correlation function, and the mean square of the derivative of realization of a random process.
Kandula, Max
2012-01-01
The Sound attenuation and dispersion in saturated gas-vapor-droplet mixture in the presence of evaporation has been investigated theoretically. The theory is based on an extension of the work of Davidson to accommodate the effects of nonlinear particle relaxation processes of mass, momentum and energy transfer on sound attenuation and dispersion. The results indicate the existence of a spectral broadening effect in the attenuation coefficient (scaled with respect to the peak value) with a decrease in droplet mass concentration. It is further shown that for large values of the droplet concentration the scaled attenuation coefficient is characterized by a universal spectrum independent of droplet mass concentration.
Suppression of nonlinear phonon relaxation in Yb:YAG thin disk via zero phonon line pumping.
Smrž, Martin; Miura, Taisuke; Chyla, Michal; Nagisetty, Siva; Novák, Ondřej; Endo, Akira; Mocek, Tomáš
2014-08-15
A quantitative comparison of conventional absorption line (940 nm) pumping and zero phonon line (ZPL) (969 nm) pumping of a Yb:YAG thin disk laser is reported. Characteristics of an output beam profile, surface temperature, and deformation of a thin disk under the different pump wavelengths are evaluated. We found that a nonlinear phonon relaxation (NPR) of the excited state in Yb:YAG, which induces nonlinear temperature rise and large aspheric deformation, did not appear in the case of a ZPL pumped Yb:YAG thin disk. This means that the advantage of ZPL pumping is not only the reduction of quantum defect but also the suppression of NPR. The latter effect is more important for high power lasers.
Directory of Open Access Journals (Sweden)
Wei-Cheng Wang
2002-06-01
Full Text Available We study the asymptotic equivalence of the Jin-Xin relaxation model and its formal limit for genuinely nonlinear $2imes 2$ conservation laws. The initial data is allowed to have jump discontinuities corresponding to centered rarefaction waves, which includes Riemann data connected by rarefaction curves. We show that, as long as the initial data is a small perturbation of a constant state, the solution for the relaxation system exists globally in time and converges, in the zero relaxation limit, to the solution of the corresponding conservation law uniformly except for an initial layer.
Mishurov, Dmytro; Voronkin, Andrii; Roshal, Alexander; Brovko, Oleksandr
2016-07-01
Cross-linked polymers on the basis of di-, tri and tetraglycidyl ethers of quercetin (3,3‧,4‧,5,7-pentahydroxyflavone) were synthesized, and then, poled in electrical field of corona discharge. Investigations of structural, thermal and optical parameters of the polymer films were carried out. It was found that the polymers obtained from di- and triglycidyl quercetin ethers had high values of macroscopic quadratic susceptibilities and substantial stability of nonlinear optical (NLO) properties after the poling. Tetraglycidyl ether of quercetin forms the polymer of lower quadratic susceptibility, which demonstrates noticeable relaxation process resulting in decrease of the NLO effect. It is supposed that the difference of the NLO properties is due to peculiarities of physical network of the polymers, namely to the ratio between numbers of hydrogen bonds formed by hydroxyl groups of chromophore fragments and by the ones of interfragmental parts of the polymeric chains.
Jung, Kwan-Jin
2009-09-01
A mathematical model to regress the nonlinear blood oxygen level-dependent (BOLD) fMRI signal has been developed by incorporating the refractory effect into the linear BOLD model of the biphasic gamma variate function. The refractory effect was modeled as a relaxation of two separate BOLD capacities corresponding to the biphasic components of the BOLD signal in analogy with longitudinal relaxation of magnetization in NMR. When tested with the published fMRI data of finger tapping, the nonlinear BOLD model with the refractory effect reproduced the nonlinear BOLD effects such as reduced poststimulus undershoot and saddle pattern in a prolonged stimulation as well as the reduced BOLD signal for repetitive stimulation.
Uncovering Molecular Relaxation Processes with Nonlinear Spectroscopies in the Deep UV
West, Brantley Andrew
Conical intersections mediate internal conversion dynamics that compete with even the fastest nuclear motions in molecular systems. Traditional kinetic models do not apply in this regime of commensurate electronic and nuclear motion because the surroundings do not maintain equilibrium throughout the relaxation process. This dissertation focuses on uncovering the physics associated with vibronic interactions at conical intersections. Of particular interest are coherent nuclear motions driven by steep excited state potential energy gradients. Technical advances have only recently made these dynamics accessible in many systems including DNA nucleobases and cyclic polyene molecules. Optical analogues of multidimensional NMR spectroscopies have recently yielded transformative insight in relaxation processes ranging from energy transfer in photosynthesis to bond making and breaking in liquids. Prior to the start of this research, such experiments had only been conducted at infrared and visible wavelengths. Applications in the ultraviolet were motivated by studies of numerous biological systems (e.g., DNA, proteins), but had been challenged by technical issues. The work presented in this dissertation combines pulse generation techniques developed in the optical physics community with spectroscopic techniques largely pioneered by physical chemists to implement two-dimensional ultraviolet spectroscopy (2DUV). This technique is applied at the shortest wavelengths and with the best signal-to-noise ratios reported to date. Sub-picosecond excited state deactivation processes provide photo stability to the DNA double helix. Vibrational energy transfer from the solute to surrounding solvent enables relaxation of the highly non-equilibrium ground state produced by fast internal conversion. In this dissertation, nonlinear spectroscopies carried out at cryogenic temperatures are used to uncover the particular nuclear modes in the solvent that primarily accept vibrational energy from
Institute of Scientific and Technical Information of China (English)
Wan Zhongping; Wang Guangrain; Lv Yibing
2011-01-01
The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty func- tion approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach.
Directory of Open Access Journals (Sweden)
Ohanyan G.G.
2010-09-01
Full Text Available The quasi-adiabatic and quasi-isotherm regimes of propagation of high-frequency perturbation are considered in a thermal relaxing gas–fluid mixture. The simplified non-linear equations are obtained. It is shown that in the absence of heat transfer and under the quasi-adiabatic regime the form of propagation is soliton, or the shock wave in quasi-isotherm regime.
Ohanyan G.G.
2010-01-01
The quasi-adiabatic and quasi-isotherm regimes of propagation of high-frequency perturbation are considered in a thermal relaxing gas–fluid mixture. The simplified non-linear equations are obtained. It is shown that in the absence of heat transfer and under the quasi-adiabatic regime the form of propagation is soliton, or the shock wave in quasi-isotherm regime.
Analysis of a Relaxation Scheme for a Nonlinear Schrödinger Equation Occurring in Plasma Physics
Oelz, Dietmar
2014-03-15
This paper is devoted to the analysis of a relaxation-type numerical scheme for a nonlinear Schrödinger equation arising in plasma physics. The scheme is shown to be preservative in the sense that it preserves mass and energy. We prove the well-posedness of the semidiscretized system and prove convergence to the solution of the time-continuous model. © 2014 © Vilnius Gediminas Technical University, 2014.
Viscoelasticity, nonlinear shear start-up, and relaxation of entangled star polymers
Snijkers, Frank
2013-07-23
We report on a detailed rheological investigation of well-defined symmetric entangled polymer stars of low functionality with varying number of arms, molar mass of the arms, and solvent content. Emphasis is placed on the response of the stars in simple shear, during start-up, and for relaxation upon flow cessation. To reduce experimental artifacts associated with edge fracture (primarily) and wall slip, we employ a homemade cone-partitioned plate fixture which was successfully implemented in recent studies. Reliable data for these highly entangled stars could be obtained for Weissenberg numbers below 300. The appearance of a stress overshoot during start-up with a corresponding strain approaching a value of 2 suggests that in the investigated shear regime the stars orient but do not stretch. This is corroborated by the fact that the empirical Cox-Merx rule appears to be validated, within experimental error. On the other hand, the (shear) rate dependent steady shear viscosity data exhibit a slope smaller than the convective constraint release slope of -1 (for linear polymers) for the investigated range of rates. The broadness of the stress overshoot reflects the broad linear relaxation spectrum of the stars. The initial stress relaxation rate, reflecting the initial loss of entanglements due to the action of convective constraint release in steady shear flow, increases with Weissenberg number. More importantly, when compared against the relevant rates for comb polymers with relatively short arms, the latter are slower at larger Weissenberg numbers. At long times, the relaxation data are consistent with the linear viscoelastic data on these systems. © 2013 American Chemical Society.
Zhang, Rui; Schweizer, Kenneth S
2012-04-21
We generalize the microscopic naïve mode coupling and nonlinear Langevin equation theories of the coupled translation-rotation dynamics of dense suspensions of uniaxial colloids to treat the effect of applied stress on shear elasticity, cooperative cage escape, structural relaxation, and dynamic and static yielding. The key concept is a stress-dependent dynamic free energy surface that quantifies the center-of-mass force and torque on a moving colloid. The consequences of variable particle aspect ratio and volume fraction, and the role of plastic versus double glasses, are established in the context of dense, glass-forming suspensions of hard-core dicolloids. For low aspect ratios, the theory provides a microscopic basis for the recently observed phenomenon of double yielding as a consequence of stress-driven sequential unlocking of caging constraints via reduction of the distinct entropic barriers associated with the rotational and translational degrees of freedom. The existence, and breadth in volume fraction, of the double yielding phenomena is predicted to generally depend on both the degree of particle anisotropy and experimental probing frequency, and as a consequence typically occurs only over a window of (high) volume fractions where there is strong decoupling of rotational and translational activated relaxation. At high enough concentrations, a return to single yielding is predicted. For large aspect ratio dicolloids, rotation and translation are always strongly coupled in the activated barrier hopping event, and hence for all stresses only a single yielding process is predicted.
El Ghazi, Haddou; Jorio, Anouar
2014-10-01
By means of a combination of Quantum Genetic Algorithm and Hartree-Fock-Roothaan method, the changes in linear, third-order nonlinear and total refractive index associated with intra-conduction band transition are investigated with and without shallow-donor impurity in wurtzite (In,Ga)N-GaN spherical quantum dot. For both cases with and without impurity, the calculation is performed within the framework of single band effective-mass and parabolic band approximations. Impurity's position and relaxation time effects are investigated. It is found that the modulation of the refractive index changes, suitable for good performance optical modulators and various infra-red optical device applications can be easily obtained by tailoring the relaxation time and the position of the impurity.
Energy Technology Data Exchange (ETDEWEB)
El Ghazi, Haddou, E-mail: hadghazi@gmail.com [LPS, Faculty of Science, Dhar El Mehrez, BP 1796 Fes-Atlas (Morocco); Special Mathematics, CPGE My Youssef, Rabat (Morocco); Jorio, Anouar [LPS, Faculty of Science, Dhar El Mehrez, BP 1796 Fes-Atlas (Morocco)
2014-10-01
By means of a combination of Quantum Genetic Algorithm and Hartree–Fock–Roothaan method, the changes in linear, third-order nonlinear and total refractive index associated with intra-conduction band transition are investigated with and without shallow-donor impurity in wurtzite (In,Ga)N–GaN spherical quantum dot. For both cases with and without impurity, the calculation is performed within the framework of single band effective-mass and parabolic band approximations. Impurity's position and relaxation time effects are investigated. It is found that the modulation of the refractive index changes, suitable for good performance optical modulators and various infra-red optical device applications can be easily obtained by tailoring the relaxation time and the position of the impurity.
Valente, Pedro C.; da Silva, Carlos B.; Pinho, Fernando T.
2013-11-01
We report a numerical study of statistically steady and decaying turbulence of FENE-P fluids for varying polymer relaxation times ranging from the Kolmogorov dissipation time-scale to the eddy turnover time. The total turbulent kinetic energy dissipation is shown to increase with the polymer relaxation time in both steady and decaying turbulence, implying a ``drag increase.'' If the total power input in the statistically steady case is kept equal in the Newtonian and the viscoelastic simulations the increase in the turbulence-polymer energy transfer naturally lead to the previously reported depletion of the Newtonian, but not the overall, kinetic energy dissipation. The modifications to the nonlinear energy cascade with varying Deborah/Weissenberg numbers are quantified and their origins investigated. The authors acknowledge the financial support from Fundação para a Ciência e a Tecnologia under grant PTDC/EME-MFE/113589/2009.
Norris, G; McConnell, G
2010-03-01
A novel bi-directional pump geometry that nonlinearly increases the nonlinear optical conversion efficiency of a synchronously pumped optical parametric oscillator (OPO) is reported. This bi-directional pumping method synchronizes the circulating signal pulse with two counter-propagating pump pulses within a linear OPO resonator. Through this pump scheme, an increase in nonlinear optical conversion efficiency of 22% was achieved at the signal wavelength, corresponding to a 95% overall increase in average power. Given an almost unchanged measured pulse duration of 260 fs under optimal performance conditions, this related to a signal wavelength peak power output of 18.8 kW, compared with 10 kW using the traditional single-pass geometry. In this study, a total effective peak intensity pump-field of 7.11 GW/cm(2) (corresponding to 3.55 GW/cm(2) from each pump beam) was applied to a 3 mm long periodically poled lithium niobate crystal, which had a damage threshold intensity of 4 GW/cm(2), without impairing crystal integrity. We therefore prove the application of this novel pump geometry provides opportunities for power-scaling of synchronously pumped OPO systems together with enhanced nonlinear conversion efficiency through relaxed damage threshold intensity conditions.
Boyanovsky, D; Holman, R; Kumar, S P; Pisarski, R D; Salgado, J; Pisarski, Rob D.
1998-01-01
The real time evolution of field condensates is solved for small and large field amplitudes in scalar theories.For small amplitudes,the quantum equations of motion for the condensate can be linearized and solved by Laplace transform. The late time evolution turns to be determined by the singularities in the complex plane (one-particle poles, two- and multi- particle cuts, Landau cuts for non-zero initial temperature). In hot scalar electrodynamics, we solve the real time evolution of field condensates with soft length scales \\sim k^{-1}>(eT)^{-1}. Transverse gauge invariant condensates relax as 1/t^2 to amplitudes determined by the quasiparticle poles. We rederive the HTL action using the non-equilibrium field theory techniques.In the nonlinear regime (for large initial energy densities) we analyze the dynamics of dissipation and relaxation in scalar theory after linear unstabilities are shut-off by the quantum back-reaction. A new time scale emerges that separates the linear from the non-linear regimes. This...
A Neurodynamic Model to Solve Nonlinear Pseudo-Monotone Projection Equation and Its Applications.
Eshaghnezhad, Mohammad; Effati, Sohrab; Mansoori, Amin
2016-09-29
In this paper, a neurodynamic model is given to solve nonlinear pseudo-monotone projection equation. Under pseudo-monotonicity condition and Lipschitz continuous condition, the projection neurodynamic model is proved to be stable in the sense of Lyapunov, globally convergent, globally asymptotically stable, and globally exponentially stable. Also, we show that, our new neurodynamic model is effective to solve the nonconvex optimization problems. Moreover, since monotonicity is a special case of pseudo-monotonicity and also since a co-coercive mapping is Lipschitz continuous and monotone, and a strongly pseudo-monotone mapping is pseudo-monotone, the neurodynamic model can be applied to solve a broader classes of constrained optimization problems related to variational inequalities, pseudo-convex optimization problem, linear and nonlinear complementarity problems, and linear and convex quadratic programming problems. Finally, several illustrative examples are stated to demonstrate the effectiveness and efficiency of our new neurodynamic model.
Řehoř, Martin; Pr&oring; ša, Vít; T&oring; ma, Karel
2016-10-01
Rigorous analysis of the response of nonlinear materials to step inputs requires one to simultaneously handle the discontinuity, differentiation, and nonlinearity. This task is however beyond the reach of the standard theories such as the classical theory of distributions and presents a considerable mathematical difficulty. New advanced mathematical tools are necessary to handle the challenge. An elegant and relatively easy-to-use framework capable of accomplishing the task is provided by the Colombeau algebra, which is a generalisation of the classical theory of distributions to the nonlinear setting. We use the Colombeau algebra formalism and derive explicit formulae describing the response of incompressible Maxwell viscoelastic fluid subject to step load/deformation in the lubricated squeeze flow setting.
Asinari, P.
2011-03-01
Boltzmann equation is one the most powerful paradigms for explaining transport phenomena in fluids. Since early fifties, it received a lot of attention due to aerodynamic requirements for high altitude vehicles, vacuum technology requirements and nowadays, micro-electro-mechanical systems (MEMs). Because of the intrinsic mathematical complexity of the problem, Boltzmann himself started his work by considering first the case when the distribution function does not depend on space (homogeneous case), but only on time and the magnitude of the molecular velocity (isotropic collisional integral). The interest with regards to the homogeneous isotropic Boltzmann equation goes beyond simple dilute gases. In the so-called econophysics, a Boltzmann type model is sometimes introduced for studying the distribution of wealth in a simple market. Another recent application of the homogeneous isotropic Boltzmann equation is given by opinion formation modeling in quantitative sociology, also called socio-dynamics or sociophysics. The present work [1] aims to improve the deterministic method for solving homogenous isotropic Boltzmann equation proposed by Aristov [2] by two ideas: (a) the homogeneous isotropic problem is reformulated first in terms of particle kinetic energy (this allows one to ensure exact particle number and energy conservation during microscopic collisions) and (b) a DVM-like correction (where DVM stands for Discrete Velocity Model) is adopted for improving the relaxation rates (this allows one to satisfy exactly the conservation laws at macroscopic level, which is particularly important for describing the late dynamics in the relaxation towards the equilibrium).
Carlen, Eric A.; Fröhlich, Jürg; Lebowitz, Joel
2016-02-01
We construct generalized grand-canonical- and canonical Gibbs measures for a Hamiltonian system described in terms of a complex scalar field that is defined on a circle and satisfies a nonlinear Schrödinger equation with a focusing nonlinearity of order p transitions" and regularity properties of field samples, are established. We then study a time evolution of this system given by the Hamiltonian evolution perturbed by a stochastic noise term that mimics effects of coupling the system to a heat bath at some fixed temperature. The noise is of Ornstein-Uhlenbeck type for the Fourier modes of the field, with the strength of the noise decaying to zero, as the frequency of the mode tends to ∞. We prove exponential approach of the state of the system to a grand-canonical Gibbs measure at a temperature and "chemical potential" determined by the stochastic noise term.
Ramaswamy, Rajesh; Sbalzarini, Ivo F; González-Segredo, Nélido
2011-01-28
Stochastic effects from correlated noise non-trivially modulate the kinetics of non-linear chemical reaction networks. This is especially important in systems where reactions are confined to small volumes and reactants are delivered in bursts. We characterise how the two noise sources confinement and burst modulate the relaxation kinetics of a non-linear reaction network around a non-equilibrium steady state. We find that the lifetimes of species change with burst input and confinement. Confinement increases the lifetimes of all species that are involved in any non-linear reaction as a reactant. Burst monotonically increases or decreases lifetimes. Competition between burst-induced and confinement-induced modulation may hence lead to a non-monotonic modulation. We quantify lifetime as the integral of the time autocorrelation function (ACF) of concentration fluctuations around a non-equilibrium steady state of the reaction network. Furthermore, we look at the first and second derivatives of the ACF, each of which is affected in opposite ways by burst and confinement. This allows discriminating between these two noise sources. We analytically derive the ACF from the linear Fokker-Planck approximation of the chemical master equation in order to establish a baseline for the burst-induced modulation at low confinement. Effects of higher confinement are then studied using a partial-propensity stochastic simulation algorithm. The results presented here may help understand the mechanisms that deviate stochastic kinetics from its deterministic counterpart. In addition, they may be instrumental when using fluorescence-lifetime imaging microscopy (FLIM) or fluorescence-correlation spectroscopy (FCS) to measure confinement and burst in systems with known reaction rates, or, alternatively, to correct for the effects of confinement and burst when experimentally measuring reaction rates.
Energy Technology Data Exchange (ETDEWEB)
Bizarri, G.; Moses, W.W. [Lawrence Berkeley Laboratory, Berkeley, CA 94720-8119 (United States); Singh, J. [Faculty of EHS, B-41, Charles Darwin University, Darwin NT 0909 (Australia); Vasil' ev, A.N., E-mail: anvasiliev@rambler.r [Institute of Nuclear Physics, Moscow State University, Moscow 119991 (Russian Federation); Williams, R.T. [Department of Physics, Wake Forest University, Winston-Salem, NC 27109 (United States)
2009-12-15
The non-proportional dependence of a scintillator's light yield on primary particle energy is believed to be influenced crucially by the interplay of non-linear kinetic terms in the radiative and non-radiative decay of excitations versus locally deposited excitation density. A calculation of energy deposition, -dE/dx, along the electron track for NaI is presented for an energy range from several electron-volt to 1 MeV. Such results can be used to specify an initial excitation distribution, if diffusion is neglected. An exactly solvable two-channel (exciton and hole(electron)) model containing 1st and 2nd order kinetic terms is constructed and used to illustrate important features seen in non-proportional light-yield curves, including a dependence on pulse shaping (detection gate width).
Edwards, Jack R.; Mcrae, D. S.
1993-01-01
An efficient implicit method for the computation of steady, three-dimensional, compressible Navier-Stokes flowfields is presented. A nonlinear iteration strategy based on planar Gauss-Seidel sweeps is used to drive the solution toward a steady state, with approximate factorization errors within a crossflow plane reduced by the application of a quasi-Newton technique. A hybrid discretization approach is employed, with flux-vector splitting utilized in the streamwise direction and central differences with artificial dissipation used for the transverse fluxes. Convergence histories and comparisons with experimental data are presented for several 3-D shock-boundary layer interactions. Both laminar and turbulent cases are considered, with turbulent closure provided by a modification of the Baldwin-Barth one-equation model. For the problems considered (175,000-325,000 mesh points), the algorithm provides steady-state convergence in 900-2000 CPU seconds on a single processor of a Cray Y-MP.
Mishima, A.; Nasu, K.
1989-03-01
The one-dimensional extended Peierls-Hubbard model with half-filled-band electrons is studied in order to clarify the lattice relaxation path of the photogenerated charge-transfer excitation in halogen-bridged mixed-valence metal complexes. The ground and excited states are calculated within mean-field theory for electrons and the adiabatic approximation for phonons. It is concluded that the main origin of the photoinduced absorption is a distant pair of the hole-polaron and the electron-polaron. This distant pair is created not from the ground state of the self-trapped exciton (STE), but from the excited states of the STE through their autodissociation. This is consistent with the experiment on the excitation energy dependence of the photoinduced absorption yield.
Marzola, Luca; Raidal, Martti
2016-11-01
Motivated by natural inflation, we propose a relaxation mechanism consistent with inflationary cosmology that explains the hierarchy between the electroweak scale and Planck scale. This scenario is based on a selection mechanism that identifies the low-scale dynamics as the one that is screened from UV physics. The scenario also predicts the near-criticality and metastability of the Standard Model (SM) vacuum state, explaining the Higgs boson mass observed at the Large Hadron Collider (LHC). Once Majorana right-handed neutrinos are introduced to provide a viable reheating channel, our framework yields a corresponding mass scale that allows for the seesaw mechanism as well as for standard thermal leptogenesis. We argue that considering singlet scalar dark matter extensions of the proposed scenario could solve the vacuum stability problem and discuss how the cosmological constant problem is possibly addressed.
Asymptotic representation of relaxation oscillations in lasers
Grigorieva, Elena V
2017-01-01
In this book we analyze relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics. The models are based on rate equations taking into account periodic modulation of parameters, optoelectronic delayed feedback, mutual coupling between lasers, intermodal interaction and other factors. With the aim to study relaxation oscillations we present the special asymptotic method of integration for ordinary differential equations and differential-difference equations. As a result, they are reduced to discrete maps. Analyzing the maps we describe analytically such nonlinear phenomena in lasers as multistability of large-amplitude relaxation cycles, bifurcations of cycles, controlled switching of regimes, phase synchronization in an ensemble of coupled systems and others. The book can be fruitful for students and technicians in nonlinear laser dynamics and in differential equations.
ON THE CENTRAL RELAXING SCHEMES I:SINGLE CONSERVATION LAWS
Institute of Scientific and Technical Information of China (English)
Hua-zhong Tang
2000-01-01
In this first paper we present a central relaxing scheme for scalar conservation laws, based on using the local relaxation approximation. Our scheme is obtained without using linear or nonlinear Riemann solvers. A cell entropy inequality is studied for the semidiscrete central relaxing scheme, and a second order MUSCL scheme is shown to be TVD in the zero relaxation limit. The next paper will extend the central relaxing scheme to multi-dimensional systems of conservation laws in curvilinear coordinates, including numerical experiments for 1D and 2D problems.
Collisionless Relaxation of Stellar Systems
Kandrup, H E
1998-01-01
The objective of the work summarised here has been to exploit and extend ideas from plasma physics and accelerator dynamics to formulate a unified description of collisionless relaxation that views violent relaxation, Landau damping, and phase mixing as (manifestations of) a single phenomenon. This approach embraces the fact that the collisionless Boltzmann equation (CBE), the basic object of the theory, is an infinite-dimensional Hamiltonian system, with the distribution function f playing the role of the fundamental dynamical variable, and that, interpreted appropriately, an evolution described by the other Hamiltonian system. Equilibrium solutions correspond to extremal points of the Hamiltonian subject to the constraints associated with Liouville's Theorem. Stable equilibria correspond to energy minima. The evolution of a system out of equilibrium involves (in general nonlinear) phase space oscillations which may -- or may not -- interfere destructively so as to damp away.
Collisionless Relaxation of Stellar Systems
Kandrup, Henry E.
1999-08-01
The objective of the work summarized here has been to exploit and extend ideas from plasma physics and accelerator dynamics to formulate a unified description of collisionless relaxation of stellar systems that views violent relaxation, Landau damping, and phase mixing as (manifestations of) a single phenomenon. This approach embraces the fact that the collisionless Boltzmann equation (CBE), the basic object of the theory, is an infinite-dimensional Hamiltonian system, with the distribution function f playing the role of the fundamental dynamical variable, and that, interpreted appropriately, an evolution described by the CBE is no different fundamentally from an evolution described by any other Hamiltonian system. Equilibrium solutions f0 correspond to extremal points of the Hamiltonian subject to the constraints associated with Liouville's Theorem. Stable equilibria correspond to energy minima. The evolution of a system out of equilibrium involves (in general nonlinear) phase space oscillations which may - or may not - interfere destructively so as to damp away.
Stress relaxation in viscous soft spheres.
Boschan, Julia; Vasudevan, Siddarth A; Boukany, Pouyan E; Somfai, Ellák; Tighe, Brian P
2017-09-27
We report the results of molecular dynamics simulations of stress relaxation tests in athermal viscous soft sphere packings close to their unjamming transition. By systematically and simultaneously varying both the amplitude of the applied strain step and the pressure of the initial condition, we access both linear and nonlinear response regimes and control the distance to jamming. Stress relaxation in viscoelastic solids is characterized by a relaxation time τ* that separates short time scales, where viscous loss is substantial, from long time scales, where elastic storage dominates and the response is essentially quasistatic. We identify two distinct plateaus in the strain dependence of the relaxation time, one each in the linear and nonlinear regimes. The height of both plateaus scales as an inverse power law with the distance to jamming. By probing the time evolution of particle velocities during relaxation, we further identify a correlation between mechanical relaxation in the bulk and the degree of non-affinity in the particle velocities on the micro scale.
Relaxation Techniques for Health
... R S T U V W X Y Z Relaxation Techniques for Health Share: On This Page What’s the ... Bottom Line? How much do we know about relaxation techniques? A substantial amount of research has been done ...
Kobayashi, M; Irisawa, H
1961-10-27
The latent period of relaxation of molluscan myocardium due to anodal current is much longer than that of contraction. Although the rate and the grade of relaxation are intimately related to both the stimulus condition and the muscle tension, the latent period of relaxation remains constant, except when the temperature of the bathing fluid is changed.
Terahertz Nonlinearity in Graphene Plasmons
Jadidi, Mohammad M; Winnerl, Stephan; Sushkov, Andrei B; Drew, H Dennis; Murphy, Thomas E; Mittendorff, Martin
2015-01-01
Sub-wavelength graphene structures support localized plasmonic resonances in the terahertz and mid-infrared spectral regimes. The strong field confinement at the resonant frequency is predicted to significantly enhance the light-graphene interaction, which could enable nonlinear optics at low intensity in atomically thin, sub-wavelength devices. To date, the nonlinear response of graphene plasmons and their energy loss dynamics have not been experimentally studied. We measure and theoretically model the terahertz nonlinear response and energy relaxation dynamics of plasmons in graphene nanoribbons. We employ a THz pump-THz probe technique at the plasmon frequency and observe a strong saturation of plasmon absorption followed by a 10 ps relaxation time. The observed nonlinearity is enhanced by two orders of magnitude compared to unpatterned graphene with no plasmon resonance. We further present a thermal model for the nonlinear plasmonic absorption that supports the experimental results.
Indentation load relaxation test
Energy Technology Data Exchange (ETDEWEB)
Hannula, S.P.; Stone, D.; Li, C.Y. (Cornell Univ., Ithaca, NY (USA))
Most of the models that are used to describe the nonelastic behavior of materials utilize stress-strain rate relations which can be obtained by a load relaxation test. The conventional load relaxation test, however, cannot be performed if the volume of the material to be tested is very small. For such applications the indentation type of test offers an attractive means of obtaining data necessary for materials characterization. In this work the feasibility of the indentation load relaxation test is studied. Experimental techniques are described together with results on Al, Cu and 316 SS. These results are compared to those of conventional uniaxial load relaxation tests, and the conversion of the load-indentation rate data into the stress-strain rate data is discussed.
Relaxation techniques for stress
... problems such as high blood pressure, stomachaches, headaches, anxiety, and depression. Using relaxation techniques can help you feel calm. These exercises can also help you manage stress and ease the effects of stress on your body.
Spectral Estimation of NMR Relaxation
Naugler, David G.; Cushley, Robert J.
2000-08-01
In this paper, spectral estimation of NMR relaxation is constructed as an extension of Fourier Transform (FT) theory as it is practiced in NMR or MRI, where multidimensional FT theory is used. nD NMR strives to separate overlapping resonances, so the treatment given here deals primarily with monoexponential decay. In the domain of real error, it is shown how optimal estimation based on prior knowledge can be derived. Assuming small Gaussian error, the estimation variance and bias are derived. Minimum bias and minimum variance are shown to be contradictory experimental design objectives. The analytical continuation of spectral estimation is constructed in an optimal manner. An important property of spectral estimation is that it is phase invariant. Hence, hypercomplex data storage is unnecessary. It is shown that, under reasonable assumptions, spectral estimation is unbiased in the context of complex error and its variance is reduced because the modulus of the whole signal is used. Because of phase invariance, the labor of phasing and any error due to imperfect phase can be avoided. A comparison of spectral estimation with nonlinear least squares (NLS) estimation is made analytically and with numerical examples. Compared to conventional sampling for NLS estimation, spectral estimation would typically provide estimation values of comparable precision in one-quarter to one-tenth of the spectrometer time when S/N is high. When S/N is low, the time saved can be used for signal averaging at the sampled points to give better precision. NLS typically provides one estimate at a time, whereas spectral estimation is inherently parallel. The frequency dimensions of conventional nD FT NMR may be denoted D1, D2, etc. As an extension of nD FT NMR, one can view spectral estimation of NMR relaxation as an extension into the zeroth dimension. In nD NMR, the information content of a spectrum can be extracted as a set of n-tuples (ω1, … ωn), corresponding to the peak maxima
MULTIDIMENSIONAL RELAXATION APPROXIMATIONS FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS
Institute of Scientific and Technical Information of China (English)
Mohammed Sea(l)d
2007-01-01
We construct and implement a non-oscillatory relaxation scheme for multidimensional hyperbolic systems of conservation laws. The method transforms the nonlinear hyperbolic system to a semilinear model with a relaxation source term and linear characteristics which can be solved numerically without using either Riemann solver or linear iterations.To discretize the relaxation system we consider a high-resolution reconstruction in space and a TVD Runge-Kutta time integration. Detailed formulation of the scheme is given for problems in three space dimensions and numerical experiments are implemented in both scalar and system cases to show the effectiveness of the method.
Perturbations and quantum relaxation
Kandhadai, Adithya
2016-01-01
We investigate whether small perturbations can cause relaxation to quantum equilibrium over very long timescales. We consider in particular a two-dimensional harmonic oscillator, which can serve as a model of a field mode on expanding space. We assume an initial wave function with small perturbations to the ground state. We present evidence that the trajectories are highly confined so as to preclude relaxation to equilibrium even over very long timescales. Cosmological implications are briefly discussed.
Observations of Nonlinear Phenomena in Rotordynamics
Ehrich, Fredric F.
Observations, analysis and understanding of nonlinear rotordynamic phenomena observed in aircraft gas turbine engines and other high-speed rotating machinery over the course of the author's career are described. Included are observations of sum-and-difference frequency response; effects of roller bearing clearance; relaxation oscillations; subharmonic response; chaotic response; and other generic nonlinear responses such as superharmonic and ultra-subharmonic response.
Molecular Relaxation in Liquids
Bagchi, Biman
2012-01-01
This book brings together many different relaxation phenomena in liquids under a common umbrella and provides a unified view of apparently diverse phenomena. It aligns recent experimental results obtained with modern techniques with recent theoretical developments. Such close interaction between experiment and theory in this area goes back to the works of Einstein, Smoluchowski, Kramers' and de Gennes. Development of ultrafast laser spectroscopy recently allowed study of various relaxation processes directly in the time domain, with time scales going down to picosecond (ps) and femtosecond (fs
Stability and suppression of turbulence in relaxing molecular gas flows
Grigoryev, Yurii N
2017-01-01
This book presents an in-depth systematic investigation of a dissipative effect which manifests itself as the growth of hydrodynamic stability and suppression of turbulence in relaxing molecular gas flows. The work describes the theoretical foundations of a new way to control stability and laminar turbulent transitions in aerodynamic flows. It develops hydrodynamic models for describing thermal nonequilibrium gas flows which allow the consideration of suppression of inviscid acoustic waves in 2D shear flows. Then, nonlinear evolution of large-scale vortices and Kelvin-Helmholtz waves in relaxing shear flows are studied. Critical Reynolds numbers in supersonic Couette flows are calculated analytically and numerically within the framework of both linear and nonlinear classical energy hydrodynamic stability theories. The calculations clearly show that the relaxation process can appreciably delay the laminar-turbulent transition. The aim of the book is to show the new dissipative effect, which can be used for flo...
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Shear stress relaxation of dental ceramics determined from creep behavior.
DeHoff, Paul H; Anusavice, Kenneth J
2004-10-01
To test the hypothesis that shear stress relaxation functions of dental ceramics can be determined from creep functions measured in a beam-bending viscometer. Stress relaxation behavior was determined from creep data for the following materials: (1) a veneering ceramic-IPS Empress2 body ceramic (E2V); (2) an experimental veneering ceramic (EXV); (3) a low expansion body porcelain-Vita VMK 68 feldspathic body porcelain (VB); (4) a high expansion body porcelain-Will Ceram feldspathic body porcelain (WCB); (5) a medium expansion opaque porcelain-Vita feldspathic opaque porcelain (VO); and (6) a high expansion opaque porcelain-Will Ceram feldspathic opaque porcelain (WCO). Laplace transform techniques were used to relate shear stress relaxation functions to creep functions for an eight-parameter, discrete viscoelastic model. Nonlinear regression analysis was performed to fit a four-term exponential relaxation function for each material at each temperature. The relaxation functions were utilized in the ANSYS finite element program to simulate creep behavior in three-point bending for each material at each temperature. Shear stress relaxation times at 575 degrees C ranged from 0.03 s for EXV to 195 s for WCO. Knowledge of the shear relaxation functions for dental ceramics at high temperatures is required input for the viscoelastic element in the ANSYS finite element program, which can used to determine transient and residual stresses in dental prostheses during fabrication.
Nonlinear dynamics of cell orientation
Safran, S. A.; de, Rumi
2009-12-01
The nonlinear dependence of cellular orientation on an external, time-varying stress field determines the distribution of orientations in the presence of noise and the characteristic time, τc , for the cell to reach its steady-state orientation. The short, local cytoskeletal relaxation time distinguishes between high-frequency (nearly perpendicular) and low-frequency (random or parallel) orientations. However, τc is determined by the much longer, orientational relaxation time. This behavior is related to experiments for which we predict the angle and characteristic time as a function of frequency.
Kinetic Actviation Relaxation Technique
Béland, Laurent Karim; El-Mellouhi, Fedwa; Joly, Jean-François; Mousseau, Normand
2011-01-01
We present a detailed description of the kinetic Activation-Relaxation Technique (k-ART), an off-lattice, self-learning kinetic Monte Carlo algorithm with on-the-fly event search. Combining a topological classification for local environments and event generation with ART nouveau, an efficient unbiased sampling method for finding transition states, k-ART can be applied to complex materials with atoms in off-lattice positions or with elastic deformations that cannot be handled with standard KMC approaches. In addition to presenting the various elements of the algorithm, we demonstrate the general character of k-ART by applying the algorithm to three challenging systems: self-defect annihilation in c-Si, self-interstitial diffusion in Fe and structural relaxation in amorphous silicon.
Collisionless relaxation in beam-plasma systems
Energy Technology Data Exchange (ETDEWEB)
Backhaus, Ekaterina Yu. [Univ. of California, Berkeley, CA (United States)
2001-01-01
This thesis reports the results from the theoretical investigations, both numerical and analytical, of collisionless relaxation phenomena in beam-plasma systems. Many results of this work can also be applied to other lossless systems of plasma physics, beam physics and astrophysics. Different aspects of the physics of collisionless relaxation and its modeling are addressed. A new theoretical framework, named Coupled Moment Equations (CME), is derived and used in numerical and analytical studies of the relaxation of second order moments such as beam size and emittance oscillations. This technique extends the well-known envelope equation formalism, and it can be applied to general systems with nonlinear forces. It is based on a systematic moment expansion of the Vlasov equation. In contrast to the envelope equation, which is derived assuming constant rms beam emittance, the CME model allows the emittance to vary through coupling to higher order moments. The CME model is implemented in slab geometry in the absence of return currents. The CME simulation yields rms beam sizes, velocity spreads and emittances that are in good agreement with particle-in-cell (PIC) simulations for a wide range of system parameters. The mechanism of relaxation is also considered within the framework of the CME system. It is discovered that the rapid relaxation or beam size oscillations can be attributed to a resonant coupling between different modes of the system. A simple analytical estimate of the relaxation time is developed. The final state of the system reached after the relaxation is complete is investigated. New and accurate analytical results for the second order moments in the phase-mixed state are obtained. Unlike previous results, these connect the final values of the second order moments with the initial beam mismatch. These analytical estimates are in good agreement with the CME model and PIC simulations. Predictions for the final density and temperature are developed that show
Fingerprinting Molecular Relaxation in Deformed Polymers
Wang, Zhe; Lam, Christopher N.; Chen, Wei-Ren; Wang, Weiyu; Liu, Jianning; Liu, Yun; Porcar, Lionel; Stanley, Christopher B.; Zhao, Zhichen; Hong, Kunlun; Wang, Yangyang
2017-07-01
The flow and deformation of macromolecules is ubiquitous in nature and industry, and an understanding of this phenomenon at both macroscopic and microscopic length scales is of fundamental and practical importance. Here, we present the formulation of a general mathematical framework, which could be used to extract, from scattering experiments, the molecular relaxation of deformed polymers. By combining and modestly extending several key conceptual ingredients in the literature, we show how the anisotropic single-chain structure factor can be decomposed by spherical harmonics and experimentally reconstructed from its cross sections on the scattering planes. The resulting wave-number-dependent expansion coefficients constitute a characteristic fingerprint of the macromolecular deformation, permitting detailed examinations of polymer dynamics at the microscopic level. We apply this approach to survey a long-standing problem in polymer physics regarding the molecular relaxation in entangled polymers after a large step deformation. The classical tube theory of Doi and Edwards predicts a fast chain retraction process immediately after the deformation, followed by a slow orientation relaxation through the reptation mechanism. This chain retraction hypothesis, which is the keystone of the tube theory for macromolecular flow and deformation, is critically examined by analyzing the fine features of the two-dimensional anisotropic spectra from small-angle neutron scattering by entangled polystyrenes. We show that the unique scattering patterns associated with the chain retraction mechanism are not experimentally observed. This result calls for a fundamental revision of the current theoretical picture for nonlinear rheological behavior of entangled polymeric liquids.
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
Extended MHD Modeling of Tearing-Driven Magnetic Relaxation
Sauppe, Joshua
2016-10-01
Driven plasma pinch configurations are characterized by the gradual accumulation and episodic release of free energy in discrete relaxation events. The hallmark of this relaxation in a reversed-field pinch (RFP) plasma is flattening of the parallel current density profile effected by a fluctuation-induced dynamo emf in Ohm's law. Nonlinear two-fluid modeling of macroscopic RFP dynamics has shown appreciable coupling of magnetic relaxation and the evolution of plasma flow. Accurate modeling of RFP dynamics requires the Hall effect in Ohm's law as well as first order ion finite Larmor radius (FLR) effects, represented by the Braginskii ion gyroviscous stress tensor. New results find that the Hall dynamo effect from / ne can counter the MHD effect from - in some of the relaxation events. The MHD effect dominates these events and relaxes the current profile toward the Taylor state, but the opposition of the two dynamos generates plasma flow in the direction of equilibrium current density, consistent with experimental measurements. Detailed experimental measurements of the MHD and Hall emf terms are compared to these extended MHD predictions. Tracking the evolution of magnetic energy, helicity, and hybrid helicity during relaxation identifies the most important contributions in single-fluid and two-fluid models. Magnetic helicity is well conserved relative to the magnetic energy during relaxation. The hybrid helicity is dominated by magnetic helicity in realistic low-beta pinch conditions and is also well conserved. Differences of less than 1 % between magnetic helicity and hybrid helicity are observed with two-fluid modeling and result from cross helicity evolution through ion FLR effects, which have not been included in contemporary relaxation theories. The kinetic energy driven by relaxation in the computations is dominated by velocity components perpendicular to the magnetic field, an effect that had not been predicted. Work performed at University of Wisconsin
Energy Technology Data Exchange (ETDEWEB)
Geniet, F; Leon, J [Physique Mathematique et Theorique, CNRS-UMR 5825, 34095 Montpellier (France)
2003-05-07
A nonlinear system possessing a natural forbidden band gap can transmit energy of a signal with a frequency in the gap, as recently shown for a nonlinear chain of coupled pendulums (Geniet and Leon 2002 Phys. Rev. Lett. 89 134102). This process of nonlinear supratransmission, occurring at a threshold that is exactly predictable in many cases, is shown to have a simple experimental realization with a mechanical chain of pendulums coupled by a coil spring. It is then analysed in more detail. First we go to different (nonintegrable) systems which do sustain nonlinear supratransmission. Then a Josephson transmission line (a one-dimensional array of short Josephson junctions coupled through superconducting wires) is shown to also sustain nonlinear supratransmission, though being related to a different class of boundary conditions, and despite the presence of damping, finiteness, and discreteness. Finally, the mechanism at the origin of nonlinear supratransmission is found to be a nonlinear instability, and this is briefly discussed here.
Fast relaxation transients in a kicked damped oscillator
Energy Technology Data Exchange (ETDEWEB)
Urquizu, Merce [Laboratori d' Estudis Geofisics ' Eduard Fontsere' , IEC, Barcelona (Spain); Correig, Antoni M. [Departament d' Astronomical i Meteorologia, Laboratori d' Estudis Geofisics Eduard Fontsere, UB Marti Franques 1, E-08028 Barcelona (Spain) and Laboratori d' Estudis Geofisics ' Eduard Fontsere' , IEC, Barcelona (Spain)]. E-mail: ton.correig@am.ub.es
2007-08-15
Although nonlinear relaxation transients are very common in nature, very few studies are devoted to its characterization, mainly due to its short time duration. In this paper, we present a study about the nature of relaxation transients in a kicked damped oscillator, in which transients are generated in terms of continuous fast changes in the parameters of the system. We have found that transient dynamics can be described, rather than in terms of bifurcation dynamics, in terms of instantaneous stretching factors, which are related to the stability of fixed points of the corresponding stroboscopic maps.
Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems
Directory of Open Access Journals (Sweden)
Hassan Saberi Nik
2014-01-01
Full Text Available We present a pseudospectral method application for solving the hyperchaotic complex systems. The proposed method, called the multistage spectral relaxation method (MSRM is based on a technique of extending Gauss-Seidel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudospectral methods to solve the resulting system on a sequence of multiple intervals. In this new application, the MSRM is used to solve famous hyperchaotic complex systems such as hyperchaotic complex Lorenz system and the complex permanent magnet synchronous motor. We compare this approach to the Runge-Kutta based ode45 solver to show that the MSRM gives accurate results.
Grueneisen relaxation photoacoustic microscopy
Wang, Lidai; Zhang, Chi; Wang, Lihong V.
2014-01-01
The temperature-dependent property of the Grueneisen parameter has been employed in photoacoustic imaging mainly to measure tissue temperature. Here we explore this property using a different approach and develop Grueneisen-relaxation photoacoustic microscopy (GR-PAM), a technique that images non-radiative absorption with confocal optical resolution. GR-PAM sequentially delivers two identical laser pulses with a micro-second-scale time delay. The first laser pulse generates a photoacoustic signal and thermally tags the in-focus absorbers. Owing to the temperature dependence of the Grueneisen parameter, when the second laser pulse excites the tagged absorbers within the thermal relaxation time, a photoacoustic signal stronger than the first one is produced. GR-PAM detects the amplitude difference between the two co-located photoacoustic signals, confocally imaging the non-radiative absorption. We greatly improved axial resolution from 45 µm to 2.3 µm and at the same time slightly improved lateral resolution from 0.63 µm to 0.41 µm. In addition, the optical sectioning capability facilitates the measurement of the absolute absorption coefficient without fluence calibration. PMID:25379919
2016-07-01
Advanced Research Projects Agency (DARPA) Dynamics-Enabled Frequency Sources (DEFYS) program is focused on the convergence of nonlinear dynamics and...Early work in this program has shown that nonlinear dynamics can provide performance advantages. However, the pathway from initial results to...dependent nonlinear stiffness observed in these devices. This work is ongoing, and will continue through the final period of this program . Reference 9
Directory of Open Access Journals (Sweden)
Trung Dung Nguyen
2014-01-01
Full Text Available Based on atomic force microscopytechnique, we found that the chondrocytes exhibits stress relaxation behavior. We explored the mechanism of this stress relaxation behavior and concluded that the intracellular fluid exuding out from the cells during deformation plays the most important role in the stress relaxation. We applied the inverse finite element analysis technique to determine necessary material parameters for porohyperelastic (PHE model to simulate stress relaxation behavior as this model is proven capable of capturing the non-linear behavior and the fluid-solid interaction during the stress relaxation of the single chondrocytes. It is observed that PHE model can precisely capture the stress relaxation behavior of single chondrocytes and would be a suitable model for cell biomechanics.
