NASA Astrophysics Data System (ADS)
Budroni, M. A.
2015-12-01
Cross diffusion, whereby a flux of a given species entrains the diffusive transport of another species, can trigger buoyancy-driven hydrodynamic instabilities at the interface of initially stable stratifications. Starting from a simple three-component case, we introduce a theoretical framework to classify cross-diffusion-induced hydrodynamic phenomena in two-layer stratifications under the action of the gravitational field. A cross-diffusion-convection (CDC) model is derived by coupling the fickian diffusion formalism to Stokes equations. In order to isolate the effect of cross-diffusion in the convective destabilization of a double-layer system, we impose a starting concentration jump of one species in the bottom layer while the other one is homogeneously distributed over the spatial domain. This initial configuration avoids the concurrence of classic Rayleigh-Taylor or differential-diffusion convective instabilities, and it also allows us to activate selectively the cross-diffusion feedback by which the heterogeneously distributed species influences the diffusive transport of the other species. We identify two types of hydrodynamic modes [the negative cross-diffusion-driven convection (NCC) and the positive cross-diffusion-driven convection (PCC)], corresponding to the sign of this operational cross-diffusion term. By studying the space-time density profiles along the gravitational axis we obtain analytical conditions for the onset of convection in terms of two important parameters only: the operational cross-diffusivity and the buoyancy ratio, giving the relative contribution of the two species to the global density. The general classification of the NCC and PCC scenarios in such parameter space is supported by numerical simulations of the fully nonlinear CDC problem. The resulting convective patterns compare favorably with recent experimental results found in microemulsion systems.
Double-diffusive layer formation
NASA Astrophysics Data System (ADS)
Zaussinger, Florian; Kupka, Friedrich; Hücker, Sebastian; Egbers, Christoph
2015-04-01
Double-diffusive convection plays an important role in geo- and astrophysical applications. The special case, where a destabilising temperature gradient counteracts a stabilising solute gradient leads to layering phenomena under certain conditions. Convectively mixed layers sandwiched in diffusive interfaces form a so-called stack. Well-known double-diffusive systems are observed in rift lakes in Africa and even from the coffee drink Latte Macciatto. Stacks of layers are also predicted to occur inside massive stars and inside giant planets. Their dynamics depend on the thermal, the solute and the momentum diffusivities, as well on the ratio of the gradients of the opposing stratifications. Since the layering process cannot be derived from linear stability analysis, the full nonlinear set of equations has to be investigated. Numerical simulations have become feasible for this task, despite the physical processes operate on a vast range of length and time scales, which is challenging for numerical hydrodynamical modelling. The oceanographically relevant case of fresh and salty water is investigated here in further details. The heat and mass transfer is compared with theoretical results and experimental measurements. Additionally, the initial dynamic of layering, the transient behaviour of a stack and the long time evolution are presented using the example of Lake Kivu and the interior of a giant planet.
NASA Astrophysics Data System (ADS)
Sutherland, Bruce; Lee, Brace
2008-11-01
Sour gas flares attempt to dispose of deadly H2S gas through combustion. What does not burn rises as a buoyant plume. But the gas is heavier than air at room temperature, so as the rising gas cools eventually it becomes negatively buoyant and descends back to the ground. Ultimately, our intent is to predict the concentrations of the gas at ground level in realistic atmospheric conditions. As a first step towards this goal we have performed laboratory experiments examining the structure of a steady state plume of hot and salty water that rises buoyantly near the source and descends as a fountain after it has cooled sufficiently. We call this a double-diffusive plume because its evolution is dictated by the different (turbulent) diffusivities of heat and salt. A temperature and conductivity probe measures both the salinity and temperature along the centreline of the plume. The supposed axisymmetric structure of the salinity concentration as it changes with height is determined by light-attenuation methods. To help interpret the results, a theory has been successfully adapted from the work of Bloomfield and Kerr (2000), who developed coupled equations describing the structure of fountains. Introducing a new empirical parameter for the relative rates of turbulent heat and salt diffusion, the predictions are found to agree favourably with experimental results.
Nonlinear diffusion and superconducting hysteresis
Mayergoyz, I.D.
1996-12-31
Nonlinear diffusion of electromagnetic fields in superconductors with ideal and gradual resistive transitions is studied. Analytical results obtained for linear and nonlinear polarizations of electromagnetic fields are reported. These results lead to various extensions of the critical state model for superconducting hysteresis.
Nonlinear Diffusion and Transient Osmosis
NASA Astrophysics Data System (ADS)
Akira, Igarashi; Lamberto, Rondoni; Antonio, Botrugno; Marco, Pizzi
2011-08-01
We investigate both analytically and numerically the concentration dynamics of a solution in two containers connected by a narrow and short channel, in which diffusion obeys a porous medium equation. We also consider the variation of the pressure in the containers due to the flow of matter in the channel. In particular, we identify a phenomenon, which depends on the transport of matter across nano-porous membranes, which we call “transient osmosis". We find that nonlinear diffusion of the porous medium equation type allows numerous different osmotic-like phenomena, which are not present in the case of ordinary Fickian diffusion. Experimental results suggest one possible candidate for transiently osmotic processes.
Double Diffusive Convection in Materials Processing
NASA Technical Reports Server (NTRS)
Ramachandra, Narayanan; Leslie, Fred W.
1999-01-01
A great number of crystals grown in space are plagued by convective motions which contribute to structural flaws. The character of these instabilities is not well understood but is associated with density variations in the presence of residual gravity (g-jitter). As a specific example, past HgCdTe crystal growth space experiments by Lehoczky and co-workers indicate radial compositional asymmetry in the grown crystals. In the case of HgCdTe the rejected component into the melt upon solidification is HgTe which is denser than the melt. The space grown crystals indicate the presence of three dimensional flow with the heavier HgTe-rich material clearly aligned with the residual gravity (0.55-1.55 micro g) vector. This flow stems from double-diffusive convection, namely, thermal and solutal buoyancy driven flow in the melt. The study of double-diffusive convection is multi-faceted and rather vast. In our investigation, we seek to focus on one specific aspect of this discipline that is of direct relevance to materials processing especially crystal growth, namely, the side ways heating regime. This problem has been widely studied, both experimentally and numerically, in the context of solar ponds wherein the system is characterized by a linear salt (solutal) gradient with an imposed lateral temperature gradient. The induced flow instabilities arise from the wide disparity between the fluid thermal diffusivity and the solute diffusivity. The extension of the analysis to practical crystal growth applications has however not been rigorously made and understood. One subtle but important difference in crystal growth systems is the fact that die system solute gradient is non-linear (typically exponential). Besides, the crystal growth problem has the added complexities of solidification, both lateral and longitudinal thermal gradients and segregation phenomena in systems where binary and ternary compounds are being grown. This paper treats the side ways heating problem alone in
Fluid dynamics of double diffusive systems
Koseff, J.R.
1989-04-07
A study of mixing processes in doubly diffusive systems is being conducted. Continuous gradients of two diffusing components (heat and salinity in our case) are being used as initial conditions, and forcing is introduced by lateral heating and surface shear. The goals of the proposed work include: (1) quantification of the effects of finite amplitude disturbances on stable, double diffusive systems, particularly with respect to lateral heating, (2) development of an improved understanding of the physical phenomena present in wind-driven shear flows in double diffusive stratified environments, (3) increasing our knowledge-base on turbulent flow in stratified environments and how to represent it, and (4) formulation of a numerical code for such flows. The work is being carried out in an experimental facility which is located in the Stanford Environmental Fluid Mechanics Laboratory, and on laboratory minicomputers and CRAY computers. In particular we are focusing on the following key issues: (1) the formation and propagation of double diffusive intrusions away from a heated wall and the effects of lateral heating on the double diffusive system; (2) the interaction between the double diffusively influenced fluxes and the turbulence induced fluxes; (3) the measurement of heat and mass fluxes; and (4) the influence of double diffusive gradients on mixed layer deepening. 1 fig.
Compact waves in microscopic nonlinear diffusion.
Hurtado, P I; Krapivsky, P L
2012-06-01
We analyze the spread of a localized peak of energy into vacuum for nonlinear diffusive processes. In contrast with standard diffusion, the nonlinearity results in a compact wave with a sharp front separating the perturbed region from vacuum. In d spatial dimensions, the front advances as t^{1/(2+da)} according to hydrodynamics, with a the nonlinearity exponent. We show that fluctuations in the front position grow as ∼t^{μ}η, where μ<1/2+da is an exponent that we measure and η is a random variable whose distribution we characterize. Fluctuating corrections to hydrodynamic profiles give rise to an excess penetration into vacuum, revealing scaling behaviors and robust features. We also examine the discharge of a nonlinear rarefaction wave into vacuum. Our results suggest the existence of universal scaling behaviors at the fluctuating level in nonlinear diffusion.
Double-Diffusive Convection in Rotational Shear
2015-03-01
CONVECTION IN ROTATIONAL SHEAR by James S. Ball March 2015 Thesis Advisor: Timour Radko Second Reader: John Colosi THIS PAGE...AND SUBTITLE 5. FUNDING NUMBERS DOUBLE-DIFFUSIVE CONVECTION IN ROTATIONAL SHEAR 6. AUTHOR(S) James S. Ball 7. PERFORMING ORGANIZATION NAME(S) AND...INTENTIONALLY LEFT BLANK ii Approved for public release;distribution is unlimited DOUBLE-DIFFUSIVE CONVECTION IN ROTATIONAL SHEAR James S. Ball
Nonlinear dynamics of a double bilipid membrane.
Sample, C; Golovin, A A
2007-09-01
The nonlinear dynamics of a biological double membrane that consists of two coupled lipid bilayers, typical of some intracellular organelles such as mitochondria or nuclei, is studied. A phenomenological free-energy functional is formulated in which the curvatures of the two parts of the double membrane and the distance between them are coupled to the lipid chemical composition. The derived nonlinear evolution equations for the double-membrane dynamics are studied analytically and numerically. A linear stability analysis is performed, and the domains of parameters are found in which the double membrane is stable. For the parameter values corresponding to an unstable membrane, numerical simulations are performed that reveal various types of complex dynamics, including the formation of stationary, spatially periodic patterns.
Numerical discretization for nonlinear diffusion filter
NASA Astrophysics Data System (ADS)
Mustaffa, I.; Mizuar, I.; Aminuddin, M. M. M.; Dasril, Y.
2015-05-01
Nonlinear diffusion filters are famously used in machine vision for image denoising and restoration. This paper presents a study on the effects of different numerical discretization of nonlinear diffusion filter. Several numerical discretization schemes are presented; namely semi-implicit, AOS, and fully implicit schemes. The results of these schemes are compared by visual results, objective measurement e.g. PSNR and MSE. The results are also compared to a Daubechies wavelet denoising method. It is acknowledged that the two preceding scheme have already been discussed in literature, however comparison to the latter scheme has not been made. The semi-implicit scheme uses an additive operator splitting (AOS) developed to overcome the shortcoming of the explicit scheme i.e., stability for very small time steps. Although AOS has proven to be efficient, from the nonlinear diffusion filter results with different discretization schemes, examples shows that implicit schemes are worth pursuing.
Enhanced nonlinear susceptibility via double-double electromagnetically induced transparency
NASA Astrophysics Data System (ADS)
Alotaibi, Hessa M. M.; Sanders, Barry C.
2016-11-01
We investigate the nonlinear optical susceptibility of an alkali-metal atom with tripod electronic configuration responsible for generating cross-phase modulation and self-phase modulation under the condition of double-double electromagnetically induced transparency. Our investigation demonstrates an enhancement in the nonlinear optical susceptibility of an alkali-metal atom by a factor of 1000 in the region of the second transparency window. This enhancement is in comparison with the atom's susceptibility in the first transparency window for the same parameters under the same conditions. Nonlinear-absorption enhancement arises by canceling Raman-gain generation, which arises when the probe and signal fields have equal intensities. At the center of the second transparency window, we obtain the condition required to attain a nonvanishing nonlinear optical susceptibility. In the bare-state picture, the coupling field must be off resonant from a bare-to-bare-state transition, while working in the semiclassical dressed picture required the signal field to be tuned off resonantly with a bare-to-dressed-state transition. The relation that governs the values of coupling- and signal-field detuning are also obtained. Our scheme exhibits the fact that the second transparency window has advantages over the first transparency window with respect to obtaining an enhanced Kerr effect, and our calculation includes simulation of both low-temperature and Doppler-broadened regimes.
Nonlinear Surface Transport in the Thin Double-Layer Limit
NASA Astrophysics Data System (ADS)
Chu, Kevin; Bazant, Martin
2006-03-01
At high applied electric fields, ionic transport within the double layer plays a significant role in the overall response of electrokinetic systems. It is well-known that surface transport processes, including surface electromigration, surface diffusion and surface advection, may impact the strength of electrokinetic phenomena by affecting both the zeta-potential and the magnitude of the tangential electric field. Therefore, it is important to include these effects when formulating the effective boundary conditions for the equations that govern electrokinetic flow outside of the double layer. In this talk, we discuss the application of a general formulation of ``surface conservation laws'' for diffuse boundary layers to derive effective boundary conditions that capture the physics of electrokinetic surface transport. Previous analyses (e.g. Deryagin & Dukhin 1969) are only valid for weak applied fields and are based on a linearization of the concentration and potential about a reference solution, but our results are fully nonlinear and hold at large applied fields as long as the double layer is sufficiently thin. We compare our nonlinear surface transport theory with existing linear analogues and apply it to the canonical problem of induced-charge electro-osmosis around a metal sphere or cylinder in a strong DC field.
Diapycnal Transport and Pattern Formation in Double-Diffusive Convection
2015-12-01
TRANSPORT AND PATTERN FORMATION IN DOUBLE-DIFFUSIVE CONVECTION by Erick L. Edwards December 2015 Dissertation Supervisor Timour Radko THIS...Dissertation 4. TITLE AND SUBTITLE DIAPYCNAL TRANSPORT AND PATTERN FORMATION IN DOUBLE- DIFFUSIVE CONVECTION 5. FUNDING NUMBERS 6. AUTHOR(S...is unlimited 12b. DISTRIBUTION CODE 13. ABSTRACT (maximum 200 words) This work analyzes the role of double-diffusive convection
NASA Astrophysics Data System (ADS)
Anwar Bég, O.; Zueco, J.; Takhar, H. S.; Bég, T. A.; Sajid, A.
2009-11-01
A boundary-layer model is described for the two-dimensional nonlinear transient thermal convection heat and mass transfer in an optically-thick fluid in a Darcian porous medium adjacent to an impulsively started vertical surface, in the presence of significant thermal radiation and buoyancy forces in an (X∗,Y∗,t∗) coordinate system. An algebraic approximation is employed to simplify the integro-differential equation of radiative transfer for unidirectional flux normal to the plate into the boundary-layer regime, by incorporating this flux term in the energy conservation equation. The conservation equations are non-dimensionalized into an (X,Y,T) coordinate system and solved using the Network Simulation Method (NSM), a robust numerical technique which demonstrates high efficiency and accuracy. The transient variation of non-dimensional streamwise velocity component (u) and temperature (T) and concentration (C) functions is computed for various selected values of Stark number (radiation-conduction interaction parameter) and Darcy number. Transient velocity (u) and steady-state local skin friction (τX) are also studied for various thermal Grashof number (Gr), species Grashof number (Gm), Schmidt number (Sc) and Stark number (N) values. These computations for the infinite permeability case (Da → ∞) are compared with previous finite difference solutions [Prasad et al. Int J Therm Sci 2007;46(12):1251-8] and shown to be in excellent agreement. An increase in Darcy number is seen to accelerate the flow and boost velocity. A decrease in Stark number (corresponding to an increase in thermal radiation heat transfer contribution) is shown to increase the velocity values. Temperature function is observed to fall in value with a rise in Da and increase with decrease in N (corresponding to an increase in thermal radiation heat transfer contribution). Applications of the study include rocket combustion chambers, astrophysical flows, spacecraft thermal fluid dynamics in
Delinating Thermohaline Double-Diffusive Rayleigh Regimes
NASA Astrophysics Data System (ADS)
Graf, T.; Walther, M.; Kolditz, O.; Liedl, R.
2013-12-01
In natural systems, convective flow induced from density differences may occur in near-coastal aquifers, atmospheric boundary layers, oceanic streams or within the earth crust. Whether an initially stable, diffusive regime evolves into a convective (stable or chaotic) regime, or vice versa, depends on the system's framing boundary conditions. A conventional parameter to express the relation between diffusive and convective forces of such a density-driven regime is Rayleigh number (Ra). While most systems are mainly dominated by only a single significant driving force (i.e. only temperature or salinity), some systems need to consider two boundary processes (e.g. deep, thus warm, haline flow in porous media). In that case, a two-dimensional, 'double-diffusive' Rayleigh system can be defined. Nield (1998) postulated a boundary between diffusive and convective regime at RaT + RaC = 4pi^2 in the first quadrant (Q1), with Rayleigh numbers for temperature and concentration respectively. The boundary in the forth quadrant (Q4) could not exactly be determined, yet the approximate position estimated. Simulations with HydroGeoSphere (Therrien, 2010) using a vertical, quadratic, homogeneous, isotropic setup confirmed the existence of the 4pi^2-boundary and revealed additional regimes (diffusive, single-roll, double-roll, chaotic) in Q1. Also, non-chaotic, oscillating patterns could be identified in Q4. More detailed investigations with OpenGeoSys (Kolditz, 2012) confirmed the preceding HGS results, and, using a 1:10-scaled domain (height:length), uncovered even more distinctive regimes (diffusive, minimum ten roles, supposely up to 25 roles, and chaotic?) in Q1, while again, oscillating patterns were found in the transition zone between diffusive and chaotic regimes in Q4. Output of numerical simulations from Q1 and Q4 show the mentioned regimes (diffusive, stable-convective, stable-oscillatory, chaotic) while results are displayed in context of a possible delination between
Arnold, J.; Kosson, D.S.; Garrabrants, A.; Meeussen, J.C.L.; Sloot, H.A. van der
2013-02-15
A robust numerical solution of the nonlinear Poisson-Boltzmann equation for asymmetric polyelectrolyte solutions in discrete pore geometries is presented. Comparisons to the linearized approximation of the Poisson-Boltzmann equation reveal that the assumptions leading to linearization may not be appropriate for the electrochemical regime in many cementitious materials. Implications of the electric double layer on both partitioning of species and on diffusive release are discussed. The influence of the electric double layer on anion diffusion relative to cation diffusion is examined.
Double-diffusive inner core convective translation
NASA Astrophysics Data System (ADS)
Deguen, Renaud; Alboussière, Thierry; Labrosse, Stéphane
2016-04-01
The hemispherical asymmetry of the inner core has been interpreted as resulting form a high-viscosity mode of inner core convection, consisting in a translation of the inner core. With melting on one hemisphere and crystallization on the other one, inner core translation would impose a strongly asymmetric buoyancy flux at the bottom of the outer core, with likely strong implications for the dynamics of the outer core and the geodynamo. The main requirement for convective instability in the inner core is an adverse radial density gradient. While older estimates of the inner core thermal conductivity favored a superadiabatic temperature gradient and the existence of thermal convection, the much higher values recently proposed makes thermal convection very unlikely. Compositional convection might be a viable alternative to thermal convection: an unstable compositional gradient may arise in the inner core either because the light elements present in the core are predicted to become increasingly incompatible as the inner core grows (Gubbins et al. 2013), or because of a possibly positive feedback of the development of the F-layer on inner core convection. Though the magnitude of the destabilizing effect of the compositional field is predicted to be similar to or smaller than the stabilizing effect of the thermal field, the huge difference between thermal and chemical diffusivities implies that double-diffusive instabilities can still arise even if the net density decreases upward. We propose here a theoretical and numerical study of double diffusive convection in the inner core that demonstrate that a translation mode can indeed exist if the compositional field is destabilizing, even if the temperature profile is subadiabatic, and irrespectively of the relative magnitude of the destabilizing compositional gradient and stabilizing temperature field. The predicted inner core translation rate is similar to the mean inner core growth rate, which is more consistent with
Double-Diffusive Layers and Phase Transitions
NASA Astrophysics Data System (ADS)
Dude, Sabine; Hansen, Ulrich
2015-04-01
Researching the thermal evolution of the Earth's mantle on numerical base is very challenging. During the last decade different approaches are put forward in oder to understand the picture of the today's Earth's mantle. One way is to incorporate all the known features and physics (plate tectonics, phase transitions, CMB-topography, ...) into numerical models and make them as complex (or 'complete') as possible to capture Earth's mantle processes and surface signals. Another way is, to take a step back and look at less complex models which account for single processes and their interaction and evolution. With these 'simpler' models one is able look in detail into the physical processes and dependencies on certain parameters. Since the knowledge of slab stagnation in the transitions zone of the Earth's mantle the question whether the mantle is or at least has been layered to some degree is still under debate. On this basis we address two important features that lead to layered mantle convection and may affect each other and with this the thermal evolution of the mantle. It is commonly known the main mantle mineral olivine pass through various phase changes with depth [1]. Detailed numerical studies had been carried out to ascertain the influence on convective motion and planetary evolution [2]. It is still heavily discussed whether the endothermic phase change at 660km depth can lead an isolated lower mantle. Most of the numerical studies favour a model which has phases of layering that are disrupted by catastrophic events. In the last years double-diffusive convection has also been intensively studied with regard to planetary mantle evolution such as pile formation and core-mantle boundary topography [3]. However, another striking feature still posing open questions are evolving layers self-organised from a previous non layered state. Considering a chemical component that influences the density of a fluid in addition to the temperature leads to dynamical phenomena
Parity breaking with a nonlinear optical double-slit configuration
NASA Astrophysics Data System (ADS)
Paltoglou, Vassilis; Efremidis, Nikolaos K.
2017-02-01
We consider an optical nonlinear interferometric setup based on Young's double-slit configuration where a nonlinear material is placed exactly after one of the two slits. We examine the effects of Kerr nonlinearity and multi-photon absorption in the resulting interference pattern. The presence of nonlinearity breaks the transverse spatial symmetry of the system, resulting to a modified intensity pattern at the observation plane as a function of the incident intensity. Our theoretical model, based on the modification of the optical path due to the presence of nonlinearity, is surprisingly accurate in predicting the intensity profile of the main lobes for a wide range of parameters. We discuss about potential applications of our model in nonlinear interferometry. Specifically, we show that it is possible to measure both the multi-photon and the Kerr coefficients of a nonlinear material based on the spatial translation of the interference pattern as a function of the incident intensity.
Dissipative double-well potential: Nonlinear stationary and pulsating modes
Zezyulin, Dmitry A.; Konotop, Vladimir V.; Alfimov, Georgy L.
2010-11-15
The analysis of nonlinear modes in a complex absorbing double-well potential supported by linear gain is presented. Families of the nonlinear modes and their bifurcations are found numerically by means of the properly modified 'shooting' method. Linear stability and dynamics of the modes are studied. It is shown that no stable modes exist in the case of attractive nonlinearity, while stable modes, including nonsymmetric ones, are found when the nonlinearity is repulsive. Varying a control parameter (e.g., the height of barrier between the wells) results in switching from one mode to another. Apart from stationary modes we have found pulsating solutions emergent from unstable modes.
Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Alsaedi, Ahmed
2017-01-01
Here two classes of viscoelastic fluids have been analyzed in the presence of Cattaneo-Christov double diffusion expressions of heat and mass transfer. A linearly stretched sheet has been used to create the flow. Thermal and concentration diffusions are characterized firstly by introducing Cattaneo-Christov fluxes. Novel features regarding Brownian motion and thermophoresis are retained. The conversion of nonlinear partial differential system to nonlinear ordinary differential system has been taken into place by using suitable transformations. The resulting nonlinear systems have been solved via convergent approach. Graphs have been sketched in order to investigate how the velocity, temperature and concentration profiles are affected by distinct physical flow parameters. Numerical values of skin friction coefficient and heat and mass transfer rates at the wall are also computed and discussed. Our observations demonstrate that the temperature and concentration fields are decreasing functions of thermal and concentration relaxation parameters. PMID:28046011
Three-dimensional flow of nanofluid with Cattaneo-Christov double diffusion
NASA Astrophysics Data System (ADS)
Hayat, Tasawar; Muhammad, Taseer; Alsaedi, Ahmed; Ahmad, Bashir
Three dimensional (3D) boundary-layer flow of viscous nanofluid has been investigated in the presence of Cattaneo-Christov double diffusion. A bi-directional linearly stretching sheet has been used to create the flow. Thermal and concentration diffusions are characterized by introducing Cattaneo-Christov fluxes. Novel attributes regarding Brownian motion and thermophoresis are retained. The conversion of nonlinear partial differential system to nonlinear ordinary differential system is done through suitable transformations. The resulting nonlinear systems are solved. Graphs have been sketched in order to investigate that how the temperature and concentration profiles are affected by distinct physical flow parameters. Further the skin friction and heat and mass transfer rates are numerically computed and discussed. Our findings depict that temperature and concentration distributions are decreasing functions of thermal and concentration relaxation parameters.
Period-Doubling Bifurcation in Nonlinear Systems
NASA Astrophysics Data System (ADS)
Mao, Jian-Min
The dependence of the critical exponents, such as the Feigenbaum ratios, of the period-doubling bifurcation on the order of critical point z is studied. The dependence is quantitatively given for one-dimensional dissipative maps. The scaling factor in the period-doubling power spectrum of a class of two-dimensional area-preserving maps is found to approach a universal limit by both fast Fourier transform and autocorrelation-function analysis. The dependence of the fractal dimension on the critical-point order is studied. The variation of the three most commonly used definitions of dimension, viz., the capacity, the information dimension, and the correlation exponent, is computed as a function of z. The numerical values agree very well with analytical estimates. The dependence of the scaling of the period-doubling bifurcation on the dimensionality of the reduced phase space is considered. Especially, the investigation of period-doubling bifurcations in four-dimensional symplectic maps indicates the existence of an universally self-similar period-doubling sequence. The fixed-point map has two unstable directions under the period-doubling operator with two relevant eigenvalues. The four orbital scaling factors have been found. As an extension of the Feigenbaum scaling law for parameter and orbital element, a many-term scaling law is suggested. For one-dimensional dissipative maps, two-dimensional area-preserving maps, and four-dimensional symplectic maps, the many-term scaling law is very well obeyed. New scaling factors have been found.
Double diffusive convection in a porous medium layer saturated with an Oldroyd nanofluid
NASA Astrophysics Data System (ADS)
Umavathi, J. C.; Sasso, Maurizio
2017-01-01
The onset of double diffusive convection in a horizontal layer of a porous medium saturated with an Oldroyd nanofluid is studied using linear and non-linear stability analysis. The modified Darcy-Oldroyd model is used for the momentum equation. The model used for the Oldroyd nanofluid incorporates the effects of Brownian motion and thermophoresis. The thermal energy equations include the diffusion and cross diffusion terms. The linear theory depends on normal mode technique and the onset criterion for stationary and oscillatory convection is derived analytically. The effects of various governing parameters viz., concentration Rayleigh number, nanofluid Lewis number, modified diffusivity ratio, Soret and Dufour parameters, Solutal Rayleigh number, Vadasz number, Lewis number, relaxation, and retardation parameters, viscosity ratio and conductivity ratio on the stationary and oscillatory convections are presented graphically. The non-linear theory based on the representation of Fourier series method is used to find the heat and mass transport. The effect of various parameters on transient heat and mass transfer is also brought out and nonlinear analysis depends on a minimal representation of double Fourier series. We also study the effect of time on transient Nusselt numbers which is found to be oscillatory when time is small. However, when time becomes very large all the three transient Nusselt values approaches to their steady state values.
Pattern formation due to non-linear vortex diffusion
NASA Astrophysics Data System (ADS)
Wijngaarden, Rinke J.; Surdeanu, R.; Huijbregtse, J. M.; Rector, J. H.; Dam, B.; Einfeld, J.; Wördenweber, R.; Griessen, R.
Penetration of magnetic flux in YBa 2Cu 3O 7 superconducting thin films in an external magnetic field is visualized using a magneto-optic technique. A variety of flux patterns due to non-linear vortex diffusion is observed: (1) Roughening of the flux front with scaling exponents identical to those observed in burning paper including two distinct regimes where respectively spatial disorder and temporal disorder dominate. In the latter regime Kardar-Parisi-Zhang behavior is found. (2) Fractal penetration of flux with Hausdorff dimension depending on the critical current anisotropy. (3) Penetration as ‘flux-rivers’. (4) The occurrence of commensurate and incommensurate channels in films with anti-dots as predicted in numerical simulations by Reichhardt, Olson and Nori. It is shown that most of the observed behavior is related to the non-linear diffusion of vortices by comparison with simulations of the non-linear diffusion equation appropriate for vortices.
Bright solitons in nonlinear media with a self-defocusing double-well nonlinearity
NASA Astrophysics Data System (ADS)
Xie, Qiongtao; Wang, Linmao; Wang, Yizhen; Shen, Zhenjiang; Fu, Jun
2014-12-01
We show that stable bright solitons can appear in a medium with spatially inhomogeneous self-defocusing (SDF) nonlinearity of a double-well structure. For a specific choice of the nonlinearity parameters, we obtain exact analytical solutions for the fundamental bright solitons. By making use of the linear stability analysis, the stability region in the parameter space for the exact fundamental bright soliton is obtained numerically. We also show the bifurcation from an antisymmetric to an asymmetric bright soliton for the SDF double-well nonlinearity.
On nonlinear conservation laws with a nonlocal diffusion term
NASA Astrophysics Data System (ADS)
Achleitner, F.; Hittmeir, S.; Schmeiser, C.
Scalar one-dimensional conservation laws with a nonlocal diffusion term corresponding to a Riesz-Feller differential operator are considered. Solvability results for the Cauchy problem in L are adapted from the case of a fractional derivative with homogeneous symbol. The main interest of this work is the investigation of smooth shock profiles. In the case of a genuinely nonlinear smooth flux function we prove the existence of such travelling waves, which are monotone and satisfy the standard entropy condition. Moreover, the dynamic nonlinear stability of the travelling waves under small perturbations is proven, similarly to the case of the standard diffusive regularisation, by constructing a Lyapunov functional.
Evolution Nonlinear Diffusion-Convection PDE Models for Spectrogram Enhancement
NASA Astrophysics Data System (ADS)
Dugnol, B.; Fernández, C.; Galiano, G.; Velasco, J.
2008-09-01
In previous works we studied the application of PDE-based image processing techniques applied to the spectrogram of audio signals in order to improve the readability of the signal. In particular we considered the implementation of the nonlinear diffusive model proposed by Álvarez, Lions and Morel [1](ALM) combined with a convective term inspired by the differential reassignment proposed by Chassandre-Mottin, Daubechies, Auger and Flandrin [2]-[3]. In this work we consider the possibility of replacing the diffusive model of ALM by diffusive terms in divergence form. In particular we implement finite element approximations of nonlinear diffusive terms studied by Chen, Levine, Rao [4] and Antontsev, Shmarev [5]-[8] with a convective term.
Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion
Del Razo, Mauricio; Pan, Wenxiao; Qian, Hong; Lin, Guang
2014-05-30
The currently existing theory of fluorescence correlation spectroscopy (FCS) is based on the linear fluctuation theory originally developed by Einstein, Onsager, Lax, and others as a phenomenological approach to equilibrium fluctuations in bulk solutions. For mesoscopic reaction-diffusion systems with nonlinear chemical reactions among a small number of molecules, a situation often encountered in single-cell biochemistry, it is expected that FCS time correlation functions of a reaction-diffusion system can deviate from the classic results of Elson and Magde [Biopolymers (1974) 13:1-27]. We first discuss this nonlinear effect for reaction systems without diffusion. For nonlinear stochastic reaction-diffusion systems there are no closed solutions; therefore, stochastic Monte-Carlo simulations are carried out. We show that the deviation is small for a simple bimolecular reaction; the most significant deviations occur when the number of molecules is small and of the same order. Extending Delbrück-Gillespie’s theory for stochastic nonlinear reactions with rapidly stirring to reaction-diffusion systems provides a mesoscopic model for chemical and biochemical reactions at nanometric and mesoscopic level such as a single biological cell.
Numerical simulation of double-diffusive finger convection
Hughes, J.D.; Sanford, W.E.; Vacher, H.L.
2005-01-01
A hybrid finite element, integrated finite difference numerical model is developed for the simulation of double-diffusive and multicomponent flow in two and three dimensions. The model is based on a multidimensional, density-dependent, saturated-unsaturated transport model (SUTRA), which uses one governing equation for fluid flow and another for solute transport. The solute-transport equation is applied sequentially to each simulated species. Density coupling of the flow and solute-transport equations is accounted for and handled using a sequential implicit Picard iterative scheme. High-resolution data from a double-diffusive Hele-Shaw experiment, initially in a density-stable configuration, is used to verify the numerical model. The temporal and spatial evolution of simulated double-diffusive convection is in good agreement with experimental results. Numerical results are very sensitive to discretization and correspond closest to experimental results when element sizes adequately define the spatial resolution of observed fingering. Numerical results also indicate that differences in the molecular diffusivity of sodium chloride and the dye used to visualize experimental sodium chloride concentrations are significant and cause inaccurate mapping of sodium chloride concentrations by the dye, especially at late times. As a result of reduced diffusion, simulated dye fingers are better defined than simulated sodium chloride fingers and exhibit more vertical mass transfer. Copyright 2005 by the American Geophysical Union.
NASA Astrophysics Data System (ADS)
Mizushima, Jiro; Izumikawa, Hayato; Fujimura, Kaoru
2016-04-01
Two-dimensional double diffusive convection of a binary fluid mixture in a square container is investigated by linear and weakly nonlinear stability analyses, numerical simulations and numerical calculations of steady solutions in the present paper. We consider an ethanol-water mixture as the binary fluid, in which the temperature and the ethanol concentration interact through the Soret effect, both affecting the fluid motion via buoyancy force. The bottom of the container is kept at a higher temperature than the top, while the side walls are assumed thermally insulating. The heat conduction state is known to become unstable to an oscillatory mode as well as a stationary mode of disturbance, and the two instability modes exchange at a set of parameter values, called codimension two point. It was reported that the convection often tend to a steady state even if the instability is induced by an oscillatory mode, which is an unusual flow property. We explore its mathematical and physical reason by formally deriving a set of amplitude equations near the codimension two point by applying the center manifold theory. It is shown that the unusual nonlinear behavior of the double diffusive convection is clearly explained from the bifurcation structure of the solutions to the set of amplitude equations.
Boundedness in a chemotaxis-haptotaxis model with nonlinear diffusion
NASA Astrophysics Data System (ADS)
Li, Yan; Lankeit, Johannes
2016-05-01
This article deals with an initial-boundary value problem for the coupled chemotaxis-haptotaxis system with nonlinear diffusion under homogeneous Neumann boundary conditions in a bounded smooth domain Ω \\subset {{{R}}n} , n = 2, 3, 4, where χ,ξ and μ are given nonnegative parameters. The diffusivity D(u) is assumed to satisfy D(u)≥slant δ {{u}m-1} for all u > 0 with some δ >0 . It is proved that for sufficiently regular initial data global bounded solutions exist whenever m>2-\\frac{2}{n} . For the case of non-degenerate diffusion (i.e. D(0) > 0) the solutions are classical; for the case of possibly degenerate diffusion (D(0)≥slant 0 ), the existence of bounded weak solutions is shown.
Experiments with a Class of Nonlinear Anti-Diffusion Schemes
NASA Astrophysics Data System (ADS)
Moini-Yekta, Shayan
The use of artificial viscosity in the simulation of viscous flows with separation, as well as inviscid flows with shocks is demonstrated first, based on standard central difference schemes. The effects of a class of nonlinear anti-diffusion schemes are studied. Furthermore, the anti-diffusion scheme is used to simulate turbulent flows over a flat plate and an ellipse, based on a primitive variable formulation in curvilinear coordinates and the artificial compressibility method. Both Baldwin-Lomax and Spalart-Allamaras models are implemented and the results are compared to those of the NASA CFL3D code. The results based on the anti-diffusion scheme are encouraging as third order upwinding results are recovered with first order upwinding with anti-diffusion.
Nonlinear saturation of trapped electron modes via perpendicular particle diffusion.
Merz, F; Jenko, F
2008-01-25
In magnetized fusion plasmas, trapped electron mode (TEM) turbulence constitutes, together with ion temperature gradient (ITG) turbulence, the dominant source of anomalous transport on ion scales. While ITG modes are known to saturate via nonlinear zonal flow generation, this mechanism is shown to be of little importance for TEM turbulence in the parameter regime explored here. Instead, a careful analysis of the statistical properties of the ExB nonlinearity in the context of gyrokinetic turbulence simulations reveals that perpendicular particle diffusion is the dominant saturation mechanism. These findings allow for the construction of a rather realistic quasilinear model of TEM induced transport.
Exact nonlinear excitations in double-degenerate plasmas
Akbari-Moghanjoughi, M.
2012-06-15
In this work, we use the conventional hydrodynamics formalism and incorporate the Chew-Goldberger-Low double-adiabatic theory to evaluate the nonlinear electrostatic ion excitations in double-degenerate (electron spin-orbit degenerate) magnetized quantum plasmas. Based on the Sagdeev pseudopotential method, an exact general pseudopotential is calculated which leads to the allowed Mach-number range criteria for such localized density structures in an anisotropic magnetized plasma. We employ the criteria on the Mach-number range for diverse magnetized quantum plasma with different equations of state. It is remarked that various plasma fractional parameters such as the system dimensionality, ion-temperature, relativistic-degeneracy, Zeeman-energy, and plasma composition are involved in the stability of an obliquely propagating nonlinear ion-acoustic wave in a double-degenerate quantum plasma. Current study is most appropriate for nonlinear wave analysis in dense astrophysical magnetized plasma environments such as white-dwarfs and neutron-star crusts where the strong magnetic fields can be present.
Diffusive limits of nonlinear hyperbolic systems with variable coefficients
NASA Astrophysics Data System (ADS)
Miyoshi, Hironari; Tsutsumi, Masayoshi
2016-09-01
We consider the initial-boundary value problem for a 2-speed system of first-order nonhomogeneous semilinear hyperbolic equations whose leading terms have a small positive parameter. Using energy estimates and a compactness lemma, we show that the diffusion limit of the sum of the solutions of the hyperbolic system, as the parameter tends to zero, verifies the nonlinear parabolic equation of the p-Laplacian type.
Multi-diffusive nonlinear Fokker-Planck equation
NASA Astrophysics Data System (ADS)
Ribeiro, Mauricio S.; Casas, Gabriela A.; Nobre, Fernando D.
2017-02-01
Nonlinear Fokker-Planck equations, characterized by more than one diffusion term, have appeared recently in literature. Here, it is shown that these equations may be derived either from approximations in a master equation, or from a Langevin-type approach. An H-theorem is proven, relating these Fokker-Planck equations to an entropy composed by a sum of contributions, each of them associated with a given diffusion term. Moreover, the stationary state of the Fokker-Planck equation is shown to coincide with the equilibrium state, obtained by extremization of the entropy, in the sense that both procedures yield precisely the same equation. Due to the nonlinear character of this equation, the equilibrium probability may be obtained, in most cases, only by means of numerical approaches. Some examples are worked out, where the equilibrium probability distribution is computed for nonlinear Fokker-Planck equations presenting two diffusion terms, corresponding to an entropy characterized by a sum of two contributions. It is shown that the resulting equilibrium distribution, in general, presents a form that differs from a sum of the equilibrium distributions that maximizes each entropic contribution separately, although in some cases one may construct such a linear combination as a good approximation for the equilibrium distribution.
NASA Astrophysics Data System (ADS)
Cherniha, Roman; King, John R.; Kovalenko, Sergii
2016-07-01
Complete descriptions of the Lie symmetries of a class of nonlinear reaction-diffusion equations with gradient-dependent diffusivity in one and two space dimensions are obtained. A surprisingly rich set of Lie symmetry algebras depending on the form of diffusivity and source (sink) in the equations is derived. It is established that there exists a subclass in 1-D space admitting an infinite-dimensional Lie algebra of invariance so that it is linearisable. A special power-law diffusivity with a fixed exponent, which leads to wider Lie invariance of the equations in question in 2-D space, is also derived. However, it is shown that the diffusion equation without a source term (which often arises in applications and is sometimes called the Perona-Malik equation) possesses no rich variety of Lie symmetries depending on the form of gradient-dependent diffusivity. The results of the Lie symmetry classification for the reduction to lower dimensionality, and a search for exact solutions of the nonlinear 2-D equation with power-law diffusivity, also are included.
Non-linear Young's double-slit experiment.
San Roman, Julio; Ruiz, Camilo; Perez, Jose Antonio; Delgado, Diego; Mendez, Cruz; Plaja, Luis; Roso, Luis
2006-04-03
The Young's double slit experiment is recreated using intense and short laser pulses. Our experiment evidences the role of the non-linear Kerr effect in the formation of interference patterns. In particular, our results evidence a mixed mechanism in which the zeroth diffraction order of each slit are mainly affected by self-focusing and self-phase modulation, while the higher orders propagate linearly. Despite of the complexity of the general problem of non-linear propagation, we demonstrate that this experiment retains its simplicity and allows for a geometrical interpretation in terms of simple optical paths. In consequence, our results may provide key ideas on experiments on the formation of interference patterns with intense laser fields in Kerr media.
NASA Astrophysics Data System (ADS)
Demberg, Kerstin; Laun, Frederik Bernd; Windschuh, Johannes; Umathum, Reiner; Bachert, Peter; Kuder, Tristan Anselm
2017-02-01
Diffusion pore imaging is an extension of diffusion-weighted nuclear magnetic resonance imaging enabling the direct measurement of the shape of arbitrarily formed, closed pores by probing diffusion restrictions using the motion of spin-bearing particles. Examples of such pores comprise cells in biological tissue or oil containing cavities in porous rocks. All pores contained in the measurement volume contribute to one reconstructed image, which reduces the problem of vanishing signal at increasing resolution present in conventional magnetic resonance imaging. It has been previously experimentally demonstrated that pore imaging using a combination of a long and a narrow magnetic field gradient pulse is feasible. In this work, an experimental verification is presented showing that pores can be imaged using short gradient pulses only. Experiments were carried out using hyperpolarized xenon gas in well-defined pores. The phase required for pore image reconstruction was retrieved from double diffusion encoded (DDE) measurements, while the magnitude could either be obtained from DDE signals or classical diffusion measurements with single encoding. The occurring image artifacts caused by restrictions of the gradient system, insufficient diffusion time, and by the phase reconstruction approach were investigated. Employing short gradient pulses only is advantageous compared to the initial long-narrow approach due to a more flexible sequence design when omitting the long gradient and due to faster convergence to the diffusion long-time limit, which may enable application to larger pores.
Double Diffusive Natural Convection in a Nuclear Waste Repository
Hao, Y; Nitao, J J; Buscheck, T A; Sun, Y
2006-07-24
In this study, we conduct a two dimensional numerical analysis of double diffusive natural convection in an emplacement drift for a nuclear waste repository. In-drift heat and moisture transport is driven by combined thermal- and compositional-induced buoyancy forces. Numerical results demonstrate buoyancy-driven convective flow patterns and configurations during both repository heat-up and cool-down phases. It is also shown that boundary conditions, particularly on the drip-shield surface, have a strong impact on in-drift convective flow and transport.
A double-serpentine diffusion path for a ternary diffusion couple
Sohn, Y.H.; Dayananda, M.A.
2000-04-19
A double-serpentine diffusion path that crosses the straight line joining the terminal alloy compositions twice on a ternary isotherm is reported for a diffusion couple assembled with two {beta} (B{sub 2}) Fe-Ni-Al alloys and annealed at 1,000 C for 2 days. The couple developed a Ni concentration profile that exhibited two regions of mass loss separated by a region of mass gain on one side of the Matano plant. With an additional couple whose path intersected the double serpentine path, ternary interdiffusion coefficients were determined at the composition of intersection. Also, average values of the ternary interdiffusion coefficients, D{sub ij}{sup Fe} (i,j = Al, Ni), were determined over selected composition ranges of the couple and employed to model the concentration profiles. The cross D{sub NiAl}{sup Fe} coefficient was negative and comparable in magnitude to the main D{sub NiNi}{sup Fe} coefficient. The double-serpentine diffusion path was characterized by large diffusional interactions among the components and appreciable variations in the interdiffusion coefficients over different compositional ranges.
Moderately nonlinear diffuse-charge dynamics under an ac voltage
NASA Astrophysics Data System (ADS)
Stout, Robert F.; Khair, Aditya S.
2015-09-01
The response of a symmetric binary electrolyte between two parallel, blocking electrodes to a moderate amplitude ac voltage is quantified. The diffuse charge dynamics are modeled via the Poisson-Nernst-Planck equations for a dilute solution of point-like ions. The solution to these equations is expressed as a Fourier series with a voltage perturbation expansion for arbitrary Debye layer thickness and ac frequency. Here, the perturbation expansion in voltage proceeds in powers of Vo/(kBT /e ) , where Vo is the amplitude of the driving voltage and kBT /e is the thermal voltage with kB as Boltzmann's constant, T as the temperature, and e as the fundamental charge. We show that the response of the electrolyte remains essentially linear in voltage amplitude at frequencies greater than the RC frequency of Debye layer charging, D /λDL , where D is the ion diffusivity, λD is the Debye layer thickness, and L is half the cell width. In contrast, nonlinear response is predicted at frequencies below the RC frequency. We find that the ion densities exhibit symmetric deviations from the (uniform) equilibrium density at even orders of the voltage amplitude. This leads to the voltage dependence of the current in the external circuit arising from the odd orders of voltage. For instance, the first nonlinear contribution to the current is O (Vo3) which contains the expected third harmonic but also a component oscillating at the applied frequency. We use this to compute a generalized impedance for moderate voltages, the first nonlinear contribution to which is quadratic in Vo. This contribution predicts a decrease in the imaginary part of the impedance at low frequency, which is due to the increase in Debye layer capacitance with increasing Vo. In contrast, the real part of the impedance increases at low frequency, due to adsorption of neutral salt from the bulk to the Debye layer.
Nonlinear evolution of double tearing mode in Hall magnetohydrodynamics
Zhang, C. L.; Ma, Z. W.
2009-12-15
Nonlinear evolution of a double tearing mode for different plasma resistivities (eta) and ion inertial lengths (d{sub i}) is investigated using Hall magnetohydrodynamics simulations. In the Hall dominant regime, the magnetic field configuration in the reconnection region evolves from Y-type to X-type geometry, which leads to fast reconnection in the nonlinear growth phase. The maximum growth rate of total kinetic energy of plasma gamma{sub max} in the explosive growth phase is found to have a d{sub i}{sup 2/5}eta{sup 1/10} scaling and the maximum total kinetic energy (E{sub k}){sub max} scales as d{sub i}{sup 4/5}. In the regime with weak Hall effect, it is found that the elongated thin current sheet formed in the early phase is broken into two X-points, forming a magnetic island in the late stage, instead of shrinking to an X-type geometry.
Geometrically nonlinear continuum thermomechanics with surface energies coupled to diffusion
NASA Astrophysics Data System (ADS)
McBride, A. T.; Javili, A.; Steinmann, P.; Bargmann, S.
2011-10-01
Surfaces can have a significant influence on the overall response of a continuum body but are often neglected or accounted for in an ad hoc manner. This work is concerned with a nonlinear continuum thermomechanics formulation which accounts for surface structures and includes the effects of diffusion and viscoelasticity. The formulation is presented within a thermodynamically consistent framework and elucidates the nature of the coupling between the various fields, and the surface and the bulk. Conservation principles are used to determine the form of the constitutive relations and the evolution equations. Restrictions on the jump in the temperature and the chemical potential between the surface and the bulk are not a priori assumptions, rather they arise from the reduced dissipation inequality on the surface and are shown to be satisfiable without imposing the standard assumptions of thermal and chemical slavery. The nature of the constitutive relations is made clear via an example wherein the form of the Helmholtz energy is explicitly given.
Nonlinear diffusion and exclusion processes with contact interactions
NASA Astrophysics Data System (ADS)
Fernando, Anthony E.; Landman, Kerry A.; Simpson, Matthew J.
2010-01-01
Exclusion processes on a regular lattice are used to model many biological and physical systems at a discrete level. The average properties of an exclusion process may be described by a continuum model given by a partial differential equation. We combine a general class of contact interactions with an exclusion process. We determine that many different types of contact interactions at the agent-level always give rise to a nonlinear diffusion equation, with a vast variety of diffusion functions D(C) . We find that these functions may be dependent on the chosen lattice and the defined neighborhood of the contact interactions. Mild to moderate contact interaction strength generally results in good agreement between discrete and continuum models, while strong interactions often show discrepancies between the two, particularly when D(C) takes on negative values. We present a measure to predict the goodness of fit between the discrete and continuous model, and thus the validity of the continuum description of a motile, contact-interacting population of agents. This work has implications for modeling cell motility and interpreting cell motility assays, giving the ability to incorporate biologically realistic cell-cell interactions and develop global measures of discrete microscopic data.
Nonlinear diffusion and exclusion processes with contact interactions.
Fernando, Anthony E; Landman, Kerry A; Simpson, Matthew J
2010-01-01
Exclusion processes on a regular lattice are used to model many biological and physical systems at a discrete level. The average properties of an exclusion process may be described by a continuum model given by a partial differential equation. We combine a general class of contact interactions with an exclusion process. We determine that many different types of contact interactions at the agent-level always give rise to a nonlinear diffusion equation, with a vast variety of diffusion functions D(C). We find that these functions may be dependent on the chosen lattice and the defined neighborhood of the contact interactions. Mild to moderate contact interaction strength generally results in good agreement between discrete and continuum models, while strong interactions often show discrepancies between the two, particularly when D(C) takes on negative values. We present a measure to predict the goodness of fit between the discrete and continuous model, and thus the validity of the continuum description of a motile, contact-interacting population of agents. This work has implications for modeling cell motility and interpreting cell motility assays, giving the ability to incorporate biologically realistic cell-cell interactions and develop global measures of discrete microscopic data.