Magnetoviscosity and relaxation in ferrofluids
Felderhof
2000-09-01
The increase in viscosity of a ferrofluid due to an applied magnetic field is discussed on the basis of a phenomenological relaxation equation for the magnetization. The relaxation equation was derived earlier from irreversible thermodynamics, and differs from that postulated by Shliomis. The two relaxation equations lead to a different dependence of viscosity on magnetic field, unless the relaxation rates are related in a specific field-dependent way. Both planar Couette flow and Poiseuille pipe flow in parallel and perpendicular magnetic field are discussed. The entropy production for these situations is calculated and related to the magnetoviscosity.
Rupp, Wolf; Simon, Karl-Heinz; Bohnert, Michael
2009-01-01
Complete relaxation can be achieved by floating in a darkened, sound-proof relaxation tank filled with salinated water kept at body temperature. Under these conditions, meditation exercises up to self-hypnosis may lead to deep relaxation with physical and mental revitalization. A user manipulated his tank, presumably to completely cut off all optical and acoustic stimuli and accidentally also covered the ventilation hole. The man was found dead in his relaxation tank. The findings suggested lack of oxygen as the cause of death.
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Nanda, Sudarsan
2013-01-01
"Nonlinear analysis" presents recent developments in calculus in Banach space, convex sets, convex functions, best approximation, fixed point theorems, nonlinear operators, variational inequality, complementary problem and semi-inner-product spaces. Nonlinear Analysis has become important and useful in the present days because many real world problems are nonlinear, nonconvex and nonsmooth in nature. Although basic concepts have been presented here but many results presented have not appeared in any book till now. The book could be used as a text for graduate students and also it will be useful for researchers working in this field.
Relaxing Behavioural Inheritance
Directory of Open Access Journals (Sweden)
Nuno Amálio
2013-05-01
Full Text Available Object-oriented (OO inheritance allows the definition of families of classes in a hierarchical way. In behavioural inheritance, a strong version, it should be possible to substitute an object of a subclass for an object of its superclass without any observable effect on the system. Behavioural inheritance is related to formal refinement, but, as observed in the literature, the refinement constraints are too restrictive, ruling out many useful OO subclassings. This paper studies behavioural inheritance in the context of ZOO, an object-oriented style for Z. To overcome refinement's restrictions, this paper proposes relaxations to the behavioural inheritance refinement rules. The work is presented for Z, but the results are applicable to any OO language that supports design-by-contract.
Coronal heating by the partial relaxation of twisted loops
Bareford, Michael; Browning, Philippa
2012-01-01
Context: Relaxation theory offers a straightforward method for estimating the energy that is released when a magnetic field becomes unstable, as a result of continual convective driving. Aims: We present new results obtained from nonlinear magnetohydrodynamic (MHD) simulations of idealised coronal loops. The purpose of this work is to determine whether or not the simulation results agree with Taylor relaxation, which will require a modified version of relaxation theory applicable to unbounded field configurations. Methods: A three-dimensional (3D) MHD Lagrangian-remap code is used to simulate the evolution of a line-tied cylindrical coronal loop model. This model comprises three concentric layers surrounded by a potential envelope; hence, being twisted locally, each loop configuration is distinguished by a piecewise-constant current profile. Initially, all configurations carry zero-net-current fields and are in ideally unstable equilibrium. The simulation results are compared with the predictions of helicity ...
Environmental Noise and Nonlinear Relaxation in Biological Systems
Spagnolo, B; Spezia, S; Curcio, L; Pizzolato, N; Dubkov, A A; Fiasconaro, A; Adorno, D Persano; Bue, P Lo; Peri, E; Colazza, S
2011-01-01
We analyse the effects of environmental noise in three different biological systems: (i) mating behaviour of individuals of \\emph{Nezara viridula} (L.) (Heteroptera Pentatomidae); (ii) polymer translocation in crowded solution; (iii) an ecosystem described by a Verhulst model with a multiplicative L\\'{e}vy noise.
Magnetic relaxation in anisotropic magnets
DEFF Research Database (Denmark)
Lindgård, Per-Anker
1971-01-01
The line shape and the kinematic and thermodynamic slowing down of the critical and paramagnetic relaxation in axially anisotropic materials are discussed. Kinematic slowing down occurs only in the longitudinal relaxation function. The thermodynamic slowing down occurs in either the transverse or...
Nonlinear microrheology of living cells
Kollmannsberger, Philip; Fabry, Ben
2009-01-01
The linear rheology of adherent cells is characterized by a power-law creep or stress relaxation response, and proportionality between stiffness and internal prestress. It is unknown whether these observations hold in the physiologically relevant nonlinear regime. We used magnetic tweezers microrheology to measure the time- and force-dependent nonlinear creep response of adherent cells. Cell deformations in response to a stepwise increasing force applied to cytoskeletally bound magnetic beads were analyzed with a nonlinear superposition approach. The creep response followed a weak power law regardless of force. Stiffness and power law exponent both increased with force, indicating stress stiffening as well as fluidization of the cytoskeleton. Softer cells showed a more pronounced stress stiffening, which is quantitatively explained by their smaller internal prestress. Stiffer and more elastic cells showed a more pronounced force-induced fluidization, consistent with predictions from soft glassy rheology. Thes...
Scheduled Relaxation Jacobi method: improvements and applications
Adsuara, J E; Cerdá-Durán, P; Aloy, M A
2015-01-01
Elliptic partial differential equations (ePDEs) appear in a wide variety of areas of mathematics, physics and engineering. Typically, ePDEs must be solved numerically, which sets an ever growing demand for efficient and highly parallel algorithms to tackle their computational solution. The Scheduled Relaxation Jacobi (SRJ) is a promising class of methods, atypical for combining simplicity and efficiency, that has been recently introduced for solving linear Poisson-like ePDEs. The SRJ methodology relies on computing the appropriate parameters of a multilevel approach with the goal of minimizing the number of iterations needed to cut down the residuals below specified tolerances. The efficiency in the reduction of the residual increases with the number of levels employed in the algorithm. Applying the original methodology to compute the algorithm parameters with more than 5 levels notably hinders obtaining optimal SRJ schemes, as the mixed (non-linear) algebraic-differential equations from which they result bec...
Localization of nonlinear excitations in curved waveguides
DEFF Research Database (Denmark)
Gaididei, Yu. B.; Christiansen, Peter Leth; Kevrekidis, P. G.;
2005-01-01
numerical simulations of the nonlinear problem and in this case localized excitations are found to persist. We found also interesting relaxational dynamics. Analogies of the present problem in context related to atomic physics and particularly to Bose–Einstein condensation are discussed....
Nonlinear and nonequilibrium dynamics in geomaterials.
TenCate, James A; Pasqualini, Donatella; Habib, Salman; Heitmann, Katrin; Higdon, David; Johnson, Paul A
2004-08-01
The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a simple macroscopic dynamical model. At even higher strains, effects due to a driven nonequilibrium state, and relaxation from it, complicate the characterization of the nonlinear behavior.
Energy-resolved hot carrier relaxation dynamics in monocrystalline plasmonic nanoantennas
Méjard, Régis; Petit, Marlène; Bouhelier, Alexandre; Cluzel, Benoît; Demichel, Olivier
2016-01-01
Hot carriers are energetic photo-excited carriers driving a large range of chemico-physical mechanisms. At the nanoscale, an efficient generation of these carriers is facilitated by illuminating plasmonic antennas. However, the ultrafast relaxation rate severally impedes their deployment in future hot-carrier based devices. In this paper, we report on the picosecond relaxation dynamics of hot carriers in plasmonic monocrystalline gold nanoantennas. The temporal dynamics of the hot carriers is experimentally investigated by interrogating the nonlinear photoluminescence response of the antenna with a spectrally-resolved two-pulse correlation configuration. We measure time-dependent nonlinearity orders varying from 1 to 8, which challenge the common interpretation of multi-photon gold luminescence. We demonstrate that the relaxation of the photo-excited carriers depends of their energies relative to the Fermi level. We find a 60 % variation in the relaxation rate for electron-hole pair energies ranging from c.a....
Zhu, Hong-Ming; Pen, Ue-Li; Chen, Xuelei; Yu, Hao-Ran
2016-01-01
We present a direct approach to non-parametrically reconstruct the linear density field from an observed non-linear map. We solve for the unique displacement potential consistent with the non-linear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to $k\\sim 1\\ h/\\mathrm{Mpc}$ with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully non-linear fields, potentially substantially expanding the BAO and RSD information content of dense large scale structure surveys, including for example SDSS main sample and 21cm intensity mapping.
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
Stability and Convergence of Relaxation Schemes to Hyperbolic Balance Laws via a Wave Operator
Miroshnikov, Alexey; Trivisa, Konstantina
2014-01-01
This article deals with relaxation approximations of nonlinear systems of hyperbolic balance laws. We introduce a class of relaxation schemes and establish their stability and convergence to the solution of hyperbolic balance laws before the formation of shocks, provided that we are within the framework of the compensated compactness method. Our analysis treats systems of hyperbolic balance laws with source terms satisfying a special mechanism which induces weak dissipation in the spirit of D...
Thermal relaxation of magnetic clusters in amorphous Hf_{57}Fe_{43} alloy
Pajic, Damir; Zadro, Kreso; Ristic, Ramir; Zivkovic, Ivica; Skoko, Zeljko; Babic, Emil
2006-01-01
The magnetization processes in binary magnetic/nonmagnetic amorphous alloy Hf_{57}Fe_{43} are investigated by the detailed measurements of magnetic hysteresis loops, temperature dependence of magnetization, relaxation of magnetization and magnetic ac susceptibility, including a nonlinear term. Blocking of magnetic moments at lower temperatures is accompanied with the slow relaxation of magnetization and magnetic hysteresis loops. All of the observed properties are explained with the superpara...
Mirigian, Stephen; Schweizer, Kenneth S.
2014-01-01
Building on the elastically collective nonlinear Langevin equation theory developed for hard spheres in the preceding paper I, we propose and implement a quasi-universal theory for the alpha relaxation of thermal liquids based on mapping them to an effective hard sphere fluid via the dimensionless compressibility. The result is a zero adjustable parameter theory that can quantitatively address in a unified manner the alpha relaxation time over 14 or more decades. The theory has no singulariti...
Complex spatiotemporal behavior in a chain of one-way nonlinearly coupled elements
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Berkemer, Rainer; Gorria, C.;
2011-01-01
The dynamics of asymmetrically coupled nonlinear elements is considered. It is shown that there are two distinctive regimes of oscillatory behavior of one-way nonlinearly coupled elements depending on the relaxation time and the strength of the coupling. In the subcritical regime when...... nonlinear model....
Can Black Hole Relax Unitarily?
Solodukhin, S. N.
2005-03-01
We review the way the BTZ black hole relaxes back to thermal equilibrium after a small perturbation and how it is seen in the boundary (finite volume) CFT. The unitarity requires the relaxation to be quasi-periodic. It is preserved in the CFT but is not obvious in the case of the semiclassical black hole the relaxation of which is driven by complex quasi-normal modes. We discuss two ways of modifying the semiclassical black hole geometry to maintain unitarity: the (fractal) brick wall and the worm-hole modification. In the latter case the entropy comes out correctly as well.
Can Black Hole Relax Unitarily?
Solodukhin, Sergey N.
2004-01-01
We review the way the BTZ black hole relaxes back to thermal equilibrium after a small perturbation and how it is seen in the boundary (finite volume) CFT. The unitarity requires the relaxation to be quasi-periodic. It is preserved in the CFT but is not obvious in the case of the semiclassical black hole the relaxation of which is driven by complex quasi-normal modes. We discuss two ways of modifying the semiclassical black hole geometry to maintain unitarity: the (fractal) brick wall and the...
Can Black Hole Relax Unitarily?
Solodukhin, S N
2004-01-01
We review the way the BTZ black hole relaxes back to thermal equilibrium after a small perturbation and how it is seen in the boundary (finite volume) CFT. The unitarity requires the relaxation to be quasi-periodic. It is preserved in the CFT but is not obvious in the case of the semiclassical black hole the relaxation of which is driven by complex quasi-normal modes. We discuss two ways of modifying the semiclassical black hole geometry to maintain unitarity: the (fractal) brick wall and the worm-hole modification. In the latter case the entropy comes out correctly as well.
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates t
Nonlinear electronic transport behavior in Indium Nitride
Energy Technology Data Exchange (ETDEWEB)
Rodrigues, Cloves G., E-mail: cloves@pucgoias.edu.br [Departamento de Fisica, Pontificia Universidade Catolica de Goias, CP 86, 74605-010 Goiania, Goias (Brazil)
2012-11-15
A theoretical study on the nonlinear transport of electrons and of the nonequilibrium temperature in n-doped Indium Nitride under influence of moderate to high electric fields (in this nonlinear domain) is presented. It is based on a nonlinear quantum kinetic theory which provides a description of the dissipative phenomena developing in the system. The electric current and the mobility in the steady state are obtained, and their dependence on the electric field strength and on the concentration (that is, a mobility dependent nonlinearly on field and concentration) is obtained and analyzed. -- Highlights: Black-Right-Pointing-Pointer We have reported on the topic of nonlinear transport (electron mobility) in n-doped InN. Black-Right-Pointing-Pointer The results evidence the presence of two distinctive regimes. Black-Right-Pointing-Pointer The dependence of the mobility on the electric field is manifested through of the relaxation times.
An Exact Relaxation of Clustering
DEFF Research Database (Denmark)
Mørup, Morten; Hansen, Lars Kai
2009-01-01
of clustering problems such as the K-means objective and pairwise clustering as well as graph partition problems, e.g., for community detection in complex networks. In particular we show that a relaxation to the simplex can be given for which the extreme solutions are stable hard assignment solutions and vice......Continuous relaxation of hard assignment clustering problems can lead to better solutions than greedy iterative refinement algorithms. However, the validity of existing relaxations is contingent on problem specific fuzzy parameters that quantify the level of similarity between the original...... versa. Based on the new relaxation we derive the SR-clustering algorithm that has the same complexity as traditional greedy iterative refinement algorithms but leading to significantly better partitions of the data. A Matlab implementation of the SR-clustering algorithm is available for download....
The relaxation & stress reduction workbook
National Research Council Canada - National Science Library
Davis, Martha; Eshelman, Elizabeth Robbins; McKay, Matthew
2008-01-01
"The Relaxation & Stress Reduction Workbook broke new ground when it was first published in 1980, detailing easy, step-by-step techniques for calming the body and mind in an increasingly overstimulated world...
Relaxation Dynamics in Heme Proteins.
Scholl, Reinhard Wilhelm
A protein molecule possesses many conformational substates that are likely arranged in a hierarchy consisting of a number of tiers. A hierarchical organization of conformational substates is expected to give rise to a multitude of nonequilibrium relaxation phenomena. If the temperature is lowered, transitions between substates of higher tiers are frozen out, and relaxation processes characteristic of lower tiers will dominate the observational time scale. This thesis addresses the following questions: (i) What is the energy landscape of a protein? How does the landscape depend on the environment such as pH and viscosity, and how can it be connected to specific structural parts? (ii) What relaxation phenomena can be observed in a protein? Which are protein specific, and which occur in other proteins? How does the environment influence relaxations? (iii) What functional form best describes relaxation functions? (iv) Can we connect the motions to specific structural parts of the protein molecule, and are these motions important for the function of the protein?. To this purpose, relaxation processes after a pressure change are studied in carbonmonoxy (CO) heme proteins (myoglobin-CO, substrate-bound and substrate-free cytochrome P450cam-CO, chloroperoxidase-CO, horseradish peroxidase -CO) between 150 K and 250 K using FTIR spectroscopy to monitor the CO bound to the heme iron. Two types of p -relaxation experiments are performed: p-release (200 to ~eq40 MPa) and p-jump (~eq40 to 200 MPa) experiments. Most of the relaxations fall into one of three groups and are characterized by (i) nonexponential time dependence and non-Arrhenius temperature dependence (FIM1( nu), FIM1(Gamma)); (ii) exponential time dependence and non-Arrhenius temperature dependence (FIM0(A_{i}to A_{j})); exponential time dependence and Arrhenius temperature dependence (FIMX( nu)). The influence of pH is studied in myoglobin-CO and shown to have a strong influence on the substate population of the
Pemrick, Suzanne M.; Edwards, Charles
1974-01-01
Glycerol-extracted rabbit psoas muscle fibers were impaled with KCl-filled glass microelectrodes. For fibers at rest-length, the potentials were significantly more negative in solutions producing relaxation than in solutions producing either rigor or contraction; further the potentials in the latter two cases were not significantly different. For stretched fibers, with no overlap between thick and thin filaments, the potentials did not differ in the rigor, the relaxation, or the contraction solutions. The potentials measured from fibers in rigor did not vary significantly with the sarcomere length. For relaxed fibers, however, the potential magnitude decreased with increasing sarcomere length. The difference between the potentials measured for rigor and relaxed fibers exhibited a nonlinear relationship with sarcomere length. The potentials from calcium-insensitive fibers were less negative in both the rigor and the relaxation solutions than those from normal fibers. When calcium-insensitive fibers had been incubated in Hasselbach and Schneider's solution plus MgCl2 or Guba-Straub's solution plus MgATP the potentials recorded upon impalement were similar in the rigor and the relaxation solution to those obtained from normal fibers in the relaxed state. It is concluded that the increase in the negative potential as the glycerinated fiber goes from rigor to relaxation may be due to an alteration in the conformation of the contractile proteins in the relaxed state. PMID:4443791
Negative magnetic relaxation in superconductors
Directory of Open Access Journals (Sweden)
Krasnoperov E.P.
2013-01-01
Full Text Available It was observed that the trapped magnetic moment of HTS tablets or annuli increases in time (negative relaxation if they are not completely magnetized by a pulsed magnetic field. It is shown, in the framework of the Bean critical-state model, that the radial temperature gradient appearing in tablets or annuli during a pulsed field magnetization can explain the negative magnetic relaxation in the superconductor.
In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D.; Leung, Daniel; Liu, Norman; Meadows, Brian K.; Gordon, Frank; Bulsara, Adi R.; Palacios, Antonio
2012-12-01
The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.
A solution of the cusp problem in relaxed halos of dark matter
Mikheeva, E; Doroshkevich, A.; Lukash, V.
2007-01-01
We propose a solution of the cusp problem in framework of the standard $\\Lambda$CDM cosmology. To do this we describe the linear and nonlinear periods of halo formation by the entropy function of dark matter particles. This approach allows us to take into account together the impact of both the processes of nonlinear relaxation of compressed matter and the small scale initial velocity perturbations in collapsed halos. We show that such random velocities lead to the random variations of the de...
Energy Technology Data Exchange (ETDEWEB)
Turchetti, G. (Bologna Univ. (Italy). Dipt. di Fisica)
1989-01-01
Research in nonlinear dynamics is rapidly expanding and its range of applications is extending beyond the traditional areas of science where it was first developed. Indeed while linear analysis and modelling, which has been very successful in mathematical physics and engineering, has become a mature science, many elementary phenomena of intrinsic nonlinear nature were recently experimentally detected and investigated, suggesting new theoretical work. Complex systems, as turbulent fluids, were known to be governed by intrinsically nonlinear laws since a long time ago, but received purely phenomenological descriptions. The pioneering works of Boltzmann and Poincare, probably because of their intrinsic difficulty, did not have a revolutionary impact at their time; it is only very recently that their message is reaching a significant number of mathematicians and physicists. Certainly the development of computers and computer graphics played an important role in developing geometric intuition of complex phenomena through simple numerical experiments, while a new mathematical framework to understand them was being developed.
Ishchuk, V. M.; Kuzenko, D. V.
2016-08-01
The paper presents results of experimental study of the dielectric constant relaxation during aging process in Pb(Zr,Ti)O3 based solid solutions (PZT) after action of external DC electric field. The said process is a long-term one and is described by the logarithmic function of time. Reversible and nonreversible relaxation process takes place depending on the field intensity. The relaxation rate depends on the field strength also, and the said dependence has nonlinear and nonmonotonic form, if external field leads to domain disordering. The oxygen vacancies-based model for description of the long-term relaxation processes is suggested. The model takes into account the oxygen vacancies on the sample's surface ends, their conversion into F+- and F0-centers under external effects and subsequent relaxation of these centers into the simple oxygen vacancies after the action termination. F-centers formation leads to the violation of the original sample's electroneutrality, and generate intrinsic DC electric field into the sample. Relaxation of F-centers is accompanied by the reduction of the electric field, induced by them, and relaxation of the dielectric constant, as consequent effect.
Seider, Warren D.; Ungar, Lyle H.
1987-01-01
Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…
Dynamical theory of spin relaxation
Field, Timothy R.; Bain, Alex D.
2013-02-01
The dynamics of a spin system is usually calculated using the density matrix. However, the usual formulation in terms of the density matrix predicts that the signal will decay to zero, and does not address the issue of individual spin dynamics. Using stochastic calculus, we develop a dynamical theory of spin relaxation, the origins of which lie in the component spin fluctuations. This entails consideration of random pure states for individual protons, and how these pure states are correctly combined when the density matrix is formulated. Both the lattice and the spins are treated quantum mechanically. Such treatment incorporates both the processes of spin-spin and (finite temperature) spin-lattice relaxation. Our results reveal the intimate connections between spin noise and conventional spin relaxation.
2016-01-01
Over recent years, several alternative relaxed clock models have been proposed in the context of Bayesian dating. These models fall in two distinct categories: uncorrelated and autocorrelated across branches. The choice between these two classes of relaxed clocks is still an open question. More fundamentally, the true process of rate variation may have both long-term trends and short-term fluctuations, suggesting that more sophisticated clock models unfolding over multiple time scales should ultimately be developed. Here, a mixed relaxed clock model is introduced, which can be mechanistically interpreted as a rate variation process undergoing short-term fluctuations on the top of Brownian long-term trends. Statistically, this mixed clock represents an alternative solution to the problem of choosing between autocorrelated and uncorrelated relaxed clocks, by proposing instead to combine their respective merits. Fitting this model on a dataset of 105 placental mammals, using both node-dating and tip-dating approaches, suggests that the two pure clocks, Brownian and white noise, are rejected in favour of a mixed model with approximately equal contributions for its uncorrelated and autocorrelated components. The tip-dating analysis is particularly sensitive to the choice of the relaxed clock model. In this context, the classical pure Brownian relaxed clock appears to be overly rigid, leading to biases in divergence time estimation. By contrast, the use of a mixed clock leads to more recent and more reasonable estimates for the crown ages of placental orders and superorders. Altogether, the mixed clock introduced here represents a first step towards empirically more adequate models of the patterns of rate variation across phylogenetic trees. This article is part of the themed issue ‘Dating species divergences using rocks and clocks’. PMID:27325829
LAVENDER AROMATERAPHY AS A RELAXANT
Directory of Open Access Journals (Sweden)
IGA Prima Dewi AP
2013-02-01
Full Text Available Aromatherapy is a kind of treatment that used aroma with aromatherapy essential oil. Extraction process from essential oil generally doing in three methods, there are distilling with water (boiled, distilling with water and steam, and distilling with steam. One of the most favorite aroma is lavender. The main content from lavender is linalyl acetate and linalool (C10H18O. Linalool is main active contents in lavender which can use for anti-anxiety (relaxation. Based on some research, the conclusion indicates that essential oil from lavender can give relaxation (carminative, sedative, reduce anxiety level and increasing mood.
Statistical mechanics of violent relaxation
Spergel, David N.; Hernquist, Lars
1992-01-01
We propose a functional that is extremized through violent relaxation. It is based on the Ansatz that the wave-particle scattering during violent dynamical processes can be approximated as a sequence of discrete scattering events that occur near a particle's perigalacticon. This functional has an extremum whose structure closely resembles that of spheroidal stellar systems such as elliptical galaxies. The results described here, therefore, provide a simple framework for understanding the physical nature of violent relaxation and support the view that galaxies are structured in accord with fundamental statistical principles.
Active optomechanics through relaxation oscillations
Princepe, Debora; Frateschi, Newton
2014-01-01
We propose an optomechanical laser based on III-V compounds which exhibits self-pulsation in the presence of a dissipative optomechanical coupling. In such a laser cavity, radiation pressure drives the mechanical degree of freedom and its back-action is caused by the mechanical modulation of the cavity loss rate. Our numerical analysis shows that even in a wideband gain material, such dissipative coupling couples the mechanical oscillation with the laser relaxation oscillations process. Laser self-pulsation is observed for mechanical frequencies below the laser relaxation oscillation frequency under sufficiently high optomechanical coupling factor.
Thermal relaxation and mechanical relaxation of rice gel
Institute of Scientific and Technical Information of China (English)
丁玉琴; 赵思明; 熊善柏
2008-01-01
Rice gel was prepared by simulating the production processes of Chinese local rice noodles,and the properties of thermal relaxation and mechanical relaxation during gelatinization were studied by differential scanning calorimetry(DSC) measurement and dynamic rheometer.The results show that during gelatinization,the molecular chains of rice starch undergo the thermal relaxation and mechanical relaxation.During the first heating and high temperature holding processes,the starch crystallites in the rice slurry melt,and the polymer chains stretch and interact,then viscoelastic gel forms.The cooling and low temperatures holding processes result in reinforced networks and decrease the viscoelasticity of the gel.During the second heating,the remaining starch crystallites further melt,the network is reinforced,and the viscoelasticity increases.The viscoelasticity,the molecular conformation and texture of the gel are adjusted by changing the temperature,and finally construct the gel with the textural characteristics of Chinese local rice noodle.
Waveform relaxation for the computational homogenization of multiscale magnetoquasistatic problems
Niyonzima, I.; Geuzaine, C.; Schöps, S.
2016-12-01
This paper proposes the application of the waveform relaxation method to the homogenization of multiscale magnetoquasistatic problems. In the monolithic heterogeneous multiscale method, the nonlinear macroscale problem is solved using the Newton-Raphson scheme. The resolution of many mesoscale problems per Gauß point allows to compute the homogenized constitutive law and its derivative by finite differences. In the proposed approach, the macroscale problem and the mesoscale problems are weakly coupled and solved separately using the finite element method on time intervals for several waveform relaxation iterations. The exchange of information between both problems is still carried out using the heterogeneous multiscale method. However, the partial derivatives can now be evaluated exactly by solving only one mesoscale problem per Gauß point.
Lattice Boltzmann model for nonlinear convection-diffusion equations.
Shi, Baochang; Guo, Zhaoli
2009-01-01
A lattice Boltzmann model for convection-diffusion equation with nonlinear convection and isotropic-diffusion terms is proposed through selecting equilibrium distribution function properly. The model can be applied to the common real and complex-valued nonlinear evolutionary equations, such as the nonlinear Schrödinger equation, complex Ginzburg-Landau equation, Burgers-Fisher equation, nonlinear heat conduction equation, and sine-Gordon equation, by using a real and complex-valued distribution function and relaxation time. Detailed simulations of these equations are performed, and it is found that the numerical results agree well with the analytical solutions and the numerical solutions reported in previous studies.
Determination of the optimal relaxation parameter in a numerical procedure for solitons propagation
Cirilo, Eliandro Rodrigues; Romeiro, Neyva Maria Lopes; Natti, Erica Regina Takano
2010-01-01
In this work, considering a numerical procedure developed to solve a system of coupled nonlinear complex differential equations, which describes the solitons propagation in dielectric optical fibers, we optimize the numerical processing time, in relation to the relaxation parameter of the procedure, for relevant groups of values of the dielectric variables of the optic fiber. Key-words: optical soliton, processing time, optimization.
Dispersion and polarization dependence of mobile carrier optical nonlinearities
Rustagi, K. C.
1984-06-01
Based on the author's earlier work, it is shown that the proper inclusion of carrier scattering should strongly modify the frequency and polarization dependence of optical nonlinearities due to mobile carriers in semiconductors. When the momentum relaxation is much faster than the energy relaxation, the intensity dependent refractive index is enhanced, the induced birefringence becomes a sharp function of the difference frequency ωa-ωb, and a collision induced stimulated Raman effect becomes important.
Nonlinear theory of kinetic instabilities near threshold
Energy Technology Data Exchange (ETDEWEB)
Berk, H.L.; Pekker, M.S. [Univ. of Texas, Austin, TX (United States). Inst. for Fusion Studies; Breizman, B.N. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies]|[Budker Inst. of Nuclear Physics, Novosibirsk (Russian Federation)
1997-05-01
A new nonlinear equation has been derived and solved for the evolution of an unstable collective mode in a kinetic system close to the threshold of linear instability. The resonant particle response produces the dominant nonlinearity, which can be calculated iteratively in the near-threshold regime as long as the mode doe snot trap resonant particles. With sources and classical relaxation processes included, the theory describes both soft nonlinear regimes, where the mode saturation level is proportional to an increment above threshold, and explosive nonlinear regimes, where the mode grows to a level that is independent of the closeness to threshold. The explosive solutions exhibit mode frequency shifting. For modes that exist in the absence of energetic particles, the frequency shift is both upward and downward. For modes that require energetic particles for their existence, there is a preferred direction of the frequency shift. The frequency shift continues even after the mode traps resonant particles.
Scheduled Relaxation Jacobi method: Improvements and applications
Adsuara, J. E.; Cordero-Carrión, I.; Cerdá-Durán, P.; Aloy, M. A.
2016-09-01
Elliptic partial differential equations (ePDEs) appear in a wide variety of areas of mathematics, physics and engineering. Typically, ePDEs must be solved numerically, which sets an ever growing demand for efficient and highly parallel algorithms to tackle their computational solution. The Scheduled Relaxation Jacobi (SRJ) is a promising class of methods, atypical for combining simplicity and efficiency, that has been recently introduced for solving linear Poisson-like ePDEs. The SRJ methodology relies on computing the appropriate parameters of a multilevel approach with the goal of minimizing the number of iterations needed to cut down the residuals below specified tolerances. The efficiency in the reduction of the residual increases with the number of levels employed in the algorithm. Applying the original methodology to compute the algorithm parameters with more than 5 levels notably hinders obtaining optimal SRJ schemes, as the mixed (non-linear) algebraic-differential system of equations from which they result becomes notably stiff. Here we present a new methodology for obtaining the parameters of SRJ schemes that overcomes the limitations of the original algorithm and provide parameters for SRJ schemes with up to 15 levels and resolutions of up to 215 points per dimension, allowing for acceleration factors larger than several hundreds with respect to the Jacobi method for typical resolutions and, in some high resolution cases, close to 1000. Most of the success in finding SRJ optimal schemes with more than 10 levels is based on an analytic reduction of the complexity of the previously mentioned system of equations. Furthermore, we extend the original algorithm to apply it to certain systems of non-linear ePDEs.
Dielectric relaxation of samarium aluminate
Energy Technology Data Exchange (ETDEWEB)
Sakhya, Anup Pradhan; Dutta, Alo; Sinha, T.P. [Bose Institute, Department of Physics, Kolkata (India)
2014-03-15
A ceramic SmAlO{sub 3} (SAO) sample is synthesized by the solid-state reaction technique. The Rietveld refinement of the X-ray diffraction pattern has been done to find the crystal symmetry of the sample at room temperature. An impedance spectroscopy study of the sample has been performed in the frequency range from 50 Hz to 1 MHz and in the temperature range from 313 K to 573 K. Dielectric relaxation peaks are observed in the imaginary parts of the spectra. The Cole-Cole model is used to analyze the dielectric relaxation mechanism in SAO. The temperature-dependent relaxation times are found to obey the Arrhenius law having an activation energy of 0.29 eV, which indicates that polaron hopping is responsible for conduction or dielectric relaxation in this material. The complex impedance plane plot of the sample indicates the presence of both grain and grain-boundary effects and is analyzed by an electrical equivalent circuit consisting of a resistance and a constant-phase element. The frequency-dependent conductivity spectra follow a double-power law due to the presence of two plateaus. (orig.)
Choosing a skeletal muscle relaxant.
See, Sharon; Ginzburg, Regina
2008-08-01
Skeletal muscle relaxants are widely used in treating musculoskeletal conditions. However, evidence of their effectiveness consists mainly of studies with poor methodologic design. In addition, these drugs have not been proven to be superior to acetaminophen or nonsteroidal anti-inflammatory drugs for low back pain. Systematic reviews and meta-analyses support using skeletal muscle relaxants for short-term relief of acute low back pain when nonsteroidal anti-inflammatory drugs or acetaminophen are not effective or tolerated. Comparison studies have not shown one skeletal muscle relaxant to be superior to another. Cyclobenzaprine is the most heavily studied and has been shown to be effective for various musculoskeletal conditions. The sedative properties of tizanidine and cyclobenzaprine may benefit patients with insomnia caused by severe muscle spasms. Methocarbamol and metaxalone are less sedating, although effectiveness evidence is limited. Adverse effects, particularly dizziness and drowsiness, are consistently reported with all skeletal muscle relaxants. The potential adverse effects should be communicated clearly to the patient. Because of limited comparable effectiveness data, choice of agent should be based on side-effect profile, patient preference, abuse potential, and possible drug interactions.
Onsager relaxation of toroidal plasmas
Energy Technology Data Exchange (ETDEWEB)
Samain, A.; Nguyen, F.
1997-01-01
The slow relaxation of isolated toroidal plasmas towards their thermodynamical equilibrium is studied in an Onsager framework based on the entropy metric. The basic tool is a variational principle, equivalent to the kinetic equation, involving the profiles of density, temperature, electric potential, electric current. New minimization procedures are proposed to obtain entropy and entropy production rate functionals. (author). 36 refs.
Relaxation properties in classical diamagnetism
Carati, A.; Benfenati, F.; Galgani, L.
2011-06-01
It is an old result of Bohr that, according to classical statistical mechanics, at equilibrium a system of electrons in a static magnetic field presents no magnetization. Thus a magnetization can occur only in an out of equilibrium state, such as that produced through the Foucault currents when a magnetic field is switched on. It was suggested by Bohr that, after the establishment of such a nonequilibrium state, the system of electrons would quickly relax back to equilibrium. In the present paper, we study numerically the relaxation to equilibrium in a modified Bohr model, which is mathematically equivalent to a billiard with obstacles, immersed in a magnetic field that is adiabatically switched on. We show that it is not guaranteed that equilibrium is attained within the typical time scales of microscopic dynamics. Depending on the values of the parameters, one has a relaxation either to equilibrium or to a diamagnetic (presumably metastable) state. The analogy with the relaxation properties in the Fermi Pasta Ulam problem is also pointed out.
2015-01-01
From the Back Cover: The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications re...
Forbidden second order optical nonlinearity of graphene
Cheng, J L; Sipe, J E
2016-01-01
We present a practical scheme to separate the contributions of the electric quadrupole-like and the magnetic dipole-like effects to the forbidden second order optical nonlinear response of graphene, and give analytic expressions for the second order optical conductivities, calculated from the independent particle approximation, with relaxation described in a phenomenological way. We predict strong second order nonlinear effects, including second harmonic generation, photon drag, and difference frequency generation. We discuss in detail the controllablity of these responses by tuning the chemical potential, where the interband optical transitions play a dominant role.
Equivalent Relaxations of Optimal Power Flow
Energy Technology Data Exchange (ETDEWEB)
Bose, S; Low, SH; Teeraratkul, T; Hassibi, B
2015-03-01
Several convex relaxations of the optimal power flow (OPF) problem have recently been developed using both bus injection models and branch flow models. In this paper, we prove relations among three convex relaxations: a semidefinite relaxation that computes a full matrix, a chordal relaxation based on a chordal extension of the network graph, and a second-order cone relaxation that computes the smallest partial matrix. We prove a bijection between the feasible sets of the OPF in the bus injection model and the branch flow model, establishing the equivalence of these two models and their second-order cone relaxations. Our results imply that, for radial networks, all these relaxations are equivalent and one should always solve the second-order cone relaxation. For mesh networks, the semidefinite relaxation and the chordal relaxation are equally tight and both are strictly tighter than the second-order cone relaxation. Therefore, for mesh networks, one should either solve the chordal relaxation or the SOCP relaxation, trading off tightness and the required computational effort. Simulations are used to illustrate these results.
The nature of relaxation processes revealed by the action signals of phase modulated light fields
Osipov, Vladimir Al; Hansen, Thorsten; Pullerits, Tõnu; Karki, Khadga Jung
2016-01-01
In the article we develop a theory of the action signals induced by the two-photon absorption of two phase modulated laser beams. In such experiments the phase of each laser beams is modulated at the frequencies $\\phi_1$ and $\\phi_2$, respectively, and the nonlinear signals are isolated at frequencies $m\\phi=m(\\phi_1-\\phi_2)$ ($m=0,1,2,\\dots$). We demonstrate that the ratio of the amplitudes of primary ($m=1$) and secondary ($m=2$) signals, $A_{\\phi}:A_{2\\phi}$, can be used as an indicator of the type of relaxation processes taking place in the material. The reference ratio value $4:1$ is achieved for the fast linear relaxation processes, and changes smoothly as the relaxation time increases. In case of bimolecular relaxation the ratio becomes a rapidly changing function of the excitation intensity. Our theoretical findings are supported by the experimental observations.
Energy Technology Data Exchange (ETDEWEB)
Yoshizawa, M. [Tohoku University, Sendai (Japan). Faculty of Engineering
1995-12-15
Large ultrafast optical nonlinearities in conjugated polymers have attracted much attention because of possible applications to nonlinear optical devices. One-dimensional systems such as conjugated polymers have localized excited states with geometrical relaxation. In this study, photoexcited states in polydiacetylene has been investigated by femtosecond Raman gain spectroscopy with 300-fs resolution. A new photoinduced Raman peak with lifetime of 1.5 ps has been observed at 1200cm{sup -1} for the first time. This peak indicates acetylene-like structure of the main chain relaxes to butatriene-like structure due to the formation of self-trapped exciting with the geometrical relaxation. The formation and decay kinetics of the Raman signals is consistent with the relaxation processes of exciting observed by femtosecond absorption spectroscopy. 8 refs., 5 figs.
Organic semiconductors: What makes the spin relax?
Bobbert, Peter A.
2010-04-01
Spin relaxation in organic materials is expected to be slow because of weak spin-orbit coupling. The effects of deuteration and coherent spin excitation show that the spin-relaxation time is actually limited by hyperfine fields.
Relaxation Techniques to Manage IBS Symptoms
... the Day Art of IBS Gallery Contact Us Relaxation Techniques to Manage IBS Symptoms Details Content Last Updated: ... Topic Psychological Treatments Understanding Stress Cognitive Behavioral Therapy Relaxation Techniques for IBS You’ve been to the doctor ...
Plasmon-mediated energy relaxation in graphene
Energy Technology Data Exchange (ETDEWEB)
Ferry, D. K. [School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287-5706 (United States); Somphonsane, R. [Department of Physics, King Mongkut' s Institute of Technology, Ladkrabang, Bangkok 10520 (Thailand); Ramamoorthy, H.; Bird, J. P. [Department of Electrical Engineering, University at Buffalo, the State University of New York, Buffalo, New York 14260-1500 (United States)
2015-12-28
Energy relaxation of hot carriers in graphene is studied at low temperatures, where the loss rate may differ significantly from that predicted for electron-phonon interactions. We show here that plasmons, important in the relaxation of energetic carriers in bulk semiconductors, can also provide a pathway for energy relaxation in transport experiments in graphene. We obtain a total loss rate to plasmons that results in energy relaxation times whose dependence on temperature and density closely matches that found experimentally.
Output Feedback Control for a Class of Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
Keylan Alimhan; Hiroshi Inaba
2006-01-01
This paper studies the global stabilization problem by an output controller for a family of uncertain nonlinear systems satisfying some relaxed triangular-type conditions and with dynamics which may not be exactly known. Using a feedback domination design method, we explicitly construct a dynamic output compensator which globally stabilizes such an uncertain nonlinear system. The usefulness of our result is illustrated with an example.
Multisplitting for linear, least squares and nonlinear problems
Energy Technology Data Exchange (ETDEWEB)
Renaut, R.
1996-12-31
In earlier work, presented at the 1994 Iterative Methods meeting, a multisplitting (MS) method of block relaxation type was utilized for the solution of the least squares problem, and nonlinear unconstrained problems. This talk will focus on recent developments of the general approach and represents joint work both with Andreas Frommer, University of Wupertal for the linear problems and with Hans Mittelmann, Arizona State University for the nonlinear problems.
Kinetic activation-relaxation technique
Béland, Laurent Karim; Brommer, Peter; El-Mellouhi, Fedwa; Joly, Jean-François; Mousseau, Normand
2011-10-01
We present a detailed description of the kinetic activation-relaxation technique (k-ART), an off-lattice, self-learning kinetic Monte Carlo (KMC) algorithm with on-the-fly event search. Combining a topological classification for local environments and event generation with ART nouveau, an efficient unbiased sampling method for finding transition states, k-ART can be applied to complex materials with atoms in off-lattice positions or with elastic deformations that cannot be handled with standard KMC approaches. In addition to presenting the various elements of the algorithm, we demonstrate the general character of k-ART by applying the algorithm to three challenging systems: self-defect annihilation in c-Si (crystalline silicon), self-interstitial diffusion in Fe, and structural relaxation in a-Si (amorphous silicon).
Kinetic activation-relaxation technique.
Béland, Laurent Karim; Brommer, Peter; El-Mellouhi, Fedwa; Joly, Jean-François; Mousseau, Normand
2011-10-01
We present a detailed description of the kinetic activation-relaxation technique (k-ART), an off-lattice, self-learning kinetic Monte Carlo (KMC) algorithm with on-the-fly event search. Combining a topological classification for local environments and event generation with ART nouveau, an efficient unbiased sampling method for finding transition states, k-ART can be applied to complex materials with atoms in off-lattice positions or with elastic deformations that cannot be handled with standard KMC approaches. In addition to presenting the various elements of the algorithm, we demonstrate the general character of k-ART by applying the algorithm to three challenging systems: self-defect annihilation in c-Si (crystalline silicon), self-interstitial diffusion in Fe, and structural relaxation in a-Si (amorphous silicon).
Brief relaxation training program for hospital employees.
Balk, Judith L; Chung, Sheng-Chia; Beigi, Richard; Brooks, Maria
2009-01-01
Employee stress leads to attrition, burnout, and increased medical costs. We aimed to assess if relaxation training leads to decreased stress levels based on questionnaire and thermal biofeedback. Thirty-minute relaxation training sessions were conducted for hospital employees and for cancer patients. Perceived Stress levels and skin temperature were analyzed before and after relaxation training.
POS Tagging Using Relaxation Labelling
Padro, L
1995-01-01
Relaxation labelling is an optimization technique used in many fields to solve constraint satisfaction problems. The algorithm finds a combination of values for a set of variables such that satisfies -to the maximum possible degree- a set of given constraints. This paper describes some experiments performed applying it to POS tagging, and the results obtained. It also ponders the possibility of applying it to word sense disambiguation.
Spin relaxation in metallic ferromagnets
Berger, L.
2011-02-01
The Elliott theory of spin relaxation in metals and semiconductors is extended to metallic ferromagnets. Our treatment is based on the two-current model of Fert, Campbell, and Jaoul. The d→s electron-scattering process involved in spin relaxation is the inverse of the s→d process responsible for the anisotropic magnetoresistance (AMR). As a result, spin-relaxation rate 1/τsr and AMR Δρ are given by similar formulas, and are in a constant ratio if scattering is by solute atoms. Our treatment applies to nickel- and cobalt-based alloys which do not have spin-up 3d states at the Fermi level. This category includes many of the technologically important magnetic materials. And we show how to modify the theory to apply it to bcc iron-based alloys. We also treat the case of Permalloy Ni80Fe20 at finite temperature or in thin-film form, where several kinds of scatterers exist. Predicted values of 1/τsr and Δρ are plotted versus resistivity of the sample. These predictions are compared to values of 1/τsr and Δρ derived from ferromagnetic-resonance and AMR experiments in Permalloy.
Arresting relaxation in Pickering Emulsions
Atherton, Tim; Burke, Chris
2015-03-01
Pickering emulsions consist of droplets of one fluid dispersed in a host fluid and stabilized by colloidal particles absorbed at the fluid-fluid interface. Everyday materials such as crude oil and food products like salad dressing are examples of these materials. Particles can stabilize non spherical droplet shapes in these emulsions through the following sequence: first, an isolated droplet is deformed, e.g. by an electric field, increasing the surface area above the equilibrium value; additional particles are then adsorbed to the interface reducing the surface tension. The droplet is then allowed to relax toward a sphere. If more particles were adsorbed than can be accommodated by the surface area of the spherical ground state, relaxation of the droplet is arrested at some non-spherical shape. Because the energetic cost of removing adsorbed colloids exceeds the interfacial driving force, these configurations can remain stable over long timescales. In this presentation, we present a computational study of the ordering present in anisotropic droplets produced through the mechanism of arrested relaxation and discuss the interplay between the geometry of the droplet, the dynamical process that produced it, and the structure of the defects observed.
Relaxation response in femoral angiography.
Mandle, C L; Domar, A D; Harrington, D P; Leserman, J; Bozadjian, E M; Friedman, R; Benson, H
1990-03-01
Immediately before they underwent femoral angiography, 45 patients were given one of three types of audiotapes: a relaxation response tape recorded for this study, a tape of contemporary instrumental music, or a blank tape. All patients were instructed to listen to their audiotape during the entire angiographic procedure. Each audiotape was played through earphones. Radiologists were not told the group assignment or tape contents. The patients given the audiotape with instructions to elicit the relaxation response (n = 15) experienced significantly less anxiety (P less than .05) and pain (P less than .001) during the procedure, were observed by radiology nurses to exhibit significantly less pain (P less than .001) and anxiety (P less than .001), and requested significantly less fentanyl citrate (P less than .01) and diazepam (P less than .01) than patients given either the music (n = 14) or the blank (n = 16) control audiotapes. Elicitation of the relaxation response is a simple, inexpensive, efficacious, and practical method to reduce pain, anxiety, and medication during femoral angiography and may be useful in other invasive procedures.
Zhu, Ming; Liu, Tingting; Wang, Shu; Zhang, Kesheng
2017-08-01
Existing two-frequency reconstructive methods can only capture primary (single) molecular relaxation processes in excitable gases. In this paper, we present a reconstructive method based on the novel decomposition of frequency-dependent acoustic relaxation spectra to capture the entire molecular multimode relaxation process. This decomposition of acoustic relaxation spectra is developed from the frequency-dependent effective specific heat, indicating that a multi-relaxation process is the sum of the interior single-relaxation processes. Based on this decomposition, we can reconstruct the entire multi-relaxation process by capturing the relaxation times and relaxation strengths of N interior single-relaxation processes, using the measurements of acoustic absorption and sound speed at 2N frequencies. Experimental data for the gas mixtures CO2-N2 and CO2-O2 validate our decomposition and reconstruction approach.
Time of relaxation in dusty plasma model
Timofeev, A. V.
2015-11-01
Dust particles in plasma may have different values of average kinetic energy for vertical and horizontal motion. The partial equilibrium of the subsystems and the relaxation processes leading to this asymmetry are under consideration. A method for the relaxation time estimation in nonideal dusty plasma is suggested. The characteristic relaxation times of vertical and horizontal motion of dust particles in gas discharge are estimated by analytical approach and by analysis of simulation results. These relaxation times for vertical and horizontal subsystems appear to be different. A single hierarchy of relaxation times is proposed.