Non-linear diffusion and pattern formation in vortex matter
NASA Astrophysics Data System (ADS)
Wijngaarden, Rinke J.; Surdeanu, R.; Huijbregtse, J. M.; Rector, J. H.; Dam, B.; Griessen, R.; Einfeld, J.; Woerdenweber, R.
2000-03-01
Penetration of magnetic flux in YBa_2Cu_3O7 superconducting thin films and crystals in externally applied magnetic fields is visualized with a magneto-optical technique. A variety of flux patterns due to non-linear vortex behavior is observed: 1. Roughening of the flux front^1 with scaling exponents identical to those observed in burning paper^2. Two regimes are found where respectively spatial disorder and temporal disorder dominate. In the latter regime Kardar-Parisi-Zhang behavior is found. 2. Roughening of the flux profile similar to the Oslo model for rice-piles. 3. Fractal penetration of flux^3 with Hausdorff dimension depending on the critical current anisotropy. 4. Penetration as 'flux-rivers'. 5. The occurrence of commensurate and incommensurate channels in films with anti-dots as predicted in numerical simulations by Reichhardt, Olson and Nori^4. By comparison with numerical simulations, it is shown that most of the observed behavior can be explained in terms of non-linear diffusion of vortices. ^1R. Surdeanu, R.J. Wijngaarden, E. Visser, J.M. Huijbregtse, J.H. Rector, B. Dam and R. Griessen, Phys.Rev. Lett. 83 (1999) 2054 ^2J. Maunuksela, M. Myllys, O.-P. Kähkönen, J. Timonen, N. Provatas, M.J. Alava, T. Ala-Nissila, Phys. Rev. Lett. 79, 1515 (1997) ^3R. Surdeanu, R.J. Wijngaarden, B. Dam, J. Rector, R. Griessen, C. Rossel, Z.F. Ren and J.H. Wang, Phys Rev B 58 (1998) 12467 ^4C. Reichhardt, C.J. Olson and F. Nori, Phys. Rev. B 58, 6534 (1998)
Double resonant processes in 1D nonlinear periodic media
NASA Astrophysics Data System (ADS)
Kuzmiak, Vladimir; Konotop, Vladimir
2001-03-01
We consider one-dimensional periodic structure consisting of alternating layers fabricated from the materials possessing \\chi^(2) nonlinearity and assume that the filling fraction and the dielectric permittivities of the slabs are chosen in such a way that resonant contions for the generation for the second and third harmonic are satisfied simultaneously. The possibility of such process is demonstrated in the structure consisting of the alternating slabs of AlGaAs and InSb. The wave evolution is described in terms of envelope function approach. By taking account three resonant waves one obtains a system of coupled-mode differential equations. One of the solutions which is of special importance is that of having a constant amplitude and the first and third harmonic having zero amplitude. We analyze the stability of the solutions and show that the use of the double resonance allows one to obtain difference generation. A particular example of such a process is fractional conversion ω arrow (2/3)ω which takes place with the participation of the mode with the frequency ω/3.
Euler buckling and nonlinear kinking of double-stranded DNA
Fields, Alexander P.; Meyer, Elisabeth A.; Cohen, Adam E.
2013-01-01
The bending stiffness of double-stranded DNA (dsDNA) at high curvatures is fundamental to its biological activity, yet this regime has been difficult to probe experimentally, and literature results have not been consistent. We created a ‘molecular vise’ in which base-pairing interactions generated a compressive force on sub-persistence length segments of dsDNA. Short dsDNA strands (<41 base pairs) resisted this force and remained straight; longer strands became bent, a phenomenon called ‘Euler buckling’. We monitored the buckling transition via Förster Resonance Energy Transfer (FRET) between appended fluorophores. For low-to-moderate concentrations of monovalent salt (up to ∼150 mM), our results are in quantitative agreement with the worm-like chain (WLC) model of DNA elasticity, without the need to invoke any ‘kinked’ states. Greater concentrations of monovalent salts or 1 mM Mg2+ induced an apparent softening of the dsDNA, which was best accounted for by a kink in the region of highest curvature. We tested the effects of all single-nucleotide mismatches on the DNA bending. Remarkably, the propensity to kink correlated with the thermodynamic destabilization of the mismatched DNA relative the perfectly complementary strand, suggesting that the kinked state is locally melted. The molecular vise is exquisitely sensitive to the sequence-dependent linear and nonlinear elastic properties of dsDNA. PMID:23956222
Experimental investigation of a double-diffused MOS structure
NASA Technical Reports Server (NTRS)
Lin, H. C.; Halsor, J. L.
1976-01-01
Self-aligned polysilicon gate technology was applied to double-diffused MOS (DMOS) construction in a manner that retains processing simplicity and effectively eliminates parasitic overlap capacitance because of the self-aligning feature. Depletion mode load devices with the same dimensions as the DMOS transistors were integrated. The ratioless feature results in smaller dimension load devices, allowing for higher density integration with no increase in the processing complexity of standard MOS technology. A number of inverters connected as ring oscillators were used as a vehicle to test the performance and to verify the anticipated benefits. The propagation time-power dissipation product and process related parameters were measured and evaluated. This report includes (1) details of the process; (2) test data and design details for the DMOS transistor, the load device, the inverter, the ring oscillator, and a shift register with a novel tapered geometry for the output stages; and (3) an analytical treatment of the effect of the distributed silicon gate resistance and capacitance on the speed of DMOS transistors.
Chen, Yunjin; Pock, Thomas
2016-08-01
Image restoration is a long-standing problem in low-level computer vision with many interesting applications. We describe a flexible learning framework based on the concept of nonlinear reaction diffusion models for various image restoration problems. By embodying recent improvements in nonlinear diffusion models, we propose a dynamic nonlinear reaction diffusion model with time-dependent parameters (i.e., linear filters and influence functions). In contrast to previous nonlinear diffusion models, all the parameters, including the filters and the influence functions, are simultaneously learned from training data through a loss based approach. We call this approach TNRD - Trainable Nonlinear Reaction Diffusion. The TNRD approach is applicable for a variety of image restoration tasks by incorporating appropriate reaction force. We demonstrate its capabilities with three representative applications, Gaussian image denoising, single image super resolution and JPEG deblocking. Experiments show that our trained nonlinear diffusion models largely benefit from the training of the parameters and finally lead to the best reported performance on common test datasets for the tested applications. Our trained models preserve the structural simplicity of diffusion models and take only a small number of diffusion steps, thus are highly efficient. Moreover, they are also well-suited for parallel computation on GPUs, which makes the inference procedure extremely fast.
Nonlinear localized eigenmodes for a Bose-Einstein condensate in a double-well potential
NASA Astrophysics Data System (ADS)
Xie, Qiongtao; Liu, Xiaoliang; Rong, Shiguang
2015-09-01
In this paper, we investigate the nonlinear localized eigenmodes for a Bose-Einstein condensate in a double-well potential. For a specific choice of the potential parameters, certain exact analytical solutions for nonlinear localized eigenmodes are presented. By applying the linear stability analysis, the stability regions of these exact nonlinear localized eigenmodes are obtained numerically. It is shown that under certain conditions, the unstable nonlinear localized modes display the breathing behavior characterized by repeated appearance of symmetric and asymmetric distributions in the two potentials. This breathing behavior is shown to arise from the symmetry breaking for these nonlinear localized eigenmodes.
NASA Astrophysics Data System (ADS)
Zhang, Ziyin; Nagy, Peter B.; Hassan, Waled
2016-02-01
Ultrasonic wave mixing has shown promising potential for assessing otherwise hidden subtle imperfections in imperfect diffusion bonds between Ti-6Al-4V components. When interrogating a diffusion bonded specimen using non-collinear shear wave mixing, both bulk and interface nonlinearity will contribute to the transmitted nonlinear signal. Although a recent study has shown that changing the transducer alignment can suppress the intrinsic nonlinearity of the surrounding material to some extent so that the interface nonlinearity could be detected more selectively, it is still difficult to distinguish different levels of bond quality based on the detected transmitted signal only. Analytical and numerical studies showed that an imperfect interface generates the same amount of nonlinear displacement in the reflected and transmitted fields. In this study, we used the reflected nonlinear interface signature to characterize diffusion bonded interfaces. Our results indicate that it is better to use the reflected nonlinear interface signature to assess the bond quality, which is in agreement with our previous analytical and numerical predictions. However, the observed random phase of the reflected signature indicates that existing nonlinear interface models are insufficient for accurately describing the nonlinear interaction of shear incident waves with high-quality diffusion bonded interfaces.
NASA Astrophysics Data System (ADS)
Cigeroglu, Ender; Samandari, Hamed
2014-11-01
Nonlinear free vibration analysis of curved double-walled carbon nanotubes (DWNTs) embedded in an elastic medium is studied in this study. Nonlinearities considered are due to large deflection of carbon nanotubes (geometric nonlinearity) and nonlinear interlayer van der Waals forces between inner and outer tubes. The differential quadrature method (DQM) is utilized to discretize the partial differential equations of motion in spatial domain, which resulted in a nonlinear set of algebraic equations of motion. The effect of nonlinearities, different end conditions, initial curvature, and stiffness of the surrounding elastic medium, and vibrational modes on the nonlinear free vibration of DWCNTs is studied. Results show that it is possible to detect different vibration modes occurring at a single vibration frequency when CNTs vibrate in the out-of-phase vibration mode. Moreover, it is observed that boundary conditions have significant effect on the nonlinear natural frequencies of the DWCNT including multiple solutions.
NASA Technical Reports Server (NTRS)
Pollmann, Konrad W.; Stodieck, Louis S.; Luttges, Marvin W.
1994-01-01
Microgravity can provide a diffusion-dominated environment for double-diffusion and diffusion-reaction experiments otherwise disrupted by buoyant convection or sedimentation. In sliding solvent diffusion cells, a diffusion interface between two liquid columns is achieved by aligning two offset sliding wells. Fluid in contact with the sliding lid of the cavities is subjected to an applied shear stress. The momentum change by the start/stop action of the well creates an additional hydrodynamical force. In microgravity, these viscous and inertial forces are sufficiently large to deform the diffusion interface and induce hydrodynamic transfer between the wells. A series of KC-135 parabolic flight experiments were conducted to characterize these effects and establish baseline data for microgravity diffusion experiments. Flow visualizations show the diffusion interface to be deformed in a sinusoidal fashion following well alignment. After the wells were separated again in a second sliding movement, the total induced liquid transfer was determined and normalized by the well aspect ratio. The normalized transfer decreased linearly with Reynolds number from 3.3 to 4.0% (w/v) for Re = 0.4 (Stokes flow) to a minimum of 1.0% for Re = 23 to 30. Reynolds numbers that provide minimum induced transfers are characterized by an interface that is highly deformed and unsuitable for diffusion measurements. Flat diffusion interfaces acceptable for diffusion measurements are obtained with Reynolds numbers on the order of 7 to 10. Microgravity experiments aboard a sounding rocket flight verified counterdiffusion of different solutes to be diffusion dominated. Ground control experiments showed enhanced mixing by double-diffusive convection. Careful selection of experimental parameters improves initial conditions and minimizes induced transfer rates.
An examination of double-diffusive processes in a mesoscale eddy in the Arctic Ocean
NASA Astrophysics Data System (ADS)
Bebieva, Yana; Timmermans, Mary-Louise
2016-01-01
Temperature and salinity measurements of an Atlantic Water mesoscale eddy in the Arctic Ocean's Canada Basin are analyzed to understand the effects of velocity shear on a range of double-diffusive processes. Double-diffusive structures in and around the eddy are examined through the transition from low shear (outside the eddy and within its solid body core) to high geostrophic shear zones at the eddy flanks. The geostrophic Richardson number takes large values where a double-diffusive staircase is observed and lowest values at the eddy flanks where geostrophic velocity is largest and a well-formed staircase is not present. A Thorpe scale analysis is used to estimate turbulent diffusivities in the flank regions. Double-diffusive and turbulent heat, salt, and buoyancy fluxes from the eddy are computed, and used to infer that the eddy decays on time scales of around 4-9 years. Fluxes highlight that Atlantic Water heat within the eddy can be fluxed downward into deeper water layers by means of both double-diffusive and turbulent mixing. Estimated lateral variations in vertical fluxes across the eddy allow for speculation that double diffusion speeds up the eddy decay, having important implications for the transfer of Atlantic Water heat in the Arctic Ocean.
Effect of carrier diffusion on the nonlinear response of optical waveguides
NASA Astrophysics Data System (ADS)
Gibbons, Wayne M.; Sarid, Dror
1987-08-01
Carrier-density-dependent changes in the propagation constant of a TE mode in a symmetric slab semiconductor waveguide are calculated with allowance for transverse diffusion effects using a self-consistent numerical method. By using the plasma theory to model the nonlinearity, it is found that the effects of transverse carrier diffusion are strongly dependent on the index profiles and waveguide geometry. If the index difference between the core and the cladding is relatively large in comparison with the nonlinear index change, diffusion can produce results that are different from the no-diffusion case. If the index difference is relatively small, diffusion does not significantly modify the nonlinear response of the waveguide.
Multigrid approaches to non-linear diffusion problems on unstructured meshes
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.; Bushnell, Dennis M. (Technical Monitor)
2001-01-01
The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.
Unifying diffusion and seepage for nonlinear gas transport in multiscale porous media
NASA Astrophysics Data System (ADS)
Song, Hongqing; Wang, Yuhe; Wang, Jiulong; Li, Zhengyi
2016-09-01
We unify the diffusion and seepage process for nonlinear gas transport in multiscale porous media via a proposed new general transport equation. A coherent theoretical derivation indicates the wall-molecule and molecule-molecule collisions drive the Knudsen and collective diffusive fluxes, and constitute the system pressure across the porous media. A new terminology, nominal diffusion coefficient can summarize Knudsen and collective diffusion coefficients. Physical and numerical experiments show the support of the new formulation and provide approaches to obtain the diffusion coefficient and permeability simultaneously. This work has important implication for natural gas extraction and greenhouse gases sequestration in geological formations.
Model coupling intraparticle diffusion/sorption, nonlinear sorption, and biodegradation processes
Karapanagioti, Hrissi K.; Gossard, Chris M.; Strevett, Keith A.; Kolar, Randall L.; Sabatini, David A.
2001-01-01
Diffusion, sorption and biodegradation are key processes impacting the efficiency of natural attenuation. While each process has been studied individually, limited information exists on the kinetic coupling of these processes. In this paper, a model is presented that couples nonlinear and nonequilibrium sorption (intraparticle diffusion) with biodegradation kinetics. Initially, these processes are studied independently (i.e., intraparticle diffusion, nonlinear sorption and biodegradation), with appropriate parameters determined from these independent studies. Then, the coupled processes are studied, with an initial data set used to determine biodegradation constants that were subsequently used to successfully predict the behavior of a second data set. The validated model is then used to conduct a sensitivity analysis, which reveals conditions where biodegradation becomes desorption rate-limited. If the chemical is not pre-equilibrated with the soil prior to the onset of biodegradation, then fast sorption will reduce aqueous concentrations and thus biodegradation rates. Another sensitivity analysis demonstrates the importance of including nonlinear sorption in a coupled diffusion/sorption and biodegradation model. While predictions based on linear sorption isotherms agree well with solution concentrations, for the conditions evaluated this approach overestimates the percentage of contaminant biodegraded by as much as 50%. This research demonstrates that nonlinear sorption should be coupled with diffusion/sorption and biodegradation models in order to accurately predict bioremediation and natural attenuation processes. To our knowledge this study is unique in studying nonlinear sorption coupled with intraparticle diffusion and biodegradation kinetics with natural media.
Nonlinear diffusion and viral spread through the leaf of a plant
NASA Astrophysics Data System (ADS)
Edwards, Maureen P.; Waterhouse, Peter M.; Munoz-Lopez, María Jesús; Anderssen, Robert S.
2016-10-01
The spread of a virus through the leaf of a plant is both spatially and temporally causal in that the present status depends on the past and the spatial spread is compactly supported and progresses outwards. Such spatial spread is known to occur for certain nonlinear diffusion processes. The first compactly supported solution for nonlinear diffusion equations appears to be that of Pattle published in 1959. In that paper, no explanation is given as to how the solution was derived. Here, we show how the solution can be derived using Lie symmetry analysis. This lays a foundation for exploring the behavior of other choices for nonlinear diffusion and exploring the addition of reaction terms which do not eliminate the compactly supported structure. The implications associated with using the reaction-diffusion equation to model the spatial-temporal spread of a virus through the leaf of a plant are discussed.
Classical momentum diffusion in double-delta-kicked particles.
Stocklin, M M A; Monteiro, T S
2006-08-01
We investigate the classical chaotic diffusion of atoms subjected to pairs of closely spaced pulses ("kicks") from standing waves of light (the 2delta-KP ). Recent experimental studies with cold atoms implied an underlying classical diffusion of a type very different from the well-known paradigm of Hamiltonian chaos, the standard map. The kicks in each pair are separated by a small time interval E<1, which together with the kick strength K, characterizes the transport. Phase space for the 2delta-KP is partitioned into momentum "cells" partially separated by momentum-trapping regions where diffusion is slow. We present here an analytical derivation of the classical diffusion for a 2delta-KP including all important correlations which were used to analyze the experimental data. We find an asymptotic (t-->infinity) regime of "hindered" diffusion: while for the standard map the diffusion rate, for K>1 , D approximately K(2)/2[1-2J(2)(K)...] oscillates about the uncorrelated rate D(0)=K(2)/2, we find analytically, that the 2delta-KP can equal, but never diffuses faster than, a random walk rate. We argue this is due to the destruction of the important classical "accelerator modes" of the standard map. We analyze the experimental regime 0.1 less or approximately KE less or approximately 1 , where quantum localization lengths L approximately Planck's (-0.75) are affected by fractal cell boundaries. We find an approximate asymptotic diffusion rate D proportional to K(3)E, in correspondence to a D proportional to K(3) regime in the standard map associated with the "golden-ratio" cantori.
Numerical Study of g-Jitter Induced Double-Diffusive Convection
NASA Technical Reports Server (NTRS)
Shu, Y.; Li, B. Q.; deGroh, Henry C.
2001-01-01
A finite element study is presented of double-diffusive convection driven by g-jitter in a microgravity environment. Mathematical formulations are presented and extensive simulations are carried out for g-jitter induced fluid flow, temperature distribution, and solutal transport in an alloy system under consideration for space flights. Computations include the use of idealized single-frequency and multi-frequency g-jitter as well as the real g-jitter data taken during an actual Space Shuttle fight. Little correlation is seen between these velocity components for the g-jitter components studied. The temperature field is basically undisturbed by convection because of a small Pr number for the fluid. The disturbance of the concentration field, however, is pronounced, and the local variation of the concentration follows the velocity oscillation in time. It is found that although the concentration field varies in both position and time, the local concentration gradient remains approximately constant in time. Numerical study further indicates that with an increase in g-jitter force (or amplitude), the nonlinear convective effects become much more obvious, which in turn drastically change the concentration fields. The simulated results computed using the g-jitter data taken during space flights show that both the velocity and concentration become random, following approximately the same pattern as the g-jitter perturbations.
The relationship between double-diffusive intrusions and staircases in the Arctic Ocean
NASA Astrophysics Data System (ADS)
Bebieva, Yana; Timmermans, Mary-Louise
2016-11-01
The origin of double-diffusive staircases in the Arctic Ocean is investigated for the particular background setting in which both temperature and salinity increase with depth. Motivated by observations that show the co-existence of thermohaline intrusions and double-diffusive staircases, a linear stability analysis is performed on the governing equations to determine the conditions under which staircases form. It is shown that a double-diffusive staircase can result from interleaving motions if the observed bulk vertical density ratio is below a critical vertical density ratio estimated for particular lateral and vertical background temperature and salinity gradients. Vertical temperature and salinity gradients dominate over horizontal gradients in determining whether staircases form. Examination of Arctic Ocean temperature and salinity measurements indicates that observations are consistent with the theory for reasonable choices of eddy diffusivity and viscosity.
Double-dark-resonance-enhanced Kerr nonlinearity in a single layer of graphene nanostructure
NASA Astrophysics Data System (ADS)
Solookinejad, Gh.; Panahi, M.; Ahmadi Sangachin, E.; Hossein Asadpour, Seyyed
2016-08-01
In this paper, a novel scheme is proposed for the giant enhanced Kerr nonlinearity in a single layer of graphene nanostructure based on quantum optics and nonlinear optical sciences. The linear and the nonlinear susceptibility of the monolayer graphene system are presented in details by using the density matrix method and perturbation theory. After deriving the equations of motion in the steady-state regime, we analytically solve the linear and nonlinear susceptibility of the system. Our numerical results show that the giant enhanced Kerr nonlinearity can be obtained in the double-dark-resonance condition with zero linear and nonlinear absorption. Our results may have potential applications in quantum information science in infrared and terahertz regimes.
A Comparison of PDE-based Non-Linear Anisotropic Diffusion Techniques for Image Denoising
Weeratunga, S K; Kamath, C
2003-01-06
PDE-based, non-linear diffusion techniques are an effective way to denoise images. In a previous study, we investigated the effects of different parameters in the implementation of isotropic, non-linear diffusion. Using synthetic and real images, we showed that for images corrupted with additive Gaussian noise, such methods are quite effective, leading to lower mean-squared-error values in comparison with spatial filters and wavelet-based approaches. In this paper, we extend this work to include anisotropic diffusion, where the diffusivity is a tensor valued function which can be adapted to local edge orientation. This allows smoothing along the edges, but not perpendicular to it. We consider several anisotropic diffusivity functions as well as approaches for discretizing the diffusion operator that minimize the mesh orientation effects. We investigate how these tensor-valued diffusivity functions compare in image quality, ease of use, and computational costs relative to simple spatial filters, the more complex bilateral filters, wavelet-based methods, and isotropic non-linear diffusion based techniques.
Comparison of PDE-based non-linear anistropic diffusion techniques for image denoising
NASA Astrophysics Data System (ADS)
Weeratunga, Sisira K.; Kamath, Chandrika
2003-05-01
PDE-based, non-linear diffusion techniques are an effective way to denoise images.In a previous study, we investigated the effects of different parameters in the implementation of isotropic, non-linear diffusion. Using synthetic and real images, we showed that for images corrupted with additive Gaussian noise, such methods are quite effective, leading to lower mean-squared-error values in comparison with spatial filters and wavelet-based approaches. In this paper, we extend this work to include anisotropic diffusion, where the diffusivity is a tensor valued function which can be adapted to local edge orientation. This allows smoothing along the edges, but not perpendicular to it. We consider several anisotropic diffusivity functions as well as approaches for discretizing the diffusion operator that minimize the mesh orientation effects. We investigate how these tensor-valued diffusivity functions compare in image quality, ease of use, and computational costs relative to simple spatial filters, the more complex bilateral filters, wavelet-based methods, and isotropic non-linear diffusion based techniques.
NASA Astrophysics Data System (ADS)
Patel, Ajay M.; Joshi, Anand Y.
2016-10-01
This paper deals with the nonlinear vibration analysis of a double walled carbon nanotube based mass sensor with curvature factor or waviness, which is doubly clamped at a source and a drain. Nonlinear vibrational behaviour of a double-walled carbon nanotube excited harmonically near its primary resonance is considered. The double walled carbon nanotube is harmonically excited by the addition of an excitation force. The modelling involves stretching of the mid plane and damping as per phenomenon. The equation of motion involves four nonlinear terms for inner and outer tubes of DWCNT due to the curved geometry and the stretching of the central plane due to the boundary conditions. The vibrational behaviour of the double walled carbon nanotube with different surface deviations along its axis is analyzed in the context of the time response, Poincaré maps and Fast Fourier Transformation diagrams. The appearance of instability and chaos in the dynamic response is observed as the curvature factor on double walled carbon nanotube is changed. The phenomenon of Periodic doubling and intermittency are observed as the pathway to chaos. The regions of periodic, sub-harmonic and chaotic behaviour are clearly seen to be dependent on added mass and the curvature factors in the double walled carbon nanotube. Poincaré maps and frequency spectra are used to explicate and to demonstrate the miscellany of the system behaviour. With the increase in the curvature factor system excitations increases and results in an increase of the vibration amplitude with reduction in excitation frequency.
Submodels of model of nonlinear diffusion in the inhomogeneous medium involving absorption
Chirkunov, Yu. A.
2015-10-15
We study the five-parameter model, describing the process of nonlinear diffusion in an inhomogeneous medium in the presence of absorption, for which the differential equation of the model admits a continuous Lie group of transformations, acting on the set of its solutions. We found six submodels of the original model of nonlinear diffusion, with different symmetry properties. Of these six submodels, the five submodels with transient absorption, for which the absorption coefficient depends on time according to a power law, represent the greatest interest with a mathematical point of view and with the point of view of physical applications. For each of these nonlinear submodels, we obtained formulas for producing new solutions that contain arbitrary constants, and we found all invariant submodels. All essentially distinct invariant solutions describing these invariant submodels are found in an explicit form or are reduced to finding the solution of nonlinear integral equations. The presence of the arbitrary constants in the integral equations that determine these solutions provide new opportunities for analytical and numerical study of boundary value problems for the received submodels and, thus, for the original model of nonlinear diffusion. For the received invariant submodels, we studied diffusion processes for which at the initial moment of the time at a fixed point is specified as a concentration and its gradient or as a concentration and its velocity. Solving of boundary value problems describing these processes is reduced to the solving of nonlinear integral equations. We established the existence and uniqueness of solutions of these boundary value problems under some additional conditions. The obtained results can be used to study the diffusion of substances, diffusion of conduction electrons and other particles, diffusion of physical fields and propagation of heat in inhomogeneous medium, and also to study a turbulence (Leith model, differential
NASA Astrophysics Data System (ADS)
Meccia, Virna L.; Simoncelli, Simona; Sparnocchia, Stefania
2016-08-01
The physical reanalysis component of the Mediterranean Forecasting System is used to construct a high-resolution three-dimensional atlas of the Turner Angle. An assessment of the model quality shows a maximum degree of agreement with observations in the water column between 150 and 1000 m depth. The mean state of the favourable conditions for double diffusion processes is evaluated and the recent decadal variability is studied in terms of changes in the water mass properties. The results show that approximately 50% of the Mediterranean Sea is favourable to double diffusion processes, from which around 47% is associated with salt fingering. The Tyrrhenian, Ionian and southwestern Mediterranean are the most vulnerable basins to salt fingering, and the strongest processes can occur in the Tyrrhenian deep waters. Diffusive convection is most likely to occur in the Ionian, Aegean and eastern Mediterranean at vertical levels deeper than 1000 m. The observed gradual warming and salinification of the Mediterranean after 1997 decreased and increased the possibilities of the occurrence of salt fingers and double diffusive convections, respectively. The climatological atlas that is presented in this paper provides a three-dimensional picture of the regions that are either doubly stable or favourable to double diffusion instability and allows for the characterization of the diffusive properties of the water masses.
NASA Astrophysics Data System (ADS)
Li, Qi; Wang, Wei-Dong; Liu, Yun; Wei, Xue-Ming
2012-02-01
A new lateral double diffused MOS (LDMOS) transistor with a double epitaxial layer formed by an n-type substrate and a p-type epitaxial layer is reported (DEL LDMOS). The mechanism of the improved breakdown characteristic is that the high electric field around the drain is reduced by substrate reverse bias, which causes the redistribution of the bulk electric field in the drift region, and the vertical blocking voltage is shared by the drain side and the source side. The numerical results indicate that the trade-off between breakdown voltage and on-resistance of the proposed device is improved greatly in comparison to that of the conventional LDMOS.
Nonlinear Diffusion Filtering of the GOCE-Based Satellite-Only Mean Dynamic Topography
NASA Astrophysics Data System (ADS)
Cunderlik, Robert; Mikula, Karol
2015-03-01
The paper presents nonlinear diffusion filtering of the GOCE-based satellite-only mean dynamic topography (MDT). Our approach is based on a numerical solution to the nonlinear diffusion equation defined on the discretized Earth’s surface using the regularized surface Perona-Malik Model. For its numerical discretization we use a surface finite volume method. A key idea is that the diffusivity coefficient depends on the edge detector. It allows effectively reduce the stripping noise while preserve important gradients in filtered data. Numerical experiments present nonlinear filtering of the geopotential evaluated from the GO_CONS_GCF_2_ DIR_R5 model on the DTU13 mean sea surface. After filtering the geopotential is transformed into the MDT.
Inexact Picard iterative scheme for steady-state nonlinear diffusion in random heterogeneous media.
Mohan, P Surya; Nair, Prasanth B; Keane, Andy J
2009-04-01
In this paper, we present a numerical scheme for the analysis of steady-state nonlinear diffusion in random heterogeneous media. The key idea is to iteratively solve the nonlinear stochastic governing equations via an inexact Picard iteration scheme, wherein the nonlinear constitutive law is linearized using the current guess of the solution. The linearized stochastic governing equations are then spatially discretized and approximately solved using stochastic reduced basis projection schemes. The approximation to the solution process thus obtained is used as the guess for the next iteration. This iterative procedure is repeated until an appropriate convergence criterion is met. Detailed numerical studies are presented for diffusion in a square domain for varying degrees of nonlinearity. The numerical results are compared against benchmark Monte Carlo simulations, and it is shown that the proposed approach provides good approximations for the response statistics at modest computational effort.
Diffusion barrier performance of novel Ti/TaN double layers for Cu metallization
NASA Astrophysics Data System (ADS)
Zhou, Y. M.; He, M. Z.; Xie, Z.
2014-10-01
Novel Ti/TaN double layers offering good stability as a barrier against Cu metallization have been made achievable by annealing in vacuum better than 1 × 10-3 Pa. Ti/TaN double layers were formed on SiO2/Si substrates by DC magnetron sputtering and then the properties of Cu/Ti/TaN/SiO2/Si film stacks were studied. It was found that the Ti/TaN double layers provide good diffusion barrier between Cu and SiO2/Si up to 750 °C for 30 min. The XRD, Auger and EDS results show that the Cu-Si compounds like Cu3Si were formed by Cu diffusion through Ti/TaN barrier for the 800 °C annealed samples. It seems that the improved diffusion barrier property of Cu/Ti/TaN/SiO2/Si stack is due to the diffusion of nitrogen along the grain boundaries in Ti layer, which would decrease the defects in Ti film and block the diffusion path for Cu diffusion with increasing annealing temperature. The failure mechanism of Ti/TaN bi-layer is similar to the Cu/TaN/Si metallization system in which Cu atoms diffuse through the grain boundary of barrier and react with silicon to form Cu3Si.
Magnetic diffusion and ion nonlinear dynamics in magnetic reconnection
NASA Astrophysics Data System (ADS)
Zenitani, S.; Shinohara, I.; Nagai, T.; Wada, T.
2013-12-01
Magnetic reconnection is a fundamental process in many plasma systems, ranging from laboratory and solar-terrestrial environments to extreme astrophysical settings. The reconnection process is controlled by magnetic dissipation physics in a small-scale region near the reconnection point (X-line), and therefore the structure of the reconnection site is of strong interest. According to the standard picture of collisionless reconnection, the X-line is surrounded by a compact electron diffusion region and by an outer ion diffusion region. While the electron region has been extensively studied, much less is known about the ion region. In this work, we examine key aspects of the ion region in magnetic reconnection. First, we evaluate the ''diffusion'' of magnetic field lines, going back to the topology theorems. Unlike in the MHD, the idealness, the frozen-in, magnetic diffusion, and the energy dissiation can be all different in a kinetic plasma. We will apply these concepts to the reconnection site in two-dimensional particle-in-cell (PIC) simulations. Importantly, in the outer part of the ion region, even though the ion ideal condition is violated, the magnetic fields are frozen to plasma fluids. This raises a serious question to the widespread definition of the ion diffusion region, based on the ion nonidealness. We further examine the ion velocity distribution function in the same region. The distribution function contains multiple populations such as global Speiser ions, local Speiser ions, and trapped ions. The particle motion of the local Speiser ions in an appropriately rotated frame explains the plasma nonidealness. The trapped ions are the first demonstration of the regular orbits in Chen & Palmadesso (1986), in self-consistent PIC simulations. They would be observational signatures in the ion current layer near reconnection sites.
Willert, Jeffrey; Park, H.; Taitano, William
2015-11-01
High-order/low-order (or moment-based acceleration) algorithms have been used to significantly accelerate the solution to the neutron transport k-eigenvalue problem over the past several years. Recently, the nonlinear diffusion acceleration algorithm has been extended to solve fixed-source problems with anisotropic scattering sources. In this paper, we demonstrate that we can extend this algorithm to k-eigenvalue problems in which the scattering source is anisotropic and a significant acceleration can be achieved. Lastly, we demonstrate that the low-order, diffusion-like eigenvalue problem can be solved efficiently using a technique known as nonlinear elimination.
Nonlinearity Effects of Lateral Density Diffusion Coefficient on Gain-Guided VCSEL Performance
NASA Technical Reports Server (NTRS)
Li, Jian-Zhong; Cheung, Samson H.; Ning, C. Z.; Biegel, Bryan (Technical Monitor)
2001-01-01
Electron and hole diffusions in the plane of semiconductor quantum wells play an important part in the static and dynamic operations of semiconductor lasers. In this paper, we apply a hydrodynamic model developed from the semiconductor Bloch equations to numerically study the effects of nonlinearity in the diffusion coefficient on single mode operation and direct modulation of a gain-guided InGaAs/GaAs multiple quantum well laser, operating not too far from threshold. We found that a small diffusion coefficient is advantageous for lowering the threshold current and increasing the modulation bandwidth. Most importantly, the effects of nonlinearity in the coefficient can be approximately reproduced by replacing the coefficient with an effective constant diffusion coefficient, which corresponds roughly to the half height density of the density distribution.
Drift-diffusion theory of symmetrical double-junction diodes
NASA Astrophysics Data System (ADS)
Schmidt, Pierre E.; Henisch, Heinz K.
1982-11-01
Using numerical methods, we have calculated the current-voltage characteristics, energy contours and carrier distributions of a symmetrical double junction diode ( n+nn+ and n+pn+). It is found that the I-V characteristics at low currents and voltages depend greatly on the doping concentration of the base region; at hihg currents, they do not. In that regime, the characteristics bunch together, and can be approximated with remarkable fidelity by the Mott-Gurney law for space-charge controlled conduction in solids. Characteristics are presented for different impurity densities and base widths.
3-D adaptive nonlinear complex-diffusion despeckling filter.
Rodrigues, Pedro; Bernardes, Rui
2012-12-01
This work aims to improve the process of speckle noise reduction while preserving edges and other relevant features through filter expansion from 2-D to 3-D. Despeckling is very important for data visual inspection and as a preprocessing step for other algorithms, as they are usually notably influenced by speckle noise. To that intent, a 3-D approach is proposed for the adaptive complex-diffusion filter. This 3-D iterative filter was applied to spectral-domain optical coherence tomography medical imaging volumes of the human retina and a quantitative evaluation of the results was performed to allow a demonstration of the better performance of the 3-D over the 2-D filtering and to choose the best total diffusion time. In addition, we propose a fast graphical processing unit parallel implementation so that the filter can be used in a clinical setting.
Complex statistics and diffusion in nonlinear disordered particle chains
Antonopoulos, Ch. G.; Bountis, T.; Skokos, Ch.; Drossos, L.
2014-06-15
We investigate dynamically and statistically diffusive motion in a Klein-Gordon particle chain in the presence of disorder. In particular, we examine a low energy (subdiffusive) and a higher energy (self-trapping) case and verify that subdiffusive spreading is always observed. We then carry out a statistical analysis of the motion, in both cases, in the sense of the Central Limit Theorem and present evidence of different chaos behaviors, for various groups of particles. Integrating the equations of motion for times as long as 10{sup 9}, our probability distribution functions always tend to Gaussians and show that the dynamics does not relax onto a quasi-periodic Kolmogorov-Arnold-Moser torus and that diffusion continues to spread chaotically for arbitrarily long times.
Double-diffusive natural convection in a fluid saturated porous cavity with a freely convecting wall
Nithiarasu, P.; Sundararajan, T.; Seetharamu, K.N.
1997-12-01
Double-diffusive natural convection in fluid saturated porous medium has been investigated using a generalized porous medium model. One of the vertical walls of the porous cavity considered is subjected to convective heat and mass transfer conditions. The results show that the flow, heat and mass transfer become sensitive to applied mass transfer coefficient in both the Darcy and non-Darcy flow regimes. It is also observed that the Sherwood number approaches a constant value as the solutal Biot number increases. Double-diffusive natural convection in fluid saturated porous medium is encountered in applications such as food processing, contaminant transport in ground water, and others.
Solution blow-up for a class of parabolic equations with double nonlinearity
Korpusov, Maxim O
2013-03-31
We consider a class of parabolic-type equations with double nonlinearity and derive sufficient conditions for finite time blow-up of its solutions in a bounded domain under the homogeneous Dirichlet condition. To prove the solution blow-up we use a modification of Levine's method. Bibliography: 13 titles.
NASA Astrophysics Data System (ADS)
Jiang, Tian; Zhang, Yong-Tao
2013-11-01
Implicit integration factor (IIF) methods are originally a class of efficient “exactly linear part” time discretization methods for solving time-dependent partial differential equations (PDEs) with linear high order terms and stiff lower order nonlinear terms. For complex systems (e.g. advection-diffusion-reaction (ADR) systems), the highest order derivative term can be nonlinear, and nonlinear nonstiff terms and nonlinear stiff terms are often mixed together. High order weighted essentially non-oscillatory (WENO) methods are often used to discretize the hyperbolic part in ADR systems. There are two open problems on IIF methods for solving ADR systems: (1) how to obtain higher than the second order global time discretization accuracy; (2) how to design IIF methods for solving fully nonlinear PDEs, i.e., the highest order terms are nonlinear. In this paper, we solve these two problems by developing new Krylov IIF-WENO methods to deal with both semilinear and fully nonlinear advection-diffusion-reaction equations. The methods can be designed for arbitrary order of accuracy. The stiffness of the system is resolved well and the methods are stable by using time step sizes which are just determined by the nonstiff hyperbolic part of the system. Large time step size computations are obtained. We analyze the stability and truncation errors of the schemes. Numerical examples of both scalar equations and systems in two and three spatial dimensions are shown to demonstrate the accuracy, efficiency and robustness of the methods.
Enhanced nonlinear optical characteristics of copper-ion-doped double crossover DNAs
NASA Astrophysics Data System (ADS)
Park, Byeongho; Lee, Byung Jic; Dugasani, Sreekantha Reddy; Cho, Youngho; Kim, Chulki; Seo, Minah; Lee, Taikjin; Jhon, Young Min; Choi, Jaebin; Lee, Seok; Park, Sung Ha; Jun, Seong Chan; Yeom, Dong-Il; Rotermund, Fabian; Kim, Jae Hun
2015-10-01
The modification of deoxyribonucleic acid (DNA) samples by sequencing the order of bases and doping copper ions opens the possibility for the design of novel nanomaterials exhibiting large optical nonlinearity. We investigated the nonlinear characteristics of copper-ion doped double crossover DNA samples for the first time to the best of our knowledge by using Z-scan and four-wave mixing methods. To accelerate the nonlinear characteristics, we prepared two types of unique DNA nanostructures composed of 148 base pairs doped with copper ions with a facile annealing method. The outstanding third-order nonlinear optical susceptibility of the copper-ion-doped DNA solution, 1.19 × 10-12 esu, was estimated by the conventional Z-scan measurement, whereas the four-wave mixing experiment was also investigated. In the visible spectral range, the copper-ion-doped DNA solution samples provided competent four-wave mixing signals with a remarkable conversion efficiency of -4.15 dB for the converted signal at 627 nm. The interactions between DNA and copper ions contribute to the enhancement of nonlinearity due to structural and functional changes. The present study signifies that the copper-ion-doped double crossover DNA is a potential candidate as a highly efficient novel material for further nonlinear optical applications.
Li, Hua; Wu, Tao
2016-10-01
A diffuse-interface model is presented in this paper for simulation of the evolution of phase transition between the liquid solution and solid gel states for physical hydrogel with nonlinear deformation. The present domain covers the gel and solution states as well as a diffuse interface between them. They are indicated by the crosslink density in such a way that the solution phase is identified as the state when the crosslink density is small, while the gel as the state if the crosslink density becomes large. In this work, a novel order parameter is thus defined as the crosslink density, which is homogeneous in each distinct phase and smoothly varies over the interface from one phase to another. In this model, the constitutive equations, imposed on the two distinct phases and the interface, are formulated by the second law of thermodynamics, which are in the same form as those derived by a different approach. The present constitutive equations include a novel Ginzburg-Landau type of free energy with a double-well profile, which accounts for the effect of crosslink density. The present governing equations include the equilibrium of forces, the conservations of mass and energy, and an additional kinetic equation imposed for phase transition, in which nonlinear deformation is considered. The equilibrium state is investigated numerically, where two stable phases are observed in the free energy profile. As case studies, a spherically symmetrical solution-gel phase transition is simulated numerically for analysis of the phase transition of physical hydrogel.
Nonlinear stability in reaction-diffusion systems via optimal Lyapunov functions
NASA Astrophysics Data System (ADS)
Lombardo, S.; Mulone, G.; Trovato, M.
2008-06-01
We define optimal Lyapunov functions to study nonlinear stability of constant solutions to reaction-diffusion systems. A computable and finite radius of attraction for the initial data is obtained. Applications are given to the well-known Brusselator model and a three-species model for the spatial spread of rabies among foxes.
Nonlinear dirac and diffusion equations in 1+1 dimensions from stochastic considerations
Maharana
2000-08-01
We generalize the method of obtaining fundamental linear partial differential equations such as the diffusion and Schrodinger equation, the Dirac, and the telegrapher's equation from a simple stochastic consideration to arrive at a certain nonlinear form of these equations. A group classification through a one-parameter group of transformations for two of these equations is also carried out.
Similarity solution to fractional nonlinear space-time diffusion-wave equation
NASA Astrophysics Data System (ADS)
Costa, F. Silva; Marão, J. A. P. F.; Soares, J. C. Alves; de Oliveira, E. Capelas
2015-03-01
In this article, the so-called fractional nonlinear space-time wave-diffusion equation is presented and discussed. This equation is solved by the similarity method using fractional derivatives in the Caputo, Riesz-Feller, and Riesz senses. Some particular cases are presented and the corresponding solutions are shown by means of 2-D and 3-D plots.
Self-similar solutions for a nonlinear radiation diffusion equation
Garnier, Josselin; Malinie, Guy; Saillard, Yves; Cherfils-Clerouin, Catherine
2006-09-15
This paper considers the hydrodynamic equations with nonlinear conduction when the internal energy and the opacity have power-law dependences in the density and in the temperature. This system models the situation in which a dense solid is brought into contact with a thermal bath. It supports self-similar solutions that depend on the surface temperature. The self-similar solution can exhibit a shock wave followed by an ablation front if the surface temperature does not increase too fast in time, but it can exhibit a heat front followed by an isothermal shock otherwise. These flows are carefully studied in order to clarify the role of the initial solid density in the energy absorption and the ablation process. Comparisons with numerical simulations show excellent agreement.
NASA Astrophysics Data System (ADS)
Cotta, R. M.; Naveira-Cotta, C. P.; Knupp, D. C.; Zotin, J. L. Z.; Pontes, P. C.
2016-09-01
This lecture offers an updated review on the Generalized Integral Transform Technique (GITT), with focus on handling complex geometries, coupled problems, and nonlinear convection-diffusion, so as to illustrate some new application paradigms. Special emphasis is given to demonstrating novel developments, such as a single domain reformulation strategy that simplifies the treatment of complex geometries, an integral balance scheme in handling multiscale problems, the adoption of convective eigenvalue problems in dealing with strongly convective formulations, and the direct integral transformation of nonlinear convection-diffusion problems based on nonlinear eigenvalue problems. Representative application examples are then provided that employ recent extensions on the Generalized Integral Transform Technique (GITT), and a few numerical results are reported to illustrate the convergence characteristics of the proposed eigenfunction expansions.
Experimental investigation of the Marangoni effect on the stability of a double-diffusive layer
NASA Technical Reports Server (NTRS)
Tanny, Josef; Chen, Chuan F.
1994-01-01
Stability experiments were carried out in 4-cm-thick, salt-stratified fluid layer by heating from below and cooling from above. The bottom boundary was rigid while the top was either free or rigid. The initial solute Rayleigh number varied from 2.5 x 10(exp 6) to 4.6 x 10(exp 7). For the rigid-free case, at initial solute Rayleigh numbers R(sub s) greater than 5.4 x 10(exp 6), thermal Marangoni instabilities were observed to onset along the free surface at a relatively low thermal Rayleigh number, R(sub t). The convection was very weak, and it had almost no effect on the concentration and temperature distributions. Double-diffusive instabilities along the top free surface were observed to onset at a higher R(sub t), with much stronger convection causing changes in the concentration and temperature distributions near the top. At a yet higher R(sub t), double-diffusive convection was observed to onset along the bottom boundary. Fluid motion in the layer then evolved into fully developed thermal convection of a homogeneous fluid without any further increase in the imposed Delta T. For layers with R(sub s) less than 5.4 x 10(exp 6), Marangoni and double-diffusive instabilities onset simultaneously along the free surface first, while double-diffusive instabilities along the bottom wall onset at a higher R(sub t).
Euler buckling and nonlinear kinking of double-stranded DNA
NASA Astrophysics Data System (ADS)
Fields, Alexander; Axelrod, Kevin; Cohen, Adam
2012-02-01
Bare double-stranded DNA is a stiff biopolymer with a persistence length of roughly 53 nm under physiological conditions. Cells and viruses employ extensive protein machinery to overcome this stiffness and bend, twist, and loop DNA to accomplish tasks such as packaging, recombination, gene regulation, and repair. The mechanical properties of DNA are of fundamental importance to the mechanism and thermodynamics of these processes, but physiologically relevant curvature has been difficult to access experimentally. We designed and synthesized a DNA hairpin construct in which base-pairing interactions generated a compressive force on a short segment of duplex DNA, inducing Euler buckling followed by bending to thermally inaccessible radii of curvature. The efficiency of F"orster resonance energy transfer (FRET) between two fluorophores covalently linked to the hairpin indicated the degree of buckling. Bulk and single-molecule measurements yielded distinctly different force-compression curves for intact DNA and for strands with single nicks, base pair mismatches, and damage sites. These results suggest that changes in local mechanical properties may play a significant role in the recognition of these features by DNA-binding proteins.
Nonlinear diffusion-wave equation for a gas in a regenerator subject to temperature gradient
NASA Astrophysics Data System (ADS)
Sugimoto, N.
2015-10-01
This paper derives an approximate equation for propagation of nonlinear thermoacoustic waves in a gas-filled, circular pore subject to temperature gradient. The pore radius is assumed to be much smaller than a thickness of thermoviscous diffusion layer, and the narrow-tube approximation is used in the sense that a typical axial length associated with temperature gradient is much longer than the radius. Introducing three small parameters, one being the ratio of the pore radius to the thickness of thermoviscous diffusion layer, another the ratio of a typical speed of thermoacoustic waves to an adiabatic sound speed and the other the ratio of a typical magnitude of pressure disturbance to a uniform pressure in a quiescent state, a system of fluid dynamical equations for an ideal gas is reduced asymptotically to a nonlinear diffusion-wave equation by using boundary conditions on a pore wall. Discussion on a temporal mean of an excess pressure due to periodic oscillations is included.
Rediscovering Hydrogel-Based Double-Diffusion Systems for Studying Biomineralization
Dorvee, Jason R.; Boskey, Adele L.; Estroff, Lara A.
2012-01-01
For those seeking to model biomineralization in vitro, hydrogels can serve as excellent models of the extracellular matrix (ECM) microenvironment. A major challenge posed in implementing such systems is the logistics involved, from fundamental engineering to experimental design. For the study of calcium phosphate (e.g., hydroxyapatite) formation, many researchers use hydrogel-based double-diffusion systems (DDSs). The various designs of these DDSs are seemingly as unique as their applications. In this Highlight, we present a survey of four distinct types of double-diffusion systems and evaluate them in the context of fundamental diffusion theory. Based upon this analysis, we present the design and evaluation of an optimized system. The techniques and framework for the evaluation and construction of a DDS presented here can be applied to any DDS that a researcher may want to implement for their particular studies of biomineralization. PMID:22962542
Nonlinear stability research on the hydraulic system of double-side rolling shear
NASA Astrophysics Data System (ADS)
Wang, Jun; Huang, Qingxue; An, Gaocheng; Qi, Qisong; Sun, Binyu
2015-10-01
This paper researches the stability of the nonlinear system taking the hydraulic system of double-side rolling shear as an example. The hydraulic system of double-side rolling shear uses unsymmetrical electro-hydraulic proportional servo valve to control the cylinder with single piston rod, which can make best use of the space and reduce reversing shock. It is a typical nonlinear structure. The nonlinear state-space equations of the unsymmetrical valve controlling cylinder system are built first, and the second Lyapunov method is used to evaluate its stability. Second, the software AMEsim is applied to simulate the nonlinear system, and the results indicate that the system is stable. At last, the experimental results show that the system unsymmetrical valve controlling the cylinder with single piston rod is stable and conforms to what is deduced by theoretical analysis and simulation. The construction and application of Lyapunov function not only provide the theoretical basis for using of unsymmetrical valve controlling cylinder with single piston rod but also develop a new thought for nonlinear stability evaluation.
Nonlinear stability research on the hydraulic system of double-side rolling shear.
Wang, Jun; Huang, Qingxue; An, Gaocheng; Qi, Qisong; Sun, Binyu
2015-10-01
This paper researches the stability of the nonlinear system taking the hydraulic system of double-side rolling shear as an example. The hydraulic system of double-side rolling shear uses unsymmetrical electro-hydraulic proportional servo valve to control the cylinder with single piston rod, which can make best use of the space and reduce reversing shock. It is a typical nonlinear structure. The nonlinear state-space equations of the unsymmetrical valve controlling cylinder system are built first, and the second Lyapunov method is used to evaluate its stability. Second, the software AMEsim is applied to simulate the nonlinear system, and the results indicate that the system is stable. At last, the experimental results show that the system unsymmetrical valve controlling the cylinder with single piston rod is stable and conforms to what is deduced by theoretical analysis and simulation. The construction and application of Lyapunov function not only provide the theoretical basis for using of unsymmetrical valve controlling cylinder with single piston rod but also develop a new thought for nonlinear stability evaluation.