Dielectric relaxation and ac conductivity of sodium tungsten phosphate glasses
Indian Academy of Sciences (India)
B Singh; P S Tarsikka; L Singh
2002-10-01
Studies of dielectric relaxation and ac conductivity have been made on three samples of sodium tungsten phosphate glasses over a temperature range of 77–420 K. Complex relative permittivity data have been analyzed using dielectric modulus approach. Conductivity relaxation frequency increases with the increase of temperature. Activation energy for conductivity relaxation has also been evaluated. Measured ac conductivity (m()) has been found to be higher than dc at low temperatures whereas at high temperature m() becomes equal to dc at all frequencies. The ac conductivity obeys the relation ac() = A over a considerable range of low temperatures. Values of exponent are nearly equal to unity at about 78 K and the values decrease non-linearly with the increase of temperature. Values of the number density of states at Fermi level ((F)) have been evaluated at 80 K assuming values of electron wave function decay constant to be 0.5 (Å)-1. Values of (F) have the order 1020 which are well within the range suggested for localized states. Present values of (F) are smaller than those for tungsten phosphate glasses.
The structure of precipitation fronts for finite relaxation time
Energy Technology Data Exchange (ETDEWEB)
Stechmann, Samuel N.; Majda, Andrew J. [New York University, Department of Mathematics and Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York, NY (United States)
2006-11-15
When convection is parameterized in an atmospheric circulation model, what types of waves are supported by the parameterization? Several studies have addressed this question by finding the linear waves of simplified tropical climate models with convective parameterizations. In this paper's simplified tropical climate model, convection is parameterized by a nonlinear precipitation term, and the nonlinearity gives rise to precipitation front solutions. Precipitation fronts are solutions where the spatial domain is divided into two regions, and the precipitation (and other model variables) changes abruptly at the boundary of the two regions. In one region the water vapor is below saturation and there is no precipitation, and in the other region the water vapor is above saturation level and precipitation is nonzero. The boundary between the two regions is a free boundary that moves at a constant speed. It is shown that only certain front speeds are allowed. The three types of fronts that exist for this model are drying fronts, slow moistening fronts, and fast moistening fronts. Both types of moistening fronts violate Lax's stability criterion, but they are robustly realizable in numerical experiments that use finite relaxation times. Remarkably, here it is shown that all three types of fronts are robustly realizable analytically for finite relaxation time. All three types of fronts may be physically unreasonable if the front spans an unrealistically large physical distance; this depends on various model parameters, which are investigated below. From the viewpoint of applied mathematics, these model equations exhibit novel phenomena as well as features in common with the established applied mathematical theories of relaxation limits for conservation laws and waves in reacting gas flows. (orig.)
5 Things To Know About Relaxation Techniques for Stress
... X Y Z 5 Things To Know About Relaxation Techniques for Stress Share: When you’re under stress, ... creating the relaxation response through regular use of relaxation techniques could counteract the negative effects of stress. Relaxation ...
Rajasekar, Shanmuganathan
2016-01-01
This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques invo...
Institute of Scientific and Technical Information of China (English)
1996-01-01
3.1 A Unified Nonlinear Feedback Functional Method for Study Both Control and Synchronization of Spatiotemporal Chaos Fang Jinqing Ali M. K. (Department of Physics, The University of Lethbridge,Lethbridge, Alberta T1K 3M4,Canada) Two fundamental questions dominate future chaos control theories.The first is the problem of controlling hyperchaos in higher dimensional systems.The second question has yet to be addressed:the problem of controlling spatiotemporal chaos in a spatiotemporal system.In recent years, control and synchronization of spatiotemporal chaos and hyperchaos have became a much more important and challenging subject. The reason for this is the control and synchronism of such behaviours have extensive and great potential of interdisciplinary applications, such as security communication, information processing, medicine and so on. However, this subject is not much known and remains an outstanding open.
Nonlinear waves in waveguides with stratification
Leble, Sergei B
1991-01-01
S.B. Leble's book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification. The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations. The reader will find new elements to the traditional approach. Various dispersion and relaxation laws for different guides are considered as well as the explicit form of projection operators, NEEs, quasi-solitons and of Darboux transforms. Special points relate to: 1. the development of a universal asymptotic method of deriving NEEs for guide propagation; 2. applications to the cases of stratified liquids, gases, solids and plasmas with various nonlinearities and dispersion laws; 3. connections between the basic problem and soliton- like solutions of the corresponding NEEs; 4. discussion of details of simple solutions in higher- order nonsingular perturbation theory.
Optimization of an amplification protocol for misfolded proteins by using relaxed control.
Coron, Jean-Michel; Gabriel, Pierre; Shang, Peipei
2015-01-01
We investigate an optimal control problem which arises in the optimization of an amplification technique for misfolded proteins. The improvement of this technique may play a role in the detection of prion diseases. The model consists in a linear system of differential equations with a nonlinear control. The appearance of oscillations in the numerical simulations is understood by using the Perron and Floquet eigenvalue theory for nonnegative irreducible matrices. Then to overcome the unsolvability of the optimal control, we relax the problem. In the two dimensional case, we solve explicitly the optimal relaxed control problem when the final time is large enough.
Stress relaxation experiments on a lamellar polystyrene-polyisoprene diblock copolymer melt
DEFF Research Database (Denmark)
Holmqvist, P.; Castelletto, V.; Hamley, I.W.;
2001-01-01
via dynamic light scattering experiments. The slowest relaxation process may be related to the shear-induced orientation of the lamellae. It is shown that time-strain separability G(t, gamma)= G(t)h(gamma) can be applied, and the damping function h(gamma) is consistent with a strongly strain......The non-linear rheology of the lamellar phase of a polystyrene-polyisoprene diblock copolymer is studied by oscillatory shear experiments. The relaxation of the shear modulus, G(t, gamma) is studied as a function of strain amplitude, gamma, up to large amplitude strains, gamma = 100%. The decay...
Relaxation parameter estimation and comparison of NLS and LLS methods for DCE MRI in the cervix
DEFF Research Database (Denmark)
Mariager, Christian; Kallehauge, Jesper; Tanderup, Kari
Dynamic Contrast Enhanced (DCE) MRI is a promising tool for tumor treatment planning. However, prior knowledge of the T1 value within each tumor voxel is needed to utilize this technique. Therefore, a T1 relaxation measurement is performed before the DCE experiment to establish a baseline, before...... any injection of contrast agent. This T1 relaxation measurement is often performed using a variable flip angle spoiled gradient recalled echo (SPGR) sequence. T1 can then be estimated using either a linear least squares (LLS) or a non-linear least squares (NLS) fitting algorithm....
Compaction and relaxation of biofilms
Valladares Linares, R.
2015-06-18
Operation of membrane systems for water treatment can be seriously hampered by biofouling. A better characterization of biofilms in membrane systems and their impact on membrane performance may help to develop effective biofouling control strategies. The objective of this study was to determine the occurrence, extent and timescale of biofilm compaction and relaxation (decompaction), caused by permeate flux variations. The impact of permeate flux changes on biofilm thickness, structure and stiffness was investigated in situ and non-destructively with optical coherence tomography using membrane fouling monitors operated at a constant crossflow velocity of 0.1 m s−1 with permeate production. The permeate flux was varied sequentially from 20 to 60 and back to 20 L m−2 h−1. The study showed that the average biofilm thickness on the membrane decreased after elevating the permeate flux from 20 to 60 L m−2 h−1 while the biofilm thickness increased again after restoring the original flux of 20 L m−2 h−1, indicating the occurrence of biofilm compaction and relaxation. Within a few seconds after the flux change, the biofilm thickness was changed and stabilized, biofilm compaction occurred faster than the relaxation after restoring the original permeate flux. The initial biofilm parameters were not fully reinstated: the biofilm thickness was reduced by 21%, biofilm stiffness had increased and the hydraulic biofilm resistance was elevated by 16%. Biofilm thickness was related to the hydraulic biofilm resistance. Membrane performance losses are related to the biofilm thickness, density and morphology, which are influenced by (variations in) hydraulic conditions. A (temporarily) permeate flux increase caused biofilm compaction, together with membrane performance losses. The impact of biofilms on membrane performance can be influenced (increased and reduced) by operational parameters. The article shows that a (temporary) pressure increase leads to more
Plasma Relaxation in Hall Magnetohydrodynamics
Shivamoggi, B K
2011-01-01
Parker's formulation of isotopological plasma relaxation process in magnetohydrodynamics (MHD) is extended to Hall MHD. The torsion coefficient alpha in the Hall MHD Beltrami condition turns out now to be proportional to the "potential vorticity." The Hall MHD Beltrami condition becomes equivalent to the "potential vorticity" conservation equation in two-dimensional hydrodynamics if the Hall MHD Lagrange multiplier beta is taken to be proportional to the "potential vorticity" as well. The winding pattern of the magnetic field lines in Hall MHD then appears to evolve in the same way as "potential vorticity" lines in 2D hydrodynamics.
Relaxing Chosen-Ciphertext Security
DEFF Research Database (Denmark)
Canetti, Ran; Krawczyk, Hugo; Nielsen, Jesper Buus
2003-01-01
Security against adaptive chosen ciphertext attacks (or, CCA security) has been accepted as the standard requirement from encryption schemes that need to withstand active attacks. In particular, it is regarded as the appropriate security notion for encryption schemes used as components within...... “for most practical purposes.” We propose a relaxed variant of CCA security, called Replayable CCA (RCCA) security. RCCA security accepts as secure the non-CCA (yet arguably secure) schemes mentioned above; furthermore, it suffices for most existing applications of CCA security. We provide three...
Shocks, singularities and oscillations in nonlinear optics and fluid mechanics
Santo, Daniele; Lannes, David
2017-01-01
The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields. .
Nonlinear Materials Characterization Facility
Federal Laboratory Consortium — The Nonlinear Materials Characterization Facility conducts photophysical research and development of nonlinear materials operating in the visible spectrum to protect...
Global exponential stabilisation of a class of nonlinear time-delay systems
Benabdallah, Amel; Echi, Nadhem
2016-12-01
This paper deals with the state and output feedback stabilisation problems for a family of nonlinear time-delay systems satisfying some relaxed triangular-type condition. The delay is supposed to be constant. Parameter-dependent control laws are used to compensate for the nonlinearities. Based on the Lyapunov-Krasovskii functionals, global exponential stability of the closed-loop systems is achieved. Finally, an extension to nonlinear time-varying delay systems is given.
Spectral properties of a confined nonlinear quantum oscillator in one and three dimensions
Energy Technology Data Exchange (ETDEWEB)
Schulze-Halberg, Axel; Gordon, Christopher R. [Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)
2013-04-15
We analyze the spectral behaviour of a nonlinear quantum oscillator model under confinement. The underlying potential is given by a harmonic oscillator interaction plus a nonlinear term that can be weakened or strengthened through a parameter. Numerical eigenvalues of the model in one and three dimensions are presented. The asymptotic behaviour of the eigenvalues for confinement relaxation and for vanishing nonlinear term in the potential is investigated. Our findings are compared with existing results.
Nonlinear singular vectors and nonlinear singular values
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A novel concept of nonlinear singular vector and nonlinear singular value is introduced, which is a natural generalization of the classical linear singular vector and linear singular value to the nonlinear category. The optimization problem related to the determination of nonlinear singular vectors and singular values is formulated. The general idea of this approach is demonstrated by a simple two-dimensional quasigeostrophic model in the atmospheric and oceanic sciences. The advantage and its applications of the new method to the predictability, ensemble forecast and finite-time nonlinear instability are discussed. This paper makes a necessary preparation for further theoretical and numerical investigations.
Relaxation of liquid bridge after droplets coalescence
Directory of Open Access Journals (Sweden)
Jiangen Zheng
2016-11-01
Full Text Available We investigate the relaxation of liquid bridge after the coalescence of two sessile droplets resting on an organic glass substrate both experimentally and theoretically. The liquid bridge is found to relax to its equilibrium shape via two distinct approaches: damped oscillation relaxation and underdamped relaxation. When the viscosity is low, damped oscillation shows up, in this approach, the liquid bridge undergoes a damped oscillation process until it reaches its stable shape. However, if the viscous effects become significant, underdamped relaxation occurs. In this case, the liquid bridge relaxes to its equilibrium state in a non-periodic decay mode. In depth analysis indicates that the damping rate and oscillation period of damped oscillation are related to an inertial-capillary time scale τc. These experimental results are also testified by our numerical simulations with COMSOL Multiphysics.
Cross relaxation in nitroxide spin labels
Marsh, Derek
2016-11-01
Cross relaxation, and mI -dependence of the intrinsic electron spin-lattice relaxation rate We , are incorporated explicitly into the rate equations for the electron-spin population differences that govern the saturation behaviour of 14N- and 15N-nitroxide spin labels. Both prove important in spin-label EPR and ELDOR, particularly for saturation recovery studies. Neither for saturation recovery, nor for CW-saturation EPR and CW-ELDOR, can cross relaxation be described simply by increasing the value of We , the intrinsic spin-lattice relaxation rate. Independence of the saturation recovery rates from the hyperfine line pumped or observed follows directly from solution of the rate equations including cross relaxation, even when the intrinsic spin-lattice relaxation rate We is mI -dependent.
Relaxation of Warped Disks: the Case of Pure Hydrodynamics
Sorathia, Kareem A; Hawley, John F
2013-01-01
Orbiting disks may exhibit bends due to a misalignment between the angular momentum of the inner and outer regions of the disk. We begin a systematic simulational inquiry into the physics of warped disks with the simplest case: the relaxation of an unforced warp under pure fluid dynamics, i.e. with no internal stresses other than Reynolds stress. We focus on the nonlinear regime in which the bend rate is large compared to the disk aspect ratio. When warps are nonlinear, strong radial pressure gradients drive transonic radial motions along the disk's top and bottom surfaces that efficiently mix angular momentum. The resulting nonlinear decay rate of the warp increases with the warp rate and the warp width, but, at least in the parameter regime studied here, is independent of the sound speed. The characteristic magnitude of the associated angular momentum fluxes likewise increases with both the local warp rate and the radial range over which the warp extends; it also increases with increasing sound speed, but m...
Utilizing RELAX NG Schemas in XML Editors
Schmied, Martin
2008-01-01
This thesis explores the possibilities of utilizing RELAX NG schemata in the process of editing XML documents. The ultimate goal of this thesis is to prototype a system supporting user while editing XML document with bound RELAX NG schema inside the Eclipse IDE. Such a system comprises two major components -- an integration of RELAX NG validator and an autocompletion engine. Design of the autocompletion engine represents the main contribution of this thesis, because similar systems are almost...
Temperature relaxation in dense plasma mixtures
Faussurier, Gérald; Blancard, Christophe
2016-09-01
We present a model to calculate temperature-relaxation rates in dense plasma mixtures. The electron-ion relaxation rates are calculated using an average-atom model and the ion-ion relaxation rates by the Landau-Spitzer approach. This method allows the study of the temperature relaxation in many-temperature electron-ion and ion-ion systems such as those encountered in inertial confinement fusion simulations. It is of interest for general nonequilibrium thermodynamics dealing with energy flows between various systems and should find broad use in present high energy density experiments.
Baryogenesis via Elementary Goldstone Higgs Relaxation
Gertov, Helene; Pearce, Lauren; Yang, Louis
2016-01-01
We extend the relaxation mechanism to the Elementary Goldstone Higgs frame- work. Besides studying the allowed parameter space of the theory we add the minimal ingredients needed for the framework to be phenomenologically viable. The very nature of the extended Higgs sector allows to consider very flat scalar potential directions along which the relaxation mechanism can be implemented. This fact translates into wider regions of applicability of the relaxation mechanism when compared to the Standard Model Higgs case. Our results show that, if the electroweak scale is not fundamental but radiatively generated, it is possible to generate the observed matter-antimatter asymmetry via the relaxation mechanism.
Dielectric relaxation studies in polyvinyl butyral
Mehendru, P. C.; Kumar, Naresh; Arora, V. P.; Gupta, N. P.
1982-10-01
Dielectric measurements have been made in thick films (˜100 μm) of polyvinyl butyral (PVB) having degree of polymerization n=1600, in the frequency range 100 Hz-100 KHz and temperature range 300-373 K. The results indicated that PVB was in the amorphous phase and observed dielectric dispersion has been assigned as the β-relaxation process. The β relaxation is of Debye type with symmetrical distribution of relaxation times. The dielectric relaxation strength Δɛ and the distribution parameters β¯ increase with temperature. The results can be qualitatively explained by assuming the hindered rotation of the side groups involving hydroxyl/acetate groups.
Relaxation and Visualization Strategies for Story Telling
Institute of Scientific and Technical Information of China (English)
冯灵林
2012-01-01
The importance of training students to tell or retell story is self - evident for mastering English language. The following activity introduces relaxation and visualization strategies for story telling.
Davies, H. C.; Turner, R. E.
1977-01-01
A dynamical relaxation technique for updating prediction models is analyzed with the help of the linear and nonlinear barotropic primitive equations. It is assumed that a complete four-dimensional time history of some prescribed subset of the meteorological variables is known. The rate of adaptation of the flow variables toward the true state is determined for a linearized f-model, and for mid-latitude and equatorial beta-plane models. The results of the analysis are corroborated by numerical experiments with the nonlinear shallow-water equations.
Nuclear relaxation via paramagnetic impurities
Dzheparov, F S; Jacquinot, J F
2002-01-01
First part of the work contains a calculation of the kinetics of nuclear relaxation via paramagnetic impurities for systems with arbitrary (including fractal) space dimension d basing on ideas, which run current for 3d objects now. A new mean-field-type theory is constructed in the second part of the work. It reproduces all results of the first part for integer d and gives a possibility to describe the process for longer time, when a crossover to Balagurov-Waks asymptotics starts to develop. Solutions of the equations of the new theory are constructed for integer d. To obtain the solutions a method of calculation of the low-energy and long-wave asymptotics for T matrix of potential scattering out of the mass shell for singular repulsive potentials is developed
Relaxing Chosen-Ciphertext Security
DEFF Research Database (Denmark)
Canetti, Ran; Krawczyk, Hugo; Nielsen, Jesper Buus
2003-01-01
Security against adaptive chosen ciphertext attacks (or, CCA security) has been accepted as the standard requirement from encryption schemes that need to withstand active attacks. In particular, it is regarded as the appropriate security notion for encryption schemes used as components within...... general protocols and applications. Indeed, CCA security was shown to suffice in a large variety of contexts. However, CCA security often appears to be somewhat too strong: there exist encryption schemes (some of which come up naturally in practice) that are not CCA secure, but seem sufficiently secure...... “for most practical purposes.” We propose a relaxed variant of CCA security, called Replayable CCA (RCCA) security. RCCA security accepts as secure the non-CCA (yet arguably secure) schemes mentioned above; furthermore, it suffices for most existing applications of CCA security. We provide three...
A solution of the cusp problem in relaxed halos of dark matter
Mikheeva, E; Lukash, V
2007-01-01
We propose a solution of the cusp problem in framework of the standard $\\Lambda$CDM cosmology. To do this we describe the linear and nonlinear periods of halo formation by the entropy function of dark matter particles. This approach allows us to take into account together the impact of both the processes of nonlinear relaxation of compressed matter and the small scale initial velocity perturbations in collapsed halos. We show that such random velocities lead to the random variations of the density profile of relaxed halos. As a rule, they suppress the formation of cusp--like halos and favor the creation of core--like ones. This approach allows us to reproduce observed rotation curves, to explain their random scatter and deviations from simulated ones.
Turbulent relaxation and meta-stable equilibrium states of an electron plasma
Rodgers, Douglas J.
A Malmberg-Penning electron trap allows for the experimental study of nearly ideal, two-dimensional (2D) inviscid (Euler) hydrodynamics. This is perhaps the simplest case of self organizing nonlinear turbulence, and is therefore a paradigm for dynamo theory, Taylor relaxation, selective decay and other nonlinear fluid processes. The dynamical relaxation of a pure electron plasma in the guiding-center-drift approximation is studied, comparing experiments, numerical simulations and statistical theories of weakly-dissipative 2D turbulence. The nonuniform metastable equilibrium states resulting from turbulent evolution are examined, and are well-described by a maximum entropy principle for constrained circulation, energy, and angular momentum. The turbulent decay of the system is also examined, and a similarity decay law is proposed which incorporates the substantial enstrophy trapped in the metastable equilibrium. This law approaches Batchelor's t-2 self-similar decay in the limit of strong turbulence, and is verified in turbulent evolution in the electron plasma experiment.
A Tropical Atmosphere Model with Moisture: Global Well-posedness and Relaxation Limit
Li, Jinkai
2015-01-01
In this paper, we consider a nonlinear interaction system between the barotropic mode and the first baroclinic mode of the tropical atmosphere with moisture; that was derived in [Frierson, D.M.W.; Majda, A.J.; Pauluis, O.M.: Dynamics of precipitation fronts in the tropical atmosphere: a novel relaxation limit, Commum. Math. Sci., 2 (2004), 591-626.] We establish the global existence and uniqueness of strong solutions to this system, with initial data in $H^1$, for each fixed convective adjustment relaxation time parameter $\\varepsilon>0$. Moreover, if the initial data enjoy slightly more regularity than $H^1$, then the unique strong solution depends continuously on the initial data. Furthermore, by establishing several appropriate $\\varepsilon$-independent estimates, we prove that the system converges to a limiting system, as the relaxation time parameter $\\varepsilon$ tends to zero, with convergence rate of the order $O(\\sqrt\\varepsilon)$. Moreover, the limiting system has a unique global strong solution, fo...
Van der Pol and the history of relaxation oscillations: toward the emergence of a concept
Ginoux, Jean-Marc
2014-01-01
Relaxation oscillations are commonly associated with the name of Balthazar van der Pol via his eponymous paper (Philosophical Magazine, 1926) in which he apparently introduced this terminology to describe the nonlinear oscillations produced by self-sustained oscillating systems such as a triode circuit. Our aim is to investigate how relaxation oscillations were actually discovered. Browsing the literature from the late 19th century, we identified four self-oscillating systems in which relaxation oscillations have been observed: i) the series dynamo machine conducted by G\\'erard-Lescuyer (1880), ii) the musical arc discovered by Duddell (1901) and investigated by Blondel (1905), iii) the triode invented by de Forest (1907) and, iv) the multivibrator elaborated by Abraham and Bloch (1917). The differential equation describing such a self-oscillating system was proposed by Poincar\\'e for the musical arc (1908), by Janet for the series dynamo machine (1919), and by Blondel for the triode (1919). Once Janet (1919)...
A suite of Mathematica notebooks for the analysis of protein main chain 15N NMR relaxation data.
Spyracopoulos, Leo
2006-12-01
A suite of Mathematica notebooks has been designed to ease the analysis of protein main chain 15N NMR relaxation data collected at a single magnetic field strength. Individual notebooks were developed to perform the following tasks: nonlinear fitting of 15N-T1 and -T2 relaxation decays to a two parameter exponential decay, calculation of the principal components of the inertia tensor from protein structural coordinates, nonlinear optimization of the principal components and orientation of the axially symmetric rotational diffusion tensor, model-free analysis of 15N-T1, -T2, and {1H}-15N NOE data, and reduced spectral density analysis of the relaxation data. The principle features of the notebooks include use of a minimal number of input files, integrated notebook data management, ease of use, cross-platform compatibility, automatic visualization of results and generation of high-quality graphics, and output of analyses in text format.
NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS
Institute of Scientific and Technical Information of China (English)
PENG SHIGE
2005-01-01
This paper deals with nonlinear expectations. The author obtains a nonlinear generalization of the well-known Kolmogorov's consistent theorem and then use it to construct filtration-consistent nonlinear expectations via nonlinear Markov chains. Compared to the author's previous results, i.e., the theory of g-expectations introduced via BSDE on a probability space, the present framework is not based on a given probability measure. Many fully nonlinear and singular situations are covered. The induced topology is a natural generalization of Lp-norms and L∞-norm in linear situations.The author also obtains the existence and uniqueness result of BSDE under this new framework and develops a nonlinear type of von Neumann-Morgenstern representation theorem to utilities and present dynamic risk measures.
Superparamagnetic relaxation of weakly interacting particles
DEFF Research Database (Denmark)
Mørup, Steen; Tronc, Elisabeth
1994-01-01
The influence of particle interactions on the superparamagnetic relaxation time has been studied by Mossbauer spectroscopy in samples of maghemite (gamma-Fe2O3) particles with different particle sizes and particle separations. It is found that the relaxation time decreases with decreasing particl...
Postextrasystolic relaxation in the dog heart
Kuijer, P.J.P.; Heethaar, R.M.; Herbschleb, J.N.; Zimmerman, A.N.E.; Meijler, F.L.
1978-01-01
Left ventricular relaxation was studied in 8 dogs using parameters derived from the left ventricular pressure: the fastest pressure fall and the time constant of pressure decline. Effects of extrasystolic rhythm interventions were examined on the relaxation parameters of the post-relative to the pre
Superparamagnetic relaxation in alpha-Fe particles
DEFF Research Database (Denmark)
Bødker, Franz; Mørup, Steen; Pedersen, Michael Stanley;
1998-01-01
The superparamagnetic relaxation time of carbon-supported alpha-Fe particles with an average size of 3.0 Mm has been studied over a large temperature range by the use of Mossbauer spectroscopy combined with AC and DC magnetization measurements. It is found that the relaxation time varies with tem...
Cross relaxation in nitroxide spin labels
DEFF Research Database (Denmark)
Marsh, Derek
2016-01-01
-label EPR and ELDOR, particularly for saturation recovery studies. Neither for saturation recovery, nor for CW-saturation EPR and CW-ELDOR, can cross relaxation be described simply by increasing the value of We, the intrinsic spin-lattice relaxation rate. Independence of the saturation recovery rates from...
Magnetization Transfer Induced Biexponential Longitudinal Relaxation
Prantner, Andrew M.; Bretthorst, G. Larry; Neil, Jeffrey J.; Garbow, Joel R.; Ackerman, Joseph J.H.
2009-01-01
Longitudinal relaxation of brain water 1H magnetization in mammalian brain in vivo is typically analyzed on a per voxel basis using a monoexponential model, thereby assigning a single relaxation time constant to all 1H magnetization within a given voxel. This approach was tested by obtaining inversion recovery data from grey matter of rats at 64 exponentially-spaced recovery times. Using Bayesian probability for model selection, brain water data were best represented by a biexponential function characterized by fast and slow relaxation components. At 4.7 T, the amplitude fraction of the rapidly relaxing component is 3.4 ± 0.7 % with a rate constant of 44 ± 12 s-1 (mean ± SD; 174 voxels from 4 rats). The rate constant of the slow relaxing component is 0.66 ± 0.04 s-1. At 11.7 T, the corresponding values are 6.9 ± 0.9 %, 19 ± 5 s-1, and 0.48 ± 0.02 s-1 (151 voxels from 4 rats). Several putative mechanisms for biexponential relaxation behavior were evaluated, and magnetization transfer between bulk water protons and non-aqueous protons was determined to be the source of biexponential longitudinal relaxation. MR methods requiring accurate quantification of longitudinal relaxation may need to take this effect explicitly into account. PMID:18759367
Windowing Waveform Relaxation of Initial Value Problems
Institute of Scientific and Technical Information of China (English)
Yao-lin Jiang
2006-01-01
We present a windowing technique of waveform relaxation for dynamic systems. An effective estimation on window length is derived by an iterative error expression provided here. Relaxation processes can be speeded up if one takes the windowing technique in advance. Numerical experiments are given to further illustrate the theoretical analysis.
Stress Relaxation in Entangled Polymer Melts
DEFF Research Database (Denmark)
Hou, Ji-Xuan; Svaneborg, Carsten; Everaers, Ralf
2010-01-01
We present an extensive set of simulation results for the stress relaxation in equilibrium and step-strained bead-spring polymer melts. The data allow us to explore the chain dynamics and the shear relaxation modulus, G(t), into the plateau regime for chains with Z=40 entanglements and into the t......We present an extensive set of simulation results for the stress relaxation in equilibrium and step-strained bead-spring polymer melts. The data allow us to explore the chain dynamics and the shear relaxation modulus, G(t), into the plateau regime for chains with Z=40 entanglements...... and into the terminal relaxation regime for Z=10. Using the known (Rouse) mobility of unentangled chains and the melt entanglement length determined via the primitive path analysis of the microscopic topological state of our systems, we have performed parameter-free tests of several different tube models. We find...
Stress and Relaxation in Relation to Personality
Directory of Open Access Journals (Sweden)
Harish Kumar Sharma
2011-09-01
Full Text Available Relaxation plays a significant role in facing stress. The aim of the present study is to see whether personality patterns determine an individual’s ability to relax. As a reaction to stress, coping is the best way to handle stress, which requires rational and conscious thinking. Does this ability to relax anyway facilitate coping reactions? A study was conducted on 100 college students. Results revealed that extraverts relax easily than introverts. In addition, if intelligence level is average or above average, relaxation does play a role in facilitating coping reactions. It suggests that in designing techniques of stress management, the personality and intelligence level must be taken into consideration to make techniques effective.
Relaxation oscillation model of hemodynamic parameters in the cerebral vessels
Cherevko, A. A.; Mikhaylova, A. V.; Chupakhin, A. P.; Ufimtseva, I. V.; Krivoshapkin, A. L.; Orlov, K. Yu
2016-06-01
Simulation of a blood flow under normality as well as under pathology is extremely complex problem of great current interest both from the point of view of fundamental hydrodynamics, and for medical applications. This paper proposes a model of Van der Pol - Duffing nonlinear oscillator equation describing relaxation oscillations of a blood flow in the cerebral vessels. The model is based on the patient-specific clinical experimental data flow obtained during the neurosurgical operations in Meshalkin Novosibirsk Research Institute of Circulation Pathology. The stability of the model is demonstrated through the variations of initial data and coefficients. It is universal and describes pressure and velocity fluctuations in different cerebral vessels (arteries, veins, sinuses), as well as in a laboratory model of carotid bifurcation. Derived equation describes the rheology of the ”blood stream - elastic vessel wall gelatinous brain environment” composite system and represents the state equation of this complex environment.
Role of atomic relaxation in hydrogen-induced amorphization
Energy Technology Data Exchange (ETDEWEB)
Katagiri, M.; Onodera, H. [National Inst. for Materials Science, Tsukuba (Japan). Computational Materials Science Center
2009-07-01
This study investigated the microscopic mechanism of hydrogen-induced amorphization (HIA) in an AB{sub 2}C{sub 15} Laves phase compounds. Molecular dynamics were used to investigate the role of size by incorporating hydrogen within various systems. The study showed that in YA{sub 12} systems, hydrogenation increased the volume, while the bulk modulus was reduced as a result of the non-linearity of the interatomic potentials. In CeNi{sub 2} systems, hydrogenation reduced the bulk modulus as a result of the negative increase of the pressure-fluctuation terms in the elastic constant. Increases in pressure fluctuations were caused by the atomic relaxation in the hydrogenation process. Atomic contraction and expansion in the CeNi{sub 2} occurred simultaneously during hydrogenation. It was concluded that the size effect in HIA facilitates elastic instability by increasing pressure fluctuations.
Magnetic Resonance Fingerprinting with short relaxation intervals.
Amthor, Thomas; Doneva, Mariya; Koken, Peter; Sommer, Karsten; Meineke, Jakob; Börnert, Peter
2017-09-01
The aim of this study was to investigate a technique for improving the performance of Magnetic Resonance Fingerprinting (MRF) in repetitive sampling schemes, in particular for 3D MRF acquisition, by shortening relaxation intervals between MRF pulse train repetitions. A calculation method for MRF dictionaries adapted to short relaxation intervals and non-relaxed initial spin states is presented, based on the concept of stationary fingerprints. The method is applicable to many different k-space sampling schemes in 2D and 3D. For accuracy analysis, T1 and T2 values of a phantom are determined by single-slice Cartesian MRF for different relaxation intervals and are compared with quantitative reference measurements. The relevance of slice profile effects is also investigated in this case. To further illustrate the capabilities of the method, an application to in-vivo spiral 3D MRF measurements is demonstrated. The proposed computation method enables accurate parameter estimation even for the shortest relaxation intervals, as investigated for different sampling patterns in 2D and 3D. In 2D Cartesian measurements, we achieved a scan acceleration of more than a factor of two, while maintaining acceptable accuracy: The largest T1 values of a sample set deviated from their reference values by 0.3% (longest relaxation interval) and 2.4% (shortest relaxation interval). The largest T2 values showed systematic deviations of up to 10% for all relaxation intervals, which is discussed. The influence of slice profile effects for multislice acquisition is shown to become increasingly relevant for short relaxation intervals. In 3D spiral measurements, a scan time reduction of 36% was achieved, maintaining the quality of in-vivo T1 and T2 maps. Reducing the relaxation interval between MRF sequence repetitions using stationary fingerprint dictionaries is a feasible method to improve the scan efficiency of MRF sequences. The method enables fast implementations of 3D spatially resolved
Gamma dosimetric parameters in some skeletal muscle relaxants
Manjunatha, H. C.
2017-09-01
We have studied the attenuation of gamma radiation of energy ranging from 84 keV to 1330 keV (^{170}Tm, ^{22} Na,^{137} Cs, and ^{60}Co) in some commonly used skeletal muscle relaxants such as tubocurarine chloride, gallamine triethiodide, pancuronium bromide, suxamethonium bromide and mephenesin. The mass attenuation coefficient is measured from the attenuation experiment. In the present work, we have also proposed the direct relation between mass attenuation coefficient (μ /ρ ) and mass energy absorption coefficient (μ _{en}/ρ ) based on the nonlinear fitting procedure. The gamma dosimetric parameters such as mass energy absorption coefficient (μ _{en}/ρ ), effective atomic number (Z_{eff}), effective electron density (N_{el}), specific {\\upgamma }-ray constant, air kerma strength and dose rate are evaluated from the measured mass attentuation coefficient. These measured gamma dosimetric parameters are compared with the theoretical values. The measured values agree with the theoretical values. The studied gamma dosimetric values for the relaxants are useful in medical physics and radiation medicine.
Theory of Activated Relaxation in Nanoscale Confined Liquids
Mirigian, Stephen; Schweizer, Kenneth
2014-03-01
We extend the recently developed Elastically Cooperative Nonlinear Langevin Equation(ECNLE) theory of activated relaxation in supercooled liquids to treat the case of geometrically confined liquids. Generically, confinement of supercooled liquids leads to a speeding up of the dynamics(with a consequent depression of the glass transition temperature) extending on the order of tens of molecular diameters away from a free surface. At present, this behavior is not theoretically well understood. Our theory interprets the speed up in dynamics in terms of two coupled effects. First, a direct surface effect, extending two to three molecular diameters from a free surface, and related to a local rearrangement of molecules with a single cage. The second is a longer ranged ``confinement'' effect, extending tens of molecular diameters from a free surface and related to the long range elastic penalty necessary for a local rearrangement. The theory allows for the calculation of relaxation time and Tg profiles within a given geometry and first principles calculations of relevant length scales. Comparison to both dynamic and pseudo-thermodynamic measurements shows reasonable agreement to experiment with no adjustable parameters.
Gamma dosimetric parameters in some skeletal muscle relaxants
Indian Academy of Sciences (India)
H C MANJUNATHA
2017-09-01
We have studied the attenuation of gamma radiation of energy ranging from 84 keV to 1330 keV $(^{170}Tm, ^{22}Na, ^{137}Cs, and ^{60}Co)$ in some commonly used skeletal muscle relaxants such as tubocurarine chloride, gallamine triethiodide, pancuronium bromide, suxamethonium bromide and mephenesin. The mass attenuation coefficient is measured from the attenuation experiment. In the present work, we have also proposed the direct relation between mass attenuation coefficient $(\\mu/\\rho)$ and mass energy absorption coefficient $(\\mu_{en}/\\rho)$ based on the nonlinear fitting procedure. The gamma dosimetric parameters such as mass energy absorption coefficient $(\\mu_{en}/\\rho)$, effective atomic number $\\rm{(Z_eff )}$, effective electron density $(N_\\rm{el})$, specific $\\gamma$-ray constant, air kerma strength and dose rate are evaluated from the measured mass attentuation coefficient. These measured gamma dosimetric parameters are compared with the theoretical values. The measured values agree with the theoretical values. The studied gamma dosimetric values for the relaxants are useful in medical physics and radiation medicine.
Domain Relaxation in Langmuir Films
Bernoff, Andrew J.; Alexander, James C.; Mann, Elizabeth K.; Mann, J. Adin; Zou, Lu; Wintersmith, Jacob R.
2007-11-01
We report on an experimental, theoretical and computational study of a molecularly thin polymer Langmuir layer domain on the surface of a subfluid. When stretched (by a transient stagnation flow), the Langmuir layer takes the form of a bola consisting of two roughly circular reservoirs connected by a thin tether. This shape relaxes to the circular minimum energy configuration. The tether is never observed to rupture, even when it is more than a hundred times as long as it is thin. We model these experiments as a free boundary problem where motion is driven by the line tension of the domain and damped by the viscosity of the subfluid. We process the digital images of the experiment to extract the domain shape, use one of these shapes as an initial condition for the numerical solution of a boundary-integral model of the underlying hydrodynamics, and compare the subsequent images of the experiment to the numerical simulation. The numerical evolutions verify that our hydrodynamical model can reproduce the observed dynamics. They also allow us to deduce the magnitude of the line tension in the system, often to within 1%.
Supervised Discrete Hashing With Relaxation.
Gui, Jie; Liu, Tongliang; Sun, Zhenan; Tao, Dacheng; Tan, Tieniu
2016-12-29
Data-dependent hashing has recently attracted attention due to being able to support efficient retrieval and storage of high-dimensional data, such as documents, images, and videos. In this paper, we propose a novel learning-based hashing method called ''supervised discrete hashing with relaxation'' (SDHR) based on ''supervised discrete hashing'' (SDH). SDH uses ordinary least squares regression and traditional zero-one matrix encoding of class label information as the regression target (code words), thus fixing the regression target. In SDHR, the regression target is instead optimized. The optimized regression target matrix satisfies a large margin constraint for correct classification of each example. Compared with SDH, which uses the traditional zero-one matrix, SDHR utilizes the learned regression target matrix and, therefore, more accurately measures the classification error of the regression model and is more flexible. As expected, SDHR generally outperforms SDH. Experimental results on two large-scale image data sets (CIFAR-10 and MNIST) and a large-scale and challenging face data set (FRGC) demonstrate the effectiveness and efficiency of SDHR.
Spin relaxation in organic semiconductors
Bobbert, Peter
2011-03-01
Intriguing magnetic field effects in organic semiconductor devices have been reported: anomalous magnetoresistance in organic spin valves and large effects of small magnetic fields on the current and luminescence of organic light-emitting diodes. Influences of isotopic substitution on these effects points at the role of hyperfine coupling. We performed studies of spin relaxation in organic semiconductors based on (i) coherent spin precession of the electron spin in an effective magnetic field consisting of a random hyperfine field and an applied magnetic field and (ii) incoherent hopping of charges. These ingredients are incorporated in a stochastic Liouville equation for the dynamics of the spin density matrix of single charges as well as pairs of charges. For single charges we find a spin diffusion length that depends on the magnetic field, explaining anomalous magnetoresistance in organic spin valves. For pairs of charges we show that the magnetic field influences formation of singlet bipolarons, in the case of like charges, and singlet and triplet excitons, in the case of opposite charges. We can reproduce different line shapes of reported magnetic field effects, including recently found effects at ultra-small fields.
Ermolenko, M. V.; Stankevich, V. V.; Buganov, O. V.; Tikhomirov, S. A.; Ganonenko, S. V.; Kuznetsov, P. I.; Yakushcheva, G. G.
2009-04-01
The nonlinear optical properties of multilayer heterostructures based on zinc chalcogenides are studied. Rapid variations in the reflection and transmission of samples excited by ultrashort laser pulses are demonstrated. The characteristic relaxation times of the induced nonlinearity are 2-5 ps and are almost independent within the experimental error on the excitation energy and temperature of a sample.
Relaxation of a 1-D gravitational system
Valageas, P
2006-01-01
We study the relaxation towards thermodynamical equilibrium of a 1-D gravitational system. This OSC model shows a series of critical energies $E_{cn}$ where new equilibria appear and we focus on the homogeneous ($n=0$), one-peak ($n=\\pm 1$) and two-peak ($n=2$) states. Using numerical simulations we investigate the relaxation to the stable equilibrium $n=\\pm 1$ of this $N-$body system starting from initial conditions defined by equilibria $n=0$ and $n=2$. We find that in a fashion similar to other long-range systems the relaxation involves a fast violent relaxation phase followed by a slow collisional phase as the system goes through a series of quasi-stationary states. Moreover, in cases where this slow second stage leads to a dynamically unstable configuration (two peaks with a high mass ratio) it is followed by a new sequence ``violent relaxation/slow collisional relaxation''. We obtain an analytical estimate of the relaxation time $t_{2\\to \\pm 1}$ through the mean escape time of a particle from its potent...
Plasma Relaxation Dynamics Moderated by Current Sheets
Dewar, Robert; Bhattacharjee, Amitava; Yoshida, Zensho
2014-10-01
Ideal magnetohydrodynamics (IMHD) is strongly constrained by an infinite number of microscopic constraints expressing mass, entropy and magnetic flux conservation in each infinitesimal fluid element, the latter preventing magnetic reconnection. By contrast, in the Taylor-relaxed equilibrium model all these constraints are relaxed save for global magnetic flux and helicity. A Lagrangian is presented that leads to a new variational formulation of magnetized fluid dynamics, relaxed MHD (RxMHD), all static solutions of which are Taylor equilibrium states. By postulating that some long-lived macroscopic current sheets can act as barriers to relaxation, separating the plasma into multiple relaxation regions, a further generalization, multi-relaxed MHD (MRxMHD), is developed. These concepts are illustrated using a simple two-region slab model similar to that proposed by Hahm and Kulsrud--the formation of an initial shielding current sheet after perturbation by boundary rippling is calculated using MRxMHD and the final island state, after the current sheet has relaxed through a reconnection sequence, is calculated using RxMHD. Australian Research Council Grant DP110102881.
Indian Academy of Sciences (India)
Madhukar N Shinde; Ravindra B Talware; Pravin G Hudge; Yogesh S Joshi; Ashok C Kumbharkhane
2012-02-01
The complex permittivity, static dielectric constant and relaxation time for 1,3-propanediol, 1,4-dioxane and their mixtures have been studied using time domain reﬂectometry (TDR). The excess permittivity, excess inverse relaxation time and Kirkwood correlation factor have also been determined at various concentrations of dioxane. Hydrogen bonded theory was applied to compute the correlation terms for the mixtures. The Bruggeman model for the nonlinear case has been ﬁtted to the dielectric data for mixtures.
Malygin, M. G.; Klahr, H.; Semenov, D.; Henning, Th.; Dullemond, C. P.
2017-09-01
Context. Hydrodynamic, non-magnetic instabilities can provide turbulent stress in the regions of protoplanetary discs, where the magneto-rotational instability can not develop. The induced motions influence the grain growth, from which formation of planetesimals begins. Thermal relaxation of the gas constrains origins of the identified hydrodynamic sources of turbulence in discs. Aims: We aim to estimate the radiative relaxation timescale of temperature perturbations in protoplanetary discs. We study the dependence of the thermal relaxation on the perturbation wavelength, the location within the disc, the disc mass, and the dust-to-gas mass ratio. We then apply thermal relaxation criteria to localise modes of the convective overstability, the vertical shear instability, and the zombie vortex instability. Methods: For a given temperature perturbation, we estimated two timescales: the radiative diffusion timescale tthick and the optically thin emission timescale tthin. The longest of these timescales governs the relaxation: trelax = max (tthick, tthin). We additionally accounted for the collisional coupling to the emitting species. Our calculations employed the latest tabulated dust and gas mean opacities. Results: The relaxation criterion defines the bulk of a typical T Tauri disc as unstable to the development of linear hydrodynamic instabilities. The midplane is unstable to the convective overstability from at most 2au and up to 40au, as well as beyond 140au. The vertical shear instability can develop between 15au and 180au. The successive generation of (zombie) vortices from a seeded noise can work within the inner 0.8au. Conclusions: A map of relaxation timescale constrains the origins of the identified hydrodynamic turbulence-driving mechanisms in protoplanetary discs. Dynamic disc modelling with the evolution of dust and gas opacities is required to clearly localise the hydrodynamic turbulence, and especially its non-linear phase.
Le Chatelier's principle with multiple relaxation channels
Gilmore, R.; Levine, R. D.
1986-05-01
Le Chatelier's principle is discussed within the constrained variational approach to thermodynamics. The formulation is general enough to encompass systems not in thermal (or chemical) equilibrium. Particular attention is given to systems with multiple constraints which can be relaxed. The moderation of the initial perturbation increases as additional constraints are removed. This result is studied in particular when the (coupled) relaxation channels have widely different time scales. A series of inequalities is derived which describes the successive moderation as each successive relaxation channel opens up. These inequalities are interpreted within the metric-geometry representation of thermodynamics.
Neural control of muscle relaxation in echinoderms.
Elphick, M R; Melarange, R
2001-03-01
Smooth muscle relaxation in vertebrates is regulated by a variety of neuronal signalling molecules, including neuropeptides and nitric oxide (NO). The physiology of muscle relaxation in echinoderms is of particular interest because these animals are evolutionarily more closely related to the vertebrates than to the majority of invertebrate phyla. However, whilst in vertebrates there is a clear structural and functional distinction between visceral smooth muscle and skeletal striated muscle, this does not apply to echinoderms, in which the majority of muscles, whether associated with the body wall skeleton and its appendages or with visceral organs, are made up of non-striated fibres. The mechanisms by which the nervous system controls muscle relaxation in echinoderms were, until recently, unknown. Using the cardiac stomach of the starfish Asterias rubens as a model, it has been established that the NO-cGMP signalling pathway mediates relaxation. NO also causes relaxation of sea urchin tube feet, and NO may therefore function as a 'universal' muscle relaxant in echinoderms. The first neuropeptides to be identified in echinoderms were two related peptides isolated from Asterias rubens known as SALMFamide-1 (S1) and SALMFamide-2 (S2). Both S1 and S2 cause relaxation of the starfish cardiac stomach, but with S2 being approximately ten times more potent than S1. SALMFamide neuropeptides have also been isolated from sea cucumbers, in which they cause relaxation of both gut and body wall muscle. Therefore, like NO, SALMFamides may also function as 'universal' muscle relaxants in echinoderms. The mechanisms by which SALMFamides cause relaxation of echinoderm muscle are not known, but several candidate signal transduction pathways are discussed here. The SALMFamides do not, however, appear to act by promoting release of NO, and muscle relaxation in echinoderms is therefore probably regulated by at least two neuronal signalling systems acting in parallel. Recently, other
Stress Relaxation in Entangled Polymer Melts
DEFF Research Database (Denmark)
Hou, Ji-Xuan; Svaneborg, Carsten; Everaers, Ralf
2010-01-01
and into the terminal relaxation regime for Z=10. Using the known (Rouse) mobility of unentangled chains and the melt entanglement length determined via the primitive path analysis of the microscopic topological state of our systems, we have performed parameter-free tests of several different tube models. We find......We present an extensive set of simulation results for the stress relaxation in equilibrium and step-strained bead-spring polymer melts. The data allow us to explore the chain dynamics and the shear relaxation modulus, G(t), into the plateau regime for chains with Z=40 entanglements...