Joo, K; Ellis, J D; Buice, E S; Spronck, J W; Munnig Schmidt, R H
2010-02-05
This paper describes a novel heterodyne laser interferometer with no significant periodic nonlinearity for linear displacement measurements. Moreover, the optical configurations have the benefit of doubling the measurement resolution when compared to its respective traditional counterparts. Experimental results show no discernable periodic nonlinearity for a retro-reflector interferometer and plane mirror interferometer configurations with a noise level below 20 pm. The incoming laser beams of the interferometers are achieved by utilizing two single mode optical fibers. To determine the stability of the optical fiber couplers a fiber delivery prototype was also built and tested.
Double-Diffusive Convection During Growth of Halides and Selenides
NASA Technical Reports Server (NTRS)
Singh, N. B.; Su, Ching-Hua; Duval, Walter M. B.
2015-01-01
several materials such as mercurous chloride, mercurous bromide, mercurous iodide, lead chloride lead bromide, lead iodide, thallium arsenic selenide, gallium selenide, zince sulfide zinc selenide and several crystals into devices. We have used both Bridgman and physical vapor transport (PVT) crystal growth methods. In the past have examined PVT growth numerically for conditions where the boundary of the enclosure is subjected to a nonlinear thermal profile. Since past few months we have been working on binary and ternary materials such as selenoiodides, doped zinc sulfides and mercurous chloro bromide and mercurous bromoiodides. In the doped and ternary materials thermal and solutal convection play extremely important role during the growth. Very commonly striations and banding is observed. Our experiments have indicated that even in highly purified source materials, homogeneity in 1-g environment is very difficult. Some of our previous numerical studies have indicated that gravity level less than 10-4 (?-g) helps in controlling the thermosolutal convection. We will discuss the ground based growth results of HgClxBr(1-x) and ZnSe growth results for the mm thick to large cm size crystals. These results will be compared with our microgravity experiments performed with this class of materials. For both HgCl-HgBr and ZnS-ZnSe the lattice parameters of the mixtures obey Vagard's law in the studied composition range. The study demonstrates that properties are very anisotropic with crystal orientation, and performance achievement requires extremely careful fabrication to utilize highest figure of merit. In addition, some parameters such as crystal growth fabrication, processing time, resolution, field of view and efficiency will be described based on novel solid solution materials. It was predicted that very similar to the pure compounds solid solutions also have very large anisotropy, and very precise oriented and homogeneous bulk and thin film crystals is required to achieve
NASA Astrophysics Data System (ADS)
Weeratunga, Sisira K.; Kamath, Chandrika
2002-05-01
Removing noise from data is often the first step in data analysis. Denoising techniques should not only reduce the noise, but do so without blurring or changing the location of the edges. Many approaches have been proposed to accomplish this; in this paper, we focus on one such approach, namely the use of non-linear diffusion operators. This approach has been studied extensively from a theoretical viewpoint ever since the 1987 work of Perona and Malik showed that non-linear filters outperformed the more traditional linear Canny edge detector. We complement this theoretical work by investigating the performance of several isotropic diffusion operators on test images from scientific domains. We explore the effects of various parameters such as the choice of diffusivity function, explicit and implicit methods for the discretization of the PDE, and approaches for the spatial discretization of the non-linear operator etc. We also compare these schemes with simple spatial filters and the more complex wavelet-based shrinkage techniques. Our empirical results show that, with an appropriate choice of parameters, diffusion-based schemes can be as effective as competitive techniques.
Nonlinear dilational mechanics of Langmuir lipid monolayers: a lateral diffusion mechanism.
Arriaga, Laura R; López-Montero, Iván; Rodríguez-García, Ruddi; Monroy, Francisco
2008-06-01
We propose a theoretical model for the nonlinear mechanical response of Langmuir lipid monolayers subjected to a dilational in-plane deformation. Lateral diffusion in conjunction with free convection has been considered to drive nonlinear mass transport in Langmuir lipid monolayers. The present model combines the conservative dynamical equations for lipid transport along the monolayer plane together with a material relationship accounting for nonlinear hypoelasticity, as experimentally observed from high-strain rheological measurements [Hilles, Adv. Colloid Interface Sci. 122, 67 (2007)]. The dynamical equations have been resolved for oscillatory nonlinear motion, the theoretical spectral amplitudes being found in quantitative agreement with the experimental values obtained from surface rheology experiments performed in Langmuir monolayers of two different lipid systems, namely DPPC and native E. Coli lipids. The presence of micrometer-sized phase coexistence domains in these lipid systems has been claimed to pump diffusive transport along the monolayer plane. This dynamical scenario defines a relaxation regime compatible with the observed nonlinear mechanical behavior.
NASA Astrophysics Data System (ADS)
Leyva, J. Francisco; Málaga, Carlos; Plaza, Ramón G.
2013-11-01
This paper studies a reaction-diffusion-chemotaxis model for bacterial aggregation patterns on the surface of thin agar plates. It is based on the non-linear degenerate cross diffusion model proposed by Kawasaki et al. (1997) [5] and it includes a suitable nutrient chemotactic term compatible with such type of diffusion, as suggested by Ben-Jacob et al. (2000) [20]. An asymptotic estimation predicts the growth velocity of the colony envelope as a function of both the nutrient concentration and the chemotactic sensitivity. It is shown that the growth velocity is an increasing function of the chemotactic sensitivity. High resolution numerical simulations using Graphic Processing Units (GPUs), which include noise in the diffusion coefficient for the bacteria, are presented. The numerical results verify that the chemotactic term enhances the velocity of propagation of the colony envelope. In addition, the chemotaxis seems to stabilize the formation of branches in the soft-agar, low-nutrient regime.
NASA Astrophysics Data System (ADS)
Ghebache, Siham; Tribeche, Mouloud
2016-04-01
Weakly nonlinear ion-acoustic (IA) double-layers (DLs), which accompany electronegative plasmas composed of positive ions, negative ions, and nonextensive electrons are investigated. A generalized Korteweg-de Vries equation with a cubic nonlinearity is derived using a reductive perturbation method. Different types of electronegative plasmas inspired from the experimental studies of Ichiki et al. (2001) are discussed. It is shown that the IA wave phase velocity, in different mixtures of negative and positive ions, decreases as the nonextensive parameter q increases, before levelling-off at a constant value for larger q. Moreover, a relative increase of Q involves an enhancement of the IA phase velocity. Existence domains of either solitary waves or double-layers are then presented and their parametric dependence is determined. Owing to the electron nonextensivity, our present plasma model can admit compressive as well as rarefactive IA-DLs.
Impurity-related nonlinear optical rectification in double quantum dot under electric field
NASA Astrophysics Data System (ADS)
Bejan, D.
2016-11-01
The characteristics of donor-impurity-related nonlinear optical rectification in asymmetric double quantum dot under electric field are investigated within the compact density-matrix formalism and the effective mass approximation. The results show that: (i) the binding energy of the ground state varies strongly with the impurity position and it is raised or decreased by the applied field, depending on the impurity position; (ii) the optical rectification spectra are rather sensitive to the impurity position and the electric field intensity; (iii) the changes in the impurity position within the double quantum dot and the electric field value may induce red or blue shift of the resonant peaks of the nonlinear optical rectification.
Extension of the double-wave-vector diffusion-weighting experiment to multiple concatenations.
Finsterbusch, Jürgen
2009-06-01
Experiments involving two diffusion-weightings in a single acquisition, so-called double- or two-wave-vector experiments, have recently been applied to measure the microscopic anisotropy in macroscopically isotropic samples or to estimate pore or compartment sizes. These informations are derived from the signal modulation observed when varying the wave vectors' orientations. However, the modulation amplitude can be small and, for short mixing times between the two diffusion-weightings, decays with increased gradient pulse lengths which hampers its detectability on whole-body MR systems. Here, an approach is investigated that involves multiple concatenations of the two diffusion-weightings in a single experiment. The theoretical framework for double-wave-vector experiments of fully restricted diffusion is adapted and the corresponding tensor approach recently presented for short mixing times extended and compared to numerical simulations. It is shown that for short mixing times (i) the extended tensor approach well describes the signal behavior observed for multiple concatenations and (ii) the relative amplitude of the signal modulation increases with the number of concatenations. Thus, the presented extension of the double-wave-vector experiment may help to improve the detectability of the signal modulations observed for short mixing times, in particular on whole-body MR systems with their limited gradient amplitudes.
Nonlinear preferential rewiring in fixed-size networks as a diffusion process.
Johnson, Samuel; Torres, Joaquín J; Marro, Joaquín
2009-05-01
We present an evolving network model in which the total numbers of nodes and edges are conserved, but in which edges are continuously rewired according to nonlinear preferential detachment and reattachment. Assuming power-law kernels with exponents alpha and beta , the stationary states which the degree distributions evolve toward exhibit a second-order phase transition-from relatively homogeneous to highly heterogeneous (with the emergence of starlike structures) at alpha=beta . Temporal evolution of the distribution in this critical regime is shown to follow a nonlinear diffusion equation, arriving at either pure or mixed power laws of exponents -alpha and 1-alpha .
Semi-analytical method for solving nonlinear heat diffusion problems in spherical medium
NASA Astrophysics Data System (ADS)
Abd-El-Malek, Mina B.; Helal, Medhat M.
2006-08-01
A semi-analytical methodology, based on the finite integral transform technique, is proposed to solve the heat diffusion problem in a spherical medium subject to nonlinear boundary conditions due to radiation exchange at the interface according to the fourth power law. The method proceeds by treating the nonlinearity term in the boundary condition as a source in the differential equation and keeping other conditions unchanged. The results obtained from this semi-analytical solutions are compared with those obtained from a numerical solution developed using an explicit finite difference method, which showed very good agreement.
Local-instantaneous filtering in the integral transform solution of nonlinear diffusion problems
NASA Astrophysics Data System (ADS)
Macêdo, E. N.; Cotta, R. M.; Orlande, H. R. B.
A novel filtering strategy is proposed to be utilized in conjunction with the Generalized Integral Transform Technique (GITT), in the solution of nonlinear diffusion problems. The aim is to optimize convergence enhancement, yielding computationally efficient eigenfunction expansions. The proposed filters include space and time dependence, extracted from linearized versions of the original partial differential system. The scheme automatically updates the filter along the time integration march, as the required truncation orders for the user requested accuracy begin to exceed a prescribed maximum system size. A fully nonlinear heat conduction example is selected to illustrate the computational performance of the filtering strategy, against the classical single-filter solution behavior.
Effects of radial diffuser hydraulic design on a double-suction centrifugal pump
NASA Astrophysics Data System (ADS)
Hou, H. C.; Zhang, Y. X.; Xu, C.; Zhang, J. Y.; Li, Z. L.
2016-05-01
In order to study effects of radial diffuser on hydraulic performance of crude oil pump, the steady CFD numerical method is applied and one large double-suction oil pump running in long-distance pipeline is considered. The research focuses on analysing the influence of its diffuser vane profile on hydraulic performance of oil pump. The four different types of cylindrical vane have been designed by in-house codes mainly including double arcs (DA), triple arcs (TA), equiangular spiral line (ES) and linear variable angle spiral line (LVS). During design process diffuser vane angles at inlet and outlet are tentatively given within a certain range and then the wrapping angle of the four types of diffuser vanes can be calculated automatically. Under the given inlet and outlet angles, the linear variable angle spiral line profile has the biggest wrapping angle and profile length which is good to delay channel diffusion but bring more friction hydraulic loss. Finally the vane camber line is thickened at the certain uniform thickness distribution and the 3D diffuser models are generated. The whole flow passage of oil pump with different types of diffusers under various flow rate conditions are numerically simulated based on RNG k-ɛ turbulent model and SIMPLEC algorithm. The numerical results show that different types of diffusers can bring about great difference on the hydraulic performance of oil pump, of which the ES profile diffuser with its proper setting angle shows the best hydraulic performance and its inner flow field is improved obviously. Compared with the head data from model sample, all designed diffusers can make a certain improvement on head characteristic. At the large flow rate conditions the hydraulic efficiency increases obviously and the best efficiency point shift to the large flow rate range. The ES profile diffuser embodies the better advantages on pump performance which can be explained theoretically that the diffuser actually acts as a diffusion
Gachet, David; Brustlein, Sophie; Rigneault, Hervé
2010-05-28
In the Young's double slit experiment, the spatial shift of the interference pattern projected onto a screen is directly related to the phase difference between the fields diffracted by the two slits. We apply this property to fields emitted by nonlinear processes and thus demonstrate background-free coherent anti-Stokes Raman scattering microscopy near an axial interface between a resonant and a nonresonant medium. This method is relevant to remove the nonresonant background in other coherent resonant processes.
Double Fourier Harmonic Balance Method for Nonlinear Oscillators by Means of Bessel Series
2014-10-16
Double Fourier harmonic balance method for nonlinear oscillators by means of Bessel series T.C. Lipscombe∗1 and C.E. Mungan†2 1Catholic University of... harmonic balance method consists in expanding the displacement of an oscillator as a Fourier cosine series in time. A key modification is proposed here, in...than the exact value. Even better, the predicted frequency for the V-ramp case turns out to be exact. Keywords: Fourier expansion, harmonic balance
Finite element method for nonlinear Riesz space fractional diffusion equations on irregular domains
NASA Astrophysics Data System (ADS)
Yang, Z.; Yuan, Z.; Nie, Y.; Wang, J.; Zhu, X.; Liu, F.
2017-02-01
In this paper, we consider two-dimensional Riesz space fractional diffusion equations with nonlinear source term on convex domains. Applying Galerkin finite element method in space and backward difference method in time, we present a fully discrete scheme to solve Riesz space fractional diffusion equations. Our breakthrough is developing an algorithm to form stiffness matrix on unstructured triangular meshes, which can help us to deal with space fractional terms on any convex domain. The stability and convergence of the scheme are also discussed. Numerical examples are given to verify accuracy and stability of our scheme.
Period doubling and other nonlinear phenomena in volcanic earthquakes and tremor
Julian, B.R.
2000-01-01
Evidence of subharmonic period-doubling cascades has recently been recognized in seismograms of volcanic tremor from several volcanoes. This phenomenon occurs only in nonlinear systems, and is the commonest route by which such systems change from periodic to chaotic behavior. It is predicted to occur in a model of volcanic tremor excitation by flow-induced vibration, and it might well also occur in other volcano-seismic source process. If the possibility of period doubling is not taken into account in interpreting spectra of tremor and long-period earthquakes, then low-frequency "sub-harmonic" oscillations may be mis-identified as normal modes of a linear acoustic resonator, leading to errors of an order of magnitude or more in inferred magma-body dimensions. This example illustrates the importance of nonlinear phenomena in attempts to understand volcano-seismic phenomena physically. Linear systems are fundamentally incapable of causing earthquakes or exciting tremor, so nonlinearity is essential to any theory of volcano-seismic phenomena. Nonlinear processes are in many respects qualitatively different from linear ones. A few of their characteristics that might be relevant in volcanoes include the possibility: (1) that damping might increase, rather than decrease, oscillation frequencies; and (2) that these frequencies might be functions of the amplitude of oscillation, so that temporal variations in spectral peak frequencies might not be manifestations of changes of conditions within the magmatic system.
Period doubling and other nonlinear phenomena in volcanic earthquakes and tremor
NASA Astrophysics Data System (ADS)
Julian, B. R.
2000-08-01
Evidence of subharmonic period-doubling cascades has recently been recognized in seismograms of volcanic tremor from several volcanoes. This phenomenon occurs only in nonlinear systems, and is the commonest route by which such systems change from periodic to chaotic behavior. It is predicted to occur in a model of volcanic tremor excitation by flow-induced vibration, and it might well also occur in other volcano-seismic source process. If the possibility of period doubling is not taken into account in interpreting spectra of tremor and long-period earthquakes, then low-frequency "sub-harmonic" oscillations may be mis-identified as normal modes of a linear acoustic resonator, leading to errors of an order of magnitude or more in inferred magma-body dimensions. This example illustrates the importance of nonlinear phenomena in attempts to understand volcano-seismic phenomena physically. Linear systems are fundamentally incapable of causing earthquakes or exciting tremor, so nonlinearity is essential to any theory of volcano-seismic phenomena. Nonlinear processes are in many respects qualitatively different from linear ones. A few of their characteristics that might be relevant in volcanoes include the possibility: (1) that damping might increase, rather than decrease, oscillation frequencies; and (2) that these frequencies might be functions of the amplitude of oscillation, so that temporal variations in spectral peak frequencies might not be manifestations of changes of conditions within the magmatic system.
DOUBLE-DIFFUSIVE INSTABILITIES OF A SHEAR-GENERATED MAGNETIC LAYER
Silvers, Lara J.; Proctor, Michael R. E.; Vasil, Geoffrey M.; Brummell, Nicholas H.
2009-09-01
Previous theoretical work has speculated about the existence of double-diffusive magnetic buoyancy instabilities of a dynamically evolving horizontal magnetic layer generated by the interaction of forced vertically sheared velocity and a background vertical magnetic field. Here, we confirm numerically that if the ratio of the magnetic to thermal diffusivities is sufficiently low then such instabilities can indeed exist, even for high Richardson number shear flows. Magnetic buoyancy may therefore occur via this mechanism for parameters that are likely to be relevant to the solar tachocline, where regular magnetic buoyancy instabilities are unlikely.
Typical and rare fluctuations in nonlinear driven diffusive systems with dissipation.
Hurtado, Pablo I; Lasanta, A; Prados, A
2013-08-01
We consider fluctuations of the dissipated energy in nonlinear driven diffusive systems subject to bulk dissipation and boundary driving. With this aim, we extend the recently introduced macroscopic fluctuation theory to nonlinear driven dissipative media, starting from the fluctuating hydrodynamic equations describing the system mesoscopic evolution. Interestingly, the action associated with a path in mesoscopic phase space, from which large-deviation functions for macroscopic observables can be derived, has the same simple form as in nondissipative systems. This is a consequence of the quasielasticity of microscopic dynamics, required in order to have a nontrivial competition between diffusion and dissipation at the mesoscale. Euler-Lagrange equations for the optimal density and current fields that sustain an arbitrary dissipation fluctuation are also derived. A perturbative solution thereof shows that the probability distribution of small fluctuations is always Gaussian, as expected from the central limit theorem. On the other hand, strong separation from the Gaussian behavior is observed for large fluctuations, with a distribution which shows no negative branch, thus violating the Gallavotti-Cohen fluctuation theorem, as expected from the irreversibility of the dynamics. The dissipation large-deviation function exhibits simple and general scaling forms for weakly and strongly dissipative systems, with large fluctuations favored in the former case but heavily suppressed in the latter. We apply our results to a general class of diffusive lattice models for which dissipation, nonlinear diffusion, and driving are the key ingredients. The theoretical predictions are compared to extensive numerical simulations of the microscopic models, and excellent agreement is found. Interestingly, the large-deviation function is in some cases nonconvex beyond some dissipation. These results show that a suitable generalization of macroscopic fluctuation theory is capable of
Langrock, Carsten; Roussev, Rostislav V; Nava, Giovanni; Minzioni, Paolo; Argiolas, Nicola; Sada, Cinzia; Fejer, Martin M
2016-08-20
Photorefractive-damage- (PRD) resistant zirconium-oxide-doped lithium niobate is investigated as a substrate for the realization of annealed proton-exchanged (APE) waveguides. Its advantages are a favorable distribution coefficient, PRD resistance comparable to magnesium-oxide-doped lithium niobate, and a proton-diffusion behavior resembling congruent lithium niobate. A 1D model for APE waveguides was developed based on a previous model for congruently melting lithium niobate. Evidence for a nonlinear index dependence on concentration was found.
Typical and rare fluctuations in nonlinear driven diffusive systems with dissipation
NASA Astrophysics Data System (ADS)
Hurtado, Pablo I.; Lasanta, A.; Prados, A.
2013-08-01
We consider fluctuations of the dissipated energy in nonlinear driven diffusive systems subject to bulk dissipation and boundary driving. With this aim, we extend the recently introduced macroscopic fluctuation theory to nonlinear driven dissipative media, starting from the fluctuating hydrodynamic equations describing the system mesoscopic evolution. Interestingly, the action associated with a path in mesoscopic phase space, from which large-deviation functions for macroscopic observables can be derived, has the same simple form as in nondissipative systems. This is a consequence of the quasielasticity of microscopic dynamics, required in order to have a nontrivial competition between diffusion and dissipation at the mesoscale. Euler-Lagrange equations for the optimal density and current fields that sustain an arbitrary dissipation fluctuation are also derived. A perturbative solution thereof shows that the probability distribution of small fluctuations is always Gaussian, as expected from the central limit theorem. On the other hand, strong separation from the Gaussian behavior is observed for large fluctuations, with a distribution which shows no negative branch, thus violating the Gallavotti-Cohen fluctuation theorem, as expected from the irreversibility of the dynamics. The dissipation large-deviation function exhibits simple and general scaling forms for weakly and strongly dissipative systems, with large fluctuations favored in the former case but heavily suppressed in the latter. We apply our results to a general class of diffusive lattice models for which dissipation, nonlinear diffusion, and driving are the key ingredients. The theoretical predictions are compared to extensive numerical simulations of the microscopic models, and excellent agreement is found. Interestingly, the large-deviation function is in some cases nonconvex beyond some dissipation. These results show that a suitable generalization of macroscopic fluctuation theory is capable of
Yuan, Zhen; Zhang, Jiang; Wang, Xiaodong; Li, Changqing
2014-01-01
We conducted a systematic investigation of the reflectance diffuse optical tomography using continuous wave (CW) measurements and nonlinear reconstruction algorithms. We illustrated and suggested how to fine-tune the nonlinear reconstruction methods in order to optimize target localization with depth-adaptive regularizations, reduce boundary noises in the reconstructed images using a logarithm based objective function, improve reconstruction quantification using transport models, and resolve crosstalk problems between absorption and scattering contrasts with the CW reflectance measurements. The upgraded nonlinear reconstruction algorithms were evaluated with a series of numerical and experimental tests, which show the potentials of the proposed approaches for imaging both absorption and scattering contrasts in the deep targets with enhanced image quality. PMID:25401014
An Inverse Model of Double Diffusive Convection in the Beaufort Sea
2009-12-01
Master’s Thesis 4. TITLE AND SUBTITLE An Inverse Model of Double Diffusive Convection in the Beaufort Sea 6. AUTHOR(S) Jeremiah E. Chaplin 5 ...convection and mixing within the homogeneous layers............................... 5 Figure 4. Ice tethered profiler system....................14...Figure 5 . Location of ITP 1-6.............................15 Figure 6. Temperature – Salinity plot for ITPs 1-6........18 Figure 7. Histogram of data
Nonlinear dynamics of bi-layered graphene sheet, double-walled carbon nanotube and nanotube bundle
NASA Astrophysics Data System (ADS)
Gajbhiye, Sachin O.; Singh, S. P.
2016-05-01
Due to strong van der Waals (vdW) interactions, the graphene sheets and nanotubes stick to each other and form clusters of these corresponding nanostructures, viz. bi-layered graphene sheet (BLGS), double-walled carbon nanotube (DWCNT) and nanotube bundle (NB) or ropes. This research work is concerned with the study of nonlinear dynamics of BLGS, DWCNT and NB due to nonlinear interlayer vdW forces using multiscale atomistic finite element method. The energy between two adjacent carbon atoms is represented by the multibody interatomic Tersoff-Brenner potential, whereas the nonlinear interlayer vdW forces are represented by Lennard-Jones 6-12 potential function. The equivalent nonlinear material model of carbon-carbon bond is used to model it based on its force-deflection relation. Newmark's algorithm is used to solve the nonlinear matrix equation governing the motion of the BLGS, DWCNT and NB. An impulse and harmonic excitations are used to excite these nanostructures under cantilevered, bridged and clamped boundary conditions. The frequency responses of these nanostructures are computed, and the dominant resonant frequencies are identified. Along with the forced vibration of these structures, the eigenvalue extraction problem of armchair and zigzag NB is also considered. The natural frequencies and corresponding mode shapes are extracted for the different length and boundary conditions of the nanotube bundle.
Observations indicative of rain-induced double diffusion in the ocean surface boundary layer
NASA Astrophysics Data System (ADS)
Walesby, K.; Vialard, J.; Minnett, P. J.; Callaghan, A. H.; Ward, B.
2015-05-01
Double diffusion can result in the formation of thermohaline staircases, typically observed in the ocean interior. The observations presented here were acquired in the ocean surface boundary layer with the autonomous microstructure Air-Sea Interaction Profiler. An intense rain event (rainfall rates of up to 35 mm/h) resulted in cooler, fresher water (up to 0.15 practical salinity unit (psu) over the upper 7-10 m) overlaying warmer, saltier water, a situation potentially conducive to double-diffusive mixing. Although not as crisp as interfaces in the interior ocean because of elevated background mixing, a total of 303 thermohaline interfaces were detected within and at the base of the fresh layer, with mean changes in temperature (T) and salinity (S) across interfaces of 20 × 10-3∘C and 22 × 10-3 psu, respectively. These results call for new studies to disambiguate whether such interfaces are formed through double-diffusive mixing or shear instabilities and understand any long-term impacts on near-surface stratification.
Swelling pressure of a divalent-rich bentonite: Diffuse double-layer theory revisited
NASA Astrophysics Data System (ADS)
Schanz, Tom; Tripathy, Snehasis
2009-05-01
Physicochemical forces are responsible for the swelling pressure development in saturated bentonites. In this paper, the swelling pressures of several compacted bentonite specimens for a range of dry density of 1.10-1.73 Mg/m3 were measured experimentally. The clay used was a divalent-rich Ca-Mg-bentonite with 12% exchangeable Na+ ions. The theoretical swelling pressure-dry density relationship for the bentonite was determined from the Gouy-Chapman diffuse double-layer theory. A comparison of experimental and theoretical results showed that the experimental swelling pressures are either smaller or greater than their theoretical counterparts within different dry density ranges. It is shown that for dry density of the clay less than about 1.55 Mg/m3, a possible dissociation of ions from the surface of the clay platelets contributed to the diffuse double-layer repulsion. At higher dry densities, the adsorptive forces due to surface and ion hydration dominated the swelling pressures of the clay. A comparison of the modified diffuse double-layer theory equations proposed in the literature to determine the swelling pressures of compacted bentonites and the experimental results for the clay in this study showed that the agreement between the calculated and experimental swelling pressure results is very good for dry densities less than 1.55 Mg/m3, whereas at higher dry densities the use of the equations was found to be limited.
Hamedi, H R; Gharamaleki, Ali Hamrah; Sahrai, Mostafa
2016-08-01
The paper is aimed at modeling the enhanced Kerr nonlinearity in a five-level double-ladder-type atomic system based on electromagnetically induced transparency (EIT) by using the semi-classical density matrix method. We present an analytical model to explain the origin of Kerr nonlinearity enhancement. The scheme also results in a several orders of magnitude increase in the Kerr nonlinearity in comparison with the well-known four- and three-level atomic systems. In addition to the steady-state case, the time-dependent Kerr nonlinearity and the switching feature of EIT-based colossal Kerr nonlinearity is investigated for the proposed system.
NASA Astrophysics Data System (ADS)
Schunert, Sebastian; Wang, Yaqi; Gleicher, Frederick; Ortensi, Javier; Baker, Benjamin; Laboure, Vincent; Wang, Congjian; DeHart, Mark; Martineau, Richard
2017-06-01
This work presents a flexible nonlinear diffusion acceleration (NDA) method that discretizes both the SN transport equation and the diffusion equation using the discontinuous finite element method (DFEM). The method is flexible in that the diffusion equation can be discretized on a coarser mesh with the only restriction that it is nested within the transport mesh and the FEM shape function orders of the two equations can be different. The consistency of the transport and diffusion solutions at convergence is defined by using a projection operator mapping the transport into the diffusion FEM space. The diffusion weak form is based on the modified incomplete interior penalty (MIP) diffusion DFEM discretization that is extended by volumetric drift, interior face, and boundary closure terms. In contrast to commonly used coarse mesh finite difference (CMFD) methods, the presented NDA method uses a full FEM discretized diffusion equation for acceleration. Suitable projection and prolongation operators arise naturally from the FEM framework. Via Fourier analysis and numerical experiments for a one-group, fixed source problem the following properties of the NDA method are established for structured quadrilateral meshes: (1) the presented method is unconditionally stable and effective in the presence of mild material heterogeneities if the same mesh and identical shape functions either of the bilinear or biquadratic type are used, (2) the NDA method remains unconditionally stable in the presence of strong heterogeneities, (3) the NDA method with bilinear elements extends the range of effectiveness and stability by a factor of two when compared to CMFD if a coarser diffusion mesh is selected. In addition, the method is tested for solving the C5G7 multigroup, eigenvalue problem using coarse and fine mesh acceleration. While NDA does not offer an advantage over CMFD for fine mesh acceleration, it reduces the iteration count required for convergence by almost a factor of two in
Relaxation of charge in monolayer graphene: Fast nonlinear diffusion versus Coulomb effects
NASA Astrophysics Data System (ADS)
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.
NASA Technical Reports Server (NTRS)
Karimbadi, H.; Krauss-Varban, D.
1992-01-01
A novel diffusion formalism that takes into account the finite width of resonances is presented. The resonance diagram technique is shown to reproduce the details of the particle orbits very accurately, and can be used to determine the acceleration/scattering in the presence of a given wave spectrum. Ways in which the nonlinear orbits can be incorporated into the diffusion equation are shown. The resulting diffusion equation is an extension of the Q-L theory to cases where the waves have large amplitudes and/or are coherent. This new equation does not have a gap at 90 deg in cases where the individual orbits can cross the gap. The conditions under which the resonance gap at 90-deg pitch angle exits are also examined.
NASA Astrophysics Data System (ADS)
Casti, Alexander Robert Richard
1999-07-01
This work explores two problems in hydrodynamic stability theory whose primary mathematical distinction is the manner in which unstable equilibria relax to a stable state. The first problem involves a dissipative fluid for which the diffusive relaxation of a linear instability is the primary saturation mechanism. The second problem arises from a conservative system where the relaxation is governed either by linear instabilities or nonlinear interactions among linearly stable modes. The dissipative problem considers thermohaline convection and the diffusive relaxation of two-dimensional, convectively unstable rolls. For this situation, the disparate diffusion rates of the heat and salt play a crucial role not only in triggering an instability, but also in dictating the nature of the saturation. We study these issues in two particular contexts. In the first case the effect of a nonlinear, basic state salt profile on the bifurcation to instability is examined, and some of the possible patterns in the weakly nonlinear regime are discussed. The second case explores the dynamics of a salt field diffusing so slowly that it does not have time to redistribute itself on the timescale over which the weakly unstable pattern develops. This necessitates a mathematical description that differs from the amplitude equations traditionally employed to capture the nonlinear saturation. The conservative system comes from astrophysics and cosmology. Motivated by the coexistence of dark and luminous matter in the cosmos, we investigate the instabilities of two interpenetrating fluids that interact only through the gravitational field. The result of primary importance is that negative energy modes may exist if the relative motion is substantial. This fact can have dramatic consequences on the nonlinear stability of the system if linearly stable waves of different energy signature conspire to resonate. In the absence of dissipative forces, the nature of the saturation must be a nonlinear
NASA Astrophysics Data System (ADS)
Duc, Nguyen Dinh; Quan, Tran Quoc
2012-09-01
An analytical investigation into the nonlinear response of thick functionally graded double-curved shallow panels resting on elastic foundations and subjected to thermal and thermomechanical loads is presented. Young's modulus and Poisson's ratio are both graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of constituents. All formulations are based on the classical shell theory with account of geometrical nonlinearity and initial geometrical imperfection in the cases of Pasternak-type elastic foundations. By applying the Galerkin method, explicit relations for the thermal load-deflection curves of simply supported curved panels are found. The effects of material and geometrical properties and foundation stiffness on the buckling and postbuckling load-carrying capacity of the panels in thermal environments are analyzed and discussed.
Nonlinear Vibration Characteristics of Fluid-Filled Double-Walled Carbon Nanotubes
NASA Astrophysics Data System (ADS)
Yan, Y.; Wang, W. Q.; Zhang, L. X.
Nonlinear vibration behaviors of double-walled carbon nanotubes (DWCNTs) with fluid inside the inner tube are investigated based on Donnell's cylindrical shell model and the more refined van der Waals (vdW) interaction formula. The Galerkin method and harmonic balance method are used to study the issue. The results obtained show that the radial vibrational modes of simply supported DWCNTs have twice the dynamical mode transitions as the frequency increases. The transitions correspond to twice the noncoaxial vibrations which play a critical role in electronic and transport properties of CNTs. Moreover, comparisons of the dynamical behaviors of fluid-filled DWCNTs with different wave numbers, radii and aspect ratios demonstrate that the amplitude-frequency curve topological forms are identical. Meanwhile, it is also concluded that the existence of fluid is significant for the value of amplitude ratio corresponding to noncoaxial vibration whereas it does not change the nonlinear vibrating topological pattern of amplitude-frequency curves.
Nonlinear modes and symmetry breaking in rotating double-well potentials
NASA Astrophysics Data System (ADS)
Li, Yongyao; Pang, Wei; Malomed, Boris A.
2012-08-01
We study modes trapped in a rotating ring carrying the self-focusing (SF) or self-defocusing (SDF) cubic nonlinearity and double-well potential cos2θ, where θ is the angular coordinate. The model, based on the nonlinear Schrödinger (NLS) equation in the rotating reference frame, describes the light propagation in a twisted pipe waveguide, as well as in other optical settings, and also a Bose-Einstein condensate (BEC) trapped in a torus and dragged by the rotating potential. In the SF and SDF regimes, five and four trapped modes of different symmetries are found, respectively. The shapes and stability of the modes and the transitions between them are studied in the first rotational Brillouin zone. In the SF regime, two symmetry-breaking transitions are found, of subcritical and supercritical types. In the SDF regime, an antisymmetry-breaking transition occurs. Ground states are identified in both the SF and SDF systems.
Nonlinear evolution of the Kelvin-Helmholtz instability in the double current sheet configuration
NASA Astrophysics Data System (ADS)
Mao, Aohua; Li, Jiquan; Liu, Jinyuan; Kishimoto, Yasuaki
2016-03-01
The nonlinear evolution of the Kelvin-Helmholtz (KH) instability driven by a radially antisymmetric shear flow in the double current sheet configuration is numerically investigated based on a reduced magnetohydrodynamic model. Simulations reveal different nonlinear fate of the KH instability depending on the amplitude of the shear flow, which restricts the strength of the KH instability. For strong shear flows far above the KH instability threshold, the linear electrostatic-type KH instability saturates and achieves a vortex flow dominated quasi-steady state of the electromagnetic (EM) KH turbulence with large-amplitude zonal flows as well as zonal fields. The magnetic surfaces are twisted significantly due to strong vortices but without the formation of magnetic islands. However, for the shear flow just over the KH instability threshold, a weak EM-type KH instability is saturated and remarkably damped by zonal flows through modifying the equilibrium shear flow. Interestingly, a secondary double tearing mode (DTM) is excited subsequently in highly damped KH turbulence, behaving as a pure DTM in a flowing plasma as described in Mao et al. [Phys. Plasmas 21, 052304 (2014)]. However, the explosive growth phenomenon is replaced by a gradually growing oscillation due to the extremely twisted islands. As a result, the release of the magnetic energy becomes slow and the global magnetic reconnection tends to be gentle. A complex nonlinear interaction between the EM KH turbulence and the DTMs occurs for the medium shear flows above the KH instability threshold, turbulent EM fluctuations experience oscillatory nonlinear growth of the DTMs, finally achieves a quasi-steady state with the interplay of the fluctuations between the DTMs and the EM KH instability.
Denoising of single-trial matrix representations using 2D nonlinear diffusion filtering.
Mustaffa, I; Trenado, C; Schwerdtfeger, K; Strauss, D J
2010-01-15
In this paper we present a novel application of denoising by means of nonlinear diffusion filters (NDFs). NDFs have been successfully applied for image processing and computer vision areas, particularly in image denoising, smoothing, segmentation, and restoration. We apply two types of NDFs for the denoising of evoked responses in single-trials in a matrix form, the nonlinear isotropic and the anisotropic diffusion filters. We show that by means of NDFs we are able to denoise the evoked potentials resulting in a better extraction of physiologically relevant morphological features over the ongoing experiment. This technique offers the advantage of translation-invariance in comparison to other well-known methods, e.g., wavelet denoising based on maximally decimated filter banks, due to an adaptive diffusion feature. We compare the proposed technique with a wavelet denoising scheme that had been introduced before for evoked responses. It is concluded that NDFs represent a promising and useful approach in the denoising of event related potentials. Novel NDF applications of single-trials of auditory brain responses (ABRs) and the transcranial magnetic stimulation (TMS) evoked electroencephalographic responses denoising are presented in this paper.
García-Sánchez, Pablo; Loucaides, Neophytos G; Ramos, Antonio
2017-02-01
Pumping of electrolytes in microchannels can be achieved with the use of microelectrodes subjected to AC potentials. Experiments have shown an influence of Faradaic currents in the pumping performance, and theoretical studies for asymmetric electrolytes suggest that induced charges in the diffusion layer play an important role. In this work we consider the case of a diffusion layer induced by an array of electrodes subjected to a traveling wave potential and we include Faradaic currents. Previous theoretical studies considered the case of very small applied voltages, which allowed for two major simplifications: (i) Butler-Volmer (B-V) equation was linearized, and (ii) the presence of gradients in ion concentration was neglected. We extend previous results and used the full nonlinear B-V equation. A comparison with the linear limit shows that the flow rate in both cases coincides for voltages around and below ≈0.25 V. For voltages larger than this, the nonlinear equations show that gradients in ion concentration appear and have an important influence, therefore, the predictions deviate from the linear model. We show that the electrical force in the diffusion layer can induce pumping either in the same or the opposite direction of the applied traveling-wave potential and it could be responsible for the reversal of the flow as observed in experiments.
NASA Astrophysics Data System (ADS)
García-Sánchez, Pablo; Loucaides, Neophytos G.; Ramos, Antonio
2017-02-01
Pumping of electrolytes in microchannels can be achieved with the use of microelectrodes subjected to AC potentials. Experiments have shown an influence of Faradaic currents in the pumping performance, and theoretical studies for asymmetric electrolytes suggest that induced charges in the diffusion layer play an important role. In this work we consider the case of a diffusion layer induced by an array of electrodes subjected to a traveling wave potential and we include Faradaic currents. Previous theoretical studies considered the case of very small applied voltages, which allowed for two major simplifications: (i) Butler-Volmer (B-V) equation was linearized, and (ii) the presence of gradients in ion concentration was neglected. We extend previous results and used the full nonlinear B-V equation. A comparison with the linear limit shows that the flow rate in both cases coincides for voltages around and below ≈0.25 V. For voltages larger than this, the nonlinear equations show that gradients in ion concentration appear and have an important influence, therefore, the predictions deviate from the linear model. We show that the electrical force in the diffusion layer can induce pumping either in the same or the opposite direction of the applied traveling-wave potential and it could be responsible for the reversal of the flow as observed in experiments.
Nonlinear Elastic J-Integral Measurements in Mode I Using a Tapered Double Cantilever Beam Geometry
NASA Technical Reports Server (NTRS)
Macon, David J.
2006-01-01
An expression for the J-integral of a nonlinear elastic material is derived for an advancing crack in a tapered double cantilever beam fracture specimen. The elastic and plastic fracture energies related to the test geometry and how these energies correlates to the crack position are discussed. The dimensionless shape factors eta(sub el and eta(sub p) are shown to be equivalent and the deformation J-integral is analyzed in terms of the eta(sub el) function. The fracture results from a structural epoxy are interpreted using the discussed approach. The magnitude of the plastic dissipation is found to strongly depend upon the initial crack shape.
Thermal Diffusivity Measurement of Zinc-Aluminum-Layered Double Hydroxide using Photoflash Technique
NASA Astrophysics Data System (ADS)
Ranjbar, Maryam; Yunus, W. Mahmood Mat.; Hussein, Mohd Zobir bin; Moksin, Mohd Maarof H. A.; Haydari, Mehdi
2008-05-01
The photoflash technique has been widely used for measuring thermal diffusivity of various types of materials. In this report thermal diffusivity of Zn-Al layered double hydroxide synthesized at different ratios of Zn to Al composition is presented. The samples were prepared using Zn(NO3)2 and Al(NO3)3 solutions at pH of 10 by drop wise addition of NaOH solution with vigorous stirring under nitrogen atmosphere. Different compositions of Zn to Al molar ratios were obtained by changing the molar ratio of Zn(NO3)2 to Al(NO3)3. The slurry formed was kept at 70 °C in an oil bath shaker for 18 h, filtered, washed and dried in an oven for 18 h at 70 °C. A simple photo flash and polyvinlidene diflouride (PVDF) film was used as light source and thermal wave detector, respectively. Thermal diffusivity of Zn-Al layered double hydroxide measure at room temperature was found increase with different compositions for Zn-Al ratio of 3-5.
The Effect of Rotation on Oscillatory Double-diffusive Convection (Semiconvection)
NASA Astrophysics Data System (ADS)
Moll, Ryan; Garaud, Pascale
2017-01-01
Oscillatory double-diffusive convection (ODDC, more traditionally called semiconvection) is a form of linear double-diffusive instability that occurs in fluids that are unstably stratified in temperature (Schwarzschild unstable), but stably stratified in chemical composition (Ledoux stable). This scenario is thought to be quite common in the interiors of stars and giant planets, and understanding the transport of heat and chemical species by ODDC is of great importance to stellar and planetary evolution models. Fluids unstable to ODDC have a tendency to form convective thermocompositional layers that significantly enhance the fluxes of temperature and chemical composition compared with microscopic diffusion. Although a number of recent studies have focused on studying properties of both layered and nonlayered ODDC, few have addressed how additional physical processes such as global rotation affect its dynamics. In this work, we study first how rotation affects the linear stability properties of rotating ODDC. Using direct numerical simulations, we then analyze the effect of rotation on properties of layered and nonlayered ODDC, and we study how the angle of the rotation axis with respect to the direction of gravity affects layering. We find that rotating systems can be broadly grouped into two categories based on the strength of rotation. The qualitative behavior in the more weakly rotating group is similar to nonrotating ODDC, but strongly rotating systems become dominated by vortices that are invariant in the direction of the rotation vector and strongly influence transport. We find that whenever layers form, rotation always acts to reduce thermal and compositional transport.
Oceanic Double-Diffusive Layer Thicknesses in the Presence of Turbulence
NASA Astrophysics Data System (ADS)
Shibley, Nicole; Timmermans, Mary-Louise
2016-11-01
Double-diffusive stratification in the ocean is characterized by staircase structures consisting of mixed layers separated by high-gradient interfaces in temperature and salinity. Several past studies have examined mechanisms that govern the observed thicknesses of staircase mixed layers. In one formalism, the mixed-layer thickness is set by layer formation that arises when a heat source is applied at the base of water that is stably-stratified in salinity; in another, the equilibrium thickness of mixed layers has been explained as the product of "merging," where thin layers continue to grow until they reach a thickness determined by a criterion relating the ratio of heat flux to salt flux and the density ratio. We extend the above two theories to consider the influence of turbulence on mixed-layer thicknesses. The study has implications for the Arctic Ocean where double-diffusive staircases are widely present, and mixed-layer thicknesses are well-resolved by ocean measurements. Our theoretical framework provides a means to determine turbulent diffusivities (in regions where microstructure measurements are not available) by considering only observations of density ratio, stratification, and layer thicknesses.
Brandt-Pollmann, U; Lebiedz, D; Diehl, M; Sager, S; Schlöder, J
2005-09-01
Theoretical and experimental studies related to manipulation of pattern formation in self-organizing reaction-diffusion processes by appropriate control stimuli become increasingly important both in chemical engineering and cellular biochemistry. In a model study, we demonstrate here exemplarily the application of an efficient nonlinear model predictive control (NMPC) algorithm to real-time optimal feedback control of pattern formation in a bacterial chemotaxis system modeled by nonlinear partial differential equations. The corresponding drift-diffusion model type is representative for many (bio)chemical systems involving nonlinear reaction dynamics and nonlinear diffusion. We show how the computed optimal feedback control strategy exploits the system inherent physical property of wave propagation to achieve desired control aims. We discuss various applications of our approach to optimal control of spatiotemporal dynamics.
NASA Astrophysics Data System (ADS)
Brandt-Pollmann, U.; Lebiedz, D.; Diehl, M.; Sager, S.; Schlöder, J.
2005-09-01
Theoretical and experimental studies related to manipulation of pattern formation in self-organizing reaction-diffusion processes by appropriate control stimuli become increasingly important both in chemical engineering and cellular biochemistry. In a model study, we demonstrate here exemplarily the application of an efficient nonlinear model predictive control (NMPC) algorithm to real-time optimal feedback control of pattern formation in a bacterial chemotaxis system modeled by nonlinear partial differential equations. The corresponding drift-diffusion model type is representative for many (bio)chemical systems involving nonlinear reaction dynamics and nonlinear diffusion. We show how the computed optimal feedback control strategy exploits the system inherent physical property of wave propagation to achieve desired control aims. We discuss various applications of our approach to optimal control of spatiotemporal dynamics.
An algorithm for solving the fractional convection diffusion equation with nonlinear source term
NASA Astrophysics Data System (ADS)
Momani, Shaher
2007-10-01
In this paper an algorithm based on Adomian's decomposition method is developed to approximate the solution of the nonlinear fractional convection-diffusion equation {∂αu}/{∂tα}={∂2u}/{∂x2}-c{∂u}/{∂x}+Ψ(u)+f(x,t),0
Computation of traveling wave fronts for a nonlinear diffusion-advection model.
Mansour, M B A
2009-01-01
This paper utilizes a nonlinear reaction-diffusion-advection model for describing the spatiotemporal evolution of bacterial growth. The traveling wave solutions of the corresponding system of partial differential equations are analyzed. Using two methods, we then find such solutions numerically. One of the methods involves the traveling wave equations and solving an initial-value problem, which leads to accurate computations of the wave profiles and speeds. The second method is to construct time-dependent solutions by solving an initial-moving boundary-value problem for the PDE system, showing another approximation for such wave solutions.
Double hit diffuse large B-cell lymphomas: diagnostic and therapeutic challenges.
Friedberg, Jonathan W
2015-03-01
Although diffuse large B-cell lymphoma (DLBCL) is curable with standard chemoimmunotherapy, over 30% of patients with advanced stage disease experience refractory disease or progression. Recent studies suggest that rearrangement of the myc oncogene occurs in approximately 10% of patients with DLBCL, and confers a very poor prognosis, particularly when there is concomitant rearrangement of bcl-2, a condition referred to as "double hit DLBCL". Using immunohistochemistry, up to 30% of patients have evidence of increased expression of myc, which occurs in both activated B-cell and germinal center type DLBCL. When bcl-2 is also positive by immunohistochemistry, prognosis is also poor. There are no randomized studies guiding treatment for patients with double hit DLBCL, but new datasets are emerging suggesting a possible role for dose-adjusted EPOCH infusional chemotherapy with rituximab. This review will conclude with a survey of novel agents which may be rationally incorporated into chemotherapy platforms for this high risk subset of DLBCL.
Hu, Weiming; Hu, Ruiguang; Xie, Nianhua; Ling, Haibin; Maybank, Stephen
2014-04-01
In this paper, we propose saliency driven image multiscale nonlinear diffusion filtering. The resulting scale space in general preserves or even enhances semantically important structures such as edges, lines, or flow-like structures in the foreground, and inhibits and smoothes clutter in the background. The image is classified using multiscale information fusion based on the original image, the image at the final scale at which the diffusion process converges, and the image at a midscale. Our algorithm emphasizes the foreground features, which are important for image classification. The background image regions, whether considered as contexts of the foreground or noise to the foreground, can be globally handled by fusing information from different scales. Experimental tests of the effectiveness of the multiscale space for the image classification are conducted on the following publicly available datasets: 1) the PASCAL 2005 dataset; 2) the Oxford 102 flowers dataset; and 3) the Oxford 17 flowers dataset, with high classification rates.
Detecting compartmental non-Gaussian diffusion with symmetrized double-PFG MRI.
Paulsen, Jeffrey L; Özarslan, Evren; Komlosh, Michal E; Basser, Peter J; Song, Yi-Qiao
2015-11-01
Diffusion in tissue and porous media is known to be non-Gaussian and has been used for clinical indications of stroke and other tissue pathologies. However, when conventional NMR techniques are applied to biological tissues and other heterogeneous materials, the presence of multiple compartments (pores) with different Gaussian diffusivities will also contribute to the measurement of non-Gaussian behavior. Here we present symmetrized double PFG (sd-PFG), which can separate these two contributions to non-Gaussian signal decay as having distinct angular modulation frequencies. In contrast to prior angular d-PFG methods, sd-PFG can unambiguously extract kurtosis as an oscillation from samples with isotropic or uniformly oriented anisotropic pores, and can generally extract a combination of compartmental anisotropy and kurtosis. The method further fixes its sensitivity with respect to the time dependence of the apparent diffusion coefficient. We experimentally demonstrate the measurement of the fourth cumulant (kurtosis) of diffusion and find it consistent with theoretical predictions. By enabling the unambiguous identification of contributions of compartmental kurtosis to the signal, sd-PFG has the potential to help identify the underlying micro-structural changes corresponding to current kurtosis based diagnostics, and act as a novel source of contrast to better resolve tissue micro-structure.
Nonlinear models for the adoption and diffusion of innovations for industrial energy conservation.
Jacobsen, Joseph J; Guastello, Stephen J
2007-10-01
Four different theoretical models for explaining the diffusion of innovation were compared for 13 energy-related innovations--the Theory of Planned Behavior, the S-curve for Diffusion of Innovations, the power law distribution, and the cusp catastrophe. The substantive concern was to explore the roles of facilitative and obstructive factors in diffusing industrial and commercial innovations. Participants were 102 industrial plant and facilities managers from sites that were among the top users of electrical energy and natural gas in the United States. They completed a survey that contained measurements of positive attitudes toward innovation, organizational resistance to innovation, and the extent to which they had investigated or adopted each of the target innovations. Seven of the 13 innovations exhibited strong cusp catastrophe models (via nonlinear regression, average R2 = .91) compared to linear alternative models (average R2 = .31) for those innovations; the S-curve for diffusion was regarded as a simplified version of the cusp. One innovation was characterized best by a power law distribution (R2 = .94), and the remaining five were characterized best by a linear model that was based on the Theory of Planned Behavior (R2 = .41). Different underlying dynamics for the various innovations were implied by these results.