Spin relaxation in nanowires by hyperfine coupling
Energy Technology Data Exchange (ETDEWEB)
Echeverria-Arrondo, C. [Department of Physical Chemistry, Universidad del Pais Vasco UPV/EHU, 48080 Bilbao (Spain); Sherman, E.Ya. [Department of Physical Chemistry, Universidad del Pais Vasco UPV/EHU, 48080 Bilbao (Spain); IKERBASQUE Basque Foundation for Science, 48011 Bilbao, Bizkaia (Spain)
2012-08-15
Hyperfine interactions establish limits on spin dynamics and relaxation rates in ensembles of semiconductor quantum dots. It is the confinement of electrons which determines nonzero hyperfine coupling and leads to the spin relaxation. As a result, in nanowires one would expect the vanishing of this effect due to extended electron states. However, even for relatively clean wires, disorder plays a crucial role and makes electron localization sufficient to cause spin relaxation on the time scale of the order of 10 ns. (copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Compact vs. Exponential-Size LP Relaxations
Energy Technology Data Exchange (ETDEWEB)
Carr, R.D.; Lancia, G.
2000-09-01
In this paper we introduce by means of examples a new technique for formulating compact (i.e. polynomial-size) LP relaxations in place of exponential-size models requiring separation algorithms. In the same vein as a celebrated theorem by Groetschel, Lovasz and Schrijver, we state the equivalence of compact separation and compact optimization. Among the examples used to illustrate our technique, we introduce a new formulation for the Traveling Salesman Problem, whose relaxation we show equivalent to the subtour elimination relaxation.
Relaxation time in disordered molecular systems
Energy Technology Data Exchange (ETDEWEB)
Rocha, Rodrigo P. [Departamento de Física, Universidade Federal de Santa Catarina, 88040-900 Florianópolis-SC (Brazil); Freire, José A., E-mail: jfreire@fisica.ufpr.br [Departamento de Física, Universidade Federal do Paraná, 81531-990 Curitiba-PR (Brazil)
2015-05-28
Relaxation time is the typical time it takes for a closed physical system to attain thermal equilibrium. The equilibrium is brought about by the action of a thermal reservoir inducing changes in the system micro-states. The relaxation time is intuitively expected to increase with system disorder. We derive a simple analytical expression for this dependence in the context of electronic equilibration in an amorphous molecular system model. We find that the disorder dramatically enhances the relaxation time but does not affect its independence of the nature of the initial state.
Nuclear magnetic resonance relaxation in multiple sclerosis
DEFF Research Database (Denmark)
Larsson, H B; Barker, G J; MacKay, A
1998-01-01
OBJECTIVES: The theory of relaxation processes and their measurements are described. An overview is presented of the literature on relaxation time measurements in the normal and the developing brain, in experimental diseases in animals, and in patients with multiple sclerosis. RESULTS...... AND CONCLUSION: Relaxation time measurements provide insight into development of multiple sclerosis plaques, especially the occurrence of oedema, demyelination, and gliosis. There is also evidence that normal appearing white matter in patients with multiple sclerosis is affected. What is now needed are fast...
1H relaxation dispersion in solutions of nitroxide radicals: Influence of electron spin relaxation
Kruk, D.; Korpała, A.; Kubica, A.; Kowalewski, J.; Rössler, E. A.; Moscicki, J.
2013-03-01
The work presents a theory of nuclear (1H) spin-lattice relaxation dispersion for solutions of 15N and 14N radicals, including electron spin relaxation effects. The theory is a generalization of the approach presented by Kruk et al. [J. Chem. Phys. 137, 044512 (2012)], 10.1063/1.4736854. The electron spin relaxation is attributed to the anisotropic part of the electron spin-nitrogen spin hyperfine interaction modulated by rotational dynamics of the paramagnetic molecule, and described by means of Redfield relaxation theory. The 1H relaxation is caused by electron spin-proton spin dipole-dipole interactions which are modulated by relative translational motion of the solvent and solute molecules. The spectral density characterizing the translational dynamics is described by the force-free-hard-sphere model. The electronic relaxation influences the 1H relaxation by contributing to the fluctuations of the inter-molecular dipolar interactions. The developed theory is tested against 1H spin-lattice relaxation dispersion data for glycerol solutions of 4-oxo-TEMPO-d16-15N and 4-oxo-TEMPO-d16-14N covering the frequency range of 10 kHz-20 MHz. The studies are carried out as a function of temperature starting at 328 K and going down to 290 K. The theory gives a consistent overall interpretation of the experimental data for both 14N and 15N systems and explains the features of 1H relaxation dispersion resulting from the electron spin relaxation.
Hydrogen sulfide and vascular relaxation
Institute of Scientific and Technical Information of China (English)
SUN Yan; TANG Chao-shu; DU Jun-bao; JIN Hong-fang
2011-01-01
Objective To review the vasorelaxant effects of hydrogen sulfide (H2S) in arterial rings in the cardiovascular system under both physiological and pathophysiological conditions and the possible mechanisms involved.Data sources The data in this review were obtained from Medline and Pubmed sources from 1997 to 2011 using the search terms "hydrogen sulfide" and ""vascular relaxation".Study selection Articles describing the role of hydrogen sulfide in the regulation of vascular activity and its vasorelaxant effects were selected.Results H2S plays an important role in the regulation of cardiovascular tone.The vasomodulatory effects of H2S depend on factors including concentration,species and tissue type.The H2S donor,sodium hydrosulfide (NarS),causes vasorelaxation of rat isolated aortic rings in a dose-dependent manner.This effect was more pronounced than that observed in pulmonary arterial rings.The expression of KATP channel proteins and mRNA in the aortic rings was increased compared with pulmonary artery rings.H2S is involved in the pathogenesis of a variety of cardiovascular diseases.Downregulation of the endogenous H2S pathway is an important factor in the pathogenesis of cardiovascular diseases.The vasorelaxant effects of H2S have been shown to be mediated by activation of KATP channels in vascular smooth muscle cells and via the induction of acidification due to activation of the CI/HCO3 exchanger.It is speculated that the mechanisms underlying the vasoconstrictive function of H2S in the aortic rings involves decreased NO production and inhibition of cAMP accumulation.Conclusion H2S is an important endogenous gasotransmitter in the cardiovascular system and acts as a modulator of vascular tone in the homeostatic regulation of blood pressure.
“I think relax, relax and it flows a lot easier”: Exploring client-generated relax strategies
Directory of Open Access Journals (Sweden)
Dianne Cirone
2014-10-01
Full Text Available Background. Some adult stroke survivors participating in Cognitive Orientation to daily Occupational Performance (CO-OP treatment programs self-generated relax strategies that have not been explored in previous CO-OP publications. The objective of this study was to describe the process by which adults with stroke used relax strategies and to explore the outcomes associated with their use. Methods. Secondary analysis of transcripts of intervention sessions from five participants was conducted. Results. All five participants applied relax strategies after initially observing a breakdown in performance that was attributed to increased fatigue or tension. The relax strategies used by the participants during their occupations included general relaxation, physical modifications to reduce tension, mental preparation, and pacing. The application of these strategies seemed to result in improved skill performance, reduced fatigue, and transfer to other activities. Conclusion. The relax strategy warrants further investigation as a potentially important therapeutic tool to improve occupational performance in individuals who have had a stroke.
Chen, Xianfeng; Zeng, Heping; Guo, Qi; She, Weilong
2015-01-01
This book presents an overview of the state of the art of nonlinear optics from weak light nonlinear optics, ultrafast nonlinear optics to electro-optical theory and applications. Topics range from the fundamental studies of the interaction between matter and radiation to the development of devices, components, and systems of tremendous commercial interest for widespread applications in optical telecommunications, medicine, and biotechnology.
Distributed nonlinear optical response
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov
2005-01-01
The purpose of the research presented here is to investigate basic physical properties in nonlinear optical materials with delayed or nonlocal nonlinearity. Soliton propagation, spectral broadening and the influence of the nonlocality or delay of the nonlinearity are the main focusses in the work...
Noncommutative Nonlinear Supersymmetry
Nishino, H; Nishino, Hitoshi; Rajpoot, Subhash
2002-01-01
We present noncommutative nonlinear supersymmetric theories. The first example is a non-polynomial Akulov-Volkov-type lagrangian with noncommutative nonlinear global supersymmetry in arbitrary space-time dimensions. The second example is the generalization of this lagrangian to Dirac-Born-Infeld lagrangian with nonlinear supersymmetry realized in dimensions D=2,3,4 and 6 (mod 8).
Fiber Nonlinearities: A Tutorial
Institute of Scientific and Technical Information of China (English)
Govind P. Agrawal
2003-01-01
Fiber nonlinearities have long been regarded as being mostly harmful for fiber-optic communication systems. Over the last few years, however, the nonlinear effects are increasingly being used for practical telecommunications applications,the Raman amplification being only one of the recent examples. In this tutorial I review the vario us nonlinear effects occurring in optical fibers from both standpoints..
Fiber Nonlinearities: A Tutorial
Institute of Scientific and Technical Information of China (English)
Govind; P.; Agrawal
2003-01-01
Fiber nonlinearities have long been regarded as being mostly harmful for fiber-optic communication systems. Over the last few years, however, the nonlinear effects are increasingly being used for practical telecommunications applications, the Raman amplification being only one of the recent examples. In this tutorial I review the various nonlinear effects occurring in optical fibers from both standpoints..
PBH tests for nonlinear systems
Kawano, Yu; Ohtsuka, Toshiyuki
2017-01-01
Recently, concepts of nonlinear eigenvalues and eigenvectors are introduced. In this paper, we establish connections between the nonlinear eigenvalues and nonlinear accessibility/observability. In particular, we provide a generalization of Popov- Belevitch-Hautus (PBH) test to nonlinear accessibilit
Enhanced four-wave mixing with nonlinear plasmonic metasurfaces
Jin, Boyuan
2016-01-01
Plasmonic metasurfaces provide an effective way to increase the efficiency of several nonlinear processes while maintaining nanoscale dimensions. In this work, nonlinear metasurfaces based on film-coupled silver nanostripes loaded with Kerr nonlinear material are proposed to achieve efficient four-wave mixing (FWM). Highly localized plasmon resonances are formed in the nanogap between the metallic film and nanostripes. The local electric field is dramatically enhanced in this subwavelength nanoregion. These properties combined with the relaxed phase matching condition due to the ultrathin area lead to a giant FWM efficiency, which is enhanced by nineteen orders of magnitude compared to a bare silver screen. In addition, efficient visible and low-THz sources can be constructed based on the proposed nonlinear metasurfaces. The FWM generated coherent wave has a directional radiation pattern and its output power is relatively insensitive to the incident angles of the excitation sources. This radiated power can be...
Ageing of the nonlinear optical susceptibility in soft matter
Energy Technology Data Exchange (ETDEWEB)
Ghofraniha, N [SMC-INFM-CNR, c/o Universita di Roma ' La Sapienza' , Piazzale Aldo Moro 2, 00185, Rome (Italy); Conti, C [Research Centre ' Enrico Fermi' , Via Panisperna 89/A, 00184 Rome (Italy); Leonardo, R Di [SOFT-INFM-CNR, c/o Universita di Roma ' La Sapienza' , Piazzale Aldo Moro 2, 00185, Rome (Italy); Ruzicka, B [SOFT-INFM-CNR, c/o Universita di Roma ' La Sapienza' , Piazzale Aldo Moro 2, 00185, Rome (Italy); Ruocco, G [SOFT-INFM-CNR, c/o Universita di Roma ' La Sapienza' , Piazzale Aldo Moro 2, 00185, Rome (Italy)
2007-05-23
We investigate the nonlinear optics response of a colloidal dispersion undergoing dynamics slowing down with age, by using Z-scan and dynamic light scattering measurements. We study the high optical nonlinearity of an organic dye (rhodamine B) dispersed in a water-clay (laponite) suspension. We consider different clay concentrations (2.0-2.6 wt%) experiencing dynamics arrest. We find that (i) the concentration dependent exponential growth of both mean relaxation time and nonlinear absorption coefficient can be individually scaled to a master curve and (ii) the scaling times are the same for the two physical quantities. These findings indicate that the optical nonlinear susceptibility exhibits the same ageing universal scaling behaviour, typical of disordered out of equilibrium systems.
Slow spin relaxation in dipolar spin ice.
Orendac, Martin; Sedlakova, Lucia; Orendacova, Alzbeta; Vrabel, Peter; Feher, Alexander; Pajerowski, Daniel M.; Cohen, Justin D.; Meisel, Mark W.; Shirai, Masae; Bramwell, Steven T.
2009-03-01
Spin relaxation in dipolar spin ice Dy2Ti2O7 and Ho2Ti2O7 was investigated using the magnetocaloric effect and susceptibility. The magnetocaloric behavior of Dy2Ti2O7 at temperatures where the orientation of spins is governed by ``ice rules`` (T Tice) revealed thermally activated relaxation; however, the resulting temperature dependence of the relaxation time is more complicated than anticipated by a mere extrapolation of the corresponding high temperature data [1]. A susceptibility study of Ho2Ti2O7 was performed at T > Tice and in high magnetic fields, and the results suggest a slow relaxation of spins analogous to the behavior reported in a highly polarized cooperative paramagnet [2]. [1] J. Snyder et al., Phys. Rev. Lett. 91 (2003) 107201. [2] B. G. Ueland et al., Phys. Rev. Lett. 96 (2006) 027216.
Energy landscape of relaxed amorphous silicon
Valiquette, Francis; Mousseau, Normand
2003-09-01
We analyze the structure of the energy landscape of a well-relaxed 1000-atom model of amorphous silicon using the activation-relaxation technique (ART nouveau). Generating more than 40 000 events starting from a single minimum, we find that activated mechanisms are local in nature, that they are distributed uniformly throughout the model, and that the activation energy is limited by the cost of breaking one bond, independently of the complexity of the mechanism. The overall shape of the activation-energy-barrier distribution is also insensitive to the exact details of the configuration, indicating that well-relaxed configurations see essentially the same environment. These results underscore the localized nature of relaxation in this material.
Precession Relaxation of Viscoelastic Oblate Rotators
Frouard, Julien
2016-01-01
Various perturbations (collisions, close encounters, YORP) destabilise the rotation of a small body, leaving it in a non-principal spin state. Then the body experiences alternating stresses generated by the inertial forces. The ensuing inelastic dissipation reduces the kinetic energy, without influencing the angular momentum. This yields nutation relaxation, i.e., evolution of the spin towards rotation about the maximal-inertia axis. Knowledge of the timescales needed to damp the nutation is crucial in studies of small bodies' dynamics. In the past, nutation relaxation has been described by an empirical quality factor introduced to parameterise the dissipation rate and to evade the discussion of the actual rheological parameters and their role in dissipation. This approach is unable to describe the dependence of the relaxation rate upon the nutation angle, because we do not know the quality factor's dependence on the frequency (which is a function of the nutation angle). This leaves open the question of relax...
Two-Body Relaxation in Cosmological Simulations
Binney, J; Binney, James; Knebe, Alexander
2002-01-01
The importance of two-body relaxation in cosmological simulations is explored with simulations in which there are two species of particles. The cases of mass ratio sqrt(2):1 and 4:1 are investigated. Simulations are run with both a fixed softening length and adaptive softening using the publicly available codes GADGET and MLAPM, respectively. The effects of two-body relaxation are detected in both the density profiles of halos and the mass function of halos. The effects are more pronounced with a fixed softening length, but even in this case they are not so large as to suggest that results obtained with one mass species are significantly affected by two-body relaxation. The simulations that use adaptive softening are slightly less affected by two-body relaxation and produce slightly higher central densities in the largest halos. They run about three times faster than the simulations that use a fixed softening length.
Structural relaxation in annealed hyperquenched basaltic glasses
DEFF Research Database (Denmark)
Guo, Xiaoju; Mauro, John C.; Potuzak, M.
2012-01-01
The enthalpy relaxation behavior of hyperquenched (HQ) and annealed hyperquenched (AHQ) basaltic glass is investigated through calorimetric measurements. The results reveal a common onset temperature of the glass transition for all the HQ and AHQ glasses under study, indicating that the primary r...... relaxation is activated at the same temperature regardless of the initial departure from equilibrium. The analysis of secondary relaxation at different annealing temperatures provides insights into the enthalpy recovery of HQ glasses.......The enthalpy relaxation behavior of hyperquenched (HQ) and annealed hyperquenched (AHQ) basaltic glass is investigated through calorimetric measurements. The results reveal a common onset temperature of the glass transition for all the HQ and AHQ glasses under study, indicating that the primary...
Vibrational energy relaxation in liquid oxygen
Everitt, K. F.; Egorov, S. A.; Skinner, J. L.
1998-09-01
We consider theoretically the relaxation from the first excited vibrational state to the ground state of oxygen molecules in neat liquid oxygen. The relaxation rate constant is related in the usual way to the Fourier transform of a certain quantum mechanical force-force time-correlation function. A result from Egelstaff allows one instead to relate the rate constant (approximately) to the Fourier transform of a classical force-force time-correlation function. This Fourier transform is then evaluated approximately by calculating three equilibrium averages from a classical molecular dynamics simulation. Our results for the relaxation times (at two different temperatures) are within a factor of 5 of the experimental relaxation times, which are in the ms range.
Analytical representations for relaxation functions of glasses
Hilfer, R.
2002-01-01
Analytical representations in the time and frequency domains are derived for the most frequently used phenomenological fit functions for non-Debye relaxation processes. In the time domain the relaxation functions corresponding to the complex frequency dependent Cole-Cole, Cole-Davidson and Havriliak-Negami susceptibilities are also represented in terms of $H$-functions. In the frequency domain the complex frequency dependent susceptibility function corresponding to the time dependent stretche...
Vibrational relaxation in very high temperature nitrogen
Hansen, C. Frederick
1991-01-01
Vibrational relaxation of N2 molecules is considered at temperatures up to 40,000 K in gas mixtures that contain electrons as well as heavy collision partners. The theory of vibrational relaxation due to N2-N2 collisions is fit to experimental data to 10,000 K by choice of the shape of the intermolecular potential and size of the collision cross section. These values are then used to extrapolate the theory to 40,000 K.
Anomalous enthalpy relaxation in vitreous silica
DEFF Research Database (Denmark)
Yue, Yuanzheng
2015-01-01
scans. It is known that the liquid fragility (i.e., the speed of the viscous slow-down of a supercooled liquid at its Tg during cooling) has impact on enthalpy relaxation in glass. Here, we find that vitreous silica (as a strong system) exhibits striking anomalies in both glass transition and enthalpy...... the fragile ones do in a structurally independent fashion. We discuss the origin of the anomalous enthalpy relaxation in the HQ vitreous silica....
Message passing with relaxed moment matching
Qi, Yuan; Guo, Yandong
2012-01-01
Bayesian learning is often hampered by large computational expense. As a powerful generalization of popular belief propagation, expectation propagation (EP) efficiently approximates the exact Bayesian computation. Nevertheless, EP can be sensitive to outliers and suffer from divergence for difficult cases. To address this issue, we propose a new approximate inference approach, relaxed expectation propagation (REP). It relaxes the moment matching requirement of expectation propagation by addin...
Protein dynamics from nuclear magnetic relaxation.
Charlier, Cyril; Cousin, Samuel F; Ferrage, Fabien
2016-05-01
Nuclear magnetic resonance is a ubiquitous spectroscopic tool to explore molecules with atomic resolution. Nuclear magnetic relaxation is intimately connected to molecular motions. Many methods and models have been developed to measure and interpret the characteristic rates of nuclear magnetic relaxation in proteins. These approaches shed light on a rich and diverse range of motions covering timescales from picoseconds to seconds. Here, we introduce some of the basic concepts upon which these approaches are built and provide a series of illustrations.
Lagrange relaxation and Dantzig-Wolfe decomposition
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui
1989-01-01
The paper concerns a large-scale linear programming problem having a block-diagonal structure with coupling constraints. It is shown that there are deep connections between the Lagrange relaxation techniques and the Dantzig-Wolfe decomposition methods......The paper concerns a large-scale linear programming problem having a block-diagonal structure with coupling constraints. It is shown that there are deep connections between the Lagrange relaxation techniques and the Dantzig-Wolfe decomposition methods...
Lagrange relaxation and Dantzig-Wolfe decomposition
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui
1989-01-01
The paper concerns a large-scale linear programming problem having a block-diagonal structure with coupling constraints. It is shown that there are deep connections between the Lagrange relaxation techniques and the Dantzig-Wolfe decomposition methods......The paper concerns a large-scale linear programming problem having a block-diagonal structure with coupling constraints. It is shown that there are deep connections between the Lagrange relaxation techniques and the Dantzig-Wolfe decomposition methods...
Trivedi, C. M.; Rana, V. A.; Hudge, P. G.; Kumbharkhane, A. C.
2016-08-01
Complex permittivity spectra of binary mixtures of varying concentrations of β-picoline and Methanol (MeOH) have been obtained using time domain reflectometry (TDR) technique over frequency range 10 MHz to 25 GHz at 283.15, 288.15, 293.15 and 298.15 K temperatures. The dielectric relaxation parameters namely static permittivity (ɛ0), high frequency limit permittivity (ɛ∞1) and the relaxation time (τ) were determined by fitting complex permittivity data to the single Debye/Cole-Davidson model. Complex nonlinear least square (CNLS) fitting procedure was carried out using LEVMW software. The excess permittivity (ɛ0E) and the excess inverse relaxation time (1/τ)E which contain information regarding molecular structure and interaction between polar-polar liquids were also determined. From the experimental data, parameters such as effective Kirkwood correlation factor (geff), Bruggeman factor (fB) and some thermo dynamical parameters have been calculated. Excess parameters were fitted to the Redlich-Kister polynomial equation. The values of static permittivity and relaxation time increase nonlinearly with increase in the mol-fraction of MeOH at all temperatures. The values of excess static permittivity (ɛ0E) and the excess inverse relaxation time (1/τ)E are negative for the studied β-picoline — MeOH system at all temperatures.
Nonlinear dynamics and complexity
Luo, Albert; Fu, Xilin
2014-01-01
This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.
Nonlinear Interaction of Waves in Geomaterials
Ostrovsky, L. A.
2009-05-01
Progress of 1990s - 2000s in studying vibroacoustic nonlinearities in geomaterials is largely related to experiments in resonance samples of rock and soils. It is now a common knowledge that many such materials are very strongly nonlinear, and they are characterized by hysteresis in the dependence between the stress and strain tensors, as well as by nonlinear relaxation ("slow time"). Elastic wave propagation in such media has many peculiarities; for example, third harmonic amplitude is a quadratic (not cubic as in classical solids) function of the main harmonic amplitude, and average wave velocity is linearly (not quadratically as usual) dependent on amplitude. The mechanisms of these peculiarities are related to complex structure of a material typically consisting of two phases: a hard matrix and relatively soft inclusions such as microcracks and grain contacts. Although most informative experimental results have been obtained in rock in the form of resonant bars, few theoretical models are yet available to describe and calculate waves interacting in such samples. In this presentation, a brief overview of structural vibroacoustic nonlinearities in rock is given first. Then, a simple but rather general approach to the description of wave interaction in solid resonators is developed based on accounting for resonance nonlinear perturbations which are cumulating from period to period. In particular, the similarity and the differences between traveling waves and counter-propagating waves are analyzed for materials with different stress-strain dependences. These data can be used for solving an inverse problem, i.e. characterizing nonlinear properties of a geomaterial by its measured vibroacoustic parameters. References: 1. L. Ostrovsky and P. Johnson, Riv. Nuovo Chimento, v. 24, 1-46, 2007 (a review); 2. L. Ostrovsky, J. Acoust. Soc. Amer., v. 116, 3348-3353, 2004.
Orientational relaxation in semiflexible dendrimers.
Kumar, Amit; Biswas, Parbati
2013-12-14
The orientational relaxation dynamics of semiflexible dendrimers are theoretically calculated within the framework of optimized Rouse-Zimm formalism. Semiflexibility is modeled through appropriate restrictions in the direction and orientation of the respective bond vectors, while the hydrodynamic interactions are included via the preaveraged Oseen tensor. The time autocorrelation function M(i)(1)(t) and the second order orientational autocorrelation function P(i)(2)(t) are analyzed as a function of the branch-point functionality and the degree of semiflexibility. Our approach of calculating M(i)(1)(t) is completely different from that of the earlier studies (A. Perico and M. Guenza J. Chem. Phys., 1985, 83, 3103; J. Chem. Phys., 1986, 84, 510), where the expression of M(i)(1)(t) obtained from earlier studies does not demarcate the flexible dendrimers from the semiflexible ones. The component of global motion of the time autocorrelation function exhibits a strong dependence on both degree of semiflexibility and branch-point functionality, while the component of pulsation motion depends only on the degree of semiflexibility. But it is difficult to distinguish the difference in the extent of pulsation motion among the compressed (0 qualitative behavior of P(i)(2)(t) obtained from our calculations closely matches with the expression for P(exact)(2)(t) in the earlier studies. Theoretically calculated spectral density, J(ω), is found to depend on the degree of semiflexibility and the branch-point functionality for the compressed and expanded conformations of semiflexible dendrimers as a function of frequency, especially in the high frequency regime, where J(ω) decays with frequency for both compressed and expanded conformations of semiflexible dendrimers. This decay of the spectral density occurs after displaying a cross-over behavior with the variation in the degree of semiflexibility in the intermediate frequency regime. The characteristic area increases with the
Dielectric relaxation spectroscopy of phlogopite mica
Energy Technology Data Exchange (ETDEWEB)
Kaur, Navjeet; Singh, Mohan; Singh, Anupinder [Department of Physics, Guru Nanak Dev University, Amritsar, Punjab 143005 (India); Awasthi, A.M. [Thermodynamics Laboratory, UGC-DAE Consortium for Scientific Research, Indore 452001 (India); Singh, Lakhwant, E-mail: lakhwant@yahoo.com [Department of Physics, Guru Nanak Dev University, Amritsar, Punjab 143005 (India)
2012-11-15
An in-depth investigation of the dielectric characteristics of annealed phlogopite mica has been conducted in the frequency range 0.1 Hz-10 MHz and over the temperature range 653-873 K through the framework of dielectric permittivity, electric modulus and conductivity formalisms. These formalisms show qualitative similarities in relaxation processes. The frequency dependence of the M Double-Prime and dc conductivity is found to obey an Arrhenius law and the activation energy of the phlogopite mica calculated both from dc conductivity and the modulus spectrum is similar, indicating that same type of charge carriers are involved in the relaxation phenomena. The electric modulus and conductivity data have been fitted with the Havriliak-Negami function. Scaling of M Prime , M Double-Prime , ac conductivity has also been performed in order to obtain insight into the relaxation mechanisms. The scaling behaviour indicates that the relaxation describes the same mechanism at different temperatures. The relaxation mechanism was also examined using the Cole-Cole approach. The study elaborates that the investigation regarding the temperature and frequency dependence of dielectric relaxation in the phlogopite mica will be helpful for various cutting edge applications of this material in electrical engineering.
Dielectric relaxation of gamma irradiated muscovite mica
Energy Technology Data Exchange (ETDEWEB)
Kaur, Navjeet [Department of Physics, Guru Nanak Dev University, Amritsar, Punjab 143005 (India); Singh, Mohan, E-mail: mohansinghphysics@gmail.com [Department of Physics, Guru Nanak Dev University, Amritsar, Punjab 143005 (India); Singh, Lakhwant [Department of Physics, Guru Nanak Dev University, Amritsar, Punjab 143005 (India); Awasthi, A.M. [Thermodynamics Laboratory, UGC-DAE Consortium for Scientific Research, Indore 452001 (India); Lochab, S.P. [Inter-University Accelerator Centre, Aruna Asaf Ali Marg, New Delhi 110067 (India)
2015-03-15
Highlights: • The present article reports the effect of gamma irradiation on the dielectric relaxation characteristics of muscovite mica. • Dielectric and electrical relaxations have been analyzed in the framework of dielectric permittivity, electric modulus and Cole–Cole formalisms. • The frequency dependent electrical conductivity has been rationalized using Johnsher’s universal power law. • The experimentally measured electric modulus and conductivity data have been fitted using Havriliak–Negami dielectric relaxation function. - Abstract: In the present research, the dielectric relaxation of gamma irradiated muscovite mica was studied in the frequency range of 0.1 Hz–10 MHz and temperature range of 653–853 K, using the dielectric permittivity, electric modulus and conductivity formalisms. The dielectric constants (ϵ′ and ϵ′′) are found to be high for gamma irradiated muscovite mica as compared to the pristine sample. The frequency dependence of the imaginary part of complex electric modulus (M′′) and dc conductivity data conforms Arrhenius law with single value of activation energy for pristine sample and two values of activation energy for gamma irradiated mica sample. The experimentally assessed electric modulus and conductivity information have been interpreted by the Havriliak–Negami dielectric relaxation explanation. Using the Cole–Cole framework, an analysis of real and imaginary characters of the electric modulus for pristine and gamma irradiated sample was executed which reflects the non-Debye relaxation mechanism.
Rounded stretched exponential for time relaxation functions.
Powles, J G; Heyes, D M; Rickayzen, G; Evans, W A B
2009-12-01
A rounded stretched exponential function is introduced, C(t)=exp{(tau(0)/tau(E))(beta)[1-(1+(t/tau(0))(2))(beta/2)]}, where t is time, and tau(0) and tau(E) are two relaxation times. This expression can be used to represent the relaxation function of many real dynamical processes, as at long times, t>tau(0), the function converges to a stretched exponential with normalizing relaxation time, tau(E), yet its expansion is even or symmetric in time, which is a statistical mechanical requirement. This expression fits well the shear stress relaxation function for model soft soft-sphere fluids near coexistence, with tau(E)Cole-Cole plots for dielectric and shear stress relaxation (both the modulus and viscosity forms). It is shown that both the dielectric spectra and dynamic shear modulus imaginary parts approach the real axis with a slope equal to 0 at high frequency, whereas the dynamic viscosity has an infinite slope in the same limit. This indicates that inertial effects at high frequency are best discerned in the modulus rather than the viscosity Cole-Cole plot. As a consequence of the even expansion in time of the shear stress relaxation function, the value of the storage modulus derived from it at very high frequency exceeds that in the infinite frequency limit (i.e., G(infinity)).
On convex relaxation of graph isomorphism.
Aflalo, Yonathan; Bronstein, Alexander; Kimmel, Ron
2015-03-10
We consider the problem of exact and inexact matching of weighted undirected graphs, in which a bijective correspondence is sought to minimize a quadratic weight disagreement. This computationally challenging problem is often relaxed as a convex quadratic program, in which the space of permutations is replaced by the space of doubly stochastic matrices. However, the applicability of such a relaxation is poorly understood. We define a broad class of friendly graphs characterized by an easily verifiable spectral property. We prove that for friendly graphs, the convex relaxation is guaranteed to find the exact isomorphism or certify its inexistence. This result is further extended to approximately isomorphic graphs, for which we develop an explicit bound on the amount of weight disagreement under which the relaxation is guaranteed to find the globally optimal approximate isomorphism. We also show that in many cases, the graph matching problem can be further harmlessly relaxed to a convex quadratic program with only n separable linear equality constraints, which is substantially more efficient than the standard relaxation involving n2 equality and n2 inequality constraints. Finally, we show that our results are still valid for unfriendly graphs if additional information in the form of seeds or attributes is allowed, with the latter satisfying an easy to verify spectral characteristic.
Fully non-linear hyper-viscoelastic modeling of skeletal muscle in compression.
Wheatley, Benjamin B; Pietsch, Renée B; Haut Donahue, Tammy L; Williams, Lakiesha N
2016-01-01
Understanding the behavior of skeletal muscle is critical to implementing computational methods to study how the body responds to compressive loading. This work presents a novel approach to studying the fully nonlinear response of skeletal muscle in compression. Porcine muscle was compressed in both the longitudinal and transverse directions under five stress relaxation steps. Each step consisted of 5% engineering strain over 1 s followed by a relaxation period until equilibrium was reached at an observed change of 1 g/min. The resulting data were analyzed to identify the peak and equilibrium stresses as well as relaxation time for all samples. Additionally, a fully nonlinear strain energy density-based Prony series constitutive model was implemented and validated with independent constant rate compressive data. A nonlinear least squares optimization approach utilizing the Levenberg-Marquardt algorithm was implemented to fit model behavior to experimental data. The results suggested the time-dependent material response plays a key role in the anisotropy of skeletal muscle as increasing strain showed differences in peak stress and relaxation time (p 0.05). The optimizing procedure produced a single set of hyper-viscoelastic parameters which characterized compressive muscle behavior under stress relaxation conditions. The utilized constitutive model was the first orthotropic, fully nonlinear hyper-viscoelastic model of skeletal muscle in compression while maintaining agreement with constitutive physical boundaries. The model provided an excellent fit to experimental data and agreed well with the independent validation in the transverse direction.
Stress-enhanced Gelation: A Dynamic Nonlinearity of Elasticity
Yao, Norman Y.; Broedersz, Chase P.; Depken, Martin; Becker, Daniel J.; Pollak, Martin R.; MacKintosh, Frederick C.; Weitz, David A.
2013-01-01
A hallmark of biopolymer networks is their sensitivity to stress, reflected by pronounced nonlinear elastic stiffening. Here, we demonstrate a distinct dynamical nonlinearity in biopolymer networks consisting of F-actin cross-linked by α-actinin-4. Applied stress delays the onset of relaxation and flow, markedly enhancing gelation and extending the regime of solid-like behavior to much lower frequencies. We show that this macroscopic network response can be accounted for at the single molecule level by the increased binding affinity of the cross-linker under load, characteristic of catch-bond-like behavior. PMID:23383843
Photo-induced nonlinear absorption in carbon nanostructures
Zatrudina, Rimma Sh.; Gribkov, Vladislav Yu.
2017-05-01
Photoinduced nonlinear absorption of new carbon nanoparticles - astralenes and two types of carbon nanoclusters was investigated. The nonlinear absorption of aqueous suspensions of astralenes and solutions of carbon nanoclusters was studied by the method of z-scanning with Nd3+ -glass laser (wavelength λ = 1064 nm) in Q-switching regimes. A numerical model of the propagation of the laser pulse in a medium with reverse saturable absorption was created. Relaxation time of the first exited state and the ratio of absorption cross-sections of the first exited and ground states for the researched types of carbon nanoparticles were determined by the numerical simulation.
Lossless Convexification of Control Constraints for a Class of Nonlinear Optimal Control Problems
Blackmore, Lars; Acikmese, Behcet; Carson, John M.,III
2012-01-01
In this paper we consider a class of optimal control problems that have continuous-time nonlinear dynamics and nonconvex control constraints. We propose a convex relaxation of the nonconvex control constraints, and prove that the optimal solution to the relaxed problem is the globally optimal solution to the original problem with nonconvex control constraints. This lossless convexification enables a computationally simpler problem to be solved instead of the original problem. We demonstrate the approach in simulation with a planetary soft landing problem involving a nonlinear gravity field.
BOOK REVIEW: Nonlinear Magnetohydrodynamics
Shafranov, V.
1998-08-01
Nonlinear magnetohydrodynamics by Dieter Biskamp is a thorough introduction to the physics of the most impressive non-linear phenomena that occur in conducting magnetoplasmas. The basic systems, in which non-trivial dynamic processes are observed, accompanied by changes of geometry of the magnetic field and the effects of energy transformation (magnetic energy into kinetic energy or the opposite effect in magnetic dynamos), are the plasma magnetic confinement systems for nuclear fusion and space plasmas, mainly the solar plasma. A significant number of the examples of the dynamic processes considered are taken from laboratory plasmas, for which an experimental check of the theory is possible. Therefore, though the book is intended for researchers and students interested in both laboratory, including nuclear fusion, and astrophysical plasmas, it is most probably closer to the first category of reader. In the Introduction the author notes that unlike the hydrodynamics of non-conducting fluids, where the phenomena caused by rapid fluid motions are the most interesting, for plasmas in a strong magnetic field the quasi-static configurations inside which the local dynamic processes occur are often the most important. Therefore, the reader will also find in this book rather traditional material on the theory of plasma equilibrium and stability in magnetic fields. In addition, it is notable that, as opposed to a linear theory, the non-linear theory, as a rule, cannot give quite definite explanations or predictions of phenomena, and consequently there are in the book many results obtained by consideration of numerical models with the use of supercomputers. The treatment of non-linear dynamics is preceded by Chapters 2 to 4, in which the basics of MHD theory are presented with an emphasis on the role of integral invariants of the magnetic helicity type, a derivation of the reduced MHD equations is given, together with examples of the exact solutions of the equilibrium
Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities
Indian Academy of Sciences (India)
Antonella Fiacca; Nikolaos Matzakos; Nikolaos S Papageorgiou; Raffaella Servadei
2001-11-01
In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all $\\mathbb{R}$. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of $\\mathbb{R}$. This case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that the problem has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial solutions (multiplicity theorem).
SINGULAR AND RAREFACTIVE SOLUTIONS TO A NONLINEAR VARIATIONAL WAVE EQUATION
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Following a recent paper of the authors in Communications in Partial Differential Equations, this paper establishes the global existence of weak solutions to a nonlinear variational wave equation under relaxed conditions on the initial data so that the solutions can contain singularities (blow-up). Propagation of local oscillations along one family of characteristics remains under control despite singularity formation in the other family of characteristics.
Effects of different "relaxing" music styles on the autonomic nervous system
Directory of Open Access Journals (Sweden)
Santiago Pérez-Lloret
2014-01-01
Full Text Available The objective of this study was to assess the effects on heart rate variability (HRV of exposure to different styles of "relaxing" music. Autonomic responses to musical stimuli were correlated with subjective preferences regarding the relaxing properties of each music style. Linear and nonlinear HRV analysis was conducted in 25 healthy subjects exposed to silence or to classical, new age or romantic melodies in a random fashion. At the end of the study, subjects were asked to choose the melody that they would use to relax. The low-to-high-frequency ratio was significantly higher when subjects were exposed to "new age" music when compared with silence (3.4 ± 0.3 vs. 2.6 ± 0.3, respectively, P < 0.02, while no differences were found with "classical" or "romantic" melodies (2.1 ± 0.4 and 2.2 ± 0.3. These results were related to a reduction in the high frequency component with "new age" compared to silence (17.4 ± 1.9 vs. 23.1 ± 1.1, respectively P < 0.004. Significant differences across melodies were also found for nonlinear HRV indexes. Subjects′ preferences did not correlate with autonomic responses to melodies. The results suggest that "new age" music induced a shift in HRV from higher to lower frequencies, independently on the music preference of the listener.
Mixed diffusive-convective relaxation of a broad beam of energetic particles in cold plasma
Carlevaro, Nakia; Falessi, Matteo V; Montani, Giovanni; Terzani, Davide; Zonca, Fulvio
2015-01-01
We revisit the applications of quasi-linear theory as a paradigmatic model for weak plasma turbulence and the associated bump-on-tail problem. The work, presented here, is built around the idea that large-amplitude or strongly shaped beams do not relax through diffusion only and that there exists an intermediate time scale where the relaxations are {\\it convective} (ballistic-like). We cast this novel idea in the rigorous form of a self-consistent nonlinear dynamical model, which generalizes the classic equations of the quasi-linear theory to "broad" beams with internal structure. We also present numerical simulation results of the relaxation of a broad beam of energetic particles in cold plasma. These generally demonstrate the mixed diffusive-convective features of supra-thermal particle transport; and essentially depend on nonlinear wave-particle interactions and phase-space structures. Taking into account modes of the stable linear spectrum is crucial for the self-consistent evolution of the distribution f...
The use of (double) relaxation oscillation SQUIDs as a sensor
Duuren, van M.J.; Brons, G.C.S.; Kattouw, H.; Flokstra, J.; Rogalla, H.
1997-01-01
Relaxation Oscillation SQUIDs (ROSs) and Double Relaxation Oscillation SQUIDs (DROSs) are based on relaxation oscillations that are induced in hysteretic dc SQUIDs by an external L-R shunt. The relaxation frequency of a ROS varies with the applied flux Φ, whereas the output of a DROS is a dc voltage
The use of (double) relaxation oscillation SQUIDs as a sensor
van Duuren, M.J.; Brons, G.C.S.; Kattouw, H.; Flokstra, Jakob; Rogalla, Horst
1997-01-01
Relaxation Oscillation SQUIDs (ROSs) and Double Relaxation Oscillation SQUIDs (DROSs) are based on relaxation oscillations that are induced in hysteretic dc SQUIDs by an external L-R shunt. The relaxation frequency of a ROS varies with the applied flux Φ, whereas the output of a DROS is a dc
A Solar Cycle Dependence of Nonlinearity in Magnetospheric Activity
Energy Technology Data Exchange (ETDEWEB)
Johnson, Jay R; Wing, Simon
2005-03-08
The nonlinear dependencies inherent to the historical K(sub)p data stream (1932-2003) are examined using mutual information and cumulant based cost as discriminating statistics. The discriminating statistics are compared with surrogate data streams that are constructed using the corrected amplitude adjustment Fourier transform (CAAFT) method and capture the linear properties of the original K(sub)p data. Differences are regularly seen in the discriminating statistics a few years prior to solar minima, while no differences are apparent at the time of solar maximum. These results suggest that the dynamics of the magnetosphere tend to be more linear at solar maximum than at solar minimum. The strong nonlinear dependencies tend to peak on a timescale around 40-50 hours and are statistically significant up to one week. Because the solar wind driver variables, VB(sub)s and dynamical pressure exhibit a much shorter decorrelation time for nonlinearities, the results seem to indicate that the nonlinearity is related to internal magnetospheric dynamics. Moreover, the timescales for the nonlinearity seem to be on the same order as that for storm/ring current relaxation. We suggest that the strong solar wind driving that occurs around solar maximum dominates the magnetospheric dynamics suppressing the internal magnetospheric nonlinearity. On the other hand, in the descending phase of the solar cycle just prior to solar minimum, when magnetospheric activity is weaker, the dynamics exhibit a significant nonlinear internal magnetospheric response that may be related to increased solar wind speed.
Energy Technology Data Exchange (ETDEWEB)
Schlüter, Steffen [School of Chemical, Biological and Environmental Engineering, Oregon State University, Corvallis Oregon USA; Department Soil Physics, Helmholtz-Centre for Environmental Research-UFZ, Halle Germany; Berg, Steffen [Shell Global Solutions International B.V., Rijswijk Netherlands; Li, Tianyi [School of Chemical, Biological and Environmental Engineering, Oregon State University, Corvallis Oregon USA; Vogel, Hans-Jörg [Department Soil Physics, Helmholtz-Centre for Environmental Research-UFZ, Halle Germany; Institut für Agrar- und Ernährungswissenschaften, Martin-Luther-Universität Halle-Wittenberg, Halle Germany; Wildenschild, Dorthe [School of Chemical, Biological and Environmental Engineering, Oregon State University, Corvallis Oregon USA
2017-06-01
The relaxation dynamics toward a hydrostatic equilibrium after a change in phase saturation in porous media is governed by fluid reconfiguration at the pore scale. Little is known whether a hydrostatic equilibrium in which all interfaces come to rest is ever reached and which microscopic processes govern the time scales of relaxation. Here we apply fast synchrotron-based X-ray tomography (X-ray CT) to measure the slow relaxation dynamics of fluid interfaces in a glass bead pack after fast drainage of the sample. The relaxation of interfaces triggers internal redistribution of fluids, reduces the surface energy stored in the fluid interfaces, and relaxes the contact angle toward the equilibrium value while the fluid topology remains unchanged. The equilibration of capillary pressures occurs in two stages: (i) a quick relaxation within seconds in which most of the pressure drop that built up during drainage is dissipated, a process that is to fast to be captured with fast X-ray CT, and (ii) a slow relaxation with characteristic time scales of 1–4 h which manifests itself as a spontaneous imbibition process that is well described by the Washburn equation for capillary rise in porous media. The slow relaxation implies that a hydrostatic equilibrium is hardly ever attained in practice when conducting two-phase experiments in which a flux boundary condition is changed from flow to no-flow. Implications for experiments with pressure boundary conditions are discussed.
Anomalous Enthalpy Relaxation in Vitreous Silica
Directory of Open Access Journals (Sweden)
Yuanzheng eYue
2015-08-01
Full Text Available It is a challenge to calorimetrically determine the glass transition temperature (Tg of vitreous silica. Here we demonstrate that this challenge mainly arises from the extreme sensitivity of the Tg to the hydroxyl content in vitreous silica, but also from the irreversibility of its glass transition when repeating the calorimetric scans. It is known that the liquid fragility (i.e., the speed of the viscous slow-down of a supercooled liquid at its Tg during cooling has impact on enthalpy relaxation in glass. Here we find that vitreous silica (as a strong system exhibits striking anomalies in both glass transition and enthalpy relaxation compared to fragile oxide systems. The anomalous enthalpy relaxation of vitreous silica is discovered by performing the hperquenching-annealing-calorimetry experiments. We argue that the strong systems like vitreous silica and vitreous Germania relax in a structurally cooperative manner, whereas the fragile ones do in a structurally independent fashion. We discuss the origin of the anomalous enthalpy relaxation in the HQ vitreous silica.
Motional Spin Relaxation in Large Electric Fields
Schmid, Riccardo; Filippone, B W
2008-01-01
We discuss the precession of spin-polarized Ultra Cold Neutrons (UCN) and $^{3}\\mathrm{He}$ atoms in uniform and static magnetic and electric fields and calculate the spin relaxation effects from motional $v\\times E$ magnetic fields. Particle motion in an electric field creates a motional $v\\times E$ magnetic field, which when combined with collisions, produces variations of the total magnetic field and results in spin relaxation of neutron and $^{3}\\mathrm{He}$ samples. The spin relaxation times $T_{1}$ (longitudinal) and $T_{2}$ (transverse) of spin-polarized UCN and $^{3}\\mathrm{He}$ atoms are important considerations in a new search for the neutron Electric Dipole Moment at the SNS \\emph{nEDM} experiment. We use a Monte Carlo approach to simulate the relaxation of spins due to the motional $v\\times E$ field for UCN and for $^{3}\\mathrm{He}$ atoms at temperatures below $600 \\mathrm{mK}$. We find the relaxation times for the neutron due to the $v\\times E$ effect to be long compared to the neutron lifetime, ...
Doppler effect induced spin relaxation boom
Zhao, Xinyu; Huang, Peihao; Hu, Xuedong
2016-03-01
We study an electron spin qubit confined in a moving quantum dot (QD), with our attention on both spin relaxation, and the product of spin relaxation, the emitted phonons. We find that Doppler effect leads to several interesting phenomena. In particular, spin relaxation rate peaks when the QD motion is in the transonic regime, which we term a spin relaxation boom in analogy to the classical sonic boom. This peak indicates that a moving spin qubit may have even lower relaxation rate than a static qubit, pointing at the possibility of coherence-preserving transport for a spin qubit. We also find that the emitted phonons become strongly directional and narrow in their frequency range as the qubit reaches the supersonic regime, similar to Cherenkov radiation. In other words, fast moving excited spin qubits can act as a source of non-classical phonons. Compared to classical Cherenkov radiation, we show that quantum dot confinement produces a small but important correction on the Cherenkov angle. Taking together, these results have important implications to both spin-based quantum information processing and coherent phonon dynamics in semiconductor nanostructures.