NASA Astrophysics Data System (ADS)
Ouyang, Wei; Mao, Weijian; Li, Wuqun; Zhang, Pan
2016-11-01
An approach for approximate direct quadratic nonlinear inversion in two-parameter (density and bulk modulus) heterogeneous acoustic media is being presented and discussed in this paper. The approach consists of two parts: the first is a linear generalized Radon transform (GRT) migration procedure based on the weighted true-amplitude summation of pre-stack seismic scattered data that is adapted to a virtually arbitrary observing system, and the second is a non-iterative quadratic inversion operation, produced from the explicit expression of amplitude radiation pattern that is acting on the migrated data. This ensures the asymptotic inversion can continue to simultaneously locate the discontinuities and reconstruct the size of the discontinuities in the perturbation parameters describing the acoustic media. We identify that the amplitude radiation pattern is the binary quadratic combination of the parameters in the process of formulating nonlinear inverse scattering problems based on second-order Born approximation. The coefficients of the quadratic terms are computed by appropriately handling the double scattering effects. These added quadratic terms provide a better amplitude correction for the parameters inversion. Through numerical tests, we show that for strong perturbations, the errors of the linear inversion are significant and unacceptable. In contrast, the quadratic nonlinear inversion can give fairly accurate inversion results and keep almost the same computational complexity as conventional GRT liner inversion.
NASA Astrophysics Data System (ADS)
Ouyang, Wei; Mao, Weijian; Li, Wuqun; Zhang, Pan
2017-02-01
An approach for approximate direct quadratic non-linear inversion in two-parameter (density and bulk modulus) heterogeneous acoustic media is being presented and discussed in this paper. The approach consists of two parts: the first is a linear generalized Radon transform (GRT) migration procedure based on the weighted true-amplitude summation of pre-stack seismic scattered data that is adapted to a virtually arbitrary observing system, and the second is a non-iterative quadratic inversion operation, produced from the explicit expression of amplitude radiation pattern that is acting on the migrated data. This ensures the asymptotic inversion can continue to simultaneously locate the discontinuities and reconstruct the size of the discontinuities in the perturbation parameters describing the acoustic media. We identify that the amplitude radiation pattern is the binary quadratic combination of the parameters in the process of formulating non-linear inverse scattering problems based on second-order Born approximation. The coefficients of the quadratic terms are computed by appropriately handling the double scattering effects. These added quadratic terms provide a better amplitude correction for the parameters inversion. Through numerical tests, we show that for strong perturbations, the errors of the linear inversion are significant and unacceptable. In contrast, the quadratic non-linear inversion can give fairly accurate inversion results and keep almost the same computational complexity as conventional GRT liner inversion.
Noid, W G; Loring, Roger F
2004-10-15
Observables in coherent, multiple-pulse infrared spectroscopy may be computed from a vibrational nonlinear response function. This response function is conventionally calculated quantum-mechanically, but the challenges in applying quantum mechanics to large, anharmonic systems motivate the examination of classical mechanical vibrational nonlinear response functions. We present an approximate formulation of the classical mechanical third-order vibrational response function for an anharmonic solute oscillator interacting with a harmonic solvent, which establishes a clear connection between classical and quantum mechanical treatments. This formalism permits the identification of the classical mechanical analog of the pure dephasing of a quantum mechanical degree of freedom, and suggests the construction of classical mechanical analogs of the double-sided Feynman diagrams of quantum mechanics, which are widely applied to nonlinear spectroscopy. Application of a rotating wave approximation permits the analytic extraction of signals obeying particular spatial phase matching conditions from a classical-mechanical response function. Calculations of the third-order response function for an anharmonic oscillator coupled to a harmonic solvent are compared to numerically correct classical mechanical results.
Badawi, Ahmed M; Rushdi, Muhammad A
2006-01-01
This paper proposes a novel algorithm for speckle reduction in medical ultrasound imaging while preserving the edges with the added advantages of adaptive noise filtering and speed. We propose a nonlinear image diffusion algorithm that incorporates two local parameters of image quality, namely, scatterer density and texture-based contrast in addition to gradient, to weight the nonlinear diffusion process. The scatterer density is proposed to replace the existing traditional measures of quality of the ultrasound diffusion process such as MSE, RMSE, SNR, and PSNR. This novel diffusion filter was then implemented using back propagation neural network for fast parallel processing of volumetric images. The experimental results show that weighting the image diffusion with these parameters produces better noise reduction and produces a better edge detection quality with reasonable computational cost. The proposed filter can be used as a preprocessing phase before applying any ultrasound segmentation or active contour model processes.
Nonlinear diffusion of indirect excitons in an ideal bilayer with an in-plane harmonic trap
NASA Astrophysics Data System (ADS)
Wang, Li; Wang, Qinglu
2009-06-01
The nonlinear diffusion of the spatially indirect excitons in an ideal bilayer with an in-plane harmonic trap is investigated based on the theories developed by Ivanov [A.L. Ivanov, Europhys. Lett. 59 (2002) 586; A.L. Ivanov, J. Phys.: Condens. Matter 16 (2004) S3629] and Rapaport et al. [R. Rapaport, G. Chen, S. Simon, O. Mitrofanov, L. Pfeiffer, P.M. Platzman, Phys. Rev. B 72 (2005) 075428]. A nonlinear equation for the diffusion of the indirect excitons in this structure is established. The two-dimensional density of the indirect excitons in this structure is calculated. The calculations show that the density adjacent to the trap center for different exciton temperatures can remain very high even long after the photo-excitation because of the confinement of the in-plane harmonic trap, and that the indirect excitons gather several tens of μm away from the trap center. The calculations are in good agreement qualitatively with the experimental results of Voros et al. [Z. Voros, D.W. Snoke, L. Pfeiffer, K. West, Phys. Rev. Lett. 97 (2006) 016803] and prove that an in-plane harmonic trap can indeed keep an exciton gas dense near its center.
Singh, A.K.; Basu, B.
1995-10-01
During alloy solidification, macrosegregation results from long range transport of solute under the influence of convective flow and leads to nonuniform quality of a solidified material. The present study is an attempt to understand the role of double diffusive convection resulting from the solutal rejection in the evolution of macrosegregation in an iron carbon system. The solidification process of an alloy is governed by conservation of heat, mass, momentum, and species and is accompanies by the evolution of latent heat and the rejection or incorporation of solute at the solid liquid interface. Using a continuum formulation, the governing equations were solved using the finite volume method. The numerical model was validated by simulating experiments on an ammonium chloride water system reported in the literature. The model was further used to study the role of double diffusive convection in the evolution of macrosegregation during solidification of Fe 1 wt pct c alloy in a rectangular cavity. Simulation of this transient process was carried out until complete solidification, and the results, depicting the influence of flow field on thermal and solutal field and vice versa, are shown at various stages of solidification. Under the given set of parameters, it was found that the thermal buoyancy affects the macrosegregation field globally, whereas the solutal buoyancy has a localized effect.
NASA Astrophysics Data System (ADS)
Iizuka, S.
1998-02-01
Potential Modification Due to C60- Production * Modifications of the Floating Potential and the Plasma Potential in a C60 Plasma * Properties of Strongly Electronegative Plasma Produced at Afterglow of Electron Cyclotron Resonance Chlorine Plasma * 2.2 Particle Accelerations * Potential Structures Due to an Electron Beam-Excited Localized HF-Discharge (Invited) * Experiments and Computer Simulations of Electric Field Spikes in Electron Beam-Plasma Interaction * Magnetosonic Waves in Multi-Ion-Species Plasmas: Nonlinear Evolution and Ion Acceleration * Observation of Repetitive Electric Field Pulses Accompanying a Short Wave Train Near the Lower Hybrid Frequency in a High-Voltage Linear Plasma Discharge * Control of Potential Profile and Energy Transport to Machine Ends along Open Magnetic Field Lines in a Tandem Mirror * Observation of Ion Acceleration in Picosecond Laser Produced Plasma Expanding across a Magnetic Field * Pellet Ablation Characteristics and the Effect on the Potential in Toroidal Plasmas (Invited) * CHAPTER 3: CROSS-FIELD ELECTRIC FIELDS, VELOCITY SHEAR, AND VORTEX FORMATION * 3.1 Cross-Field Potential Structures * Laboratory Simulation of Transverse Magnetic Field Effects on Dynamics of Plasma Streams in Magnetosphere * Double-Layer-like and Sheath-like Potential Structures across Magnetic Field Lines * Relaxation of Virtual Cathode Oscillations due to Transverse Effects in a Crossed-Field Diode * Control of Radial Potential Profile and Related Low-Frequency Fluctuations in an ECR-Produced Plasma * Potential Formation in Magnetized Dusty Plasma * Potential Measurement Using Electrostatic Probe in Tokamak Boundary Plasma * Studies on Radial Electric Field and Confinement in Toroidal Plasmas (Invited) * 3.2 Velocity Shear * Space Chamber Investigations of Transverse Velocity Shear Driven Plasma Waves * Observations of the Velocity-Shear-Driven Instability in a Sodium Plasma (Invited) * The Effect of Negative Ions and Neutral Particle Collisions on the
Wang, Sijia; Peterson, Daniel J.; Gatenby, J. C.; Li, Wenbin; Grabowski, Thomas J.; Madhyastha, Tara M.
2017-01-01
Correction of echo planar imaging (EPI)-induced distortions (called “unwarping”) improves anatomical fidelity for diffusion magnetic resonance imaging (MRI) and functional imaging investigations. Commonly used unwarping methods require the acquisition of supplementary images during the scanning session. Alternatively, distortions can be corrected by nonlinear registration to a non-EPI acquired structural image. In this study, we compared reliability using two methods of unwarping: (1) nonlinear registration to a structural image using symmetric normalization (SyN) implemented in Advanced Normalization Tools (ANTs); and (2) unwarping using an acquired field map. We performed this comparison in two different test-retest data sets acquired at differing sites (N = 39 and N = 32). In both data sets, nonlinear registration provided higher test-retest reliability of the output fractional anisotropy (FA) maps than field map-based unwarping, even when accounting for the effect of interpolation on the smoothness of the images. In general, field map-based unwarping was preferable if and only if the field maps were acquired optimally. PMID:28270762
Magnetic Damping of g-Jitter Induced Double-Diffusive Convection
NASA Technical Reports Server (NTRS)
Shu, Y.; Li, B. Q.; deGroh, H. C.
2001-01-01
This paper describes a numerical study of the g-jitter driven double diffusive convective flows, thermal and concentration distributions in binary alloy melt systems subject to an external magnetic field. The study is based on the finite element solution of transient magnetohydrodynamic equations governing the momentum, thermal and solutal transport in the melt pool. Numerical simulations are conducted using the synthesized single- and multi- frequency g-jitter as well as the real g-jitter data taken during space flights with or without an applied magnetic field. It is found that for the conditions studied, the main melt flow follows approximately a lineal- superposition of velocity components induced by individual g-jitter components, regardless of whether a magnetic field exists or not. The flow field is characterized by a recirculating double diffusive convection loop oscillating in time with a defined frequency equal to that of the driving g-jitter force. An applied magnetic field has little effect on the oscillating recirculating pattern, except around the moment in time when the flow reverses its direction. The field has no effect on the oscillation period, but it changes the phase angle. It is very effective in suppressing the flow intensity and produces a notable reduction of the solutal striation and time fluctuations in the melt. For a given magnetic field strength, the magnetic damping effect is more pronounced on the velocity associated with the largest g-jitter component present and/or the g-jitter spiking peaks. A stronger magnetic field is more effective in suppressing the melt convection and also is more helpful in bringing the convection in phase with the g-jitter driving force. The applied field is particularly useful in suppressing the effect of real g-jitter spikes on both flow and solutal distributions. With appropriately selected magnetic fields, the convective flows caused by g-jitter can be reduced sufficiently and diffusion dominant
Effect of cation ordering on oxygen vacancy diffusion pathways in double perovskites
Uberuaga, Blas Pedro; Pilania, Ghanshyam
2015-07-08
Perovskite structured oxides (ABO_{3}) are attractive for a number of technological applications, including as superionics because of the high oxygen conductivities they exhibit. Double perovskites (AA’BB’O_{6}) provide even more flexibility for tailoring properties. Using accelerated molecular dynamics, we examine the role of cation ordering on oxygen vacancy mobility in one model double perovskite SrLaTiAlO_{6}. We find that the mobility of the vacancy is very sensitive to the cation ordering, with a migration energy that varies from 0.6 to 2.7 eV. In the extreme cases, the mobility is both higher and lower than either of the two end member single perovskites. Further, the nature of oxygen vacancy diffusion, whether one-dimensional, two-dimensional, or three-dimensional, also varies with cation ordering. We correlate the dependence of oxygen mobility on cation structure to the distribution of Ti^{4+} cations, which provide unfavorable environments for the positively charged oxygen vacancy. The results demonstrate the potential of using tailored double perovskite structures to precisely control the behavior of oxygen vacancies in these materials.
Effect of cation ordering on oxygen vacancy diffusion pathways in double perovskites
Uberuaga, Blas Pedro; Pilania, Ghanshyam
2015-07-08
Perovskite structured oxides (ABO3) are attractive for a number of technological applications, including as superionics because of the high oxygen conductivities they exhibit. Double perovskites (AA’BB’O6) provide even more flexibility for tailoring properties. Using accelerated molecular dynamics, we examine the role of cation ordering on oxygen vacancy mobility in one model double perovskite SrLaTiAlO6. We find that the mobility of the vacancy is very sensitive to the cation ordering, with a migration energy that varies from 0.6 to 2.7 eV. In the extreme cases, the mobility is both higher and lower than either of the two end member single perovskites.more » Further, the nature of oxygen vacancy diffusion, whether one-dimensional, two-dimensional, or three-dimensional, also varies with cation ordering. We correlate the dependence of oxygen mobility on cation structure to the distribution of Ti4+ cations, which provide unfavorable environments for the positively charged oxygen vacancy. The results demonstrate the potential of using tailored double perovskite structures to precisely control the behavior of oxygen vacancies in these materials.« less
NASA Astrophysics Data System (ADS)
Wang, Wei; Ma, Wanbiao; Lai, Xiulan
2017-01-01
From a biological perspective, a diffusive virus infection dynamic model with nonlinear functional response, absorption effect and chemotaxis is proposed. In the model, the diffusion of virus consists of two parts, the random diffusion and the chemotactic movement. The chemotaxis flux of virus depends not only on their own density, but also on the density of infected cells, and the density gradient of infected cells. The well posedness of the proposed model is deeply investigated. For the proposed model, the linear stabilities of the infection-free steady state E0 and the infection steady state E* are extensively performed. We show that the threshold dynamics can be expressed by the basic reproduction number R0 of the model without chemotaxis. That is, the infection-free steady state E0 is globally asymptotically stable if R0 < 1, and the virus is uniformly persistent if R0 > 1. In addition, we use the cross iteration method and the Schauder's fixed point theorem to prove the existence of travelling wave solutions connecting the infection-free steady state E0 and the infection steady state E* by constructing a pair of upper-lower solutions. At last, numerical simulations are presented to confirm theoretical findings.
Basko, D M
2014-02-01
We study the discrete nonlinear Schröinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved but, on the other, strong enough for the dynamics of the normal mode amplitudes to be chaotic for almost all modes. We show that in this regime and in the limit of high temperature, the macroscopic density ρ satisfies the nonlinear diffusion equation with a density-dependent diffusion coefficient, D(ρ) = D(0)ρ(2). An explicit expression for D(0) is obtained in terms of the eigenfunctions and eigenvalues of the linear problem, which is then evaluated numerically. The role of the second conserved quantity (energy) in the transport is also quantitatively discussed.
Janvier, M; Kishimoto, Y; Li, J Q
2011-11-04
The onset of abrupt magnetic reconnection events, observed in the nonlinear evolution of double tearing modes (DTM), is investigated via reduced resistive magnetohydrodynamic simulations. We have identified the critical threshold for the parameters characterizing the linear DTM stability leading to the bifurcation to the explosive dynamics. A new type of secondary instability is discovered that is excited once the magnetic islands on each rational surface reach a critical structure characterized here by the width and the angle rating their triangularization. This new instability is an island structure-driven nonlinear instability, identified as the trigger of the subsequent nonlinear dynamics which couples flow and flux perturbations. This instability only weakly depends on resistivity.
Double-Diffusive Finger Convection: Flow Field Evolution in a Hele-Shaw Cell
COOPER,CLAY A.; GLASS JR.,ROBERT J.; TYLER,SCOTT W.
2000-12-21
Double-diffusive finger convection is a hydrodynamic instability that can occur when two components with different diffusivities are oppositely stratified with respect to the fluid density gradient as a critical condition is exceeded. Laboratory experiments were designed using sodium chloride and sucrose solutions in a Hele-Shaw cell. A high resolution, full field, light transmission technique was used to study the development of the instability. The initial buoyancy ratio (R{sub p}), which is a ratio of fluid density contributions by the two solutes, was varied systematically in the experiments so that the range of parameter space spanned conditions that were nearly stable (R{sub p} = 2.8) to those that were moderately unstable (R{sub p} = 1.4). In systems of low R{sub p}, fingers develop within several minutes, merge with adjacent fingers, form conduits, and stall before newer-generated fingers travel through the conduits and continue the process. Solute fluxes in low R{sub p} systems quickly reach steady state and are on the order of 10{sup {minus}6} m{sup 2} sec{sup {minus}1}. In the higher R{sub p} experiments, fingers are slower to evolve and do not interact as dynamically as in the lower R{sub p} systems. Our experiment with initial R{sub p} = 2.8 exhibited flux on the order of that expected for a similar diffusive system (i.e., 10{sup {minus}7} m{sup 2} sec{sup {minus}1}), although the structures were very different than the pattern of transport expected in a diffusing system. Mass flux decayed as t{sup 1/2} in two experiments each with initial R{sub p} = 2.4 and 2.8.
Multiple secondary islands formation in nonlinear evolution of double tearing mode simulations
NASA Astrophysics Data System (ADS)
Guo, W.; Ma, J.; Yu, Z.
2017-03-01
A new numerical code solving the conservative perturbed resistive magnetohydrodynamic (MHD) model is developed. Numerical tests of the ideal Kelvin-Helmholtz instability and the resistive double tearing mode (DTM) show its capability in solving linear and nonlinear MHD instabilities. The nonlinear DTM evolution in 2D geometry is numerically investigated with low guiding field B z 0 , short half-distance y 0 between the equilibrium current sheets, and small resistivity η. The interaction of islands on the two initial current sheets may generate an unstable flow driven current sheet with a high length-to-thickness aspect ratio (α), and multiple secondary islands can form. In general, the length-to-thickness aspect ratio α and the number of secondary islands increase with decreasing guide field B z 0 , decreasing half-distance y 0 , and increasing Lundquist number of the flow driven current sheet S L although the dependence may be non-monotonic. The reconnection rate dependence on S L , B z 0 , and y 0 is also investigated.
NASA Astrophysics Data System (ADS)
Fernandes, Ryan I.; Fairweather, Graeme
2012-08-01
An alternating direction implicit (ADI) orthogonal spline collocation (OSC) method is described for the approximate solution of a class of nonlinear reaction-diffusion systems. Its efficacy is demonstrated on the solution of well-known examples of such systems, specifically the Brusselator, Gray-Scott, Gierer-Meinhardt and Schnakenberg models, and comparisons are made with other numerical techniques considered in the literature. The new ADI method is based on an extrapolated Crank-Nicolson OSC method and is algebraically linear. It is efficient, requiring at each time level only O(N) operations where N is the number of unknowns. Moreover, it is shown to produce approximations which are of optimal global accuracy in various norms, and to possess superconvergence properties.
Basko, D.M.
2011-07-15
Research Highlights: > In a one-dimensional disordered chain of oscillators all normal modes are localized. > Nonlinearity leads to chaotic dynamics. > Chaos is concentrated on rare chaotic spots. > Chaotic spots drive energy exchange between oscillators. > Macroscopic transport coefficients are obtained. - Abstract: The subject of this study is the long-time equilibration dynamics of a strongly disordered one-dimensional chain of coupled weakly anharmonic classical oscillators. It is shown that chaos in this system has a very particular spatial structure: it can be viewed as a dilute gas of chaotic spots. Each chaotic spot corresponds to a stochastic pump which drives the Arnold diffusion of the oscillators surrounding it, thus leading to their relaxation and thermalization. The most important mechanism of equilibration at long distances is provided by random migration of the chaotic spots along the chain, which bears analogy with variable-range hopping of electrons in strongly disordered solids. The corresponding macroscopic transport equations are obtained.
Median-prior tomography reconstruction combined with nonlinear anisotropic diffusion filtering
NASA Astrophysics Data System (ADS)
Yan, Jianhua; Yu, Jun
2007-04-01
Positron emission tomography (PET) is becoming increasingly important in the fields of medicine and biology. Penalized iterative algorithms based on maximum a posteriori (MAP) estimation for image reconstruction in emission tomography place conditions on which types of images are accepted as solutions. The recently introduced median root prior (MRP) favors locally monotonic images. MRP can preserve sharp edges, but a steplike streaking effect and much noise are still observed in the reconstructed image, both of which are undesirable. An MRP tomography reconstruction combined with nonlinear anisotropic diffusion interfiltering is proposed for removing noise and preserving edges. Analysis shows that the proposed algorithm is capable of producing better reconstructed images compared with those reconstructed by conventional maximum-likelihood expectation maximization (MLEM), MAP, and MRP-based algorithms in PET image reconstruction.
NASA Astrophysics Data System (ADS)
Passalacqua, Paola; Do Trung, Tien; Foufoula-Georgiou, Efi; Sapiro, Guillermo; Dietrich, William E.
2010-03-01
A geometric framework for the automatic extraction of channels and channel networks from high-resolution digital elevation data is introduced in this paper. The proposed approach incorporates nonlinear diffusion for the preprocessing of the data, both to remove noise and to enhance features that are critical to the network extraction. Following this preprocessing, channels are defined as curves of minimal effort, or geodesics, where the effort is measured on the basis of fundamental geomorphological characteristics such as flow accumulation area and isoheight contours curvature. The merits of the proposed methodology, and especially the computational efficiency and accurate localization of the extracted channels, are demonstrated using light detection and ranging (lidar) data of the Skunk Creek, a tributary of the South Fork Eel River basin in northern California.
A Priori Estimates for Fractional Nonlinear Degenerate Diffusion Equations on Bounded Domains
NASA Astrophysics Data System (ADS)
Bonforte, Matteo; Vázquez, Juan Luis
2015-10-01
We investigate quantitative properties of the nonnegative solutions to the nonlinear fractional diffusion equation, , posed in a bounded domain, , with m > 1 for t > 0. As we use one of the most common definitions of the fractional Laplacian , 0 < s < 1, in a bounded domain with zero Dirichlet boundary conditions. We consider a general class of very weak solutions of the equation, and obtain a priori estimates in the form of smoothing effects, absolute upper bounds, lower bounds, and Harnack inequalities. We also investigate the boundary behaviour and we obtain sharp estimates from above and below. In addition, we obtain similar estimates for fractional semilinear elliptic equations. Either the standard Laplacian case s = 1 or the linear case m = 1 are recovered as limits. The method is quite general, suitable to be applied to a number of similar problems.
Stochastic dynamics and control of a driven nonlinear spin chain: the role of Arnold diffusion
NASA Astrophysics Data System (ADS)
Chotorlishvili, L.; Toklikishvili, Z.; Berakdar, J.
2009-09-01
We study a chain of nonlinear interacting spins driven by a static and a time-dependent magnetic field. The aim is to identify the conditions for the locally and temporally controlled spin switching. Analytical and full numerical calculations show the possibility of stochastic control if the underlying semiclassical dynamics is chaotic. This is achievable by tuning the external field parameters according to the method described in this paper. We show analytically for a finite spin chain that Arnold diffusion is the underlying mechanism for the present stochastic control. Quantum mechanically we consider the regime where the classical dynamics is regular or chaotic. For the latter we utilize the random matrix theory. The efficiency and the stability of the non-equilibrium quantum spin states are quantified by the time dependence of the Bargmann angle related to the geometric phases of the states.
Simulation of diffuse-charge capacitance in electric double layer capacitors
NASA Astrophysics Data System (ADS)
Sun, Ning; Gersappe, Dilip
2017-01-01
We use a Lattice Boltzmann Model (LBM) in order to simulate diffuse-charge dynamics in Electric Double Layer Capacitors (EDLCs). Simulations are carried out for both the charge and the discharge processes on 2D systems of complex random electrode geometries (pure random, random spheres and random fibers). The steric effect of concentrated solutions is considered by using a Modified Poisson-Nernst-Planck (MPNP) equations and compared with regular Poisson-Nernst-Planck (PNP) systems. The effects of electrode microstructures (electrode density, electrode filler morphology, filler size, etc.) on the net charge distribution and charge/discharge time are studied in detail. The influence of applied potential during discharging process is also discussed. Our studies show how electrode morphology can be used to tailor the properties of supercapacitors.