Role of Relaxation on the Giant Permittivity and Electrical Properties of CaCu3Ti4O12 Ceramics
Zhao, Xuetong; Ren, Lulu; Liao, Ruijin; Li, Jianying; Yang, Lijun; Wang, Feipeng
2016-06-01
CaCu3Ti4O12 (CCTO) ceramics were synthesized under various sintering conditions to investigate the role of relaxation on permittivity and electrical properties. Two relaxation processes that respectively related to grain and to domain boundary at a temperature as low as 223 K were fitted according to the Cole-Cole theory. The results indicate that both relaxations largely account for the giant permittivity of CCTO ceramics. Moreover, the relaxation behaviors of grain and of the grain boundary can be processed via impedance plots that vary from 113 K to 473 K. It is shown that longer sintering duration leads to lower resistance of grain and of grain boundary: e.g., from 3200 Ω to 810 Ω and 1.76 MΩ to 0.48 MΩ, respectively. The activation energy related to grain-boundary relaxation drops from 1.14 eV to 0.80 eV, while the value of grain stays unchanged at about 0.11 eV. The Schottky barrier of the CCTO sample decreases from 0.65 eV to 0.57 eV. It is also proposed that the nonlinearity of current-voltage property for CCTO ceramics may be strongly related to the relaxation processes of grain boundaries.
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Robust Output Feedback Control for a Class of Nonlinear Systems with Input Unmodeled Dynamics
Institute of Scientific and Technical Information of China (English)
Ming-Zhe Hou; Ai-Guo Wu; Guang-Ren Dua
2008-01-01
The robust global stabilization problem of a class of uncertain nonlinear systems with input unmodeled dynamics is considered using output feedback, where the uncertain nonlinear terms satisfy a far more relaxed condition than the existing triangular- type condition. Under the assumption that the input unmodeled dynamics is minimum-phase and of relative degree zero, a dynamic output compensator is explicitly constructed based on the nonseparation principle. An example illustrates the usefulness of the proposed method.
Reduced-Complexity Semidefinite Relaxations of Optimal Power Flow Problems
DEFF Research Database (Denmark)
Andersen, Martin Skovgaard; Hansson, Anders; Vandenberghe, Lieven
2014-01-01
We propose a new method for generating semidefinite relaxations of optimal power flow problems. The method is based on chordal conversion techniques: by dropping some equality constraints in the conversion, we obtain semidefinite relaxations that are computationally cheaper, but potentially weaker......, than the standard semidefinite relaxation. Our numerical results show that the new relaxations often produce the same results as the standard semidefinite relaxation, but at a lower computational cost....
Ionescu, Tudor C.; Scherpen, Jacquelien M. A.
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain linearization results that correspond to the notion of a cross Gramian for symmetric linear systems. Furthermore, first steps towards relations with the singular value functions of the nonlinear Hankel operator are studied and yield promising results.
Directory of Open Access Journals (Sweden)
W. L. Fouché
1983-03-01
Full Text Available In this article we discuss some aspects of nonlinear functional analysis. It included reviews of Banach’s contraction theorem, Schauder’s fixed point theorem, globalising techniques and applications of homotopy theory to nonlinear functional analysis. The author emphasises that fundamentally new ideas are required in order to achieve a better understanding of phenomena which contain both nonlinear and definite infinite dimensional features.
Nonlinear Electrodynamics and QED
2003-01-01
The limits of linear electrodynamics are reviewed, and possible directions of nonlinear extension are explored. The central theme is that the qualitative character of the empirical successes of quantum electrodynamics must be used as a guide for understanding the nature of the nonlinearity of electrodynamics at the subatomic level. Some established theories of nonlinear electrodynamics, namely, those of Mie, Born, and Infeld are presented in the language of the modern geometrical and topologi...
Current leakage relaxation and charge trapping in ultra-porous low-k materials
Energy Technology Data Exchange (ETDEWEB)
Borja, Juan; Plawsky, Joel L., E-mail: plawsky@rpi.edu; Gill, William N. [Howard P. Isermann Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180 (United States); Lu, T.-M. [Department of Physics, Rensselaer Polytechnic Institute, Troy, New York 12180 (United States); Bakhru, Hassaram [University at Albany' s College of Nanoscale Science and Engineering (CNSE), Albany, New York 12203 (United States)
2014-02-28
Time dependent dielectric failure has become a pivotal aspect of interconnect design as industry pursues integration of sub-22 nm process-technology nodes. Literature has provided key information about the role played by individual species such as electrons, holes, ions, and neutral impurity atoms. However, no mechanism has been shown to describe how such species interact and influence failure. Current leakage relaxation in low-k dielectrics was studied using bipolar field experiments to gain insight into how charge carrier flow becomes impeded by defects within the dielectric matrix. Leakage current decay was correlated to injection and trapping of electrons. We show that current relaxation upon inversion of the applied field can be described by the stretched exponential function. The kinetics of charge trapping events are consistent with a time-dependent reaction rate constant, k=k{sub 0}⋅(t+1){sup β−1}, where 0 < β < 1. Such dynamics have previously been observed in studies of charge trapping reactions in amorphous solids by W. H. Hamill and K. Funabashi, Phys. Rev. B 16, 5523–5527 (1977). We explain the relaxation process in charge trapping events by introducing a nonlinear charge trapping model. This model provides a description on the manner in which the transport of mobile defects affects the long-tail current relaxation processes in low-k films.
Current leakage relaxation and charge trapping in ultra-porous low-k materials
Borja, Juan; Plawsky, Joel L.; Lu, T.-M.; Bakhru, Hassaram; Gill, William N.
2014-02-01
Time dependent dielectric failure has become a pivotal aspect of interconnect design as industry pursues integration of sub-22 nm process-technology nodes. Literature has provided key information about the role played by individual species such as electrons, holes, ions, and neutral impurity atoms. However, no mechanism has been shown to describe how such species interact and influence failure. Current leakage relaxation in low-k dielectrics was studied using bipolar field experiments to gain insight into how charge carrier flow becomes impeded by defects within the dielectric matrix. Leakage current decay was correlated to injection and trapping of electrons. We show that current relaxation upon inversion of the applied field can be described by the stretched exponential function. The kinetics of charge trapping events are consistent with a time-dependent reaction rate constant, k =k0ṡ(t+1)β -1, where 0 < β < 1. Such dynamics have previously been observed in studies of charge trapping reactions in amorphous solids by W. H. Hamill and K. Funabashi, Phys. Rev. B 16, 5523-5527 (1977). We explain the relaxation process in charge trapping events by introducing a nonlinear charge trapping model. This model provides a description on the manner in which the transport of mobile defects affects the long-tail current relaxation processes in low-k films.
Leiser, Randolph J.; Rotstein, Horacio G.
2017-08-01
Oscillations in far-from-equilibrium systems (e.g., chemical, biochemical, biological) are generated by the nonlinear interplay of positive and negative feedback effects operating at different time scales. Relaxation oscillations emerge when the time scales between the activators and the inhibitors are well separated. In addition to the large-amplitude oscillations (LAOs) or relaxation type, these systems exhibit small-amplitude oscillations (SAOs) as well as abrupt transitions between them (canard phenomenon). Localized cluster patterns in networks of relaxation oscillators consist of one cluster oscillating in the LAO regime or exhibiting mixed-mode oscillations (LAOs interspersed with SAOs), while the other oscillates in the SAO regime. Because the individual oscillators are monostable, localized patterns are a network phenomenon that involves the interplay of the connectivity and the intrinsic dynamic properties of the individual nodes. Motivated by experimental and theoretical results on the Belousov-Zhabotinsky reaction, we investigate the mechanisms underlying the generation of localized patterns in globally coupled networks of piecewise-linear relaxation oscillators where the global feedback term affects the rate of change of the activator (fast variable) and depends on the weighted sum of the inhibitor (slow variable) at any given time. We also investigate whether these patterns are affected by the presence of a diffusive type of coupling whose synchronizing effects compete with the symmetry-breaking global feedback effects.
Van der Pol and the history of relaxation oscillations: toward the emergence of a concept.
Ginoux, Jean-Marc; Letellier, Christophe
2012-06-01
Relaxation oscillations are commonly associated with the name of Balthazar van der Pol via his paper (Philosophical Magazine, 1926) in which he apparently introduced this terminology to describe the nonlinear oscillations produced by self-sustained oscillating systems such as a triode circuit. Our aim is to investigate how relaxation oscillations were actually discovered. Browsing the literature from the late 19th century, we identified four self-oscillating systems in which relaxation oscillations have been observed: (i) the series dynamo machine conducted by Gérard-Lescuyer (1880), (ii) the musical arc discovered by Duddell (1901) and investigated by Blondel (1905), (iii) the triode invented by de Forest (1907), and (iv) the multivibrator elaborated by Abraham and Bloch (1917). The differential equation describing such a self-oscillating system was proposed by Poincaré for the musical arc (1908), by Janet for the series dynamo machine (1919), and by Blondel for the triode (1919). Once Janet (1919) established that these three self-oscillating systems can be described by the same equation, van der Pol proposed (1926) a generic dimensionless equation which captures the relevant dynamical properties shared by these systems. Van der Pol's contributions during the period of 1926-1930 were investigated to show how, with Le Corbeiller's help, he popularized the "relaxation oscillations" using the previous experiments as examples and, turned them into a concept.
Energy Technology Data Exchange (ETDEWEB)
Ji, Aimin; Yin, Xu; Yuan, Minghai [Hohai University, Changzhou (China)
2015-09-15
There are two problems in Collaborative optimization (CO): (1) the local optima arising from the selection of an inappropriate initial point; (2) the low efficiency and accuracy root in inappropriate relaxation factors. To solve these problems, we first develop the Latin hypercube design (LHD) to determine an initial point of optimization, and then use the non-linear programming by quadratic Lagrangian (NLPQL) to search for the global solution. The effectiveness of the initial point selection strategy is verified by three benchmark functions with some dimensions and different complexities. Then we propose the Adaptive relaxation collaborative optimization (ARCO) algorithm to solve the inconsistency between the system level and the disciplines level, and in this method, the relaxation factors are determined according to the three separated stages of CO respectively. The performance of the ARCO algorithm is compared with the standard collaborative algorithm and the constant relaxation collaborative algorithm with a typical numerical example, which indicates that the ARCO algorithm is more efficient and accurate. Finally, we propose a Hybrid collaborative optimization (HCO) approach, which integrates the selection strategy of initial point with the ARCO algorithm. The results show that HCO can achieve the global optimal solution without the initial value and it also has advantages in convergence, accuracy and robustness. Therefore, the proposed HCO approach can solve the CO problems with applications in the spindle and the speed reducer.
Kono, Mitsuo
2010-01-01
A nonlinearity is one of the most important notions in modern physics. A plasma is rich in nonlinearities and provides a variety of behaviors inherent to instabilities, coherent wave structures and turbulence. The book covers the basic concepts and mathematical methods, necessary to comprehend nonlinear problems widely encountered in contemporary plasmas, but also in other fields of physics and current research on self-organized structures and magnetized plasma turbulence. The analyses make use of strongly nonlinear models solved by analytical techniques backed by extensive simulations and available experiments. The text is written for senior undergraduates, graduate students, lecturers and researchers in laboratory, space and fusion plasmas.
Nonlinear magnetic metamaterials.
Shadrivov, Ilya V; Kozyrev, Alexander B; van der Weide, Daniel W; Kivshar, Yuri S
2008-12-08
We study experimentally nonlinear tunable magnetic metamaterials operating at microwave frequencies. We fabricate the nonlinear metamaterial composed of double split-ring resonators where a varactor diode is introduced into each resonator so that the magnetic resonance can be tuned dynamically by varying the input power. We demonstrate that at higher powers the transmission of the metamaterial becomes power-dependent and, as a result, such metamaterial can demonstrate various nonlinear properties. In particular, we study experimentally the power-dependent shift of the transmission band and demonstrate nonlinearity-induced enhancement (or suppression) of wave transmission. (c) 2008 Optical Society of America
Organic nonlinear optical materials
Umegaki, S.
1987-01-01
Recently, it became clear that organic compounds with delocalized pi electrons show a great nonlinear optical response. Especially, secondary nonlinear optical constants of more than 2 digits were often seen in the molecular level compared to the existing inorganic crystals such as LiNbO3. The crystallization was continuously tried. Organic nonlinear optical crystals have a new future as materials for use in the applied physics such as photomodulation, optical frequency transformation, opto-bistabilization, and phase conjugation optics. Organic nonlinear optical materials, e.g., urea, O2NC6H4NH2, I, II, are reviewed with 50 references.
Nonlinearity-reduced interferometer
Wu, Chien-ming
2007-12-01
Periodic nonlinearity is a systematic error limiting the accuracy of displacement measurements at the nanometer level. It results from many causes such as the frequency mixing, polarization mixing, polarization-frequency mixing, and the ghost reflections. An interferometer having accuracy in displacement measurement of less than one-nanometer is necessary in nanometrology. To meet the requirement, the periodic nonlinearity should be less than deep sub-nanometer. In this paper, a nonlinearity-reduced interferometry has been proposed. Both the linear- and straightness-interferometer were tested. The developed interferometer demonstrated of a residual nonlinearity less than 25 pm.
Mozart versus new age music: relaxation states, stress, and ABC relaxation theory.
Smith, Jonathan C; Joyce, Carol A
2004-01-01
Smith's (2001) Attentional Behavioral Cognitive (ABC) relaxation theory proposes that all approaches to relaxation (including music) have the potential for evoking one or more of 15 factor-analytically derived relaxation states, or "R-States" (Sleepiness, Disengagement, Rested / Refreshed, Energized, Physical Relaxation, At Ease/Peace, Joy, Mental Quiet, Childlike Innocence, Thankfulness and Love, Mystery, Awe and Wonder, Prayerfulness, Timeless/Boundless/Infinite, and Aware). The present study investigated R-States and stress symptom-patterns associated with listening to Mozart versus New Age music. Students (N = 63) were divided into three relaxation groups based on previously determined preferences. Fourteen listened to a 28-minute tape recording of Mozart's Eine Kleine Nachtmusik and 14 listened to a 28-minute tape of Steven Halpern's New Age Serenity Suite. Others (n = 35) did not want music and instead chose a set of popular recreational magazines. Participants engaged in their relaxation activity at home for three consecutive days for 28 minutes a session. Before and after each session, each person completed the Smith Relaxation States Inventory (Smith, 2001), a comprehensive questionnaire tapping 15 R-States as well as the stress states of somatic stress, worry, and negative emotion. Results revealed no differences at Session 1. At Session 2, those who listened to Mozart reported higher levels of At Ease/Peace and lower levels of Negative Emotion. Pronounced differences emerged at Session 3. Mozart listeners uniquely reported substantially higher levels of Mental Quiet, Awe and Wonder, and Mystery. Mozart listeners reported higher levels, and New Age listeners slightly elevated levels, of At Ease/Peace and Rested/Refreshed. Both Mozart and New Age listeners reported higher levels of Thankfulness and Love. In summary, those who listened to Mozart's Eine Kleine Nachtmusik reported more psychological relaxation and less stress than either those who listened to
Directory of Open Access Journals (Sweden)
Nicolas Garraud
2017-05-01
Full Text Available The design and validation of a magnetic particle spectrometer (MPS system used to study the linear and nonlinear behavior of magnetic nanoparticle suspensions is presented. The MPS characterizes the suspension dynamic response, both due to relaxation and saturation effects, which depends on the magnetic particles and their environment. The system applies sinusoidal excitation magnetic fields varying in amplitude and frequency and can be configured for linear measurements (1 mT at up to 120 kHz and nonlinear measurements (50 mT at up to 24 kHz. Time-resolved data acquisition at up to 4 MS/s combined with hardware and software-based signal processing allows for wide-band measurements up to 50 harmonics in nonlinear mode. By cross-calibrating the instrument with a known sample, the instantaneous sample magnetization can be quantitatively reconstructed. Validation of the two MPS modes are performed for iron oxide and cobalt ferrite suspensions, exhibiting Néel and Brownian relaxation, respectively.
On topological relaxations of chromatic conjectures
Simonyi, Gábor
2010-01-01
There are several famous unsolved conjectures about the chromatic number that were relaxed and already proven to hold for the fractional chromatic number. We discuss similar relaxations for the topological lower bound(s) of the chromatic number. In particular, we prove that such a relaxed version is true for the Behzad-Vizing conjecture and also discuss the conjectures of Hedetniemi and of Hadwiger from this point of view. For the latter, a similar statement was already proven in an earlier paper of the first author with G. Tardos, our main concern here is that the so-called odd Hadwiger conjecture looks much more difficult in this respect. We prove that the statement of the odd Hadwiger conjecture holds for large enough Kneser graphs and Schrijver graphs of any fixed chromatic number.
Vibrational and Rotational Energy Relaxation in Liquids
DEFF Research Database (Denmark)
Petersen, Jakob
the intramolecular dynamics during photodissociation is investigated. The apparent agreement with quantum mechanical calculations is shown to be in contrast to the applicability of the individual approximations used in deriving the model from a quantum mechanical treatment. In the spirit of the Bersohn-Zewail model......, the vibrational energy relaxation of I2 subsequent to photodissociation and recombination in CCl4 is studied using classical Molecular Dynamics simulations. The vibrational relaxation times and the time-dependent I-I pair distribution function are compared to new experimental results, and a qualitative agreement...... is found in both cases. Furthermore, the rotational energy relaxation of H2O in liquid water is studied via simulations and a power-and-work analysis. The mechanism of the energy transfer from the rotationally excited H2O molecule to its water neighbors is elucidated, i.e. the energy-accepting degrees...
Relaxation and Diffusion in Complex Systems
Ngai, K L
2011-01-01
Relaxation and Diffusion in Complex Systems comprehensively presents a variety of experimental evidences of universal relaxation and diffusion properties in complex materials and systems. The materials discussed include liquids, glasses, colloids, polymers, rubbers, plastic crystals and aqueous mixtures, as well as carbohydrates, biomolecules, bioprotectants and pharmaceuticals. Due to the abundance of experimental data, emphasis is placed on glass-formers and the glass transition problem, a still unsolved problem in condensed matter physics and chemistry. The evidence for universal properties of relaxation and diffusion dynamics suggests that a fundamental physical law is at work. The origin of the universal properties is traced to the many-body effects of the interaction, rigorous theory of which does not exist at the present time. However, using solutions of simplified models as guides, key quantities have been identified and predictions of the universal properties generated. These predictions from Ngai’...
Substrate stress relaxation regulates cell spreading
Chaudhuri, Ovijit; Gu, Luo; Darnell, Max; Klumpers, Darinka; Bencherif, Sidi A.; Weaver, James C.; Huebsch, Nathaniel; Mooney, David J.
2015-02-01
Studies of cellular mechanotransduction have converged upon the idea that cells sense extracellular matrix (ECM) elasticity by gauging resistance to the traction forces they exert on the ECM. However, these studies typically utilize purely elastic materials as substrates, whereas physiological ECMs are viscoelastic, and exhibit stress relaxation, so that cellular traction forces exerted by cells remodel the ECM. Here we investigate the influence of ECM stress relaxation on cell behaviour through computational modelling and cellular experiments. Surprisingly, both our computational model and experiments find that spreading for cells cultured on soft substrates that exhibit stress relaxation is greater than cells spreading on elastic substrates of the same modulus, but similar to that of cells spreading on stiffer elastic substrates. These findings challenge the current view of how cells sense and respond to the ECM.
Excited-state relaxation of some aminoquinolines
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available The absorption and fluorescence spectra, fluorescence quantum yields and lifetimes, and fluorescence rate constants ( k f of 2-amino-3-( 2 ′ -benzoxazolylquinoline (I, 2-amino-3-( 2 ′ -benzothiazolylquinoline (II, 2-amino-3-( 2 ′ -methoxybenzothiazolyl-quinoline (III, 2-amino-3-( 2 ′ -benzothiazolylbenzoquinoline (IV at different temperatures have been measured. The shortwavelength shift of fluorescence spectra of compounds studied (23–49 nm in ethanol as the temperature decreases (the solvent viscosity increases points out that the excited-state relaxation process takes place. The rate of this process depends essentially on the solvent viscosity, but not the solvent polarity. The essential increasing of fluorescence rate constant k f (up to about 7 times as the solvent viscosity increases proves the existence of excited-state structural relaxation consisting in the mutual internal rotation of molecular fragments of aminoquinolines studied, followed by the solvent orientational relaxation.
Improved memristor-based relaxation oscillator
Mosad, Ahmed G.
2013-09-01
This paper presents an improved memristor-based relaxation oscillator which offers higher frequency and wider tunning range than the existing reactance-less oscillators. It also has the capability of operating on two positive supplies or alternatively a positive and negative supply. Furthermore, it has the advantage that it can be fully integrated on-chip providing an area-efficient solution. On the other hand, The oscillation concept is discussed then a complete mathematical analysis of the proposed oscillator is introduced. Furthermore, the power consumption of the new relaxation circuit is discussed and validated by the PSPICE circuit simulations showing an excellent agreement. MATLAB results are also introduced to demonstrate the resistance range and the corresponding frequency range which can be obtained from the proposed relaxation oscillator. © 2013 Elsevier Ltd.
Interactive Image Enhancement by Fuzzy Relaxation
Institute of Scientific and Technical Information of China (English)
Shang-Ming Zhou; John Q.Can; Li-Da Xu; Robert John
2007-01-01
In this paper, an interactive image enhancement (HE) technique based on fuzzy relaxation is presented, which allows the user to select different intensity levels for enhancement and intermit the enhancement process according to his/her preference in applications. First, based on an analysis of the convergence of a fuzzy relaxation algorithm for image contrast enhancement, an improved version of this algorithm, which is called FuzzIIE Method 1, is suggested by deriving a relationship between the convergence regions and the parameters in the transformations defined in the algorithm. Then a method called FuzzIIE Method 2 is introduced by using a different fuzzy relaxation function, in which there is no need to re-select the parameter values for interactive image enhancement. Experimental results are presented demonstrating the enhancement capabilities of the proposed methods under different conditions.
Formal Proofs for Nonlinear Optimization
Directory of Open Access Journals (Sweden)
Victor Magron
2015-01-01
Full Text Available We present a formally verified global optimization framework. Given a semialgebraic or transcendental function f and a compact semialgebraic domain K, we use the nonlinear maxplus template approximation algorithm to provide a certified lower bound of f over K.This method allows to bound in a modular way some of the constituents of f by suprema of quadratic forms with a well chosen curvature. Thus, we reduce the initial goal to a hierarchy of semialgebraic optimization problems, solved by sums of squares relaxations. Our implementation tool interleaves semialgebraic approximations with sums of squares witnesses to form certificates. It is interfaced with Coq and thus benefits from the trusted arithmetic available inside the proof assistant. This feature is used to produce, from the certificates, both valid underestimators and lower bounds for each approximated constituent.The application range for such a tool is widespread; for instance Hales' proof of Kepler's conjecture yields thousands of multivariate transcendental inequalities. We illustrate the performance of our formal framework on some of these inequalities as well as on examples from the global optimization literature.
Relaxation Dynamics of Semiflexible Fractal Macromolecules
Directory of Open Access Journals (Sweden)
Jonas Mielke
2016-07-01
Full Text Available We study the dynamics of semiflexible hyperbranched macromolecules having only dendritic units and no linear spacers, while the structure of these macromolecules is modeled through T-fractals. We construct a full set of eigenmodes of the dynamical matrix, which couples the set of Langevin equations. Based on the ensuing relaxation spectra, we analyze the mechanical relaxation moduli. The fractal character of the macromolecules reveals itself in the storage and loss moduli in the intermediate region of frequencies through scaling, whereas at higher frequencies, we observe the locally-dendritic structure that is more pronounced for higher stiffness.
Dynamics of cosmological relaxation after reheating
Choi, Kiwoon; Sekiguchi, Toyokazu
2016-01-01
We examine if the cosmological relaxation mechanism, which was proposed recently as a new solution to the hierarchy problem, can be compatible with high reheating temperature well above the weak scale. As the barrier potential disappears at high temperature, the relaxion rolls down further after the reheating, which may ruin the successful implementation of the relaxation mechanism. It is noted that if the relaxion is coupled to a dark gauge boson, the new frictional force arising from dark gauge boson production can efficiently slow down the relaxion motion, which allows the relaxion to be stabilized after the electroweak phase transition for a wide range of model parameters, while satisfying the known observational constraints.
Synthetic aperture radar autofocus via semidefinite relaxation.
Liu, Kuang-Hung; Wiesel, Ami; Munson, David C
2013-06-01
The autofocus problem in synthetic aperture radar imaging amounts to estimating unknown phase errors caused by unknown platform or target motion. At the heart of three state-of-the-art autofocus algorithms, namely, phase gradient autofocus, multichannel autofocus (MCA), and Fourier-domain multichannel autofocus (FMCA), is the solution of a constant modulus quadratic program (CMQP). Currently, these algorithms solve a CMQP by using an eigenvalue relaxation approach. We propose an alternative relaxation approach based on semidefinite programming, which has recently attracted considerable attention in other signal processing problems. Experimental results show that our proposed methods provide promising performance improvements for MCA and FMCA through an increase in computational complexity.
Depicting Vortex Stretching and Vortex Relaxing Mechanisms
Institute of Scientific and Technical Information of China (English)
符松; 李启兵; 王明皓
2003-01-01
Different from many existing studies on the paranetrization of vortices, we investigate the effectiveness of two new parameters for identifying the vortex stretching and vortex relaxing mechanisms. These parameters are invariants and identify three-dimensional flow structures only, i.e. they diminish in two-dimensional flows. This is also unlike the existing vortex identification approaches which deliver information in two-dimensional flows. The present proposals have been successfully applied to identify the stretching and relaxing vortices in compressible mixing layers and natural convection flows.
Global Optimization Algorithm for Nonlinear Sum of Ratios Problems%非线性比式和问题的全局优化算法
Institute of Scientific and Technical Information of China (English)
焦红伟; 郭运瑞; 陈永强
2008-01-01
In this paper,a global optimization algorithm is proposed for nonlinear sum of ratios problem(P).The algorithm works by globally solving problem(P1)that is equivalent to problem(P),by utilizing linearization technique a linear relaxation programming of the(P1)is then obtained.The proposed algorithm is convergent to the global minimum of(P1)through the successive refinement of linear relaxation of the feasible region of objective function and solutions of a series of linear relaxation programming.Numerical results indicate that the proposed algorithm is feasible and can be used to globally solve nonlinear sum of ratios problems(P).
Tarrío-Saavedra, Javier; González, Cécilia Galindo; Naya, Salvador; López-Beceiro, Jorge
2017-01-01
This study investigated a methodology based on image processing and statistics to characterize and model the deformation upon controlled and uniform magnetic field and the relaxation under zero field of droplets observed in aqueous solutions of sodium alginate incorporating magnetic maghemite nanoparticles stabilized by adsorption of citrate ions. The changes of droplet geometry were statistically analyzed using a new approach based on the data obtained from optical microscopy, image processing, nonlinear regression, evolutionary optimization, analysis of variance and resampling. Image enhancement and then image segmentation (Gaussian mixture modeling) processes were applied to extract features with reliable information of droplets dimensions from optical micrographs. The droplets deformation and relaxation trends were accurately adjusted by the Kohlrausch-Williams-Watts (KWW) function and a mean relaxation time was obtained by fitting the time evolution of geometry parameters. It was found to be proportional to the initial radius of the spherical droplets and was associated to interfacial tension. PMID:28081239
Nonlinear dielectric effects in liquids: a guided tour
Richert, Ranko
2017-09-01
Dielectric relaxation measurements probe how the polarization of a material responds to the application of an external electric field, providing information on structure and dynamics of the sample. In the limit of small fields and thus linear response, such experiments reveal the properties of the material in the same thermodynamic state it would have in the absence of the external field. At sufficiently high fields, reversible changes in enthalpy and entropy of the system occur even at constant temperature, and these will in turn alter the polarization responses. The resulting nonlinear dielectric effects feature field induced suppressions (saturation) and enhancements (chemical effect) of the amplitudes, as well as time constant shifts towards faster (energy absorption) and slower (entropy reduction) dynamics. This review focuses on the effects of high electric fields that are reversible and observed at constant temperature for single component glass-forming liquids. The experimental challenges involved in nonlinear dielectric experiments, the approaches to separating and identifying the different sources of nonlinear behavior, and the current understanding of how high electric fields affect dielectric materials will be discussed. Covering studies from Debye’s initial approach to the present state-of-the-art, it will be emphasized what insight can be gained from the nonlinear responses that are not available from dielectric relaxation results obtained in the linear regime.
Lasers for nonlinear microscopy.
Wise, Frank
2013-03-01
Various versions of nonlinear microscopy are revolutionizing the life sciences, almost all of which are made possible because of the development of ultrafast lasers. In this article, the main properties and technical features of short-pulse lasers used in nonlinear microscopy are summarized. Recent research results on fiber lasers that will impact future instruments are also discussed.
Eaton, D F
1991-07-19
The current state of materials development in nonlinear optics is summarized, and the promise of these materials is critically evaluated. Properties and important materials constants of current commercial materials and of new, promising, inorganic and organic molecular and polymeric materials with potential in second- and third-order nonlinear optical applications are presented.
Billings, S. A.
1988-03-01
Time and frequency domain identification methods for nonlinear systems are reviewed. Parametric methods, prediction error methods, structure detection, model validation, and experiment design are discussed. Identification of a liquid level system, a heat exchanger, and a turbocharge automotive diesel engine are illustrated. Rational models are introduced. Spectral analysis for nonlinear systems is treated. Recursive estimation is mentioned.
Ionescu, T. C.; Scherpen, J. M. A.; Korytowski, A; Malanowski, K; Mitkowski, W; Szymkat, M
2009-01-01
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Christiansen, Peter Leth; Torner, L.
1999-01-01
We show that with the quasi-phase-matching technique it is possible to fabricate stripes of nonlinearity that trap and guide light like waveguides. We investigate an array of such stripes and find that when the stripes are sufficiently narrow, the beam dynamics is governed by a quadratic nonlinear...
Controllability in nonlinear systems
Hirschorn, R. M.
1975-01-01
An explicit expression for the reachable set is obtained for a class of nonlinear systems. This class is described by a chain condition on the Lie algebra of vector fields associated with each nonlinear system. These ideas are used to obtain a generalization of a controllability result for linear systems in the case where multiplicative controls are present.
Menon, P. K. A.; Badgett, M. E.; Walker, R. A.
1992-01-01
Trajectory-control laws based on singular-perturbation theory and nonlinear dynamical modeling. Nonlinear maneuver autopilot commands flight-test trajectories of F-15 airplane. Underlying theory of controller enables separation of variables processed in fast and slow control loops, reducing amount of computation required.
Nonlinear optics and photonics
He, Guang S
2015-01-01
This book provides a comprehensive presentation on most of the major topics in nonlinear optics and photonics, with equal emphasis on principles, experiments, techniques, and applications. It covers many major new topics including optical solitons, multi-photon effects, nonlinear photoelectric effects, fast and slow light , and Terahertz photonics. Chapters 1-10 present the fundamentals of modern nonlinear optics, and could be used as a textbook with problems provided at the end of each chapter. Chapters 11-17 cover the more advanced topics of techniques and applications of nonlinear optics and photonics, serving as a highly informative reference for researchers and experts working in related areas. There are also 16 pages of color photographs to illustrate the visual appearances of some typical nonlinear optical effects and phenomena. The book could be adopted as a textbook for both undergraduates and graduate students, and serve as a useful reference work for researchers and experts in the fields of physics...
Lugiato, Luigi; Brambilla, Massimo
2015-01-01
Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.
Collection Development: Relaxation & Meditation, September 1, 2010
Lettus, Dodi
2010-01-01
One of the first books to document the relationship between stress and physical and emotional health was "The Relaxation Response" by Herbert Benson, M.D., with Miriam Z. Klipper. Originally published in 1975, the book grew out of Benson's observations as a cardiologist and his research as a fellow at Harvard Medical School. Benson's study of…
BRIEF REPORT: The colour relaxation equation
Xiaofei, Zhang; Jiarong, Li
1996-03-01
Colour diffusion in quark - gluon plasma (QGP) is investigated from the transport equations of QGP. The pure non-Abelian collision term describing the colour diffusion in QGP is obtained, the expression for colour relaxation time is derived and the physical picture of the colour diffusion in QGP is shown.
Control linearity and jitter of relaxation oscillators
Gierkink, Sander Laurentius Johannes
1999-01-01
The body of this thesis (chapters 3,4 and 5) deals with the analysis and improvement of a specific class of voltage- or current controlled oscillators (VCO’s respectively CCO’s) called relaxation oscillators. Before going into detail on this particular class of oscillators, first the function and ap
Relaxation for Children. (Revised and Expanded Edition.)
Rickard, Jenny
Intended as a guide to reduce negative stress in children, this book suggests relaxation and meditation techniques to help children cope with stressful events. Part 1 provides an introduction to the format of the book. Part 2 contains summaries of the 10 sessions that make up the program. Each session has six sequential stages in which students…
Relaxation of polarized nuclei in superconducting rhodium
DEFF Research Database (Denmark)
Knuuttila, T.A.; Tuoriniemi, J.T.; Lefmann, K.
2000-01-01
Nuclear spin lattice relaxation rates were measured in normal and superconducting (sc) rhodium with nuclear polarizations up to p = 0.55. This was sufficient to influence the sc state of Rh, whose T, and B-c, are exceptionally low. Because B-c
Collection Development: Relaxation & Meditation, September 1, 2010
Lettus, Dodi
2010-01-01
One of the first books to document the relationship between stress and physical and emotional health was "The Relaxation Response" by Herbert Benson, M.D., with Miriam Z. Klipper. Originally published in 1975, the book grew out of Benson's observations as a cardiologist and his research as a fellow at Harvard Medical School. Benson's study of…
Redheffer representations and relaxed commutant lifting
ter Horst, S.
2011-01-01
It is well known that the solutions of a (relaxed) commutant lifting problem can be described via a linear fractional representation of the Redheffer type. The coefficients of such Redheffer representations are analytic operator-valued functions defined on the unit disc D of the complex plane. In th
Vibrational relaxation of pure liquid water
Lindner, J; Vohringer, P; Pshenichnikov, MS; Cringus, D; Wiersma, DA; Mostovoy, M; Vöhringer, Peter; Pshenichnikov, Maxim S.
2006-01-01
Multicolor infrared ultrafast spectroscopy is applied to investigate the vibrational relaxation dynamics in liquid water at room temperature. In a sequence of experiments, both the stretching and the bending mode are photoexcited and probed. A unified model, capable of the reproduction of as much as
Relaxation Treatment for Insomnia: A Component Analysis.
Woolfolk, Robert L.; McNulty, Terrence F.
1983-01-01
Compared four relaxation treatments for sleep onset insomnia with a waiting-list control. Treatments varied in presence or absence of muscular tension-release instructions and in foci of attention. Results showed all treatment conditions reduced latency of sleep onset and fatigue; visual focusing best reduced the number of nocturnal awakenings.…
Generalized approach to non-exponential relaxation
Indian Academy of Sciences (India)
R M Pickup; R Cywinski; C Pappas; P Fouquet; B Farago; P Falus
2008-11-01
Non-exponential relaxation is a universal feature of systems as diverse as glasses, spin glasses, earthquakes, financial markets and the universe. Complex relaxation results from hierarchically constrained dynamics with the strength of the constraints being directly related to the form of the relaxation, which changes from a simple exponential to a stretched exponential and a power law by increasing the constraints in the system. A global and unified approach to non-exponentiality was first achieved by Weron and was further generalized by Brouers and Sotolongo-Costa, who applied the concept of non-extensive entropy introduced by Tsallis to the relaxation of disordered systems. These concepts are now confronted with experimental results on the classical metallic spin glasses CuMn, AuFe and the insulating system EuSrS. The revisited data have also be complemented by new results on several compositions of the classical CuMn spin glass and on systems, like CoGa and CuCo, the magnetic behaviour of which is believed to arise from magnetic clusters and should be characteristic for superparamagnetism.
Relaxation dynamics of multilayer triangular Husimi cacti
Galiceanu, Mircea; Jurjiu, Aurel
2016-09-01
We focus on the relaxation dynamics of multilayer polymer structures having, as underlying topology, the Husimi cactus. The relaxation dynamics of the multilayer structures is investigated in the framework of generalized Gaussian structures model using both Rouse and Zimm approaches. In the Rouse type-approach, we determine analytically the complete eigenvalues spectrum and based on it we calculate the mechanical relaxation moduli (storage and loss modulus) and the average monomer displacement. First, we monitor these physical quantities for structures with a fixed generation number and we increase the number of layers, such that the linear topology will smoothly come into play. Second, we keep constant the size of the structures, varying simultaneously two parameters: the generation number of the main layer, G, and the number of layers, c. This fact allows us to study in detail the crossover from a pure Husimi cactus behavior to a predominately linear chain behavior. The most interesting situation is found when the two limiting topologies cancel each other. For this case, we encounter in the intermediate frequency/time domain regions of constant slope for different values of the parameter set (G, c) and we show that the number of layers follows an exponential-law of G. In the Zimm-type approach, which includes the hydrodynamic interactions, the quantities that describe the mechanical relaxation dynamics do not show scaling behavior as in the Rouse model, except the limiting case, namely, a very high number of layers and low generation number.
Noise in (double) relaxation oscillation SQUIDs
Adelerhof, Derk Jan; Adelerhof, Derk Jan; Flokstra, Jakob; Rogalla, Horst
1994-01-01
We have modelled the effect of two intrinsic noise sources on the flux noise spectral density of (Double) Relaxation Oscillation SQUIDs ((D)ROSs) based on hysteretic Josephson tunnel junctions. An important noise source is the spread in the critical current of the SQUID due to thermal fluctuations.
Reactor flush time correction in relaxation experiments
den Otter, M.W.; Bouwmeester, Henricus J.M.; Boukamp, Bernard A.; Verweij, H.
2001-01-01
The present paper deals with the analysis of experimental data from conductivity relaxation experiments. It is shown that evaluation of the chemical diffusion and surface transfer coefficients for oxygen by use of this technique is possible only if accurate data for the conductivity transient can be
Completely generalized multivalued nonlinear quasi-variational inclusions
Directory of Open Access Journals (Sweden)
Zeqing Liu
2002-01-01
Full Text Available We introduce and study a new class of completely generalized multivalued nonlinear quasi-variational inclusions. Using the resolvent operator technique for maximal monotone mappings, we suggest two kinds of iterative algorithms for solving the completely generalized multivalued nonlinear quasi-variational inclusions. We establish both four existence theorems of solutions for the class of completely generalized multivalued nonlinear quasi-variational inclusions involving strongly monotone, relaxed Lipschitz, and generalized pseudocontractive mappings, and obtain a few convergence results of iterative sequences generated by the algorithms. The results presented in this paper extend, improve, and unify a lot of results due to Adly, Huang, Jou-Yao, Kazmi, Noor, Noor-Al-Said, Noor-Noor, Noor-Noor-Rassias, Shim-Kang-Huang-Cho, Siddiqi-Ansari, Verma, Yao, and Zhang.
Global optimization of truss topology with discrete bar areas—Part I: Theory of relaxed problems
DEFF Research Database (Denmark)
Achtziger, Wolfgang; Stolpe, Mathias
2008-01-01
. The main issue of the paper and of the approach lies in the fact that the relaxed nonlinear optimization problem can be formulated as a quadratic program (QP). Here the paper generalizes and extends the available theory from the literature. Although the Hessian of this QP is indefinite, it is possible...... to circumvent the non-convexity and to calculate global optimizers. Moreover, the QPs to be treated in the branch-and-bound search tree differ from each other just in the objective function. In Part I we give an introduction to the problem and collect all theory and related proofs for the treatment...
Scalerandi, M; Johnson, P A
2003-01-01
Local interaction simulation approach simulations of the ultrasonic wave propagation in multi-grained materials have succeeded in reproducing most of the recently observed nonclassical nonlinear effects, such as stress-strain hysteresis and discrete memory in quasi-static experiments and a downwards shift of the resonance frequency and the generation of odd harmonics at specific amplitude rates in dynamics experiments. By including a simple mechanism of thermally activated random transitions, we can predict the occurrence of experimentally observed effects, such as the conditioning and relaxation of the specimen. Experiments are also suggested for a quantitative assessment of the validity of the model.
Wang, Yingwei; Mu, Haoran; Li, Xiaohong; Yuan, Jian; Chen, Jiazhang; Xiao, Si; Bao, Qiaoliang; Gao, Yongli; He, Jun
2016-05-01
We report the large nonlinear response and ultrafast carrier relaxation dynamics of a graphene-Bi2Te3 heterostructure produced by two-step chemical vapour deposition. The nonlinear refractive index reaches n2 = 0.2 × 10-7 cm2/W at the telecommunication wavelength of 1550 nm, which is almost seven orders of magnitude larger than that of the bulk Si material. Additionally, a pump-probe experiment is performed to investigate the ultrafast dynamic process (intraband relaxation time τ1 = 270 ± 20 fs; interband relaxation time τ2 = 3.6 ± 0.2 ps) of the graphene-Bi2Te3 heterostructure. Then, based on the donor-acceptor structure model, we propose a theoretical model to explain the dynamic relaxation process. Our results show that the graphene-Bi2Te3 heterostructure is a promising saturable absorber for ultrafast pulse laser applications at telecommunication wavelengths.
Fast numerical methods for mixed-integer nonlinear model-predictive control
Kirches, Christian
2011-01-01
Christian Kirches develops a fast numerical algorithm of wide applicability that efficiently solves mixed-integer nonlinear optimal control problems. He uses convexification and relaxation techniques to obtain computationally tractable reformulations for which feasibility and optimality certificates can be given even after discretization and rounding.
Load Relaxation of Olivine Single Crystals
Cooper, R. F.; Stone, D. S.; Plookphol, T.
2016-12-01
Single crystals of ferromagnesian olivine (San Carlos, AZ, peridot; Fo90-92) have been deformed in both uniaxial creep and load relaxation under conditions of ambient pressure, T = 1500ºC and pO2 = 10-10 atm; creep stresses were in the range 40 ≤ σ1 (MPa) ≤ 220. The crystals were oriented such that the applied stress was parallel to [011]c, which promotes single slip on the slowest slip system in olivine, (010)[001]. The creep rates at steady state match well the results of earlier investigators, as does the stress sensitivity (a power-law exponent of n = 3.6). Dislocation microstructures, including spatial distribution of low-angle (subgrain) boundaries, additionally confirm previous investigations. Inverted primary creep (an accelerating strain rate with an increase in stress) was observed. Load-relaxation, however, produced a singular response—a single hardness curve—regardless of the magnitude of creep stress or total accumulated strain preceding relaxation. The log-stress v. log-strain rate data from load-relaxation and creep experiments overlap to within experimental error. The load-relaxation behavior is distinctly different that that described for other crystalline solids, where the flow stress is affected strongly by work hardening such that a family of distinct hardness curves is generated, which are related by a scaling function. The response of olivine for the conditions studied, thus, indicates flow that is rate-limited by dislocation glide, reflecting specifically a high intrinsic lattice resistance (Peierls stress).
Ziv, Naomi; Rotem, Tomer; Arnon, Zahi; Haimov, Iris
2008-01-01
A large percentage of older people suffer from chronic insomnia, affecting many aspects of life quality and well-being. Although insomnia is most often treated with medication, a growing number of studies demonstrate the efficiency of various relaxation techniques. The present study had three aims: first, to compare two relaxation techniques--music relaxation and progressive muscular relaxation--on various objective and subjective measures of sleep quality; second, to examine the effect of these techniques on anxiety and depression; and finally, to explore possible relationships between the efficiency of both techniques and personality variables. Fifteen older adults took part in the study. Following one week of base-line measurements of sleep quality, participants followed one week of music relaxation and one week of progressive muscular relaxation before going to sleep. Order of relaxation techniques was controlled. Results show music relaxation was more efficient in improving sleep. Sleep efficiency was higher after music relaxation than after progressive muscular relaxation. Moreover, anxiety was lower after music relaxation. Progressive muscular relaxation was related to deterioration of sleep quality on subjective measures. Beyond differences between the relaxation techniques, extraverts seemed to benefit more from both music and progressive muscular relaxation. The advantage of non-pharmacological means to treat insomnia, and the importance of taking individual differences into account are discussed.
Enhanced four-wave mixing with nonlinear plasmonic metasurfaces.
Jin, Boyuan; Argyropoulos, Christos
2016-06-27
Plasmonic metasurfaces provide an effective way to increase the efficiency of several nonlinear processes while maintaining nanoscale dimensions. In this work, nonlinear metasurfaces based on film-coupled silver nanostripes loaded with Kerr nonlinear material are proposed to achieve efficient four-wave mixing (FWM). Highly localized plasmon resonances are formed in the nanogap between the metallic film and nanostripes. The local electric field is dramatically enhanced in this subwavelength nanoregion. These properties combined with the relaxed phase matching condition due to the ultrathin area lead to a giant FWM efficiency, which is enhanced by nineteen orders of magnitude compared to a bare silver screen. In addition, efficient visible and low-THz sources can be constructed based on the proposed nonlinear metasurfaces. The FWM generated coherent wave has a directional radiation pattern and its output power is relatively insensitive to the incident angles of the excitation sources. This radiated power can be further enhanced by increasing the excitation power. The dielectric nonlinear material placed in the nanogap is mainly responsible for the ultrastrong FWM response. Compact and efficient wave mixers and optical sources spanning different frequency ranges are envisioned to be designed based on the proposed nonlinear metasurface designs.
Gang, Zhou
2008-01-01
Nonlinear Schrodinger / Gross-Pitaevskii equations play a central role in the understanding of nonlinear optical and macroscopic quantum systems. The large time dynamics of such systems is governed by interactions of the nonlinear ground state manifold, discrete neutral modes (``excited states'') and dispersive radiation. Systems with symmetry, in spatial dimensions larger than one, typically have degenerate neutral modes. Thus, we study the large time dynamics of systems with degenerate neutral modes. This requires a new normal form (nonlinear matrix Fermi Golden Rule) governing the system's large time asymptotic relaxation to the ground state (soliton) manifold.
Lacot, Eric; Girardeau, Vadim; Hugon, Olivier; Jacquin, Olivier
2016-01-01
In this article, we study the non-linear coupling between the stationary (i.e. the beating modulation signal) and transient (i.e. the laser quantum noise) dynamics of a laser subjected to frequency shifted optical feedback. We show how the noise power spectrum and more specifically the relaxation oscillation frequency of the laser are modified under different optical feedback condition. Specifically we study the influence of (i) the amount of light returning to the laser cavity and (ii) the initial detuning between the frequency shift and intrinsic relaxation frequency. The present work shows how the relaxation frequency is related to the strength of the beating signal and the shape of the noise power spectrum gives an image of the Transfer Modulation Function (i.e. of the amplification gain) of the nonlinear-laser dynamics.The theoretical predictions, confirmed by numerical resolutions, are in good agreements with the experimental data.
Extending the EGP constitutive model for polymer glasses to multiple relaxation times
van Breemen, L. C. A.; Klompen, E. T. J.; Govaert, L. E.; Meijer, H. E. H.
2011-10-01
The one-mode EGP (Eindhoven glassy polymer) model captures the plastic flow at yield and post-yield quantitatively, but behaves poor in the non-linear viscoelastic pre-yield region. Since a proper description here is important in cases of complex loading and unloading situations, such as e.g. in indentation and scratching, an extension to non-linear modeling is required using a spectrum of relaxation times. It is shown that such a reference spectrum can be obtained from simple tensile tests. It shifts to shorter times under the influence of stress and is independent of the two important time-dependent processes in polymers: the strain rate applied during testing and the aging time during storage and use. The multi-mode model is critically tested and proves quantitative in describing the intrinsic polymer response and, based thereupon, in predicting the correct response in tensile testing, including necking, in flat tip indentation and in notched loading.
Zweig, George
2016-05-01
An earlier paper characterizing the linear mechanical response of the organ of Corti [J. Acoust. Soc. Am. 138, 1102-1121 (2015)] is extended to the nonlinear domain. Assuming the existence of nonlinear oscillators nonlocally coupled through the pressure they help create, the oscillator equations are derived and examined when the stimuli are modulated tones and clicks. The nonlinearities are constrained by the requirements of oscillator stability and the invariance of zero crossings in the click response to changes in click amplitude. The nonlinear oscillator equations for tones are solved in terms of the fluid pressure that drives them, and its time derivative, presumably a proxy for forces created by outer hair cells. The pressure equation is reduced to quadrature, the integrand depending on the oscillators' responses. The resulting nonlocally coupled nonlinear equations for the pressure, and oscillator amplitudes and phases, are solved numerically in terms of the fluid pressure at the stapes. Methods for determining the nonlinear damping directly from measurements are described. Once the oscillators have been characterized from their tone and click responses, the mechanical response of the cochlea to natural sounds may be computed numerically. Signal processing inspired by cochlear mechanics opens up a new area of nonlocal nonlinear time-frequency analysis.
Two-body relaxation in modified Newtonian dynamics
Ciotti, L
2004-01-01
A naive extension to MOND of the standard computation of the two-body relaxation time Tb implies that Tb is comparable to the crossing time regardless of the number N of stars in the system. This computation is questionable in view of the non-linearity of MOND's field equation. A non-standard approach to the calculation of Tb is developed that can be extended to MOND whenever discreteness noise generates force fluctuations that are small compared to the mean-field force. It is shown that this approach yields standard Newtonian results for systems in which the mean density profile is either plane-parallel or spherical. In the plane-parallel case we find that in the deep-MOND regime Tbb scales with N as in the Newtonian case, but is shorter by the square of the factor by which MOND enhances the gravitational force over its Newtonian value for the same system. Application of these results to dwarf galaxies and groups and clusters of galaxies reveals that in MOND luminosity segregation should be far advanced in g...
Agrawal, Govind P
2001-01-01
The Optical Society of America (OSA) and SPIE - The International Society for Optical Engineering have awarded Govind Agrawal with an honorable mention for the Joseph W. Goodman Book Writing Award for his work on Nonlinear Fiber Optics, 3rd edition.Nonlinear Fiber Optics, 3rd Edition, provides a comprehensive and up-to-date account of the nonlinear phenomena occurring inside optical fibers. It retains most of the material that appeared in the first edition, with the exception of Chapter 6, which is now devoted to the polarization effects relevant for light propagation in optical
Will Nonlinear Backcalculation Help?
DEFF Research Database (Denmark)
Ullidtz, Per
2000-01-01
demonstrates, that treating the subgrade as a nonlinear elastic material, can result in more realistic moduli and a much better agreement between measured and calculated stresses and strains.The response of nonlinear elastic materials can be calculated using the Finite Element Method (FEM). A much simpler...... approach is to use the Method of Equivalent Thicknesses (MET), modified for a nonlinear subgrade. The paper includes an example where moduli backcalculated using FEM, linear elastic theory and MET are compared. Stresses and strains predicted by the three methods are also compared to measured values...
Nonlinear graphene metamaterial
Nikolaenko, Andrey E; Atmatzakis, Evangelos; Luo, Zhiqiang; Shen, Ze Xiang; De Angelis, Francesco; Boden, Stuart A; Di Fabrizio, Enzo; Zheludev, Nikolay I
2012-01-01
We demonstrate that the broadband nonlinear optical response of graphene can be resonantly enhanced by more than an order of magnitude through hybridization with a plasmonic metamaterial,while retaining an ultrafast nonlinear response time of ~1 ps. Transmission modulation close to ~1% is seen at a pump uence of ~0.03 mJ/cm^2 at the wavelength of ~1600 nm. This approach allows to engineer and enhance graphene's nonlinearity within a broad wavelength range enabling applications in optical switching, mode-locking and pulse shaping.
[Brain activity during different stages of the relaxation process].
gorev, A S; Kovaleva, A V; Panova, E N; Gorbacheva, A K
2012-01-01
A group of adults participated in experiment in which they were asked to reach relaxed state by using relaxation techniques (active relaxation) and to maintain this state without any technique (passive relaxation). Some changes of EEG-characteristics during relaxation were analyzed. This experiment includes four situations (different functional states): baselinel, active relaxation, passive relaxation, baseline2. EEG was recorded from 10 cortical leads: O1, O2, TPO (left and right), P3, P4, C3, C4, F3 and F4. A comparative EEG analysis was done for 10 frequency bands from 5 to 40 Hz. In each experimental situation we revealed general trends for EEG parameters and also some specific changes in EEG, which characterized brain organization during passive and active relaxed states.
Multigrid Methods for Nonlinear Problems: An Overview
Energy Technology Data Exchange (ETDEWEB)
Henson, V E
2002-12-23
Since their early application to elliptic partial differential equations, multigrid methods have been applied successfully to a large and growing class of problems, from elasticity and computational fluid dynamics to geodetics and molecular structures. Classical multigrid begins with a two-grid process. First, iterative relaxation is applied, whose effect is to smooth the error. Then a coarse-grid correction is applied, in which the smooth error is determined on a coarser grid. This error is interpolated to the fine grid and used to correct the fine-grid approximation. Applying this method recursively to solve the coarse-grid problem leads to multigrid. The coarse-grid correction works because the residual equation is linear. But this is not the case for nonlinear problems, and different strategies must be employed. In this presentation we describe how to apply multigrid to nonlinear problems. There are two basic approaches. The first is to apply a linearization scheme, such as the Newton's method, and to employ multigrid for the solution of the Jacobian system in each iteration. The second is to apply multigrid directly to the nonlinear problem by employing the so-called Full Approximation Scheme (FAS). In FAS a nonlinear iteration is applied to smooth the error. The full equation is solved on the coarse grid, after which the coarse-grid error is extracted from the solution. This correction is then interpolated and applied to the fine grid approximation. We describe these methods in detail, and present numerical experiments that indicate the efficacy of them.
The Nonlinear Rheology of Electrorheological Fluids
Martin, James E.
1998-03-01
When a colloidal suspension is exposed to a uniaxial electric field the polarized particles chain along field lines causing a macroscopic "solidification" of the fluid, the basis of the so-called electrorheological (ER) effect. Likewise, in a rotating electric field particles form sheets in the plane of the field, which we call the rotary ER effect. Both of these fluids exhibit a nonlinear, shear thinning rheology, due to shear-induced structural relaxations. Because the fluid stress can be controlled by the applied field, a number of applications are possible, including electromechanical actuators, clutches, and active vibration dampers. To design these devices, and to develop effective control loop algorithms, it is necessary to understand the strongly nonlinear rheology of these fluids. We have used time-resolved, two-dimensional light scattering on a concentrated colloidal silica fluid in steady and oscillatory shear to demonstrate that the fragmentation and aggregation of chain-like particle microstructures is the cause of flow nonlinearities. We show that the light scattering is an indirect measure of the fluid stress. These observations form the basis of a kinetic chain model we developed to describe the nonlinear dynamics of the microstructures in ER fluids in nonstationary shear flows. Understanding the microstructural dynamics then leads us to a theory of the macroscopic rheology of these fluids in nonstationary, low Reynolds number flows. Finally, we have conducted extensive large-scale (1000-10000 particles) simulations of these fluids in steady and oscillatory shear, and will compare these results to theory and experiment.
Characteristics of the secondary relaxation process in soft colloidal suspensions
Saha, Debasish; Joshi, Yogesh M.; Bandyopadhyay, Ranjini
2015-11-01
A universal secondary relaxation process, known as the Johari-Goldstein (J-G) β-relaxation process, appears in glass formers. It involves all parts of the molecule and is particularly important in glassy systems because of its very close relationship with the α-relaxation process. However, the absence of a J-G β-relaxation mode in colloidal glasses raises questions regarding its universality. In the present work, we study the microscopic relaxation processes in Laponite suspensions, a model soft glassy material, by dynamic light scattering (DLS) experiments. α- and β-relaxation timescales are estimated from the autocorrelation functions obtained by DLS measurements for Laponite suspensions with different concentrations, salt concentrations and temperatures. Our experimental results suggest that the β-relaxation process in Laponite suspensions involves all parts of the constituent Laponite particle. The ergodicity breaking time is also seen to be correlated with the characteristic time of the β-relaxation process for all Laponite concentrations, salt concentrations and temperatures. The width of the primary relaxation process is observed to be correlated with the secondary relaxation time. The secondary relaxation time is also very sensitive to the concentration of Laponite. We measure primitive relaxation timescales from the α-relaxation time and the stretching exponent (β) by applying the coupling model for highly correlated systems. The order of magnitude of the primitive relaxation time is very close to the secondary relaxation time. These observations indicate the presence of a J-G β-relaxation mode for soft colloidal suspensions of Laponite.
Relaxation of Magnetic Nanoparticle Chain without Applied Field*
Institute of Scientific and Technical Information of China (English)
HE Liang-Ming
2011-01-01
The relaxation ofa one-dimensional magnetic nanoparticle linear chain with lattice constant a is investigated in absence of applied field. There is an equilibrium state (or steady state) where all magnetic moments of particles lie along the chain (x-axis), back to which the magnetic nanoparticle chain at other state will relax. It is found that the relaxation time Tx is determined by Tx = 10β × a3. This relaxation is compared with that of single magnetic nanoparticle system.
Multipolar nonlinear nanophotonics
Smirnova, Daria
2016-01-01
Nonlinear nanophotonics is a rapidly developing field with many useful applications for a design of nonlinear nanoantennas, light sources, nanolasers, sensors, and ultrafast miniature metadevices. A tight confinement of the local electromagnetic fields in resonant photonic nanostructures can boost nonlinear optical effects, thus offering versatile opportunities for subwavelength control of light. To achieve the desired functionalities, it is essential to gain flexible control over the near- and far-field properties of nanostructures. Thus, both modal and multipolar analyses are widely exploited for engineering nonlinear scattering from resonant nanoscale elements, in particular for enhancing the near-field interaction, tailoring the far-field multipolar interference, and optimization of the radiation directionality. Here, we review the recent advances in this recently emerged research field ranging from metallic structures exhibiting localized plasmonic resonances to hybrid metal-dielectric and all-dielectric...
Solitons in nonlinear lattices
Kartashov, Yaroslav V; Torner, Lluis
2010-01-01
This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of the nonlinearity, and their combinations with linear lattices. A majority of the results obtained, thus far, in this field and reviewed in this article are theoretical. Nevertheless, relevant experimental settings are surveyed too, with emphasis on perspectives for implementation of the theoretical predictions in the experiment. Physical systems discussed in the review belong to the realms of nonlinear optics (including artificial optical media, such as photonic crystals, and plasmonics) and Bose-Einstein condensation (BEC). The solitons are considered in one, two, and three dimensions (1D, 2D, and 3D). Basic properties of the solitons presented in the review are their existence, stability, and mobility. Although the field is still far from completion, general conclusions c...
Directory of Open Access Journals (Sweden)
Shakeeb Bin Hasan
2014-12-01
Full Text Available Contrary to traditional optical elements, plasmonic antennas made from nanostructured metals permit the localization of electromagnetic fields on length scales much smaller than the wavelength of light. This results in huge amplitudes for the electromagnetic field close to the antenna being conducive for the observation of nonlinear effects already at moderate pump powers. Thus, these antennas exhibit a promising potential to achieve optical frequency conversion and all-optical control of light at the nano-scale. This opens unprecedented opportunities for ultrafast nonlinear spectroscopy, sensing devices, on-chip optical frequency conversion, nonlinear optical metamaterials, and novel photon sources. Here, we review some of the recent advances in exploiting the potential of plasmonic antennas to realize robust nonlinear applications.
Leburn, Christopher; Reid, Derryck
2013-01-01
The field of ultrafast nonlinear optics is broad and multidisciplinary, and encompasses areas concerned with both the generation and measurement of ultrashort pulses of light, as well as those concerned with the applications of such pulses. Ultrashort pulses are extreme events – both in terms of their durations, and also the high peak powers which their short durations can facilitate. These extreme properties make them powerful experiment tools. On one hand, their ultrashort durations facilitate the probing and manipulation of matter on incredibly short timescales. On the other, their ultrashort durations can facilitate high peak powers which can drive highly nonlinear light-matter interaction processes. Ultrafast Nonlinear Optics covers a complete range of topics, both applied and fundamental in nature, within the area of ultrafast nonlinear optics. Chapters 1 to 4 are concerned with the generation and measurement of ultrashort pulses. Chapters 5 to 7 are concerned with fundamental applications of ultrasho...
DEFF Research Database (Denmark)
Nguyen-Duy, Khiem
and remains the prime source of energy in non-terrestrial applications such as those in sky-explorers. However, a renewable energy source is expensive, bulky, and its performance is weather dependent, which make testing of downstream converters very difficult. As a result, a nonlinear source emulator (NSE......) is a good solution to solve the problems associated with the use of real nonlinear sources in testing phases. However, a recent technical survey conducted during this work shows that most existing NSEs have only been concerned with simulating nonlinear systems in terrestrial applications. Furthermore......, their dynamic performance were not fast enough in order to imitate how a real nonlinear energy source would react under extreme conditions and operation modes. Particularly, a system in the sky can experience a step change of sunlight irradiation. Moreover, operation modes may include load step between nominal...
Introduction to nonlinear science
Nicolis, G
1995-01-01
One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex, nonlinear or chaotic, behavior. In this book, the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications drawn from the physical, engineering, and biological sciences. Some of the interesting topics covered include: dynamical systems with a finite number of degrees of freedom, linear stability analysis of fixed points, nonlinear behavior of fixed points, bifurcation analysis, spatially distributed systems, broken symmetries, pattern formation, and chaotic dynamics. The author makes a special effort to provide a logical connection between ordinary dynamical systems and spatially extended systems, and to balance the emphasis on chaotic behavior and more classical nonlinear behavior. He also develops a statistical approach to complex systems and compares it to traditional deterministi...
Nonlinear magnetoinductive transmission lines
Lazarides, Nikos; Tsironis, G P
2011-01-01
Power transmission in one-dimensional nonlinear magnetic metamaterials driven at one end is investigated numerically and analytically in a wide frequency range. The nonlinear magnetic metamaterials are composed of varactor-loaded split-ring resonators which are coupled magnetically through their mutual inductances, forming thus a magnetoiductive transmission line. In the linear limit, significant power transmission along the array only appears for frequencies inside the linear magnetoinductive wave band. We present analytical, closed form solutions for the magnetoinductive waves transmitting the power in this regime, and their discrete frequency dispersion. When nonlinearity is important, more frequency bands with significant power transmission along the array may appear. In the equivalent circuit picture, the nonlinear magnetoiductive transmission line driven at one end by a relatively weak electromotive force, can be modeled by coupled resistive-inductive-capacitive (RLC) circuits with voltage-dependent cap...
Optimization under Nonlinear Constraints
1982-01-01
In this paper a timesaving method is proposed for maximizing likelihood functions when the parameter space is subject to nonlinear constraints, expressible as second order polynomials. The suggested approach is especially attractive when dealing with systems with many parameters.
Nonlinearity in nanomechanical cantilevers
DEFF Research Database (Denmark)
Villanueva Torrijo, Luis Guillermo; Karabalin, R. B.; Matheny, M. H.
2013-01-01
Euler-Bernoulli beam theory is widely used to successfully predict the linear dynamics of micro-and nanocantilever beams. However, its capacity to characterize the nonlinear dynamics of these devices has not yet been rigorously assessed, despite its use in nanoelectromechanical systems development....... These findings underscore the delicate balance between inertial and geometric nonlinear effects in the fundamental mode, and strongly motivate further work to develop theories beyond the Euler-Bernoulli approximation. DOI: 10.1103/PhysRevB.87.024304....... In this article, we report the first highly controlled measurements of the nonlinear response of nanomechanical cantilevers using an ultralinear detection system. This is performed for an extensive range of devices to probe the validity of Euler-Bernoulli theory in the nonlinear regime. We find that its...
Nonlinear Stokes Mueller Polarimetry
Samim, Masood; Barzda, Virginijus
2015-01-01
The Stokes Mueller polarimetry is generalized to include nonlinear optical processes such as second- and third-harmonic generation, sum- and difference-frequency generations. The overall algebraic form of the polarimetry is preserved, where the incoming and outgoing radiations are represented by column vectors and the intervening medium is represented by a matrix. Expressions for the generalized nonlinear Stokes vector and the Mueller matrix are provided in terms of coherency and correlation matrices, expanded by higher-dimensional analogues of Pauli matrices. In all cases, the outgoing radiation is represented by the conventional $4\\times 1$ Stokes vector, while dimensions of the incoming radiation Stokes vector and Mueller matrix depend on the order of the process being examined. In addition, relation between nonlinear susceptibilities and the measured Mueller matrices are explicitly provided. Finally, the approach of combining linear and nonlinear optical elements is discussed within the context of polarim...
Nonlinear optics response of semiconductor quantum wells under high magnetic fields
Energy Technology Data Exchange (ETDEWEB)
Chemla, D.S.
1993-07-01
Recent investigations on the nonlinear optical response of semiconductor quantum wells in a strong perpendicular magnetic field, H, are reviewed. After some introductory material the evolution of the linear optical properties of GaAs QW`s as a function of H is discussed; an examination is made of how the magneto-excitons (MX) extrapolate continuously between quasi-2D QW excitons (X) when H = 0, and pairs of Landau levels (LL) when H {yields} {infinity}. Next, femtosecond time resolved investigations of their nonlinear optical response are presented; the evolution of MX-MX interactions with increasing H is stressed. Finally, how, as the dimensionality is reduced by application of H, the number of scattering channels is limited and relaxation of electron-hole pairs is affected. How nonlinear optical spectroscopy can be exploited to access the relaxation of angular momentum within magneto-excitons is also discussed.
General decay of solutions of a nonlinear system of viscoelastic wave equations
Said-Houari, Belkacem
2011-04-16
This work is concerned with a system of two viscoelastic wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we prove that, for certain class of relaxation functions and for some restrictions on the initial data, the rate of decay of the total energy depends on those of the relaxation functions. This result improves many results in the literature, such as the ones in Messaoudi and Tatar (Appl. Anal. 87(3):247-263, 2008) and Liu (Nonlinear Anal. 71:2257-2267, 2009) in which only the exponential and polynomial decay rates are considered. © 2011 Springer Basel AG.
Two-temperature reaction and relaxation rates
Kolesnichenko, E.; Gorbachev, Yu.
2016-09-01
Within the method of solving the kinetic equations for gas mixtures with internal degrees of freedom developed by the authors and based on the approximate summational invariants (ASI) concept, gas-dynamic equations for a multi-temperature model for the spatially inhomogeneous case are derived. For the two-temperature case, the expressions for the non-equilibrium reaction and relaxation rates are obtained. Special attention is drawn to corresponding thermodynamic equations. Different possibilities of introducing the gas-dynamic variables related to the internal degrees of freedom are considered. One is based on the choice of quantum numbers as the ASI, while the other is based on the choice of internal (vibrational) energy as the ASI. Limits to a one-temperature situation are considered in all the cases. For the cutoff harmonic oscillator model, explicit expressions for the reaction and relaxation rates are derived.
Microplastic relaxations of single and polycrystalline molybdenum
Energy Technology Data Exchange (ETDEWEB)
Pichl, W.; Weiss, B. [Wien Univ. (Austria). Inst. fuer Materialphysik; Chen, D.L.
1998-05-01
The microplasticity of high-purity molybdenum single crystals and of Mo polycrystals of technical purity has been investigated by relaxation step tests in uniaxial compression. A new model for the evaluation of relaxation tests in the microplastic range of b.c.c metals is presented which takes into account the decrease of the mobile dislocation density due to exhaustion of non-screw dislocations. The model allows an independent determination of the activation volume and of the microstructure parameters controlling dislocation exhaustion. The results indicate that in the high-purity single crystals the deformation rate is controlled by interactions of non-screw dislocations with the grown-in network. In the polycrystals additional interactions with impurity atoms seem to occur. In the single crystals the activity and subsequent exhaustion of two different glide systems was observed, followed by a gradual onset of screw dislocation motion. (orig.) 26 refs.
Electron-vibration relaxation in oxygen plasmas
Laporta, V.; Heritier, K. L.; Panesi, M.
2016-06-01
An ideal chemical reactor model is used to study the vibrational relaxation of oxygen molecules in their ground electronic state, X3Σg-, in presence of free electrons. The model accounts for vibrational non-equilibrium between the translational energy mode of the gas and the vibrational energy mode of individual molecules. The vibrational levels of the molecules are treated as separate species, allowing for non-Boltzmann distributions of their population. The electron and vibrational temperatures are varied in the range [0-20,000] K. Numerical results show a fast energy transfer between oxygen molecules and free electron, which causes strong deviation of the vibrational distribution function from Boltzmann distribution, both in heating and cooling conditions. Comparison with Landau-Teller model is considered showing a good agreement for electron temperature range [2000-12,000] K. Finally analytical fit of the vibrational relaxation time is given.
Modeling aftershocks as a stretched exponential relaxation
Mignan, A.
2015-11-01
The decay rate of aftershocks has been modeled as a power law since the pioneering work of Omori in the late nineteenth century. Although other expressions have been proposed in recent decades to describe the temporal behavior of aftershocks, the number of model comparisons remains limited. After reviewing the aftershock models published from the late nineteenth century until today, I solely compare the power law, pure exponential and stretched exponential expressions defined in their simplest forms. By applying statistical methods recommended recently in applied mathematics, I show that all aftershock sequences tested in three regional earthquake catalogs (Southern and Northern California, Taiwan) and with three declustering techniques (nearest-neighbor, second-order moment, window methods) follow a stretched exponential instead of a power law. These results infer that aftershocks are due to a simple relaxation process, in accordance with most other relaxation processes observed in Nature.
Relaxation time estimation in surface NMR
Grunewald, Elliot D.; Walsh, David O.
2017-03-21
NMR relaxation time estimation methods and corresponding apparatus generate two or more alternating current transmit pulses with arbitrary amplitudes, time delays, and relative phases; apply a surface NMR acquisition scheme in which initial preparatory pulses, the properties of which may be fixed across a set of multiple acquisition sequence, are transmitted at the start of each acquisition sequence and are followed by one or more depth sensitive pulses, the pulse moments of which are varied across the set of multiple acquisition sequences; and apply processing techniques in which recorded NMR response data are used to estimate NMR properties and the relaxation times T.sub.1 and T.sub.2* as a function of position as well as one-dimensional and two-dimension distributions of T.sub.1 versus T.sub.2* as a function of subsurface position.
Relaxation Based Electrical Simulation for VLSI Circuits
Directory of Open Access Journals (Sweden)
S. Rajkumar
2012-06-01
Full Text Available Electrical circuit simulation was one of the first CAD tools developed for IC design. The conventional circuit simulators like SPICE and ASTAP were designed initially for the cost effective analysis of circuits containing a few hundred transistors or less. A number of approaches have been used to improve the performances of congenital circuit simulators for the analysis of large circuits. Thereafter relaxation methods was proposed to provide more accurate waveforms than standard circuit simulators with up to two orders of magnitude speed improvement for large circuits. In this paper we have tried to highlights recently used waveform and point relaxation techniques for simulation of VLSI circuits. We also propose a simple parallelization technique and experimentally demonstrate that we can solve digital circuits with tens of million transistors in a few hours.
Electrochemical relaxation at electrically conducting polymers
Nateghi, M. R.; zarandi, M. B.
2008-08-01
In this study, slow relaxation (SR) associated with the electroreduction of polyaniline (PAn) films during polarization to high cathodic potentials was investigated by cyclic voltammetry technique. Anodic voltammetric currents were used as experimental variable to indicate the relaxation occurring in PAn films deposited electrochemically on the Pt electrode surface. The dependence of SR on polymer film thickness, waiting potential, and mobility of the doped anion was investigated. Percolation threshold potential for heteropolyanion doped PAn was estimated to be between 150 and 200 mV depending on polymer thickness on the electrode surface. A new model of the conducting to insulating conversion is described by the percolation theory and mobility gap changes during the process.
Electrochemical relaxation at electrically conducting polymers
Energy Technology Data Exchange (ETDEWEB)
Nateghi, M R [Department of Chemistry, Islamic Azad University, Yazd-Branch, Yazd (Iran, Islamic Republic of); Zarandi, M B [Department of physics, Yazd University, Yazd (Iran, Islamic Republic of)
2008-08-15
In this study, slow relaxation (SR) associated with the electroreduction of polyaniline (PAn) films during polarization to high cathodic potentials was investigated by cyclic voltammetry technique. Anodic voltammetric currents were used as experimental variable to indicate the relaxation occurring in PAn films deposited electrochemically on the Pt electrode surface. The dependence of SR on polymer film thickness, waiting potential, and mobility of the doped anion was investigated. Percolation threshold potential for heteropolyanion doped PAn was estimated to be between 150 and 200 mV depending on polymer thickness on the electrode surface. A new model of the conducting to insulating conversion is described by the percolation theory and mobility gap changes during the process.
Relaxation time estimation in surface NMR
Energy Technology Data Exchange (ETDEWEB)
Grunewald, Elliot D.; Walsh, David O.
2017-03-21
NMR relaxation time estimation methods and corresponding apparatus generate two or more alternating current transmit pulses with arbitrary amplitudes, time delays, and relative phases; apply a surface NMR acquisition scheme in which initial preparatory pulses, the properties of which may be fixed across a set of multiple acquisition sequence, are transmitted at the start of each acquisition sequence and are followed by one or more depth sensitive pulses, the pulse moments of which are varied across the set of multiple acquisition sequences; and apply processing techniques in which recorded NMR response data are used to estimate NMR properties and the relaxation times T.sub.1 and T.sub.2* as a function of position as well as one-dimensional and two-dimension distributions of T.sub.1 versus T.sub.2* as a function of subsurface position.
Multi-region relaxed magnetohydrodynamics with flow
Dennis, G R; Dewar, R L; Hole, M J
2014-01-01
We present an extension of the multi-region relaxed magnetohydrodynamics (MRxMHD) equilibrium model that includes plasma flow. This new model is a generalization of Woltjer's model of relaxed magnetohydrodynamics equilibria with flow. We prove that as the number of plasma regions becomes infinite our extension of MRxMHD reduces to ideal MHD with flow. We also prove that some solutions to MRxMHD with flow are not time-independent in the laboratory frame, and instead have 3D structure which rotates in the toroidal direction with fixed angular velocity. This capability gives MRxMHD potential application to describing rotating 3D MHD structures such as 'snakes' and long-lived modes.
Multi-region relaxed magnetohydrodynamics with flow
Energy Technology Data Exchange (ETDEWEB)
Dennis, G. R., E-mail: graham.dennis@anu.edu.au; Dewar, R. L.; Hole, M. J. [Research School of Physics and Engineering, Australian National University, ACT 0200 (Australia); Hudson, S. R. [Princeton Plasma Physics Laboratory, PO Box 451, Princeton, New Jersey 08543 (United States)
2014-04-15
We present an extension of the multi-region relaxed magnetohydrodynamics (MRxMHD) equilibrium model that includes plasma flow. This new model is a generalization of Woltjer's model of relaxed magnetohydrodynamics equilibria with flow. We prove that as the number of plasma regions becomes infinite, our extension of MRxMHD reduces to ideal MHD with flow. We also prove that some solutions to MRxMHD with flow are not time-independent in the laboratory frame, and instead have 3D structure which rotates in the toroidal direction with fixed angular velocity. This capability gives MRxMHD potential application to describing rotating 3D MHD structures such as 'snakes' and long-lived modes.
Braided magnetic fields: equilibria, relaxation and heating
Pontin, D I; Russell, A J B; Hornig, G
2015-01-01
We examine the dynamics of magnetic flux tubes containing non-trivial field line braiding (or linkage), using mathematical and computational modelling. The key results obtained from recent modelling efforts are summarised, in the context of testable predictions for the laboratory. We discuss the existence of braided force-free equilibria, and demonstrate that for a field anchored at perfectly-conducting plates, these equilibria exist and contain current sheets whose thickness scales inversely with the braid complexity - as measured for example by the topological entropy. By contrast, for a periodic domain braided exact equilibria typically do not exist, while approximate equilibria contain thin current sheets. In the presence of resistivity, reconnection is triggered at the current sheets and a turbulent relaxation ensues. We discuss the properties of this relaxation, and in particular the existence of constraints that may mean that the final state is not the linear force-free field predicted by Taylor's hypo...
Relaxation matching algorithm for moving photogrammetry
Guo, Lei; Liu, Ke; Miao, Yinxiao; Zhu, Jigui
2015-02-01
Moving photogrammetry is an application of close range photogrammetry in industrial measurement to realize threedimensional coordinate measurement within large-scale volume. This paper describes an approach of relaxation matching algorithm applicable to moving photogrammetry according to the characteristics of accurate matching result of different measuring images. This method uses neighborhood matching support to improve the matching rate after coarse matching based on epipolar geometry constraint and precise matching using three images. It reflects the overall matching effect of all points, that means when a point is matched correctly, the matching results of those points round it must be correct. So for one point considered, the matching results of points round it are calculated to judge whether its result is correct. Analysis indicates that relaxation matching can eliminate the mismatching effectively and acquire 100% rate of correct matching. It will play a very important role in moving photogrammetry to ensure the following implement of ray bundle adjustment.
Relaxation and Diffusion for the Kicked Rotor
Khodas, M A
2000-01-01
The dynamics of the kicked-rotor, that is a paradigm for a mixed system, where the motion in some parts of phase space is chaotic and in other parts is regular is studied statistically. The evolution (Frobenius-Perron) operator of phase space densities in the chaotic component is calculated in presence of noise, and the limit of vanishing noise is taken is taken in the end of calculation. The relaxation rates (related to the Ruelle resonances) to the invariant equilibrium density are calculated analytically within an approximation that improves with increasing stochasticity. The results are tested numerically. The global picture of relaxation to the equilibrium density in the chaotic component when the system is bounded and of diffusive behavior when it is unbounded is presented.
Modeling Aftershocks as a Stretched Exponential Relaxation
Mignan, Arnaud
2015-01-01
The decay rate of aftershocks has been modeled as a power law since the pioneering work of Omori in the late nineteenth century. Considered the second most fundamental empirical law after the Gutenberg-Richter relationship, the power law paradigm has rarely been challenged by the seismological community. By taking a view of aftershock research not biased by prior conceptions of Omori power law decay and by applying statistical methods recommended in applied mathematics, I show that all aftershock sequences tested in three regional earthquake catalogs (Southern and Northern California, Taiwan) and with three declustering techniques (nearest-neighbor, second-order moment, window methods) follow a stretched exponential instead of a power law. These results infer that aftershocks are due to a simpler relaxation process than originally thought, in accordance with most other relaxation processes observed in Nature.
Relaxation in Technique Leading to New Beginnings().
Koritar, Endre
2016-12-01
This paper explores how standard analytic technique may result in a repetition of past traumatic experiences in the transference and countertransference analytic situation. Relaxation and elasticity of technique can lead to re-integration of previously fragmented ego functions, and in remembering and re-experiencing of previously repressed symbolic representations of fragmenting past traumatic experiences, resulting in neocatharsis and working through, thus healing wounds and scars sustained in self development. This healing process will be described through a detailed depiction of an analytic process introducing relaxation of technique, in a response by the analyst, to the patient's Orpha (self-protective) function. Responsiveness to the patient's implicitly or explicitly expressed needs, in the analytic space, may require a departure from standard technique for a deeper level of dynamic work where symbolization of unrepresented emotional experiences becomes possible.
Adaptive and Nonlinear Control
1992-02-29
in [22], we also applied the concept of zero dynamics to the problem of exact linearization of a nonlinear control system by dynamic feedback. Exact ...nonlinear systems, although it was well-known that the conditions for exact linearization are very stringent and consequently do not apply to a broad...29th IEEE Conference n Decision and Control, Invited Paper delivered by Dr. Gilliam. Exact Linearization of Zero Dynamics, 29th IEEE Conference on
Nonlinear Optics and Turbulence
1992-10-01
currently at Queen Mary College, London Patrick Dunne, (Ph.D., 1987, M.I.T., Hydrodynamic Stability, Nonlinear Waves), 1987-1988. Alecsander Dyachenko...U I I I U I I 3 9 3 V. BIOGRAPHIES A. FACULTY BRUCE BAYLY, 31, Ph.D. 1986, Princeton University. Postdoctoral visiting member 1986-88 at Courant...Caputo, A. C. Newell, and M. Shelley , "Nonlinear Wave Propagation Through a Random Medium and Soliton Tunneling", Integrable Systems and
RELAXATION TIME LIMITS PROBLEM FOR HYDRODYNAMIC MODELS IN SEMICONDUCTOR SCIENCE
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this article, two relaxation time limits, namely, the momentum relaxation time limit and the energy relaxation time limit are considered. By the compactness argument, it is obtained that the smooth solutions of the multidimensional nonisentropic Euler-Poisson problem converge to the solutions of an energy transport model or a drift diffusion model, respectively, with respect to different time scales.
Relaxation Techniques for Handicapped Children: A Review of Literature.
Zipkin, Dvora
1985-01-01
The paper discusses four major relaxation training approaches used with handicapped children: progressive muscle relaxation, biofeedback, yoga, and mental relaxation, which includes guided fantasy, imagery, and meditation. Descriptions of these techniques, the effects of their use with various populations, and reviews of recent studies of their…
Relaxation Criteria for Iterated Traffic Simulations
Kelly, Terence; Nagel, Kai
Iterative transportation microsimulations adjust traveler route plans by iterating between a microsimulation and a route planner. At each iteration, the route planner adjusts individuals' route choices based on the preceding microsimulations. Empirically, this process yields good results, but it is usually unclear when to stop the iterative process when modeling real-world traffic. This paper investigates several criteria to judge relaxation of the iterative process, emphasizing criteria related to traveler decision-making.
Dimension reduction for systems with slow relaxation
Venkataramani, Shankar C; Restrepo, Juan M
2016-01-01
We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model reduction, and build a mathematical framework for analyzing the reduced models. We introduce the notions of universal and asymptotic filters to characterize `optimal' model reductions. We discuss how our methods apply to the practically important problem of modeling oil spills.
p-q growth via relaxation methods
Directory of Open Access Journals (Sweden)
Irene Benedetti
2004-01-01
Full Text Available Local Lipschitz continuity of local minimizers of vectorial integrals ∫Ω f(x,Dudx is proved when f satisfies p-q growth condition and ξ↦f(x,ξ is not convex. The uniform convexity and the radial structure condition with respect to the last variable are assumed only at infinity. In the proof, we use semicontinuity and relaxation results for functionals with nonstandard growth.
Models of Flux Tubes from Constrained Relaxation
Indian Academy of Sciences (India)
Α. Mangalam; V. Krishan
2000-09-01
We study the relaxation of a compressible plasma to an equilibrium with flow. The constraints of conservation of mass, energy, angular momentum, cross-helicity and relative magnetic helicity are imposed. Equilibria corresponding to the energy extrema while conserving these invariants for parallel flows yield three classes of solutions and one of them with an increasing radial density profile, relevant to solar flux tubes is presented.
Active nematic gels as active relaxing solids
Turzi, Stefano S
2017-01-01
I put forward a continuum theory for active nematic gels, defined as fluids or suspensions of orientable rodlike objects endowed with active dynamics, that is based on symmetry arguments and compatibility with thermodynamics. The starting point is our recent theory that models (passive) nematic liquid crystals as relaxing nematic elastomers. The interplay between viscoelastic response and active dynamics of the microscopic constituents is naturally taken into account. By contrast with standar...
Relaxation time measurements by an electronic method.
Brousseau, R.; Vanier, J.
1973-01-01
Description of a simple electronic system that permits the direct measurement of time constants of decaying signals. The system was used in connection with relaxation experiments on hydrogen and rubidium masers and was found to operate well. The use of a computing counter in the systems gives the possibility of making averages on several experiments and obtaining the standard deviation of the results from the mean. The program for the computing counter is given.
Controlling spin relaxation with a cavity
Bienfait, A.; Pla, J. J.; Kubo, Y.; Zhou, X.; Stern, M.; Lo, C. C.; Weis, C. D.; Schenkel, T.; Vion, D.; Esteve, D.; Morton, J. J. L.; Bertet, P.
2016-03-01
Spontaneous emission of radiation is one of the fundamental mechanisms by which an excited quantum system returns to equilibrium. For spins, however, spontaneous emission is generally negligible compared to other non-radiative relaxation processes because of the weak coupling between the magnetic dipole and the electromagnetic field. In 1946, Purcell realized that the rate of spontaneous emission can be greatly enhanced by placing the quantum system in a resonant cavity. This effect has since been used extensively to control the lifetime of atoms and semiconducting heterostructures coupled to microwave or optical cavities, and is essential for the realization of high-efficiency single-photon sources. Here we report the application of this idea to spins in solids. By coupling donor spins in silicon to a superconducting microwave cavity with a high quality factor and a small mode volume, we reach the regime in which spontaneous emission constitutes the dominant mechanism of spin relaxation. The relaxation rate is increased by three orders of magnitude as the spins are tuned to the cavity resonance, demonstrating that energy relaxation can be controlled on demand. Our results provide a general way to initialize spin systems into their ground state and therefore have applications in magnetic resonance and quantum information processing. They also demonstrate that the coupling between the magnetic dipole of a spin and the electromagnetic field can be enhanced up to the point at which quantum fluctuations have a marked effect on the spin dynamics; as such, they represent an important step towards the coherent magnetic coupling of individual spins to microwave photons.
Yang, Qianli; Pitkow, Xaq
2015-03-01
Most interesting natural sensory stimuli are encoded in the brain in a form that can only be decoded nonlinearly. But despite being a core function of the brain, nonlinear population codes are rarely studied and poorly understood. Interestingly, the few existing models of nonlinear codes are inconsistent with known architectural features of the brain. In particular, these codes have information content that scales with the size of the cortical population, even if that violates the data processing inequality by exceeding the amount of information entering the sensory system. Here we provide a valid theory of nonlinear population codes by generalizing recent work on information-limiting correlations in linear population codes. Although these generalized, nonlinear information-limiting correlations bound the performance of any decoder, they also make decoding more robust to suboptimal computation, allowing many suboptimal decoders to achieve nearly the same efficiency as an optimal decoder. Although these correlations are extremely difficult to measure directly, particularly for nonlinear codes, we provide a simple, practical test by which one can use choice-related activity in small populations of neurons to determine whether decoding is suboptimal or optimal and limited by correlated noise. We conclude by describing an example computation in the vestibular system where this theory applies. QY and XP was supported by a grant from the McNair foundation.
Nonlinear Multiantenna Detection Methods
Directory of Open Access Journals (Sweden)
Chen Sheng
2004-01-01
Full Text Available A nonlinear detection technique designed for multiple-antenna assisted receivers employed in space-division multiple-access systems is investigated. We derive the optimal solution of the nonlinear spatial-processing assisted receiver for binary phase shift keying signalling, which we refer to as the Bayesian detector. It is shown that this optimal Bayesian receiver significantly outperforms the standard linear beamforming assisted receiver in terms of a reduced bit error rate, at the expense of an increased complexity, while the achievable system capacity is substantially enhanced with the advent of employing nonlinear detection. Specifically, when the spatial separation expressed in terms of the angle of arrival between the desired and interfering signals is below a certain threshold, a linear beamformer would fail to separate them, while a nonlinear detection assisted receiver is still capable of performing adequately. The adaptive implementation of the optimal Bayesian detector can be realized using a radial basis function network. Two techniques are presented for constructing block-data-based adaptive nonlinear multiple-antenna assisted receivers. One of them is based on the relevance vector machine invoked for classification, while the other on the orthogonal forward selection procedure combined with the Fisher ratio class-separability measure. A recursive sample-by-sample adaptation procedure is also proposed for training nonlinear detectors based on an amalgam of enhanced -means clustering techniques and the recursive least squares algorithm.
Nonlinear systems in medicine.
Higgins, John P
2002-01-01
Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states.
Effect of relaxation on adiabatic following
Energy Technology Data Exchange (ETDEWEB)
Nayfeh, M.H.
1976-09-01
A solution is presented for the damped optical Bloch equations under the excitation of a smooth pulse by first deriving three independent third-order equations of the Bloch vector components. Each equation is reduced to quadratures by assuming that the logarithmic time derivative of the field amplitude is small compared to the Rabi frequency. This results in an approximate summation of the infinite-order time-dependent perturbation in the field amplitude. The relaxation-dependent induced damping of the population inversion is calculated. Also calculated are additional relaxation-dependent contributions to the intensity-dependent refractive index. The time-integrated intensity contribution tends to cause line asymmetry, which becomes, at later times, linear in ..gamma../sub 2/ when ..gamma../sub 2/ very-much-greater-than ..gamma../sub 1/ and zero when 2..gamma../sub 2/ = ..gamma../sub 1/, where ..gamma../sub 1/ and ..gamma../sub 2/ are the atomic energy and phase-changing relaxations, respectively. The dependence of the spectral broadening on pulse length, pressure, and length of the sample is discussed. (AIP)
Graph Matching: Relax at Your Own Risk.
Lyzinski, Vince; Fishkind, Donniell E; Fiori, Marcelo; Vogelstein, Joshua T; Priebe, Carey E; Sapiro, Guillermo
2016-01-01
Graph matching-aligning a pair of graphs to minimize their edge disagreements-has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and connectomics. Its attention can be partially attributed to its computational difficulty. Although many heuristics have previously been proposed in the literature to approximately solve graph matching, very few have any theoretical support for their performance. A common technique is to relax the discrete problem to a continuous problem, therefore enabling practitioners to bring gradient-descent-type algorithms to bear. We prove that an indefinite relaxation (when solved exactly) almost always discovers the optimal permutation, while a common convex relaxation almost always fails to discover the optimal permutation. These theoretical results suggest that initializing the indefinite algorithm with the convex optimum might yield improved practical performance. Indeed, experimental results illuminate and corroborate these theoretical findings, demonstrating that excellent results are achieved in both benchmark and real data problems by amalgamating the two approaches.
Cortex phellodendri Extract Relaxes Airway Smooth Muscle
Directory of Open Access Journals (Sweden)
Qiu-Ju Jiang
2016-01-01
Full Text Available Cortex phellodendri is used to reduce fever and remove dampness and toxin. Berberine is an active ingredient of C. phellodendri. Berberine from Argemone ochroleuca can relax airway smooth muscle (ASM; however, whether the nonberberine component of C. phellodendri has similar relaxant action was unclear. An n-butyl alcohol extract of C. phellodendri (NBAECP, nonberberine component was prepared, which completely inhibits high K+- and acetylcholine- (ACH- induced precontraction of airway smooth muscle in tracheal rings and lung slices from control and asthmatic mice, respectively. The contraction induced by high K+ was also blocked by nifedipine, a selective blocker of L-type Ca2+ channels. The ACH-induced contraction was partially inhibited by nifedipine and pyrazole 3, an inhibitor of TRPC3 and STIM/Orai channels. Taken together, our data demonstrate that NBAECP can relax ASM by inhibiting L-type Ca2+ channels and TRPC3 and/or STIM/Orai channels, suggesting that NBAECP could be developed to a new drug for relieving bronchospasm.
Probing relaxation times in graphene quantum dots
Volk, Christian; Neumann, Christoph; Kazarski, Sebastian; Fringes, Stefan; Engels, Stephan; Haupt, Federica; Müller, André; Stampfer, Christoph
2013-01-01
Graphene quantum dots are attractive candidates for solid-state quantum bits. In fact, the predicted weak spin-orbit and hyperfine interaction promise spin qubits with long coherence times. Graphene quantum dots have been extensively investigated with respect to their excitation spectrum, spin-filling sequence and electron-hole crossover. However, their relaxation dynamics remain largely unexplored. This is mainly due to challenges in device fabrication, in particular concerning the control of carrier confinement and the tunability of the tunnelling barriers, both crucial to experimentally investigate decoherence times. Here we report pulsed-gate transient current spectroscopy and relaxation time measurements of excited states in graphene quantum dots. This is achieved by an advanced device design that allows to individually tune the tunnelling barriers down to the low megahertz regime, while monitoring their asymmetry. Measuring transient currents through electronic excited states, we estimate a lower bound for charge relaxation times on the order of 60–100 ns. PMID:23612294
Tension and relaxation in the individual.
Newbury, C R
1979-06-01
Increasing materialism in society is resulting in more wide spread nervous tension in all age groups. While some degree of nervous tension is necessary in everyday living, its adverse effects require that we must learn to bring it under control. Total tension is shown to have two components: a controllable element arising from factors in the environment and the inbuilt uncontrollable residue which is basic in the individual temperament. The effects of excessive or uncontrolled stress can be classified as 1) emotional reactions such as neurotic behaviour (anxiety hypochondria, hysteria, phobia, depression obsessions and compulsions) or psychotic behaviour and 2) psychosomatic reactions (nervous asthma, headache, insomnia, heart attack). Nervous energy can be wastefully expended by such factors as loss of temper, wrong attitudes to work, job frustration and marital strains. Relaxation is the only positive way to control undesirable nervous tension and its techniques require to be learned. A number of techniques (progressive relaxation, differential relaxation, hypnosis, the use of biofeedback, Yoga and Transcendental Meditation) are described and their application to dental practice is discussed.
Relaxation strategies for patients during dermatologic surgery.
Shenefelt, Philip D
2010-07-01
Patient stress and anxiety are common preoperatively and during dermatologic procedures and surgeries. Stress and anxiety can occasionally interfere with performance of procedures or surgery and can induce hemodynamic instability, such as elevated blood pressure or syncope, as well as producing considerable discomfort for some patients. Detection of excess stress and anxiety in patients can allow the opportunity for corrective or palliative measures. Slower breathing, biofeedback, progressive muscular relaxation, guided imagery, hypnosis, meditation and music can help calm and rebalance the patient's autonomic nervous system and immune functioning. Handheld miniaturized heart rate variability biofeedback devices are now available. The relaxation response can easily be taught. Guided imagery can be recorded or live. Live rapid induction hypnosis followed by deepening and then self-guided imagery requires no experience on the part of the patient but does require training and experience on the part of a provider. Recorded hypnosis inductions may also be used. Meditation generally requires more prior experience and training, but is useful when the patient already is skilled in it. Live, guided meditation or meditation recordings may be used. Relaxing recorded music from speakers or headphones or live performance music may also be employed to ease discomfort and improve the patient's attitude for dermatologic procedures and surgeries.
Ideal relaxation of the Hopf fibration
Smiet, Christopher Berg; Candelaresi, Simon; Bouwmeester, Dirk
2017-07-01
Ideal magnetohydrodynamics relaxation is the topology-conserving reconfiguration of a magnetic field into a lower energy state where the net force is zero. This is achieved by modeling the plasma as perfectly conducting viscous fluid. It is an important tool for investigating plasma equilibria and is often used to study the magnetic configurations in fusion devices and astrophysical plasmas. We study the equilibrium reached by a localized magnetic field through the topology conserving relaxation of a magnetic field based on the Hopf fibration in which magnetic field lines are closed circles that are all linked with one another. Magnetic fields with this topology have recently been shown to occur in non-ideal numerical simulations. Our results show that any localized field can only attain equilibrium if there is a finite external pressure, and that for such a field a Taylor state is unattainable. We find an equilibrium plasma configuration that is characterized by a lowered pressure in a toroidal region, with field lines lying on surfaces of constant pressure. Therefore, the field is in a Grad-Shafranov equilibrium. Localized helical magnetic fields are found when plasma is ejected from astrophysical bodies and subsequently relaxes against the background plasma, as well as on earth in plasmoids generated by, e.g., a Marshall gun. This work shows under which conditions an equilibrium can be reached and identifies a toroidal depression as the characteristic feature of such a configuration.
Handbook of nonlinear optical crystals
Dmitriev, Valentin G; Nikogosyan, David N
1991-01-01
This Handbook of Nonlinear Optical Crystals provides a complete description of the properties and applications of nonlinear crystals In addition, it presents the most important equations for calculating the main parameters of nonlinear frequency converters This comprehensive reference work will be of great value to all scientists and engineers working in nonlinear optics, quantum electronics and laser physics
Interpreting the nonlinear dielectric response of glass-formers in terms of the coupling model
Energy Technology Data Exchange (ETDEWEB)
Ngai, K. L. [CNR-IPCF, Largo Bruno Pontecorvo 3, I-56127 Pisa, Italy and Dipartimento di Fisica, Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa (Italy)
2015-03-21
Nonlinear dielectric measurements at high electric fields of glass-forming glycerol and propylene carbonate initially were carried out to elucidate the dynamic heterogeneous nature of the structural α-relaxation. Recently, the measurements were extended to sufficiently high frequencies to investigate the nonlinear dielectric response of faster processes including the so-called excess wing (EW), appearing as a second power law at high frequencies in the loss spectra of many glass formers without a resolved secondary relaxation. While a strong increase of dielectric constant and loss is found in the nonlinear dielectric response of the α-relaxation, there is a lack of significant change in the EW. A surprise to the experimentalists finding it, this difference in the nonlinear dielectric properties between the EW and the α-relaxation is explained in the framework of the coupling model by identifying the EW investigated with the nearly constant loss (NCL) of caged molecules, originating from the anharmonicity of the intermolecular potential. The NCL is terminated at longer times (lower frequencies) by the onset of the primitive relaxation, which is followed sequentially by relaxation processes involving increasing number of molecules until the terminal Kohlrausch α-relaxation is reached. These intermediate faster relaxations, combined to form the so-called Johari-Goldstein (JG) β-relaxation, are spatially and dynamically heterogeneous, and hence exhibit nonlinear dielectric effects, as found in glycerol and propylene carbonate, where the JG β-relaxation is not resolved and in D-sorbitol where it is resolved. Like the linear susceptibility, χ{sub 1}(f), the frequency dispersion of the third-order dielectric susceptibility, χ{sub 3}(f), was found to depend primarily on the α-relaxation time, and independent of temperature T and pressure P. I show this property of the frequency dispersions of χ{sub 1}(f) and χ{sub 3}(f) is the characteristic of the many
Nonlinear Approaches in Engineering Applications
Jazar, Reza
2012-01-01
Nonlinear Approaches in Engineering Applications focuses on nonlinear phenomena that are common in the engineering field. The nonlinear approaches described in this book provide a sound theoretical base and practical tools to design and analyze engineering systems with high efficiency and accuracy and with less energy and downtime. Presented here are nonlinear approaches in areas such as dynamic systems, optimal control and approaches in nonlinear dynamics and acoustics. Coverage encompasses a wide range of applications and fields including mathematical modeling and nonlinear behavior as applied to microresonators, nanotechnologies, nonlinear behavior in soil erosion,nonlinear population dynamics, and optimization in reducing vibration and noise as well as vibration in triple-walled carbon nanotubes. This book also: Provides a complete introduction to nonlinear behavior of systems and the advantages of nonlinearity as a tool for solving engineering problems Includes applications and examples drawn from the el...
Lehrer, Paul M.
1978-01-01
Compared physiological effects of progressive relaxation, alpha feedback, and a no-treatment condition. Nonpatients showed more psychophysiological habituation than patients in response to hearing very loud tones and to reaction time tasks. Patients showed greater physiological response to relaxation than nonpatients. After relaxation, autonomic…
Relaxation of a highly deformed elastic filament at a fluid interface
Prasath, S Ganga; Govindarajan, Rama; Menon, Narayanan
2016-01-01
We perform experiments to investigate the relaxation of a highly deformed elastic filament at a liquid-air interface. The dynamics for filaments of differing length, diameter and elastic modulus collapse to a single curve when the time-dependence is scaled by a time scale $\\tau = 8 \\pi \\mu L_o^4/B$. The relaxation, however, is completed in a very small fraction of the time $\\tau$. Even though the time scale $\\tau$ can be obtained by balancing the linear bending and viscous forces, it appears to control the highly nonlinear regime of our experiments. Nonlinear numerical simulations show that the force due to tension along the filament is comparable to the bending force, producing a net elastic restoring force that is much smaller than either term. We perform particle image velocimetry at the liquid-air interface to support the results of the numerics. Finally, we find that when the filament is initialized in asymmetric shapes, it rapidly goes to a shape with symmetric stresses. This symmetrisation process is e...
LOW-FREQUENCY DIELECTRIC RELAXATION IN SILVER STEARATE LAYERS
Directory of Open Access Journals (Sweden)
Smirnov, A.P.
2016-05-01
Full Text Available The low-frequency dielectric relaxation process in silver stearate layers was studied. The increasing of dielectric permittivity with frequency decreasing and temperature increasing in studied sample are associated with the dipole-relaxation polarization mechanisms. The dispersion of loss factor could be connected with the contribution of relaxation mechanism and conductivity. The shape of the Cole-Cole diagram shows that silver stearate is a non-Debye dielectric material characterized by a wide distribution of relaxators, according to the Cole-Cole relaxation model.
Effects of different "relaxing" music styles on the autonomic nervous system.
Perez-Lloret, Santiago; Diez, Joaquín; Domé, María Natalia; Delvenne, Andrea Alvarez; Braidot, Nestor; Cardinali, Daniel P; Vigo, Daniel Eduardo
2014-01-01
The objective of this study was to assess the effects on heart rate variability (HRV) of exposure to different styles of "relaxing" music. Autonomic responses to musical stimuli were correlated with subjective preferences regarding the relaxing properties of each music style. Linear and nonlinear HRV analysis was conducted in 25 healthy subjects exposed to silence or to classical, new age or romantic melodies in a random fashion. At the end of the study, subjects were asked to choose the melody that they would use to relax. The low-to-high-frequency ratio was significantly higher when subjects were exposed to "new age" music when compared with silence (3.4 ± 0.3 vs. 2.6 ± 0.3, respectively, P romantic" melodies (2.1 ± 0.4 and 2.2 ± 0.3). These results were related to a reduction in the high frequency component with "new age" compared to silence (17.4 ± 1.9 vs. 23.1 ± 1.1, respectively P music induced a shift in HRV from higher to lower frequencies, independently on the music preference of the listener.
Goldberger, Ary L.; Bhargava, Valmik; West, Bruce J.; Mandell, Arnold J.
1985-10-01
Changing the coupling of electronic relaxation oscillators may be associated with the emergence of complex periodic behavior. The electrocardiographic record of a patient with the “sick sinus syndrome” demonstrated periodic behavior including subharmonic bifurcations in an attractor of his interbeat interval. Such nonlinear dynamics which may emerge from alterations in the coupling of oscillating pacemakers are not predicted by traditional models in cardiac electrophysiology. An understanding of the nonlinear behavior of physical and mathematical systems may generalize to pathophysiological processes.
Two-Level Dipolar System in a Heat Bath: High-Pump Power Effects in the Nonlinear Optical Responses
Paz, J. L.; León-Torres, J. R.; Lascano, Luis; Alvarado, Ysaias J.; Costa-Vera, Cesar
2017-06-01
Using the four-wave mixing spectroscopy, we analyze the nonlinear optical properties in a strongly driven two-level system, using a perturbative treatment where, the pump field is considered at all orders, second order in the probe, and first order for the signal field, when the stochastic effects of the solvent are considered. Significant variations in the nonlinear optical properties due mainly to changes in the probe intensity, chemical concentrations, and transversal relaxation times are observed.
Magneto-dependent stress relaxation of magnetorheological gels
Xu, Yangguang
2017-09-01
The stress relaxation behaviors of magnetorheological (MR) gels under stepwise shear loading are systematically investigated. The particle-enhanced effect, the magneto-induced effect, and the temperature-enhanced effect on the stress relaxation of MR gels are discussed. For further analysis of the magneto-induced stress relaxation mechanism in MR gels, a phenomenological model is established to describe the stress relaxation behavior of the matrix and the magnetic particle chains. All characteristic parameters introduced in the model, i.e. relaxation time, instantaneous modulus, and stable modulus, have well-defined physical meanings and are fitted based on the experimental results. The influence of each parameter on the macroscopic response is discussed and it is found that the relaxation stress induced by the magneto-mechanical coupling effect plays an important role in the stress relaxation process of MR gels.
Wölfle, Stephanie E; Chaston, Daniel J; Goto, Kenichi; Sandow, Shaun L; Edwards, Frank R; Hill, Caryl E
2011-05-15
Blood flow is adjusted to tissue demand through rapidly ascending vasodilatations resulting from conduction of hyperpolarisation through vascular gap junctions. We investigated how these dilatations can spread without attenuation if mediated by an electrical signal. Cremaster muscle arterioles were studied in vivo by simultaneously measuring membrane potential and vessel diameter. Focal application of acetylcholine elicited hyperpolarisations which decayed passively with distance from the local site,while dilatation spread upstream without attenuation. Analysis of simultaneous recordings at the local site revealed that hyperpolarisation and dilatation were only linearly related over a restricted voltage range to a threshold potential, beyond which dilatation was maximal. Experimental data could be simulated in a computational model with electrotonic decay of hyperpolarisation but imposition of this threshold. The model was tested by reducing the amplitude of the local hyperpolarisation which led to entry into the linear range closer to the local site and decay of dilatation. Serial section electron microscopy and light dye treatment confirmed that the spread of dilatation occurred through the endothelium and that the two cell layers were tightly coupled. Generality of the mechanism was demonstrated by applying the model to the attenuated propagation of dilatation found in larger arteries.We conclude that long distance spread of locally initiated dilatations is not due to a regenerative electrical phenomenon, but rather a restricted linear relationship between voltage and vessel tone, which minimises the impact of electrotonic decay of voltage. Disease-related alterations in endothelial coupling or ion channel expression could therefore decrease the ability to adjust blood flow to meet metabolic demand.
Nonlinear Stochastic Flutter of a Cantilever Wing with Joint Relaxation and Random Loading
2008-02-21
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A Numerical Study of Automated Dynamic Relaxation for Nonlinear Static Tensioned Structures.
1987-10-01
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Convergence of Chahine's nonlinear relaxation inversion method used for limb viewing remote sensing
Chu, W. P.
1985-01-01
The application of Chahine's (1970) inversion technique to remote sensing problems utilizing the limb viewing geometry is discussed. The problem considered here involves occultation-type measurements and limb radiance-type measurements from either spacecraft or balloon platforms. The kernel matrix of the inversion problem is either an upper or lower triangular matrix. It is demonstrated that the Chahine inversion technique always converges, provided the diagonal elements of the kernel matrix are nonzero.
Cariati, Elena; Ugo, Renato; Santoro, Giuseppe; Tordin, Elisa; Sorace, Lorenzo; Caneschi, Andrea; Sironi, Angelo; Macchi, Piero; Casati, Nicola
2010-12-06
New Co(II) members of the family of multifunctional materials of general formula [DAMS](4)[M(2)Co(C(2)O(4))(6)]·2DAMBA·2H(2)O (M(III) = Rh, Fe, Cr; DAMBA = para-dimethylaminobenzaldehyde and [DAMS(+)] = trans-4-(4-dimethylaminostyryl)-1-methylpyridinium) have been isolated and characterized. Such new hybrid mixed metal oxalates are isostructural with the previously investigated containing Zn(II), Mn(II), and Ni(II). This allows to preserve the exceptional second harmonic generation (SHG) activity, due to both the large molecular quadratic hyperpolarizability of [DAMS(+)] and the efficiency of the crystalline network which organizes [DAMS(+)] into head-to-tail arranged J-type aggregates, and to further tune the magnetic properties. In particular, the magnetic data of the Rh(III) derivative demonstrate that high spin octacoordinated Co(II) centers behave very similarly to the hexacoordinated Co(II) ones, being dominated by a large orbital contribution. The Cr(III) derivative is characterized by ferromagnetic Cr(III)-Co(II) interactions. Most relevantly, the Fe(III) compound is characterized by a moderate antiferromagnetic interaction between Fe(III) and Co(II), resulting in a ferrimagnetic like structure. Its low temperature dynamic magnetic properties were found to follow a thermally activated behavior (τ(0) = 8.6 × 10(-11) s and ΔE = 21.4 K) and make this a candidate for the second oxalate-based single chain magnet (SCM) reported up to date, a property which in this case is coupled to the second order non linear optical (NLO) ones.
Energy Technology Data Exchange (ETDEWEB)
Davis, C.G.
1990-01-01
The advent of nonlinear pulsation theory really coincides with the development of the large computers after the second world war. Christy and Stobbie were the first to make use of finite difference techniques on computers to model the bumps'' observed in the classical Cepheid light and velocity curves, the so-called Hertzsprung'' sequence. Following this work a more sophisticated analysis of the light and velocity curves from the models was made by Simon and Davis using Fourier techniques. Recently a simpler amplitude equation formalism has been developed that helps explain this resonance mechanism. The determination of Population I Cepheid masses by nonlinear methods will be discussed. For the lower mass objects, such as RR Lyrae and BL Her. stars, we find general agreement using evolutionary masses and nonlinear pulsation theory. An apparent difficulty of nonlinear pulsation theory occurs in the understanding of double'' mode pulsation, which will also be discussed. Recent studies in nonlinear pulsation theory have dealt with the question of mode selection, period doubling and the trends towards chaotic behavior such as is observed in the transition from W Virginis to RV Tauri-like stars. 10 refs., 1 fig., 2 tabs.
High Relaxivity Gd(III)–DNA Gold Nanostars: Investigation of Shape Effects on Proton Relaxation
Rotz, Matthew W.; Culver, Kayla S. B.; Parigi, Giacomo; MacRenaris, Keith W.; Luchinat, Claudio; Odom, Teri W.; Meade, Thomas J.
2015-01-01
Gadolinium(III) nanoconjugate contrast agents (CAs) have distinct advantages over their small-molecule counterparts in magnetic resonance imaging. In addition to increased Gd(III) payload, a significant improvement in proton relaxation efficiency, or relaxivity (r1), is often observed. In this work, we describe the synthesis and characterization of a nanoconjugate CA created by covalent attachment of Gd(III) to thiolated DNA (Gd(III)–DNA), followed by surface conjugation onto gold nanostars (DNA–Gd@stars). These conjugates exhibit remarkable r1 with values up to 98 mM−1 s−1. Additionally, DNA–Gd@stars show efficient Gd(III) delivery and biocompatibility in vitro and generate significant contrast enhancement when imaged at 7 T. Using nuclear magnetic relaxation dispersion analysis, we attribute the high performance of the DNA–Gd@stars to an increased contribution of second-sphere relaxivity compared to that of spherical CA equivalents (DNA–Gd@spheres). Importantly, the surface of the gold nanostar contains Gd(III)–DNA in regions of positive, negative, and neutral curvature. We hypothesize that the proton relaxation enhancement observed results from the presence of a unique hydrophilic environment produced by Gd(III)–DNA in these regions, which allows second-sphere water molecules to remain adjacent to Gd(III) ions for up to 10 times longer than diffusion. These results establish that particle shape and second-sphere relaxivity are important considerations in the design of Gd(III) nanoconjugate CAs. PMID:25723190
Lu, Zijie; Manias, Evangelos; MacDonald, Digby D.; Lanagan, Michael
2009-10-01
Dielectric spectra of dimethyl sulfoxide (DMSO)/water mixtures, over the entire concentration range, have been measured using the transmission line method at frequencies from 45 MHz to 26 GHz and at temperatures of 298-318 K. The relaxation times of the mixtures show a maximum at an intermediate molar fraction of DMSO. The specific structure of mixtures in different concentration regions was determined by the dielectric relaxation dynamics, obtained from the effect of temperature on the relaxation time. A water structure "breaking effect" is observed in dilute aqueous solutions. The average number of hydrogen bonds per water molecule in these mixtures is found to be reduced compared to pure water. The increase in the dielectric relaxation time in DMSO/water mixtures is attributed to the spatial (steric) constraints of DMSO molecules on the hydrogen-bond network, rather than being due to hydrophobic hydration of the methyl groups. The interaction between water and DMSO by hydrogen bonding reaches a maximum at a DMSO molar fraction of 0.33, reflected by the maximum activation enthalpy for dielectric relaxation in this concentration, suggesting the formation of a stoichiometric compound, H2O-DMSO-H2O. In highly concentrated solutions, negative activation entropies are observed, indicating the presence of aggregates of DMSO molecules. A distinct antiparallel arrangement of dipoles is obtained for neat DMSO in the liquid state according to the Kirkwood correlation factor (gK = 0.5), calculated from the static permittivity. The similarity of the dielectric behavior of pure DMSO and DMSO-rich mixtures suggests that dipole-dipole interactions contribute significantly to the rotational relaxation process in these solutions.
Nonlinear damping effects in spin torque dynamics of magnetic tunnel junctions
Barsukov, Igor; Chen, Yu-Jin; Lee, Han Kyu; Goncalves, Alexandre; Katine, Jordan; Arias, Rodrigo; Ivanov, Boris; Krivorotov, Ilya
2015-03-01
Performance of nanoscale spin torque devices such as memory (STT-MRAM) and auto-oscillators critically depends on magnetic relaxation. It is commonly assumed that magnetization dynamics in the presence of spin torque can be understood as simple competition between antidamping arising from spin torque and Gilbert damping of the free layer. However our experiments reveal that the situation is more complex and that nonlinear damping processes in the free layer of magnetic tunnel junction (MTJ) nanopillars can strongly alter spin torque driven dynamics. We study elliptical MTJ nanopillars with in-plane magnetizations of the free layer and SAF layers by spin torque ferromagnetic resonance. We find an excitation spectrum associated with standing spin waves of the free layer. By varying the external field, the energy of a higher-order spin wave mode becomes twice the energy of the main mode. This opens up a nonlinear, resonant relaxation channel, giving rise to a damping increase of approximately 20 percent. With increasing spin torque provided by a DC bias current, we find that this relaxation channel competes with antidamping in a nonlinear manner, increasingly contributing to and even dominating the relaxation at subcritical currents.
Relaxation techniques for pain management in labour.
Smith, Caroline A; Levett, Kate M; Collins, Carmel T; Crowther, Caroline A
2011-12-07
Many women would like to avoid pharmacological or invasive methods of pain management in labour and this may contribute towards the popularity of complementary methods of pain management. This review examined currently available evidence supporting the use of relaxation therapies for pain management in labour. To examine the effects of relaxation methods for pain management in labour on maternal and perinatal morbidity. We searched the Cochrane Pregnancy and Childbirth Group's Trials Register (30 November 2010), The Cochrane Complementary Medicine Field's Trials Register (November 2011), the Cochrane Central Register of Controlled Trials (The Cochrane Library 2010, Issue 4), MEDLINE (1966 to 30 November 2010), CINAHL (1980 to 30 November 2010), the Australian and New Zealand Clinical Trial Registry (30 November 2010), Chinese Clinical Trial Register (30 November 2010), Current Controlled Trials (30 November 2010), ClinicalTrials.gov, (30 November 2010) ISRCTN Register (30 November 2010), National Centre for Complementary and Alternative Medicine (NCCAM) (30 November 2010) and the WHO International Clinical Trials Registry Platform (30 November 2010). Randomised controlled trials comparing relaxation methods with standard care, no treatment, other non-pharmacological forms of pain management in labour or placebo. Three review authors independently assessed trials for inclusion and extracted data. Data were checked for accuracy. Two review authors independently assessed trial quality. We attempted to contact study authors for additional information. We included 11 studies (1374 women) in the review. Relaxation was associated with a reduction in pain intensity during the latent phase (mean difference (MD) -1.25, 95% confidence interval (CI) -1.97 to -0.53, one trial, 40 women) and active phase of labour (MD -2.48, 95% CI -3.13 to 0.83, two trials, 74 women). There was evidence of improved outcomes from relaxation instruction with increased satisfaction with pain
Nonlinear elastic waves in materials
Rushchitsky, Jeremiah J
2014-01-01
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...
Nonlinear Dynamic Force Spectroscopy
Björnham, Oscar
2016-01-01
Dynamic force spectroscopy (DFS) is an experimental technique that is commonly used to assess information of the strength, energy landscape, and lifetime of noncovalent bio-molecular interactions. DFS traditionally requires an applied force that increases linearly with time so that the bio-complex under investigation is exposed to a constant loading rate. However, tethers or polymers can modulate the applied force in a nonlinear regime. For example, bacterial adhesion pili and polymers with worm-like chain properties are examples of structures that show nonlinear force responses. In these situations, the theory for traditional DFS cannot be readily applied. In this work we expand the theory for DFS to also include nonlinear external forces while still maintaining compatibility with the linear DFS theory. To validate the theory we modeled a bio-complex expressed on a stiff, an elastic and a worm-like chain polymer, using Monte Carlo methods, and assessed the corresponding rupture force spectra. It was found th...
Nonlinear optomechanical paddle nanocavities
Kaviani, Hamidreza; Wu, Marcelo; Ghobadi, Roohollah; Barclay, Paul E
2014-01-01
A photonic crystal optomechanical system combining strong nonlinear optomechanical coupling, low effective mass and large optical mode spacing is introduced. This nanoscale "paddle nanocavity" device supports mechanical resonances with effective mass of 300--600 fg which couple nonlinearly to co-localized optical modes with a quadratic optomechanical coupling coefficient $g^{(2)} > 2\\pi\\times400$ MHz/nm$^2$, and a two phonon to single photon optomechanical coupling rate $\\Delta \\omega_0 > 2\\pi\\times 16$ Hz. This coupling relies on strong phonon-photon interactions in a structure whose optical mode spectrum is highly non--degenerate. Simulations indicate that nonlinear optomechanical readout of thermally driven motion in these devices should be observable for T $> 50 $ mK, and that measurement of phonon shot noise is achievable.
Nonlinear dynamics of structures
Oller, Sergio
2014-01-01
This book lays the foundation of knowledge that will allow a better understanding of nonlinear phenomena that occur in structural dynamics. This work is intended for graduate engineering students who want to expand their knowledge on the dynamic behavior of structures, specifically in the nonlinear field, by presenting the basis of dynamic balance in non‐linear behavior structures due to the material and kinematics mechanical effects. Particularly, this publication shows the solution of the equation of dynamic equilibrium for structure with nonlinear time‐independent materials (plasticity, damage and frequencies evolution), as well as those time dependent non‐linear behavior materials (viscoelasticity and viscoplasticity). The convergence conditions for the non‐linear dynamic structure solution are studied, and the theoretical concepts and its programming algorithms are presented.
Nonlinear Photonic Crystal Fibers
DEFF Research Database (Denmark)
Hansen, Kim Per
2004-01-01
, leading to reduced mode confinement and dispersion flexibility. In this thesis, we treat the nonlinear photonic crystal fiber – a special sub-class of photonic crystal fibers, the core of which has a diameter comparable to the wavelength of the light guided in the fiber. The small core results in a large...... nonlinear coefficient and in various applications, it is therefore possible to reduce the required fiber lengths quite dramatically, leading to increased stability and efficiency. Furthermore, it is possible to design these fibers with zero-dispersion at previously unreachable wavelengths, paving the way...... for completely new applications, especially in and near the visible wavelength region. One such application is supercontinuum generation. Supercontinuum generation is extreme broadening of pulses in a nonlinear medium (in this case a small-core fiber), and depending on the dispersion of the fiber, it is possible...
Schmidt, Bruno E; Ernotte, Guilmot; Clerici, Matteo; Morandotti, Roberto; Ibrahim, Heide; Legare, Francois
2016-01-01
In the framework of linear optics, light fields do not interact with each other in a medium. Yet, when their field amplitude becomes comparable to the electron binding energies of matter, the nonlinear motion of these electrons emits new dipole radiation whose amplitude, frequency and phase differ from the incoming fields. Such high fields are typically achieved with ultra-short, femtosecond (1fs = 10-15 sec.) laser pulses containing very broad frequency spectra. Here, the matter not only couples incoming and outgoing fields but also causes different spectral components to interact and mix through a convolution process. In this contribution, we describe how frequency domain nonlinear optics overcomes the shortcomings arising from this convolution in conventional time domain nonlinear optics1. We generate light fields with previously inaccessible properties because the uncontrolled coupling of amplitudes and phases is turned off. For example, arbitrary phase functions are transferred linearly to the second har...
Nonlinear optomechanics with graphene
Shaffer, Airlia; Patil, Yogesh Sharad; Cheung, Hil F. H.; Wang, Ke; Vengalattore, Mukund
2016-05-01
To date, studies of cavity optomechanics have been limited to exploiting the linear interactions between the light and mechanics. However, investigations of quantum signal transduction, quantum enhanced metrology and manybody physics with optomechanics each require strong, nonlinear interactions. Graphene nanomembranes are an exciting prospect for realizing such studies due to their inherently nonlinear nature and low mass. We fabricate large graphene nanomembranes and study their mechanical and optical properties. By using dark ground imaging techniques, we correlate their eigenmode shapes with the measured dissipation. We study their hysteretic response present even at low driving amplitudes, and their nonlinear dissipation. Finally, we discuss ongoing efforts to use these resonators for studies of quantum optomechanics and force sensing. This work is supported by the DARPA QuASAR program through a Grant from the ARO.
Nonlinear Analysis of Buckling
Directory of Open Access Journals (Sweden)
Psotný Martin
2014-06-01
Full Text Available The stability analysis of slender web loaded in compression was presented. To solve this problem, a specialized computer program based on FEM was created. The nonlinear finite element method equations were derived from the variational principle of minimum of potential energy. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm was used. Corresponding levels of the total potential energy were defined. The peculiarities of the effects of the initial imperfections were investigated. Special attention was focused on the influence of imperfections on the post-critical buckling mode. The stable and unstable paths of the nonlinear solution were separated. Obtained results were compared with those gained using ANSYS system.
Nonlinear Metamaterials for Holography
Almeida, Euclides; Prior, Yehiam
2015-01-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multi-layer metamaterial holograms where by the nonlinear process of Third Harmonic Generation, a background free image is formed at a new frequency which is the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analyzed and prospects for future device applications are discussed.
Multidimensional nonlinear descriptive analysis
Nishisato, Shizuhiko
2006-01-01
Quantification of categorical, or non-numerical, data is a problem that scientists face across a wide range of disciplines. Exploring data analysis in various areas of research, such as the social sciences and biology, Multidimensional Nonlinear Descriptive Analysis presents methods for analyzing categorical data that are not necessarily sampled randomly from a normal population and often involve nonlinear relations. This reference not only provides an overview of multidimensional nonlinear descriptive analysis (MUNDA) of discrete data, it also offers new results in a variety of fields. The first part of the book covers conceptual and technical preliminaries needed to understand the data analysis in subsequent chapters. The next two parts contain applications of MUNDA to diverse data types, with each chapter devoted to one type of categorical data, a brief historical comment, and basic skills peculiar to the data types. The final part examines several problems and then concludes with suggestions for futu...
Smith, Jonathan C; Karmin, Aaron D
2002-12-01
This study examined idiosyncratic reality claims, that is, irrational or paranormal beliefs often claimed to enhance relaxation and happiness and reduce stress. The Smith Idiosyncratic Reality Claims Inventory and the Smith Relaxation Dispositions Inventory (which measures relaxation and stress dispositions, or enduring states of mind frequently associated with relaxation or stress) were given to 310 junior college student volunteers. Principal components factor analysis with varimax rotation identified five idiosyncratic reality claim factors: belief in Literal Christianity; Magic; Space Aliens: After Death experiences; and Miraculous Powers of Meditation, Prayer, and Belief. No factor correlated with increased relaxation dispositions Peace, Energy, or Joy, or reduced dispositional somatic stress, worry, or negative emotion on the Smith Relaxation Dispositions Inventory. It was concluded that idiosyncratic reality claims may not be associated with reported relaxation, happiness, or stress. In contrast, previous research strongly supported self-affirming beliefs with few paranormal assumptions display such an association.
Nonlinear airship aeroelasticity
Bessert, N.; Frederich, O.
2005-12-01
The aeroelastic derivatives for today's aircraft are calculated in the concept phase using a standard procedure. This scheme has to be extended for large airships, due to various nonlinearities in structural and aerodynamic behaviour. In general, the structural model of an airship is physically as well as geometrically nonlinear. The main sources of nonlinearity are large deformations and the nonlinear material behaviour of membranes. The aerodynamic solution is also included in the nonlinear problem, because the deformed airship influences the surrounding flow. Due to these nonlinearities, the aeroelastic problem for airships can only be solved by an iterative procedure. As one possibility, the coupled aerodynamic and structural dynamic problem was handled using linked standard solvers. On the structural side, the Finite-Element program package ABAQUS was extended with an interface to the aerodynamic solver VSAERO. VSAERO is based on the aerodynamic panel method using potential flow theory. The equilibrium of the internal structural and the external aerodynamic forces leads to the structural response and a trimmed flight state for the specified flight conditions (e.g. speed, altitude). The application of small perturbations around a trimmed state produces reaction forces and moments. These constraint forces are then transferred into translational and rotational acceleration fields by performing an inertia relief analysis of the disturbed structural model. The change between the trimmed flight state and the disturbed one yields the respective aeroelastic derivatives. By including the calculated derivatives in the linearised equation of motion system, it is possible to judge the stability and controllability of the investigated airship.
Structural relaxation in viscous metallic liquids
Energy Technology Data Exchange (ETDEWEB)
Meyer, A. [National Inst. of Standards and Technology (BFRL), Gaithersburg, MD (United States)]|[Technische Univ. Muenchen, Muenchen (Germany); Wuttke, J.; Petry, W. [Technische Univ. Muenchen, Muenchen (Germany); Schober, H. [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France); Randl, O.G. [Manufacture Michelin, Clermont-Ferrand (France)
1999-11-01
Recently, metallic alloys have been found that exhibit extremely large viscosities in the liquid state. These liquids can be quenched into bulk metallic glasses at relatively modest cooling rates. In contrast to simple metals the structural relaxation of these systems show a two step decay in the liquid state. This behaviour has long been known for molecular or ionic glass formers in their under-cooled liquid state. Applying an analysis previously used for the glass formers (mode-coupling theory) a full quantitative description of the neutron data is obtained for these metallic liquids. (authors) 3 refs., 2 figs.
Nondepolarizing relaxants: new concepts and new drugs.
Kopman, A
1993-01-01
Less than a decade ago, the only nondepolarizing neuromuscular blocking drugs available to the anesthetist were traditional long-acting drugs such as pancuronium and d-tubocurarine. The revolution that began 10 years ago in our use of relaxants promises to continue unabated into the next decade. Changes in our clinical use of these drugs will be sparked not just by the introduction of new drugs but also by a greater understanding of the pharmacokinetic/pharmacodynamic principles that govern onset and recovery.
Thermal Stress Relaxation of Nonhomogeneous Coatings
Institute of Scientific and Technical Information of China (English)
无
1999-01-01
Nonhomogeneous coatings (NCs) are new type of engineering structures that is not yet fully understood. One important aspect in the mechanical analysis of NCs is to determine the gradient distribution that creates the maximum thermal stress relaxation. This paper employs numerical analysis using the finite element metho d and experimental analysis using moire interference to study the stress distrib ution in NCs. Attention focused on the edge effect stresses in the coating/subst rate structures and their dependence on the different gradient distributions of this new kind of composite structure.
Reflexogenic relaxation gastroduodenography by the acupuncture method
Energy Technology Data Exchange (ETDEWEB)
Rabkin, I.Kh.; Tsibulyak, V.N.; Mnatsakyan, K.A.; Kondorskaya, I.L.; Galkina, T.V.
The communication is based upon the results of x-ray examination of the stomach and duodenum in 63 patients with stenoses of the pyloroduodenal zone, cicatrical deformities of the duodenal bulb, bulbar ulcer, duodenal organic lesions, and functional stenosis of the loop. First a routine X-ray examination of the stomach and duodenum was performed using barium-water mixture, then followed acupuncture aimed at hypotension in the definite points of the floor of the auricle where branches of the vagus innervating the stomach and duodenum are located. As distinct from pharmacological relaxation this method produces a purpose-oriented selective effect.
Compatible Relaxation and Coarsening in Algebraic Multigrid
Energy Technology Data Exchange (ETDEWEB)
Brannick, J J; Falgout, R D
2009-09-22
We introduce a coarsening algorithm for algebraic multigrid (AMG) based on the concept of compatible relaxation (CR). The algorithm is significantly different from standard methods, most notably because it does not rely on any notion of strength of connection. We study its behavior on a number of model problems, and evaluate the performance of an AMG algorithm that incorporates the coarsening approach. Lastly, we introduce a variant of CR that provides a sharper metric of coarse-grid quality and demonstrate its potential with two simple examples.
Relaxed Operational Semantics of Concurrent Programming Languages
Directory of Open Access Journals (Sweden)
Gustavo Petri
2012-08-01
Full Text Available We propose a novel, operational framework to formally describe the semantics of concurrent programs running within the context of a relaxed memory model. Our framework features a "temporary store" where the memory operations issued by the threads are recorded, in program order. A memory model then specifies the conditions under which a pending operation from this sequence is allowed to be globally performed, possibly out of order. The memory model also involves a "write grain," accounting for architectures where a thread may read a write that is not yet globally visible. Our formal model is supported by a software simulator, allowing us to run litmus tests in our semantics.
Strain modulations as a mechanism to reduce stress relaxation in laryngeal tissues.
Directory of Open Access Journals (Sweden)
Eric J Hunter
Full Text Available Vocal fold tissues in animal and human species undergo deformation processes at several types of loading rates: a slow strain involved in vocal fold posturing (on the order of 1 Hz or so, cyclic and faster posturing often found in speech tasks or vocal embellishment (1-10 Hz, and shear strain associated with vocal fold vibration during phonation (100 Hz and higher. Relevant to these deformation patterns are the viscous properties of laryngeal tissues, which exhibit non-linear stress relaxation and recovery. In the current study, a large strain time-dependent constitutive model of human vocal fold tissue is used to investigate effects of phonatory posturing cyclic strain in the range of 1 Hz to 10 Hz. Tissue data for two subjects are considered and used to contrast the potential effects of age. Results suggest that modulation frequency and extent (amplitude, as well as the amount of vocal fold overall strain, all affect the change in stress relaxation with modulation added. Generally, the vocal fold cover reduces the rate of relaxation while the opposite is true for the vocal ligament. Further, higher modulation frequencies appear to reduce the rate of relaxation, primarily affecting the ligament. The potential benefits of cyclic strain, often found in vibrato (around 5 Hz modulation and intonational inflection, are discussed in terms of vocal effort and vocal pitch maintenance. Additionally, elderly tissue appears to not exhibit these benefits to modulation. The exacerbating effect such modulations may have on certain voice disorders, such as muscle tension dysphonia, are explored.
Chashei, I. V.; Fahr, H. J.
Charge-exchange processes between interstellar H-/O-atoms and protons of the bulk of the interstellar plasma flow downstream of the outer bowshock in the heliospheric interface induce secondary ions leading to non-relaxated velocity distribution functions. The relaxation of these freshly induced ions towards an equilibrium distribution occurs due to Coulomb interactions and wave-particle interactions with the background turbulence. Since Coulomb interactions are of low relevance, we study here in detail the effect of wave-particle interactions. To find the turbulence levels in the interface we consider the MHD-wave transformation at the outer shock surface between the interface and the local interstellar plasma. The turbulence in the outer interface region is shown to be dominated by incompressible Alfvén waves both for cases of quasiparallel and quasiperpendicular shocks. Also we show that waves propagating towards the shock are more intensive than those propagating away from it. The level of Alfvén turbulence in the interface is estimated using the recent data on local interstellar turbulence deduced from observations of interstellar scintillations of distant radiosources. Two proton relaxation processes are considered: quasilinear resonant interactions with Alfvén waves and non-linear self-induced wave-particle scattering. The corresponding diffusion coefficients are estimated, and typical time periods for protons and oxygen ions relaxation are shown to be of the same order of magnitude as H-/O-atoms passage time over the extent of the interface. This indicates that perturbed ion distribution functions must be expected there.
Dielectric dispersion and relaxations in (PVA-PEO)-ZnO polymer nanocomposites
Choudhary, Shobhna
2017-10-01
The organic-inorganic nanocomposite materials consisted of poly(vinyl alcohol) (PVA) and poly(ethylene oxide) (PEO) blend matrix (50/50 wt%) dispersed with zinc oxide (ZnO) nanoparticles have been prepared by the aqueous solution-cast method. The dielectric dispersion and relaxation processes in these polymer nanocomposite (PNC) films (i.e., (PVA-PEO)-x wt% ZnO; x = 0, 1, 3 or 5) have been investigated over the frequency range from 20 Hz to 1 MHz by employing the dielectric relaxation spectroscopy (DRS). Influence of ZnO contents on the complex dielectric permittivity, electrical conductivity, electric modulus and impedance properties of these PNC materials has been explored. The dielectric permittivity and the relaxation time values corresponding to polymers cooperative chain segmental motion significantly change with the variation of ZnO contents in the PVA-PEO blend matrix at ambient temperature. The temperature dependent relaxation times and dc conductivity values of (PVA-PEO)-3 wt% ZnO film have been investigated which obey the Arrhenius behaviour. The dielectric permittivity of the film as a function of temperature exhibits linear behaviour at radio frequencies and non-linear variation at lower audio frequencies. X-ray diffraction measurements confirm a huge decrease in crystalline phase of the polymer blend matrix on the addition of 1 wt% ZnO nanoparticles. These PNC materials have low values of dielectric permittivity and electrical conductivity which confirm their suitability as novel flexible-type polymer nanodielectric for the insulation in microelectronic devices, whereas the fast chain segmental dynamics and high amorphous phase reveal these materials as a potential candidate for the preparation of nanocomposite solid polymer electrolytes.
Dietrich, Olaf; Levin, Johannes; Ahmadi, Seyed-Ahmad; Plate, Annika; Reiser, Maximilian F; Bötzel, Kai; Giese, Armin; Ertl-Wagner, Birgit
2017-04-01
The aim of this study is to evaluate the MR imaging behavior of ferrous (Fe(2+)) and ferric (Fe(3+)) iron ions in order to develop a noninvasive technique to quantitatively differentiate between both forms of iron. MRI was performed at 3 T in a phantom consisting of 21 samples with different concentrations of ferrous and ferric chloride solutions (between 0 and 10 mmol/L). A multi-echo spoiled gradient-echo pulse sequence with eight echoes was used for both T 2* and quantitative susceptibility measurements. The transverse relaxation rate, R 2* = 1/T 2*, was determined by nonlinear exponential fitting based on the mean signals in each sample. The susceptibilities, χ, of the samples were calculated after phase unwrapping and background field removal by fitting the spatial convolution of a unit dipole response to the measured internal field map. Relaxation rate changes, ΔR 2*(c Fe), and susceptibility changes, Δχ(c Fe), their linear slopes, as well as the ratios ΔR 2*(c Fe) / Δχ(c Fe) were determined for all concentrations. The linear slopes of the relaxation rate were (12.5 ± 0.4) s(-1)/(mmol/L) for Fe(3+) and (0.77 ± 0.09) s(-1)/(mmol/L) for Fe(2+) (significantly different, z test P relaxation behaviors in MRI but similar susceptibility patterns. These properties can be used to differentiate ferrous and ferric samples.
Agrawal, Govind
2012-01-01
Since the 4e appeared, a fast evolution of the field has occurred. The 5e of this classic work provides an up-to-date account of the nonlinear phenomena occurring inside optical fibers, the basis of all our telecommunications infastructure as well as being used in the medical field. Reflecting the big developments in research, this new edition includes major new content: slow light effects, which offers a reduction in noise and power consumption and more ordered network traffic-stimulated Brillouin scattering; vectorial treatment of highly nonlinear fibers; and a brand new chapter o
DEFF Research Database (Denmark)
Mosegaard, Klaus
2012-01-01
For non-linear inverse problems, the mathematical structure of the mapping from model parameters to data is usually unknown or partly unknown. Absence of information about the mathematical structure of this function prevents us from presenting an analytical solution, so our solution depends on our......-heuristics are inefficient for large-scale, non-linear inverse problems, and that the 'no-free-lunch' theorem holds. We discuss typical objections to the relevance of this theorem. A consequence of the no-free-lunch theorem is that algorithms adapted to the mathematical structure of the problem perform more efficiently than...
Fundamentals of nonlinear optics
Powers, Peter E
2011-01-01
Peter Powers's rigorous but simple description of a difficult field keeps the reader's attention throughout. … All chapters contain a list of references and large numbers of practice examples to be worked through. … By carefully working through the proposed problems, students will develop a sound understanding of the fundamental principles and applications. … the book serves perfectly for an introductory-level course for second- and third-order nonlinear optical phenomena. The author's writing style is refreshing and original. I expect that Fundamentals of Nonlinear Optics will fast become pop
Tunable nonlinear graphene metasurfaces
Smirnova, Daria A; Kivshar, Yuri S; Khanikaev, Alexander B
2015-01-01
We introduce the concept of nonlinear graphene metasurfaces employing the controllable interaction between a graphene layer and a planar metamaterial. Such hybrid metasurfaces support two types of subradiant resonant modes, asymmetric modes of structured metamaterial elements ("metamolecules") and graphene plasmons exhibiting strong mutual coupling and avoided dispersion crossing. High tunability of graphene plasmons facilitates strong interaction between the subradiant modes, modifying the spectral position and lifetime of the associated Fano resonances. We demonstrate that strong resonant interaction, combined with the subwavelength localization of plasmons, leads to the enhanced nonlinear response and high efficiency of the second-harmonic generation.
Nonlinear effects in optical fibers
Ferreira, Mario F
2011-01-01
Cutting-edge coverage of nonlinear phenomena occurring inside optical fibers Nonlinear fiber optics is a specialized part of fiber optics dealing with optical nonlinearities and their applications. As fiber-optic communication systems have become more advanced and complex, the nonlinear effects in optical fibers have increased in importance, as they adversely affect system performance. Paradoxically, the same nonlinear phenomena also offer the promise of addressing the bandwidth bottleneck for signal processing for future ultra-high speed optical networks. Nonlinear Effects in Optical Fiber
Dielectric relaxations investigation of a synthesized epoxy resin polymer
Jilani, Wissal; Mzabi, Nissaf; Gallot-Lavallée, Olivier; Fourati, Najla; Zerrouki, Chouki; Zerrouki, Rachida; Guermazi, Hajer
2015-04-01
A diglycidylether of bisphenol A (DGEBA) epoxy resin was synthesized, and cured with 3,3'-diaminodiphenyl sulfone (DDS) at a curing temperature of 120 °C. The relaxation properties of the realized polymers were studied by two complementary techniques: dielectric relaxation spectroscopy (DRS), in the temperature range 173-393K and in the frequency interval 10-1-106 Hz, and thermally stimulated depolarization current (TSDC) with a windowing polarization process. Current-voltage (I-V) measurements were also carried out to study interfacial relaxations. Dielectric data were analyzed in terms of permittivity and electric modulus variations. Three relaxation processes ( γ, β and α) have been identified. They were found to be frequency and temperature dependent and were interpreted in terms of the Havriliak-Negami approach. Relaxation parameters were determined by fitting the experimental data. The temperature dependence of the relaxation time was well fitted by the Arrhenius law for secondary relaxations, while the Vogel-Fulcher-Tamann model was found to better fit the τ( T) variations for α relaxation. We found τ 0 = 4.9 10-12 s, 9.6 10-13 s and 1.98 10-7 s for γ, β and α relaxations, respectively. The obtained results were found to be consistent with those reported in the literature. Due to the calculation of the low-frequency data of dielectric loss by the Hamon approximation, the Maxwell-Wagner-Sillars (MWS) relaxation was highlighted.
Relaxation training after stroke: potential to reduce anxiety.
Kneebone, Ian; Walker-Samuel, Natalie; Swanston, Jennifer; Otto, Elisabeth
2014-01-01
To consider the feasibility of setting up a relaxation group to treat symptoms of post stroke anxiety in an in-patient post-acute setting; and to explore the effectiveness of relaxation training in reducing self-reported tension. A relaxation group protocol was developed in consultation with a multidisciplinary team and a user group. Over a period of 24 months, 55 stroke patients attended group autogenic relaxation training on a rehabilitation ward. Attendance ranged between one and eleven sessions. Self-reported tension was assessed pre and post relaxation training using the Tension Rating Circles (TRCs). The TRCs identified a significant reduction in self-reported tension from pre to post training, irrespective of the number of sessions attended; z = -3.656, p stroke rehabilitation shows potential. Self-reported tension decreased after attendance at relaxation training. The TRCs proved acceptable to group members, but should be validated against standard anxiety measures. Further exploration of the application of relaxation techniques in clinical practice is desirable. Implications for Rehabilitation Anxiety is prevalent after stroke and likely affects rehabilitation outcomes. Relaxation training is a well proven treatment for anxiety in the non-stroke population. A significant within session reduction in tension, a hallmark symptom of anxiety, was evidenced via group relaxation training delivered in a post-acute, in-patient stroke unit setting. Relaxation training a shows promise as a treatment for anxiety after stroke.
The mechanics of mouse skeletal muscle when shortening during relaxation.
Barclay, C J; Lichtwark, G A
2007-01-01
The dynamic properties of relaxing skeletal muscle have not been well characterised but are important for understanding muscle function during terrestrial locomotion, during which a considerable fraction of muscle work output can be produced during relaxation. The purpose of this study was to characterise the force-velocity properties of mouse skeletal muscle during relaxation. Experiments were performed in vitro (21 degrees C) using bundles of fibres from mouse soleus and EDL muscles. Isovelocity shortening was applied to muscles during relaxation following short tetanic contractions. Using data from different contractions with different shortening velocities, curves relating force output to shortening velocity were constructed at intervals during relaxation. The velocity component included contributions from shortening of both series elastic component (SEC) and contractile component (CC) because force output was not constant. Early in relaxation force-velocity relationships were linear but became progressively more curved as relaxation progressed. Force-velocity curves late in relaxation had the same curvature as those for the CC in fully activated muscles but V(max) was reduced to approximately 50% of the value in fully activated muscles. These results were the same for slow- and fast-twitch muscles and for relaxation following maximal tetani and brief, sub-maximal tetani. The measured series elastic compliance was used to partition shortening velocity between SEC and CC. The curvature of the CC force-velocity relationship was constant during relaxation. The SEC accounted for most of the shortening and work output during relaxation and its power output during relaxation exceeded the maximum CC power output. It is proposed that unloading the CC, without any change in its overall length, accelerated cross-bridge detachment when shortening was applied during relaxation.
Simulations of coherent nonlinear optical response of molecular vibronic dimers
Perlík, Václav
2016-01-01
We have implemented vibronic dynamics for simulations of the third order coherent response of electronic dimers. In the present communication we provide the full and detailed description of the dynamical model, recently used for simulations of chlorophyll-carotenoid dyads, terylene dimers, or hypericin. We allow for explicit vibronic level structure, by including selected vibrational modes into a "system". Bath dynamics include the Landau-Teller vibrational relaxation, electronic dephasing, and nonlinear vibronic (to bath) coupling. Simulations combine effects of transport and dephasing between vibronic levels. Transport is described by master equation within secular approximation, phase is accumulated in cumulants and its calculation follows the transport pathways during waiting time period.
Jameson, A.
1976-01-01
A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.
Dielectric relaxation of CdO nanoparticles
Tripathi, Ramna; Dutta, Alo; Das, Sayantani; Kumar, Akhilesh; Sinha, T. P.
2016-02-01
Nanoparticles of cadmium oxide have been synthesized by soft chemical route using thioglycerol as the capping agent. The crystallite size is determined by X-ray diffraction technique and the particle size is obtained by transmission electron microscope. The band gap of the material is obtained using Tauc relation to UV-visible absorption spectrum. The photoluminescence emission spectra of the sample are measured at various excitation wavelengths. The molecular components in the material have been analyzed by FT-IR spectroscopy. The dielectric dispersion of the material is investigated in the temperature range from 313 to 393 K and in the frequency range from 100 Hz to 1 MHz by impedance spectroscopy. The Cole-Cole model is used to describe the dielectric relaxation of the system. The scaling behavior of imaginary part of impedance shows that the relaxation describes the same mechanism at various temperatures. The frequency-dependent electrical data are also analyzed in the framework of conductivity and electrical modulus formalisms. The frequency-dependent conductivity spectra are found to obey the power law.
Transverse relaxation of scalar-coupled protons.
Segawa, Takuya F; Baishya, Bikash; Bodenhausen, Geoffrey
2010-10-25
In a preliminary communication (B. Baishya, T. F. Segawa, G. Bodenhausen, J. Am. Chem. Soc. 2009, 131, 17538-17539), we recently demonstrated that it is possible to obtain clean echo decays of protons in biomolecules despite the presence of homonuclear scalar couplings. These unmodulated decays allow one to determine apparent transverse relaxation rates R(2) (app) of individual protons. Herein, we report the observation of R(2) (app) for three methyl protons, four amide H(N) protons, and all 11 backbone H(α) protons in cyclosporin A. If the proton resonances overlap, their R(2) (app) rates can be measured by transferring their magnetization to neighboring (13)C nuclei, which are less prone to overlap. The R(2) (app) rates of protons attached to (13)C are faster than those attached to (12)C because of (13)C-(1)H dipolar interactions. The differences of these rates allow the determination of local correlation functions. Backbone H(N) and H(α) protons that have fast decay rates R(2) (app) also feature fast longitudinal relaxation rates R(1) and intense NOESY cross peaks that are typical of crowded environments. Variations of R(2) (app) rates of backbone H(α) protons in similar amino acids reflect differences in local environments.
Relaxing effect of rose oil on humans.
Hongratanaworakit, Tapanee
2009-02-01
One increasingly popular type of alternative therapy is aromatherapy, but scientific validation in this field is still rare. The aim of this study was to investigate the effect of rose oil (Rosa damascena Mill, Rosaceae) on human autonomic parameters and emotional responses in healthy subjects after transdermal absorption. In order to exclude any olfactory stimulation the inhalation of the fragrances was prevented by breathing masks. Forty healthy volunteers participated in the experiments. Five autonomic parameters, i.e. blood pressure, breathing rate, blood oxygen saturation, pulse rate, and skin temperature, were recorded. Emotional responses were assessed by means of rating scales. Compared to placebo, rose oil caused significant decreases of breathing rate, blood oxygen saturation and systolic blood pressure, which indicate a decrease of autonomic arousal. At the emotional level, subjects in the rose oil group rated themselves as more calm, more relaxed and less alert than subjects in the control group. These findings are likely to represent a relaxing effect of the rose oil and provide some evidence for the use of rose oil in aromatherapy, such as causing relief of depression and stress in humans.
Viscosity bound versus the universal relaxation bound
Hod, Shahar
2017-10-01
For gauge theories with an Einstein gravity dual, the AdS/CFT correspondence predicts a universal value for the ratio of the shear viscosity to the entropy density, η / s = 1 / 4 π. The holographic calculations have motivated the formulation of the celebrated KSS conjecture, according to which all fluids conform to the lower bound η / s ≥ 1 / 4 π. The bound on η / s may be regarded as a lower bound on the relaxation properties of perturbed fluids and it has been the focus of much recent attention. In particular, it was argued that for a class of field theories with Gauss-Bonnet gravity dual, the shear viscosity to entropy density ratio, η / s, could violate the conjectured KSS bound. In the present paper we argue that the proposed violations of the KSS bound are strongly constrained by Bekenstein's generalized second law (GSL) of thermodynamics. In particular, it is shown that physical consistency of the Gauss-Bonnet theory with the GSL requires its coupling constant to be bounded by λGB ≲ 0 . 063. We further argue that the genuine physical bound on the relaxation properties of physically consistent fluids is ℑω(k > 2 πT) > πT, where ω and k are respectively the proper frequency and the wavenumber of a perturbation mode in the fluid.
A Simple Holographic Superconductor with Momentum Relaxation
Kim, Keun-Young; Park, Miok
2015-01-01
We study a holographic superconductor model with momentum relaxation due to massless scalar fields linear to spatial coordinates($\\psi_I = \\beta \\delta_{Ii} x^i$), where $\\beta$ is the strength of momentum relaxation. In addition to the original superconductor induced by the chemical potential($\\mu$) at $\\beta=0$, there exists a new type of superconductor induced by $\\beta$ even at $\\mu=0$. It may imply a new `pairing' mechanism of particles and antiparticles interacting with $\\beta$, which may be interpreted as `impurity'. Two parameters $\\mu$ and $\\beta$ compete in forming superconducting phase. As a result, the critical temperature behaves differently depending on $\\beta/\\mu$. It decreases when $\\beta/\\mu$ is small and increases when $\\beta/\\mu$ is large, which is a novel feature compared to other models. After analysing ground states and phase diagrams for various $\\beta/\\mu$, we study optical electric($\\sigma$), thermoelectric($\\alpha$), and thermal($\\bar{\\kappa}$) conductivities. When the system undergo...
Nonlinear elliptic systems with exponential nonlinearities
Directory of Open Access Journals (Sweden)
Said El Manouni
2002-12-01
Full Text Available In this paper we investigate the existence of solutions for {gather*} -mathop{m div}( a(| abla u | ^N| abla u |^{N-2}u = f(x,u,v quad mbox{in } Omega -mathop{m div}(a(| abla v| ^N| abla v |^{N-2}v = g(x,u,v quad mbox{in } Omega u(x = v(x = 0 quad mbox{on }partial Omega. end{gather*} Where $Omega$ is a bounded domain in ${mathbb{R}}^N$, $Ngeq 2$, $f$ and $g$ are nonlinearities having an exponential growth on $Omega$ and $a$ is a continuous function satisfying some conditions which ensure the existence of solutions.
Energy Technology Data Exchange (ETDEWEB)
Vignes, Ryan M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). National Ignition Facility and Photon Sciences; Soules, Thomas F. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). National Ignition Facility and Photon Sciences; Stolken, James S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). National Ignition Facility and Photon Sciences; Settgast, Randolph R. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). National Ignition Facility and Photon Sciences; Elhadj, Selim [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). National Ignition Facility and Photon Sciences; Matthews, Manyalibo J. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). National Ignition Facility and Photon Sciences; Mauro, J.
2012-12-17
In a fully coupled thermomechanical model of the nanoscale deformation in amorphous SiO_{2} due to laser heating is presented. Direct measurement of the transient, nonuniform temperature profiles was used to first validate a nonlinear thermal transport model. Densification due to structural relaxation above the glass transition point was modeled using the Tool-Narayanaswamy (TN) formulation for the evolution of structural relaxation times and fictive temperature. TN relaxation parameters were derived from spatially resolved confocal Raman scattering measurements of Si–O–Si stretching mode frequencies. These thermal and microstructural data were used to simulate fictive temperatures which are shown to scale nearly linearly with density, consistent with previous measurements from Shelby et al. Volumetric relaxation coupled with thermal expansion occurring in the liquid-like and solid-like glassy states lead to residual stresses and permanent deformation which could be quantified. But, experimental surface deformation profiles between 1700 and 2000 K could only be reconciled with our simulation by assuming a roughly 2 × larger liquid thermal expansion for a-SiO_{2} with a temperature of maximum density ~150 K higher than previously estimated by Bruckner et al. Calculated stress fields agreed well with recent laser-induced critical fracture measurements, demonstrating accurate material response prediction under processing conditions of practical interest.
Nonlinearity and disorder: Classification and stability of nonlinear impurity modes
DEFF Research Database (Denmark)
Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole
2001-01-01
We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of no...
Generalized Nonlinear Yule Models
Lansky, Petr; Polito, Federico; Sacerdote, Laura
2016-10-01
With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.
Ritz, Christian; Parmigiani, Giovanni
2009-01-01
R is a rapidly evolving lingua franca of graphical display and statistical analysis of experiments from the applied sciences. This book provides a coherent treatment of nonlinear regression with R by means of examples from a diversity of applied sciences such as biology, chemistry, engineering, medicine and toxicology.
Gorban, A. N.; Karlin, I.V.
2003-01-01
Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research. Contents: The Boltzmann equation, Phenomenology and Quasi-chemical representation of the Boltzmann equation, Kinetic models, Discrete velocity models, Direct simulation, Lattice Gas and Lattice Boltzmann models, Minimal Boltzmann models for flows at low Knudsen number, Other kinetic equati...
Intramolecular and nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Davis, M.J. [Argonne National Laboratory, IL (United States)
1993-12-01
Research in this program focuses on three interconnected areas. The first involves the study of intramolecular dynamics, particularly of highly excited systems. The second area involves the use of nonlinear dynamics as a tool for the study of molecular dynamics and complex kinetics. The third area is the study of the classical/quantum correspondence for highly excited systems, particularly systems exhibiting classical chaos.
DEFF Research Database (Denmark)
Jørgensen, Michael Finn
1995-01-01
It is generally very difficult to solve nonlinear systems, and such systems often possess chaotic solutions. In the rare event that a system is completely solvable, it is said to integrable. Such systems never have chaotic solutions. Using the Inverse Scattering Transform Method (ISTM) two...
Nonlinear phased array imaging
Croxford, Anthony J.; Cheng, Jingwei; Potter, Jack N.
2016-04-01
A technique is presented for imaging acoustic nonlinearity within a specimen using ultrasonic phased arrays. Acoustic nonlinearity is measured by evaluating the difference in energy of the transmission bandwidth within the diffuse field produced through different focusing modes. The two different modes being classical beam forming, where delays are applied to different element of a phased array to physically focus the energy at a single location (parallel firing) and focusing in post processing, whereby one element at a time is fired and a focused image produced in post processing (sequential firing). Although these two approaches are linearly equivalent the difference in physical displacement within the specimen leads to differences in nonlinear effects. These differences are localized to the areas where the amplitude is different, essentially confining the differences to the focal point. Direct measurement at the focal point are however difficult to make. In order to measure this the diffuse field is used. It is a statistical property of the diffuse field that it represents the total energy in the system. If the energy in the diffuse field for both the sequential and parallel firing case is measured then the difference between these, within the input signal bandwidth, is largely due to differences at the focal spot. This difference therefore gives a localized measurement of where energy is moving out of the transmission bandwidth due to nonlinear effects. This technique is used to image fatigue cracks and other damage types undetectable with conventional linear ultrasonic measurements.
Generalized Nonlinear Yule Models
Lansky, Petr; Polito, Federico; Sacerdote, Laura
2016-11-01
With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.
Trirefringence in nonlinear metamaterials
De Lorenci, Vitorio A
2012-01-01
We study the propagation of electromagnetic waves in the limit of geometrical optics for a class of nearly transparent nonlinear uniaxial metamaterials for which their permittivity tensors present a negative principal component. Their permeability are assumed positive and dependent on the electric field. We show that light waves experience triple refraction -- trirefringence. Additionally to the ordinary wave, two extraordinary waves propagate in such media.
Borghi, M.; Castellan, C.; Signorini, S.; Trenti, A.; Pavesi, L.
2017-09-01
Silicon photonics is a technology based on fabricating integrated optical circuits by using the same paradigms as the dominant electronics industry. After twenty years of fervid development, silicon photonics is entering the market with low cost, high performance and mass-manufacturable optical devices. Until now, most silicon photonic devices have been based on linear optical effects, despite the many phenomenologies associated with nonlinear optics in both bulk materials and integrated waveguides. Silicon and silicon-based materials have strong optical nonlinearities which are enhanced in integrated devices by the small cross-section of the high-index contrast silicon waveguides or photonic crystals. Here the photons are made to strongly interact with the medium where they propagate. This is the central argument of nonlinear silicon photonics. It is the aim of this review to describe the state-of-the-art in the field. Starting from the basic nonlinearities in a silicon waveguide or in optical resonator geometries, many phenomena and applications are described—including frequency generation, frequency conversion, frequency-comb generation, supercontinuum generation, soliton formation, temporal imaging and time lensing, Raman lasing, and comb spectroscopy. Emerging quantum photonics applications, such as entangled photon sources, heralded single-photon sources and integrated quantum photonic circuits are also addressed at the end of this review.
Nonlinear fibre optics overview
DEFF Research Database (Denmark)
Travers, J. C.; Frosz, Michael Henoch; Dudley, J. M.
2010-01-01
, provides a background to the associated nonlinear optical processes, treats the generation mechanisms from continuous wave to femtosecond pulse pump regimes and highlights the diverse applications. A full discussion of numerical methods and comprehensive computer code are also provided, enabling readers...
Tsia, Kevin K.; Jalali, Bahram
2010-05-01
An intriguing optical property of silicon is that it exhibits a large third-order optical nonlinearity, with orders-ofmagnitude larger than that of silica glass in the telecommunication band. This allows efficient nonlinear optical interaction at relatively low power levels in a small footprint. Indeed, we have witnessed a stunning progress in harnessing the Raman and Kerr effects in silicon as the mechanisms for enabling chip-scale optical amplification, lasing, and wavelength conversion - functions that until recently were perceived to be beyond the reach of silicon. With all the continuous efforts developing novel techniques, nonlinear silicon photonics is expected to be able to reach even beyond the prior achievements. Instead of providing a comprehensive overview of this field, this manuscript highlights a number of new branches of nonlinear silicon photonics, which have not been fully recognized in the past. In particular, they are two-photon photovoltaic effect, mid-wave infrared (MWIR) silicon photonics, broadband Raman effects, inverse Raman scattering, and periodically-poled silicon (PePSi). These novel effects and techniques could create a new paradigm for silicon photonics and extend its utility beyond the traditionally anticipated applications.
Leitao, J C; Gerlach, M; Altmann, E G
2016-01-01
One of the most celebrated findings in complex systems in the last decade is that different indexes y (e.g., patents) scale nonlinearly with the population~x of the cities in which they appear, i.e., $y\\sim x^\\beta, \\beta \
Nonlinear Gravitational Lagrangians revisited
Magnano, Guido
2016-01-01
The Legendre transformation method, applied in 1987 to deal with purely metric gravitational Lagrangians with nonlinear dependence on the Ricci tensor, is extended to metric-affine models and is shown to provide a concise and insightful comparison of the dynamical content of the two variational frameworks.
Nonlinearities in Microwave Superconductivity
Ledenyov, Dimitri O.; Ledenyov, Viktor O.
2012-01-01
The research is focused on the modeling of nonlinear properties of High Temperature Superconducting (HTS) thin films, using Bardeen, Cooper, Schrieffer and Lumped Element Circuit theories, with purpose to enhance microwave power handling capabilities of microwave filters and optimize design of microwave circuits in micro- and nano- electronics.
Nonlinear tsunami generation mechanism
Directory of Open Access Journals (Sweden)
M. A. Nosov
2001-01-01
Full Text Available The nonlinear mechanism of long gravitational surface water wave generation by high-frequency bottom oscillations in a water layer of constant depth is investigated analytically. The connection between the surface wave amplitude and the parameters of bottom oscillations and source length is investigated.
DEFF Research Database (Denmark)
Mosekilde, Erik
Through a significant number of detailed and realistic examples this book illustrates how the insights gained over the past couple of decades in the fields of nonlinear dynamics and chaos theory can be applied in practice. Aomng the topics considered are microbiological reaction systems, ecological...
Terahertz semiconductor nonlinear optics
DEFF Research Database (Denmark)
Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias
2013-01-01
nonlinearity in doped semiconductors originates from the near-instantaneous heating of free electrons in the ponderomotive potential created by electric field of the THz pulse, leading to ultrafast increase of electron effective mass by intervalley scattering. Modification of effective mass in turn leads...
Institute of Scientific and Technical Information of China (English)
YANG Yan; HAO Yue; ZHANG Jincheng; WANG Chong; FENG Qian
2006-01-01
The effects of strain relaxation of AlGaN barrier layer on the conduction band profile, electron concentration and two-dimensional gas (2DEG) sheet charge density in a high Al-content AlGaN/GaN high electron mobility transistor (HEMT) are calculated by self-consistently solving Poisson's and Schr(o)dinger's equations. The effect of strain relaxation on dc I-V characteristics of AlxGa1-xN/GaN HEMT is obtained by developing a nonlinear charge-control model that describes the accurate relation of 2DEG sheet charge density and gate voltage. The model predicts a highest 2DEG sheet charge density of 2.42×1013 cm-2 and maximum saturation current of 2482.8 mA/mm at a gate bias of 2 V for 0.7 μm Al0.50Ga0.50N/GaN HEMT with strain relaxation r =0 and 1.49×1013 cm-2 and 1149.7 mA/mm with strain relaxation r =1. The comparison between simulations and physical measurements shows a good agreement. Results show that the effect of strain relaxation must be considered when analyzing the characteristics of high Al-content AlGaN/GaN HEMT theoretically, and the performance of the devices is improved by decreasing the strain relaxation of AlGaN barrier layer.
Petrov, Oleg V.; Stapf, Siegfried
2017-06-01
This work addresses the problem of a compact and easily comparable representation of multi-exponential relaxation data. It is often convenient to describe such data in a few parameters, all being of physical significance and easy to interpret, and in such a way that enables a model-free comparison between different groups of samples. Logarithmic moments (LMs) of the relaxation time constitute a set of parameters which are related to the characteristic relaxation time on the log-scale, the width and the asymmetry of an underlying distribution of exponentials. On the other hand, the calculation of LMs does not require knowing the actual distribution function and is reduced to a numerical integration of original data. The performance of this method has been tested on both synthetic and experimental NMR relaxation data which differ in a signal-to-noise ratio, the sampling range and the sampling rate. The calculation of two lower-order LMs, the log-mean time and the log-variance, has proved robust against deficiencies of the experiment such as scattered data point and incomplete sampling. One may consider using them as such to monitor formation of a heterogeneous structure, e.g., in phase separation, vitrification, polymerization, hydration, aging, contrast agent propagation processes. It may also assist in interpreting frequency and temperature dependences of relaxation, revealing a crossover from slow to fast exchange between populations. The third LM was found to be a less reliable quantity due to its susceptibility to the noise and must be used with caution.
Andersen, D.; Hull, R.
2017-02-01
The effect of asymmetric interfacial strain configurations upon the generation of misfit dislocation arrays in lattice mismatched epitaxy is considered. For example, elastic strain relaxation for Si1-xGex/Si(110) films is uniaxial, assuming glide on {111} planes as expected for the diamond cubic system, which leads to asymmetric strain relief. Here, we extend our previously developed relaxation model for generation of dislocation arrays in SiGe/Si, by accounting for how the different energetics of asymmetrically strained films affect the kinetics of the relaxation process. Similarly, non-polar III-nitride epitaxial films have asymmetric strain from the outset of growth due to the different c/a lattice parameter ratios. In both systems, the asymmetric strain is represented by an additional term in the misfit dislocation applied stress equation. In SiGe/Si(110), a simple elasticity analysis of the strain produced by the uniaxial array of dislocations predicts that the relaxation orthogonal to the dislocation line direction occurs at a faster rate than predicted by purely biaxial strain relief due to the contributions of the strain parallel to the dislocations. This difference is because the strain parallel to the dislocation line directions continues to resolve stress onto the misfit dislocations even as the orthogonal strain is minimized. As a result, the minimum strain energy is predicted to occur for a dislocation spacing, which produces tensile layer strain in the orthogonal direction. Such tensile strain may modify the (opto)electronic properties of a Si, Ge, or GeSi epilayer but is only predicted to occur for advanced stages of relaxation. These asymmetric derivations are applicable to any thin film system where strain is not strictly biaxial.
Immersed boundary lattice Boltzmann model based on multiple relaxation times.
Lu, Jianhua; Han, Haifeng; Shi, Baochang; Guo, Zhaoli
2012-01-01
As an alterative version of the lattice Boltzmann models, the multiple relaxation time (MRT) lattice Boltzmann model introduces much less numerical boundary slip than the single relaxation time (SRT) lattice Boltzmann model if some special relationship between the relaxation time parameters is chosen. On the other hand, most current versions of the immersed boundary lattice Boltzmann method, which was first introduced by Feng and improved by many other authors, suffer from numerical boundary slip as has been investigated by Le and Zhang. To reduce such a numerical boundary slip, an immerse boundary lattice Boltzmann model based on multiple relaxation times is proposed in this paper. A special formula is given between two relaxation time parameters in the model. A rigorous analysis and the numerical experiments carried out show that the numerical boundary slip reduces dramatically by using the present model compared to the single-relaxation-time-based model.
Nuclear spin relaxation in liquids theory, experiments, and applications
Kowalewski, Jozef
2006-01-01
Nuclear magnetic resonance (NMR) is widely used across many fields because of the rich data it produces, and some of the most valuable data come from the study of nuclear spin relaxation in solution. While described to varying degrees in all major NMR books, spin relaxation is often perceived as a difficult, if not obscure, topic, and an accessible, cohesive treatment has been nearly impossible to find.Collecting relaxation theory, experimental techniques, and illustrative applications into a single volume, this book clarifies the nature of the phenomenon, shows how to study it, and explains why such studies are worthwhile. Coverage ranges from basic to rigorous theory and from simple to sophisticated experimental methods, and the level of detail is somewhat greater than most other NMR texts. Topics include cross-relaxation, multispin phenomena, relaxation studies of molecular dynamics and structure, and special topics such as relaxation in systems with quadrupolar nuclei and paramagnetic systems.Avoiding ove...
Hyperfine relaxation of an optically pumped cesium vapor
Energy Technology Data Exchange (ETDEWEB)
Tornos, J.; Amare, J.C.
1986-07-01
The relaxation of hyperfine orientation indirectly induced by optical pumping with a sigma-polarized D/sub 1/-light in a cesium vapor in the presence of Ar is experimentally studied. The detection technique ensures the absence of quadrupole relaxation contributions in the relaxation signals. The results from the dependences of the hyperfine relaxation rate on the temperature and argon pressure are: diffusion coefficient of Cs in Ar, D/sub 0/ = 0.101 +- 0.010 cm/sup 2/s/sup -1/ at 0/sup 0/C and 760 Torr; relaxation cross section by Cs-Ar collisions, sigma/sub c/ = (104 +- 5) x 10/sup -23/ cm/sup 2/; relaxation cross section by Cs-Cs (spin exchange) collisions, sigma/sub e//sub x/ = (1.63 +- 0.13) x 10/sup -14/ cm/sup 2/.
Cross-relaxation in multiple pulse NQR spin-locking
Energy Technology Data Exchange (ETDEWEB)
Beltjukov, P. A.; Kibrik, G. E. [Perm State University, Physics Department (Russian Federation); Furman, G. B., E-mail: gregoryf@bgu.ac.il; Goren, S. D. [Ben Gurion University, Physics Department (Israel)
2008-01-15
The experimental and theoretical NQR multiple-pulse spin locking study of cross-relaxation process in solids containing nuclei of two different sorts I > 1/2 and S = 1/2 coupled by the dipole-dipole interactions and influenced by an external magnetic field. Two coupled equations for the inverse spin temperatures of the both spin systems describing the mutual spin lattice relaxation and the cross-relaxation were obtained using the method of the nonequilibrium state operator. It is shown that the relaxation process is realized with non-exponential time dependence describing by a sum of two exponents. The cross relaxation time is calculated as a function of the multiple-pulse field parameters which agree with the experimental data. The calculated magnetization cross relaxation time vs the strength of the applied magnetic field agrees well with the obtained experimental data.
Nonlinear Optical Terahertz Technology Project
National Aeronautics and Space Administration — Our approach is based on high-Q optical WGM resonators made with a nonlinear crystal. Such resonators have been demonstrated to dramatically enhance nonlinear...
Phase retrieval using nonlinear diversity.
Lu, Chien-Hung; Barsi, Christopher; Williams, Matthew O; Kutz, J Nathan; Fleischer, Jason W
2013-04-01
We extend the Gerchberg-Saxton algorithm to phase retrieval in a nonlinear system. Using a tunable photorefractive crystal, we experimentally demonstrate the noninterferometric technique by reconstructing an unknown phase object from optical intensity measurements taken at different nonlinear strengths.
Strong nonlinear oscillators analytical solutions
Cveticanin, Livija
2017-01-01
This book outlines an analytical solution procedure of the pure nonlinear oscillator system, offering a solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter. Includes exercises.
Nonlinear Magnetic Phenomena in Highly Polarized Target Materials
Kiselev, Yu F
2007-01-01
The report introduces and surveys nonlinear magnetic phenomena which have been observed at high nuclear polarizations in polarized targets of the SMC and of the COMPASS collaborations at CERN. Some of these phenomena, namely the frequency modulation eect and the distortion of the NMR line shape, promote the development of the polarized target technique. Others, as the spin-spin cross-relaxation between spin subsystems can be used for the development of quantum statistical physics. New findings bear on an electromagnetic noise and the spectrally resolved radiation from LiD with negatively polarized nuclei detected by low temperature bolometers. These nonlinear phenomena need to be taken into account for achieving the ultimate polarizations.
Anharmonic effects in simple physical models: introducing undergraduates to nonlinearity
Christian, J. M.
2017-09-01
Given the pervasive character of nonlinearity throughout the physical universe, a case is made for introducing undergraduate students to its consequences and signatures earlier rather than later. The dynamics of two well-known systems—a spring and a pendulum—are reviewed when the standard textbook linearising assumptions are relaxed. Some qualitative effects of nonlinearity can be anticipated from symmetry (e.g., inspection of potential energy functions), and further physical insight gained by applying a simple successive-approximation method that might be taught in parallel with courses on classical mechanics, ordinary differential equations, and computational physics. We conclude with a survey of how these ideas have been deployed on programmes at a UK university.
Nonlinear conductivity and the ringdown of currents in metallic holography
Withers, Benjamin
2016-01-01
We study the electric and heat current response resulting from an electric field quench in a holographic model of momentum relaxation at nonzero charge density. After turning the electric field off, currents return to equilibrium as governed by the vector quasi-normal modes of the dual black brane, whose spectrum depends qualitatively on a parameter controlling the strength of inhomogeneity. We explore the dynamical phase diagram as a function of this parameter, showing that signatures of incoherent transport become identifiable as an oscillatory ringdown of the heat current. We also study nonlinear conductivity by holding the electric field constant. For small electric fields a balance is reached between the driving electric field and the momentum sink -- a steady state described by DC linear response. For large electric fields Joule heating becomes important and the black branes exhibit significant time dependence. In a regime where the rate of temperature increase is small, the nonlinear electrical conduct...
Analytical approximations for the amplitude and period of a relaxation oscillator
Directory of Open Access Journals (Sweden)
Golkhou Vahid
2009-01-01
Full Text Available Abstract Background Analysis and design of complex systems benefit from mathematically tractable models, which are often derived by approximating a nonlinear system with an effective equivalent linear system. Biological oscillators with coupled positive and negative feedback loops, termed hysteresis or relaxation oscillators, are an important class of nonlinear systems and have been the subject of comprehensive computational studies. Analytical approximations have identified criteria for sustained oscillations, but have not linked the observed period and phase to compact formulas involving underlying molecular parameters. Results We present, to our knowledge, the first analytical expressions for the period and amplitude of a classic model for the animal circadian clock oscillator. These compact expressions are in good agreement with numerical solutions of corresponding continuous ODEs and for stochastic simulations executed at literature parameter values. The formulas are shown to be useful by permitting quick comparisons relative to a negative-feedback represillator oscillator for noise (10× less sensitive to protein decay rates, efficiency (2× more efficient, and dynamic range (30 to 60 decibel increase. The dynamic range is enhanced at its lower end by a new concentration scale defined by the crossing point of the activator and repressor, rather than from a steady-state expression level. Conclusion Analytical expressions for oscillator dynamics provide a physical understanding for the observations from numerical simulations and suggest additional properties not readily apparent or as yet unexplored. The methods described here may be applied to other nonlinear oscillator designs and biological circuits.
Tanimura, Y; Steffen, T
2000-01-01
The relaxation processes in a quantum system nonlinearly coupled to a harmonic Gaussian-Markovian heat bath are investigated by the quantum Fokker-Planck equation in the hierarchy form. This model describes frequency fluctuations in the quantum system with an arbitrary correlation time and thus
Steffen, T; Tanimura, Y
2000-01-01
The quantum Fokker-Planck equation is derived for a system nonlinearly coupled to a harmonic oscillator bath. The system-bath interaction is assumed to be linear in the bath coordinates but quadratic in the system coordinate. The relaxation induced dynamics of a harmonic system are investigated by s
Bai, Ruiliang; Basser, Peter J; Briber, Robert M; Horkay, Ferenc
2014-03-15
Water self-diffusion coefficients and longitudinal relaxation rates in sodium polyacrylate solutions and gels were measured by NMR, as a function of polymer content and structure in a physiological concentration range of monovalent and divalent cations, Ca(2+) and Na(+). Several physical models describing the self-diffusion of the solvent were applied and compared. A free-volume model was found to be in good agreement with the experimental results over a wide range of polymer concentrations. The longitudinal relaxation rate exhibited linear dependence on polymer concentration below a critical concentration and showed non-linear behavior at higher concentrations. Both the water self-diffusion and relaxation were less influenced by the polymer in the gel state than in the uncrosslinked polymer solutions. The effect of Na(+) on the mobility of water molecules was practically undetectable. By contrast, addition of Ca(2+) strongly increased the longitudinal relaxation rate while its effect on the self-diffusion coefficient was much less pronounced.
Intraband Relaxation and Its Influences on Quantum Dot Lasers
Institute of Scientific and Technical Information of China (English)
DENG Sheng-Ling; HUANG Yong-Zhen; YU Li-Juan
2005-01-01
@@ A comprehensive two-level numerical model is developed to describe carrier distribution in a quantum-dot laser. Light-emission spectra with different intraband relaxation rates (2ps, 7.5ps and 20ps) are calculated and analysed to investigate the influence of relaxation rates on performance of the quantum-dot laser. The results indicate that fast intraband relaxation favours not only the ground state single mode operation but also the higher injection efficiency.
Relaxation of quadrupole orientation in an optically pumped alkali vapour
Energy Technology Data Exchange (ETDEWEB)
Bernabeu, E.; Tornos, J.
1985-04-01
The relaxation of quadrupole orientation (alignment) in an optically pumped alkali vapour is theoretically studied by taking into account the relaxation processes by alkali-buffer gas, alkali-alkali with spin exchange and alkali-cell wall (diffusion process) collisions. The relaxation transients of the quadrupole orientation are obtained by introducing a first-order weak-pumping approximation (intermediate pumping) less restrictive than the usually considered (zeroth order) one.
Measuring Propellant Stress Relaxation Modulus Using Dynamic Mechanical Analyzer
2017-03-29
P. N., Singh, P. P., and Bhattacharya, B., “Determination of Activation Energy of Relaxation Events in Composite Solid Propellants by Dynamic...Article 3. DATES COVERED (From - To) 04 August 2016 – 29 March 2017 4. TITLE AND SUBTITLE Measuring Propellant Stress Relaxation Modulus Using Dynamic...ERC 14. ABSTRACT A method for determining the stress relaxation master curve of solid rocket propellants was developed. The propellant was tested in
Optical Nonlinearities and Ultrafast Carrier Dynamics in Semiconductor Quantum Dots
Energy Technology Data Exchange (ETDEWEB)
Klimov, V.; McBranch, D.; Schwarz, C.
1998-08-10
Low-dimensional semiconductors have attracted great interest due to the potential for tailoring their linear and nonlinear optical properties over a wide-range. Semiconductor nanocrystals (NC's) represent a class of quasi-zero-dimensional objects or quantum dots. Due to quantum cordhement and a large surface-to-volume ratio, the linear and nonlinear optical properties, and the carrier dynamics in NC's are significantly different horn those in bulk materials. napping at surface states can lead to a fast depopulation of quantized states, accompanied by charge separation and generation of local fields which significantly modifies the nonlinear optical response in NC's. 3D carrier confinement also has a drastic effect on the energy relaxation dynamics. In strongly confined NC's, the energy-level spacing can greatly exceed typical phonon energies. This has been expected to significantly inhibit phonon-related mechanisms for energy losses, an effect referred to as a phonon bottleneck. It has been suggested recently that the phonon bottleneck in 3D-confined systems can be removed due to enhanced role of Auger-type interactions. In this paper we report femtosecond (fs) studies of ultrafast optical nonlinearities, and energy relaxation and trap ping dynamics in three types of quantum-dot systems: semiconductor NC/glass composites made by high temperature precipitation, ion-implanted NC's, and colloidal NC'S. Comparison of ultrafast data for different samples allows us to separate effects being intrinsic to quantum dots from those related to lattice imperfections and interface properties.
Cubication of Conservative Nonlinear Oscillators
Belendez, Augusto; Alvarez, Mariela L.; Fernandez, Elena; Pascual, Immaculada
2009-01-01
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear…
Terahertz Nonlinear Optics in Semiconductors
DEFF Research Database (Denmark)
Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias C.
2013-01-01
We demonstrate the nonlinear optical effects – selfphase modulation and saturable absorption of a single-cycle THz pulse in a semiconductor. Resulting from THz-induced modulation of Drude plasma, these nonlinear optical effects, in particular, lead to self-shortening and nonlinear spectral...
Fault Detection for Nonlinear Systems
DEFF Research Database (Denmark)
Stoustrup, Jakob; Niemann, H.H.
1998-01-01
The paper describes a general method for designing fault detection and isolation (FDI) systems for nonlinear processes. For a rich class of nonlinear systems, a nonlinear FDI system can be designed using convex optimization procedures. The proposed method is a natural extension of methods based...
Extreme nonlinearities in InAs/InP nanowire gain media: the two-photon induced laser
DEFF Research Database (Denmark)
Capua, Amir; Kami, Ouri; Eisenstein, Gadi;
2012-01-01
We demonstrate a novel laser oscillation scheme in an InAs / InP wire-like quantum dash gain medium. A short optical pulse excites carriers by two photon absorption which relax to the energy levels providing gain thereby enabling laser oscillations. The nonlinear dynamic interaction is analyzed...... and quantified using multi-color pump-probe measurements and shows a highly efficient nonlinear two photon excitation process which is larger by more than an order of magnitude compared to common quantum well and bulk gain media. The dynamic response of the nonlinearly induced laser line is characterized...
On the Relaxation Dynamics of Disordered Systems
Dobramysl, Ulrich
We investigate the properties of two distinct disordered systems: the two-species predator-prey Lotka-Volterra model with rate variability, and an elastic line model to simulate vortex lines in type-II superconductors. We study the effects of intrinsic demographic variability with inheritance in the reaction rates of the Lotka-Volterra model via zero-dimensional Monte Carlo simulations as well as two-dimensional lattice simulations. Individuals of each species are assigned inheritable predation efficiencies during their creation, leading to evolutionary dynamics and thus population-level optimization. We derive an effective subspecies mean-field theory and compare its results to our numerical data. Furthermore, we introduce environmental variability via quenched spatial reaction-rate randomness. We investigate the competing effects and relative importance of the two types of variability, and find that both lead to a remarkable enhancement of the species densities, while the aforementioned optimization effects are essentially neutral in the densities. Additionally, we collected extinction time histograms for small systems and find a marked increase in the stability of the populations against extinction due to the presence of variability. We employ an elastic line model to investigate the steady-state properties and non-equilibrium relaxation kinetics of magnetic vortex lines in disordered type-II superconductors. To this end, we developed a versatile and efficient Langevin molecular dynamics simulation code, allowing us to do a careful study of samples with or without vortex-vortex interactions or disorder allows us to disentangle the various complex relaxational features present in this system and investigate their origin. In particular, we compare disordered samples with randomly distributed point defects versus correlated columnar defects. We extract two-time quantities such as the mean-square displacement, the height and density correlations, to investigate the
Relaxation Behaviour of Lithium-Borosilicate Glasses
Directory of Open Access Journals (Sweden)
D. B. Thombre
2014-01-01
Full Text Available Three systems of lithium borosilicate (LBS glasses namely SI 42.5Li2O: (57.5-x B2O3: xSiO2, SII 42.5Li2O: xB2O3 :( 57.5-x SiO2 where x=0, 5, 10, 20, and 30, and SIII (100-2x Li2O: xB2O3: xSiO2 where x=30, 28.75, 27.5, 25, and 22.5, are prepared using conventional melt quenching technique. Functional dependence of conductivity on temperature in the range from 523- 673K and frequency in the range from 10Hz to 13 MHz is studied. In order to analyze electrical conductivity the microscopic parameters such as ionic jump distance and barrier height are necessary. These parameters can be understood properly on the basis of the models proposed by Almond and Elliott. As frequency increases from 1MHz to 13MHz, the Tmin shifts towards low temperature side. According to this model the charge transfer is a thermally activated process and provides a correlation between the barrier height (W and the hopping length (R. The fitting of conductivity data into Almond-West type power law behavior σ = σ(o + Aωs yielded power law exponent(s. Electrical conductivity data fitted well in Elliott’s model, which is true only for amorphous materials. The temperature dependence of frequency exponent s exhibits a minimum (smin at a particular temperature (Tmin . . From the scaling behavior of the ac conductivity it is seen that all the curves scaled better, suggesting that s is temperature independent. It is observed that smin shifts to lower temperature, which shows that electrical conductivity of glassy solid electrolytes is the manifestation of ionic dynamic processes. The superposition of the reduced conductivity at all temperatures shows relaxation mechanism is temperature independent. Analysis of modulus formalism with a distribution of relaxation times using KWW stretched exponential function, the stretching exponent, β, is depend on temperature. The analysis of the temperature variation of the M″ peak indicates the relaxation process is thermally activated
Electrical Relaxation in ULTEM® and ULTEM® Containing Mesoporous Silica
Turo, Andrew; Edmondson, Charles E.; Lomax, Joseph F.; Bendler, John T.; Fontanella, John J.; Wintersgill, Mary C.
2008-08-01
Mesoporous silica has been added to Ultem® 1000 polyetherimide using solution casting. The mesoporous silica that was added was either uncoated or coated with polystyrene. Audio frequency dielectric relaxation studies were then carried out over the temperature range 5.5 to 550 K. Several interesting results were obtained. First, the uncoated mesoporous silica caused essentially no change in the relaxation spectrum of pure Ultem®. The polystyrene coated mesoporous silica caused rather large changes. The most striking example is the introduction of a new relaxation. This relaxation occurs at about 150 K and 1000 Hz as showing in fig. 1 via the open circles.
Importance of relaxation techniques in cognitive therapy for anxiety
National Research Council Canada - National Science Library
Alice Rodrigues Willhelm; Ilana Andretta; Mariana Steiger Ungaretti
2015-01-01
.... The CBT treatment for anxiety disorders suggests cognitive techniques of restructuring and cognitive flexibilization and behavioral techniques such as exposure, systematic desensitization and body relaxation techniques...
Institute of Scientific and Technical Information of China (English)
肖立志; 杜有如; 叶朝辉
1996-01-01
Nuclear magnetic resonance (NMR) relaxation of fluids in porous media is affected by the solid-liquid interface. Quantitative determination of the surface relaxivity is significantly important for both investigation and application of relaxation mechanisms in porous media. A method to estimate the surface relaxivity with the combination of relaxation and diffusion measurements is proposed. According to this method, a criterion for testing the current diffusion and relaxation theory for porous media is available.
Nonlinear electrostatic drift Kelvin-Helmholtz instability
Sharma, Avadhesh C.; Srivastava, Krishna M.
1993-01-01
Nonlinear analysis of electrostatic drift Kelvin-Helmholtz instability is performed. It is shown that the analysis leads to the propagation of the weakly nonlinear dispersive waves, and the nonlinear behavior is governed by the nonlinear Burger's equation.
Directory of Open Access Journals (Sweden)
Stanford Shateyi
2015-01-01
Full Text Available The present study investigates entropy generation on a magnetohydrodynamic flow and heat transfer of a Maxwell fluid using a spectral relaxation method. The method is based on simple iteration schemes formed by reduction of the order of the momentum equation followed by a rearrangement of the resulting governing nonlinear equation systems which are then solved using spectral methods. The velocity and temperature profiles are obtained numerically and used to generate the entropy generation number. Entropy generation increased with the Reynolds number, the magnetic parameter and the dimensionless group parameter while decreased for higher Prandtl numbers. The effect of the flow parameters on the velocity and temperature of the flow were also investigated. The results were validated using the bvp4c where the spectral relaxation method was found to be accurate and rapidly convergent to the numerical results.
Liu, Qing; He, Ya-Ling
2015-11-01
In this paper, a double multiple-relaxation-time lattice Boltzmann model is developed for simulating transient solid-liquid phase change problems in porous media at the representative elementary volume scale. The model uses two different multiple-relaxation-time lattice Boltzmann equations, one for the flow field and the other for the temperature field with nonlinear latent heat source term. The model is based on the generalized non-Darcy formulation, and the solid-liquid interface is traced through the liquid fraction which is determined by the enthalpy-based method. The present model is validated by numerical simulations of conduction melting in a semi-infinite space, solidification in a semi-infinite corner, and convection melting in a square cavity filled with porous media. The numerical results demonstrate the efficiency and accuracy of the present model for simulating transient solid-liquid phase change problems in porous media.
Liu, Qing
2015-01-01
In this paper, a double multiple-relaxation-time lattice Boltzmann model is developed for simulating transient solid-liquid phase change problems in porous media at the representative elementary volume scale. The model uses two different multiple-relaxation-time lattice Boltzmann equations, one for the flow field and the other for the temperature field with nonlinear latent heat source term. The model is based on the generalized non-Darcy formulation, and the solid-liquid phase change interface is traced through the liquid fraction which is determined by the enthalpy method. The model is validated by numerical simulations of conduction melting in a semi-infinite space, solidification in a semi-infinite corner, and convection melting in a square cavity filled with porous media. The numerical results demonstrate the efficiency and accuracy of the present model for simulating transient solid-liquid phase change problems in porous media.
Directory of Open Access Journals (Sweden)
S. S. Motsa
2014-01-01
Full Text Available This paper introduces two novel numerical algorithms for the efficient solution of coupled systems of nonlinear boundary value problems. The methods are benchmarked against existing methods by finding dual solutions of the highly nonlinear system of equations that model the flow of a viscoelastic liquid of Oldroyd-B type in a channel of infinite extent. The methods discussed here are the spectral relaxation method and spectral quasi-linearisation method. To verify the accuracy and efficiency of the proposed methods a comparative evaluation of the performance of the methods against established numerical techniques is given.
Internal relaxation time in immersed particulate materials
Rognon, P; Gay, C
2009-01-01
We study the dynamics of the solid to liquid transition for a model material made of elastic particles immersed in a viscous fluid. The interaction between particle surfaces includes their viscous lubrication, a sharp repulsion when they get closer than a tuned steric length and their elastic deflection induced by those two forces. We use Soft Dynamics to simulate the dynamics of this material when it experiences a step increase in the shear stress and a constant normal stress. We observe a long creep phase before a substantial flow eventually establishes. We find that the typical creep time relies on an internal relaxation process, namely the separation of two particles driven by the applied stress and resisted by the viscous friction. This mechanism should be relevant for granular pastes, living cells, emulsions and wet foams.
Spirooxazine Photoisomerization and Relaxation in Polymer Matrices
Directory of Open Access Journals (Sweden)
Maria Larkowska
2011-01-01
Full Text Available 9′-Hydroxy-1,3,3-trimethylspiro[indoline-2,3′[3H]naphtha[2,1-b]-1,4oxazine] (SPO-7OH was used in studies of photochromic transformations in polymer matrices. Illumination with UV lamp caused opening the spirostructure of the oxazine with formation of open merocyanine species absorbing at ca. 610 nm. The kinetic studies of thermal relaxation of the open form showed that this process can be described with a biexponential function including both photochemical reaction and rheological behaviour of the polymeric environment. Basing on Arrhenius plot of the rate constant ascribed to the photochemical reaction, the activation energy was determined, which was 66.1 and 84.7 kJ/mole for poly(methyl methacrylate-co-butyl methacrylate and poly(vinylpyrrolidone matrix, respectively.
Relaxation and resonances in fluctuating dielectric systems
Garcia-Colin, L. S.; del Castillo, L. F.
1989-09-01
In this paper we show how the ideas behind extended irreversible thermodynamics are used to generate a systematic treatment of the relaxation and resonance phenomena in the propagation and absorption of electromagnetic energy in dielectric materials in a nonequilibrium state. Two cases are discussed: the first, in which the forced oscillations arising from the correlation between the fluctuations of the polarization vector and the electric field are neglected, and the second, in which this term is taken into account. In both cases we show how the main equations serve to make a connection between the macroscopic approach followed here and a number of results obtained for both, gases and polar liquids using molecular models. The results obtained here are compared with previous work on this problem, and new effects arising from the second case are pointed out.