Fluxes across double-diffusive interfaces : a one-dimensional turbulence study.
Kerstein, Alan R.; Lignell, David O.; Gonzalez-Juez, Esteban Daniel
2010-11-01
The parameterization of the fluxes of heat and salt across double-diffusive interfaces is of interest in geophysics, astrophysics, and engineering. The present work is a parametric study of these fluxes using one-dimensional-turbulence (ODT) simulations. Its main distinction is that it considers a parameter space larger than previous studies. Specifically, this work considers the effect on the fluxes of the stability parameter R{sub {rho}}, Rayleigh number Ra, Prandtl number, Lewis number, and Richardson number. The ratio Ra/R{sub {rho}} is found to be a dominant parameter. Here Ra/R{sub {rho}} can be seen as a ratio of destabilizing and stabilizing effects. Trends predicted by the simulations are in good agreement with previous models and available measurements.
Flow reversal of fully developed double diffusive mixed convection in a vertical channel
NASA Astrophysics Data System (ADS)
Makhatar, Nur Asiah Mohd; Saleh, Habibis; Hashim, Ishak
2015-10-01
The mixed convection flow within a vertical channel having internal heat generation at a rate proportional to a power of the temperature difference is considered. The analysis is concerning the studies of occurrence of flow reversal and the effects of three dimensionless parameters, identified as the internal heat parameter (G), a mixed convection parameter (λ) and the exponent (p) in the local heating term on the fully developed double diffusive mixed convection flow in a vertical channel. The governing equations are solved numerically via MAPLE. It was found that flow reversal occurs with larger values of internal heat parameter and mixed convection parameter, but smaller values of local-heating exponent. They also show that, unlike the internal heat parameter and the local-heating exponent, the mixed convection parameter do not give any significant effect on the temperature.
Fu, W.S.; Ke, W.W.
2000-01-01
A double diffusive natural convection in a rectangular enclosure filled with porous medium is investigated numerically. The distribution of porosity is based upon the random porosity model. The Darcy-Brinkman-Forchheimer model is used and the factors of heat flux, mean porosity and standard deviation are taken into consideration. The SIMPLEC method with iterative processes is adopted to solve the governing equations. The effects of the random porosity model on the distributions of local Nusselt number are remarkable and the variations of the local Nusselt number become disordered. The contribution of latent heat transfer to the total heat transfer of the high Rayleigh number is larger than that of the low Rayleigh number and the variations of the latent heat transfer are not in order.
Fujimoto, Cy H.; Alam, Todd Michael; Cherry, Brian Ray; Cornelius, Christopher James
2005-02-01
Solid-state {sup 1}H magic angle spinning (MAS) NMR was used to investigate sulfonated Diels-Alder poly(phenlylene) polymer membranes. Under high spinning speed {sup 1}H MAS conditions, the proton environments of the sulfonic acid and phenylene polymer backbone are resolved. A double-quantum (DQ) filter using the rotor-synchronized back-to-back (BABA) NMR multiple-pulse sequence allowed the selective suppression of the sulfonic proton environment in the {sup 1}H MAS NMR spectra. This DQ filter in conjunction with a spin diffusion NMR experiment was then used to measure the domain size of the sulfonic acid component within the membrane. In addition, the temperature dependence of the sulfonic acid spin-spin relaxation time (T{sub 2}) was determined, providing an estimate of the activation energy for the proton dynamics of the dehydrated membrane.
Yang, Zhixin; Wang, Shaowei; Zhao, Moli; Li, Shucai; Zhang, Qiangyong
2013-01-01
The onset of double diffusive convection in a viscoelastic fluid-saturated porous layer is studied when the fluid and solid phase are not in local thermal equilibrium. The modified Darcy model is used for the momentum equation and a two-field model is used for energy equation each representing the fluid and solid phases separately. The effect of thermal non-equilibrium on the onset of double diffusive convection is discussed. The critical Rayleigh number and the corresponding wave number for the exchange of stability and over-stability are obtained, and the onset criterion for stationary and oscillatory convection is derived analytically and discussed numerically.
Lattice Boltzmann methods for some 2-D nonlinear diffusion equations:Computational results
Elton, B.H.; Rodrigue, G.H. . Dept. of Applied Science Lawrence Livermore National Lab., CA ); Levermore, C.D. . Dept. of Mathematics)
1990-01-01
In this paper we examine two lattice Boltzmann methods (that are a derivative of lattice gas methods) for computing solutions to two two-dimensional nonlinear diffusion equations of the form {partial derivative}/{partial derivative}t u = v ({partial derivative}/{partial derivative}x D(u){partial derivative}/{partial derivative}x u + {partial derivative}/{partial derivative}y D(u){partial derivative}/{partial derivative}y u), where u = u({rvec x},t), {rvec x} {element of} R{sup 2}, v is a constant, and D(u) is a nonlinear term that arises from a Chapman-Enskog asymptotic expansion. In particular, we provide computational evidence supporting recent results showing that the methods are second order convergent (in the L{sub 1}-norm), conservative, conditionally monotone finite difference methods. Solutions computed via the lattice Boltzmann methods are compared with those computed by other explicit, second order, conservative, monotone finite difference methods. Results are reported for both the L{sub 1}- and L{sub {infinity}}-norms.
Cell-centered nonlinear finite-volume methods for the heterogeneous anisotropic diffusion problem
NASA Astrophysics Data System (ADS)
Terekhov, Kirill M.; Mallison, Bradley T.; Tchelepi, Hamdi A.
2017-02-01
We present two new cell-centered nonlinear finite-volume methods for the heterogeneous, anisotropic diffusion problem. The schemes split the interfacial flux into harmonic and transversal components. Specifically, linear combinations of the transversal vector and the co-normal are used that lead to significant improvements in terms of the mesh-locking effects. The harmonic component of the flux is represented using a conventional monotone two-point flux approximation; the component along the parameterized direction is treated nonlinearly to satisfy either positivity of the solution as in [29], or the discrete maximum principle as in [9]. In order to make the method purely cell-centered, we derive a homogenization function that allows for seamless interpolation in the presence of heterogeneity following a strategy similar to [46]. The performance of the new schemes is compared with existing multi-point flux approximation methods [3,5]. The robustness of the scheme with respect to the mesh-locking problem is demonstrated using several challenging test cases.
From convection rolls to finger convection in double-diffusive turbulence
Verzicco, Roberto; Lohse, Detlef
2016-01-01
Double-diffusive convection (DDC), which is the buoyancy-driven flow with fluid density depending on two scalar components, is ubiquitous in many natural and engineering environments. Of great interests are scalars' transfer rate and flow structures. Here we systematically investigate DDC flow between two horizontal plates, driven by an unstable salinity gradient and stabilized by a temperature gradient. Counterintuitively, when increasing the stabilizing temperature gradient, the salinity flux first increases, even though the velocity monotonically decreases, before it finally breaks down to the purely diffusive value. The enhanced salinity transport is traced back to a transition in the overall flow pattern, namely from large-scale convection rolls to well-organized vertically oriented salt fingers. We also show and explain that the unifying theory of thermal convection originally developed by Grossmann and Lohse for Rayleigh–Bénard convection can be directly applied to DDC flow for a wide range of control parameters (Lewis number and density ratio), including those which cover the common values relevant for ocean flows. PMID:26699474
NASA Astrophysics Data System (ADS)
Yang, Yantao; Verzicco, Roberto; Lohse, Detlef
2016-11-01
In the upper layers of the tropical and subtropical ocean, step-like mean profiles for both temperature and salinity are often observed, a phenomenon referred to as thermohaline staircase. It consists of alternatively stacked mixing layers, and finger layers with sharp gradients in both mean temperature and salinity. It is believed that thermohaline staircases are caused by double diffusive convection (DDC), i.e. the convection flow with fluid density affected by two different scalars. Here we conducted direct numerical simulations of DDC bounded by two parallel plates and aimed to realise the multi-layer state similar to the oceanic thermohaline staircase. We applied an unstable salinity difference and a stable temperature difference across the two plates. We gradually increased the salinity Rayleigh number RaS , i.e. the strength of salinity difference, and fixed the relative strength of temperature difference. When RaS is high enough the flow undergoes a transition from a single finger layer to a triple layer state, where one mixing layer emerges between two finger layers. Such triple layer state is stable up to the turbulent diffusive time scale. The finger-layer height is larger for higher RaS . The dependences of the scalar fluxes on RaS were also investigated. Supported by Dutch FOM Foundation and NWO rpogramme MCEC; Computing resources from SURFSara and PRACE project 2015133124.
Nonlinear anisotropic diffusion filtering of three-dimensional image data from two-photon microscopy
NASA Astrophysics Data System (ADS)
Broser, Philip J.; Schulte, Roland; Roth, A.; Helmchen, Fritjof; Waters, Jack; Lang, Stefan; Sakmann, Bert J.; Wittum, Gabriel
2005-03-01
Two-photon microscopy in combination with novel fluorescent labeling techniques enables imaging of three-dimensional neuronal morphologies in intact brain tissue. In principle it is now possible to automatically reconstruct the dendritic branching patterns of neurons from 3D fluorescence image stacks. In practice however, the signal-to-noise ratio can be low, in particular in the case of thin dendrites or axons imaged relatively deep in the tissue. Here we present a nonlinear anisotropic diffusion filter that enhances the signal-to-noise ratio while preserving the original dimensions of the structural elements. The key idea is to use structural information in the raw data -- the local moments of inertia -- to locally control the strength and direction of diffusion filtering. A cylindrical dendrite, for example, is effectively smoothed only parallel to its longitudinal axis, not perpendicular to it. This is demonstrated for artificial data as well as for in vivo 2-photon microscopic data from pyramidal neurons of rat neocortex. In both cases noise is averaged out along the dendrites, leading to bridging of apparent gaps, while dendritic diameters are not affected. The filter is a valuable general tool for smoothing cellular processes and is well suited for preparing data for subsequent image segmentation and neuron reconstruction.
Characterization of double diffusive convection step and heat budget in the deep Arctic Ocean
NASA Astrophysics Data System (ADS)
Zhou, S.; Lu, Y.
2013-12-01
In this paper, we explore the hydrographic structure and heat budget in deep Canada Basin using data measured with McLane-Moored-Profilers (MMPs), bottom-pressure-recorders (BPRs), and conductivity-temperature-depth (CTD) profilers. From the bottom upward, a homogenous bottom layer and its overlaying double diffusive convection (DDC) steps are well identified at Mooring A (75oN, 150oW). We find that the deep water is in weak diapycnal mixing because the effective diffusivity of the bottom layer is ~1.8×10-5 m 2s-1 while that of the other steps is ~10-6 m 2s-1. The vertical heat flux through DDC steps is evaluated with different methods. We find that the heat flux (0.1-11 mWm-2) is much smaller than geothermal heating (~50 mWm-2), which suggests that the stack of DDC steps acts as a thermal barrier in the deep basin. Moreover, the temporal distributions of temperature and salinity differences across the interface are exponential, while those of heat flux and effective diffusivity are found to be approximately log-normal. Both are the result of strong intermittency. Between 2003 and 2011, temperature fluctuation close to the sea floor distributed asymmetrically and skewed towards positive values, which provides direct indication that geothermal heating is transferred into ocean. Both BPR and CTD data suggest that geothermal heating, not the warming of upper ocean, is the dominant mechanism responsible for the warming of deep water. As the DDC steps prevent the vertical heat transfer, geothermal heating will be unlikely to have significant effect on the middle and upper oceans.
Characterization of double diffusive convection steps and heat budget in the deep Arctic Ocean
NASA Astrophysics Data System (ADS)
Zhou, Sheng-Qi; Lu, Yuan-Zheng
2013-12-01
In this paper, we explore the hydrographic structure and heat budget in the deep Canada Basin by using data measured with McLane-Moored-Profilers (MMP), bottom pressure recorders (BPR), and conductivity-temperature-depth (CTD) profilers. Upward from the bottom, a homogeneous bottom layer and its overlaying double diffusive convection (DDC) steps are well identified at Mooring A (75°N,150°W). We find that the deep water is in weak diapycnal mixing because the effective diffusivity of the bottom layer is ˜1.8 × 10-5 m2s-1, while that of the other steps is ˜10-6 m2s-1. The vertical heat flux through the DDC steps is evaluated by using different methods. We find that the heat flux (0.1-11 mWm -2) is much smaller than geothermal heating (˜50 mWm -2). This suggests that the stack of DDC steps acts as a thermal barrier in the deep basin. Moreover, the temporal distributions of temperature and salinity differences across the interface are exponential, whereas those of heat flux and effective diffusivity are found to be approximately lognormal. Both are the result of strong intermittency. Between 2003 and 2011, temperature fluctuations close to the sea floor were distributed asymmetrically and skewed toward positive values, which provide a direct observation that geothermal heating was transferred into the ocean. Both BPR and CTD data suggest that geothermal heating and not the warming of the upper ocean is the dominant mechanism responsible for the warming of deep water. As the DDC steps prevent vertical heat transfer, geothermal heating is unlikely to have a significant effect on the middle and upper Arctic Ocean.
Diffuse magnetic neutron scattering in the highly frustrated double perovskite Ba2YRuO6
Nilsen, Gøran. J.; Thompson, Corey M.; Ehlers, Georg; ...
2015-02-23
Here we investigated diffuse magnetic scattering in the highly frustrated double perovskite Ba2YRuO6 using polarized neutrons. Consistent with previous reports, the material shows two apparent transitions at 47 and 36 K to an eventual type I face-centered-cubic magnetic ground state. The (100) magnetic reflection shows different behavior from the five other observed reflections upon heating from 1.8 K, with the former broadening well beyond the resolution limit near 36 K. Closer examination of the latter group reveals a small, but clear, increase in peak widths between 36 and 47 K, indicating that this regime is dominated by short-range spin correlations.more » Diffuse magnetic scattering persists above 47 K near the position of (100) to at least 200 K, consistent with strong frustration. Reverse Monte Carlo (RMC) modeling of the diffuse scattering from 45 to 200 K finds that the spin-spin correlations between nearest and next-nearest neighbors are antiferromagnetic and ferromagnetic, respectively, at temperatures near the upper ordering temperature, but both become antiferromagnetic and of similar magnitude above 100 K. The significance of this unusual crossover is discussed in light of the super-superexchange interactions between nearest and next-nearest neighbors in this material and the demands of type I order. The dimensionality of the correlations is addressed by reconstructing the scattering in the (hk0) plane using the RMC spin configurations. This indicates that one-dimensional spin correlations dominate at temperatures close to the first transition. In addition, a comparison between mean-field calculations and (hk0) scattering implies that further neighbor couplings play a significant role in the selection of the ground state. Finally, the results and interpretation are compared with those recently published for monoclinic Sr2YRuO6, and similarities and differences are emphasized.« less
NASA Astrophysics Data System (ADS)
Kim, Nayong; Harale, Aadesh; Tsotsis, Theodore T.; Sahimi, Muhammad
2007-12-01
Nanoporous layered double hydroxide (LDH) materials have wide applications, ranging from being good adsorbents for gases (particularly CO2) and liquid ions to membranes and catalysts. They also have applications in medicine, environmental remediation, and electrochemistry. Their general chemical composition is [M1-xIIMxIII(OH-)2]x+[Xn/mm -•nH2O], where M represents a metallic cation (of valence II or III), and Xn/mm - is an m-valence inorganic, or heteropolyacid, or organic anion. We study diffusion and adsorption of CO2 in a particular LDH with MII=Mg, MIII=Al, and x ≃0.71, using an atomistic model developed based on energy minimization and molecular dynamics simulations, together with a modified form of the consistent-valence force field. The adsorption isotherms and self-diffusivity of CO2 in the material are computed over a range of temperature, using molecular simulations. The computed diffusivities are within one order of magnitude of the measured ones at lower temperatures, while agreeing well with the data at high temperatures. The measured and computed adsorption isotherms agree at low loadings, but differ by about 25% at high loadings. Possible reasons for the differences between the computed properties and the experimental data are discussed, and a model for improving the accuracy of the computed properties is suggested. Also studied are the material's hydration and swelling properties. As water molecules are added to the pore space, the LDH material swells to some extent, with the hydration energy exhibiting interesting variations with the number of the water molecules added. The implications of the results are discussed.
Double Diffusive Convection in Jupiter as a result of H/He demixing
NASA Astrophysics Data System (ADS)
Nettelmann, N.; Fortney, J. J.; Garaud, P.
2013-12-01
Demixing of hydrogen and helium with subsequent He rain has long been suggested to occur in giant planets once they have sufficiently cooled down during their evolution. Its occurrence is Jupiter is suggested by the observed atmospheric helium depletion. He rain in a giant planet may cause a gradual increase of the helium abundance with depth, in contrast to full homogeneity or a sharp increase in form of a layer boundary as assumed for convenience in traditional models. In the presence of a stabilizing compositional and a destabilizing temperature gradient, large-scale convection may be inhibited (Ledoux-stable) and replaced by layered double diffusive (LDD) or oscillatory double diffusive (ODD) convection as recently studied in hydrodynamical simulations (Mirouh, Garaud+2012; Wood, Garaud, Stellmach 2013), or even a purely diffusive stable state. We here investigate the present structure of Jupiter in light of a helium gradient due to assumed He sedimentation, and the possible occurrence of LDD and ODD convection, or a stably stratified demixing region. For that purpose we apply the published ab initio data based phase diagram of Lorenzen et al (2009, 2011), which yields the demixing temperature as a function of pressure and He abundance, and invert it to obtain the helium gradient along Jupiter's pressure-temperature profile. In a first step, we find a He gradient between 1 and ~4 Mbars. In a second step, we compute the super-adiabaticity in the demixing region that is required to get the observed heat flux transported through that region, assuming that the flux is due to LDD convection as described by Wood+2013, using the transport parameter values along the Jupiter adiabat of French et al 2012, ApJS. If fine-tuning the parameters, e.g. the layer thickness, we can indeed find a super-adiabaticity profile that is consistent with the assumption of LDD convection. However, for a wider range of parameter values, such as layer thicknesses above ~1 km, the ratio of
Roxin, Alex; Ledberg, Anders
2008-01-01
The response behaviors in many two-alternative choice tasks are well described by so-called sequential sampling models. In these models, the evidence for each one of the two alternatives accumulates over time until it reaches a threshold, at which point a response is made. At the neurophysiological level, single neuron data recorded while monkeys are engaged in two-alternative choice tasks are well described by winner-take-all network models in which the two choices are represented in the firing rates of separate populations of neurons. Here, we show that such nonlinear network models can generally be reduced to a one-dimensional nonlinear diffusion equation, which bears functional resemblance to standard sequential sampling models of behavior. This reduction gives the functional dependence of performance and reaction-times on external inputs in the original system, irrespective of the system details. What is more, the nonlinear diffusion equation can provide excellent fits to behavioral data from two-choice decision making tasks by varying these external inputs. This suggests that changes in behavior under various experimental conditions, e.g. changes in stimulus coherence or response deadline, are driven by internal modulation of afferent inputs to putative decision making circuits in the brain. For certain model systems one can analytically derive the nonlinear diffusion equation, thereby mapping the original system parameters onto the diffusion equation coefficients. Here, we illustrate this with three model systems including coupled rate equations and a network of spiking neurons. PMID:18369436
Khan, Waqar A; Uddin, Md Jashim; Ismail, A I Md
2013-01-01
The effects of hydrodynamic and thermal slip boundary conditions on the double-diffusive free convective flow of a nanofluid along a semi-infinite flat solid vertical plate are investigated numerically. It is assumed that free stream is moving. The governing boundary layer equations are non-dimensionalized and transformed into a system of nonlinear, coupled similarity equations. The effects of the controlling parameters on the dimensionless velocity, temperature, solute and nanofluid concentration as well as on the reduced Nusselt number, reduced Sherwood number and the reduced nanoparticle Sherwood number are investigated and presented graphically. To the best of our knowledge, the effects of hydrodynamic and thermal slip boundary conditions have not been investigated yet. It is found that the reduced local Nusselt, local solute and the local nanofluid Sherwood numbers increase with hydrodynamic slip and decrease with thermal slip parameters.
Khan, Waqar A.; Uddin, Md Jashim; Ismail, A. I. Md.
2013-01-01
The effects of hydrodynamic and thermal slip boundary conditions on the double-diffusive free convective flow of a nanofluid along a semi-infinite flat solid vertical plate are investigated numerically. It is assumed that free stream is moving. The governing boundary layer equations are non-dimensionalized and transformed into a system of nonlinear, coupled similarity equations. The effects of the controlling parameters on the dimensionless velocity, temperature, solute and nanofluid concentration as well as on the reduced Nusselt number, reduced Sherwood number and the reduced nanoparticle Sherwood number are investigated and presented graphically. To the best of our knowledge, the effects of hydrodynamic and thermal slip boundary conditions have not been investigated yet. It is found that the reduced local Nusselt, local solute and the local nanofluid Sherwood numbers increase with hydrodynamic slip and decrease with thermal slip parameters. PMID:23533566
Koopmans, Peter J.; Frost, Robert; Miller, Karla L.
2015-01-01
Purpose To propose a method to reduce the slab boundary artifacts in three‐dimensional multislab diffusion MRI. Methods Bloch simulation is used to investigate the effects of multiple factors on slab boundary artifacts, including characterization of residual errors on diffusion quantification. A nonlinear inversion method is proposed to simultaneously estimate the slab profile and the underlying (corrected) image. Results Correction results of numerical phantom and in vivo data demonstrate that the method can effectively remove slab boundary artifacts for diffusion data. Notably, the nonlinear inversion is also successful at short TR, a regimen where previously proposed methods (slab profile encoding and weighted average) retain residual artifacts in both diffusion‐weighted images and diffusion metrics (mean diffusion coefficient and fractional anisotropy). Conclusion The nonlinear inversion for removing slab boundary artifacts provides improvements over existing methods, particularly at the short TRs required to maximize SNR efficiency. Magn Reson Med 76:1183–1195, 2016. © 2015 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. PMID:26510172
Fournier, R.O.
1990-01-01
Much has been published about double-diffusive convection as a mechanism for explaining variations in composition and temperature within all-liquid natural systems. However, relatively little is known about the applicability of this phenomenon within the heterogeneous rocks of currently active geothermal systems where primary porosity may control fluid flow in some places and fractures may control it in others. The main appeal of double-diffusive convection within hydrothermal systems is-that it is a mechanism that may allow efficient transfer of heat mainly by convection, while at the same time maintaining vertical and lateral salinity gradients. The Salton Sea geothermal system exhibits the following reservoir characteristics: (1) decreasing salinity and temperature from bottom to top and center toward the sides, (2) a very high heat flow from the top of the system that seems to require a major component of convective transfer of heat within the chemically stratified main reservoir, and (3) a relatively uniform density of the reservoir fluid throughout the system at all combinations of subsurface temperature, pressure, and salinity. Double-diffusive convection can account for these characteristics very nicely whereas other previously suggested models appear to account either for the thermal structure or for the salinity variations, but not both. Hydrologists, reservoir engineers, and particularly geochemists should consider the possibility and consequences of double-diffusive convection when formulating models of hydrothermal processes, and of the response of reservoirs to testing and production. ?? 1990.
NASA Astrophysics Data System (ADS)
Yamaguchi, Takao; Hozumi, Hiroaki; Hirano, Yuta; Tobita, Kazuhiro; Kurosawa, Yoshio
2014-01-01
In this paper, we newly propose a fast computation method for the nonlinear transient responses including coupling between nonlinear springs and sound proof structures having porous materials using FEM. In this method, we extend our numerical method named as Modal Strain and Kinetic Method (i.e. MSKE method proposed previously by Yamaguchi who is one of the authors) from linear damping analysis to nonlinear dynamic analysis. We assume that the restoring force of the spring has cubic nonlinearity and linear hysteresis damping. To calculate damping properties for soundproof structures including elastic body, viscoelastic body and porous body, displacement vectors as common unknown variable are solved under coupled condition. The damped sound fields in the porous materials are defined by complex effective density and complex bulk modulus. The discrete equations in physical coordinate for this system are transformed into nonlinear ordinary coupled differential equations using normal coordinates corresponding to linear natural modes. Further, using MSKE method, modal damping can be derived approximately under coupled conditions between hysteresis damping of viscoelastic materials, damping of the springs and damping due to flow resistance in porous materials. The modal damping is used for the nonlinear differential equation to compute nonlinear transient responses.
Sun, Dajun D; Lee, Ping I
2015-04-06
The importance of rate of supersaturation generation on the kinetic solubility profiles of amorphous systems has recently been shown by us; however, the previous focus was limited to constant rates of supersaturation generation. The objective of the current study is to further examine the effect of nonlinear rate profiles of supersaturation generation in amorphous systems, including (1) instantaneous or infinite rate (i.e., initial degree of supersaturation), (2) first-order rate (e.g., from dissolution of amorphous drug particles), and (3) matrix diffusion regulated rate (e.g., drug release from amorphous solid dispersions (ASDs) based on cross-linked poly(2-hydroxyethyl methacrylate) (PHEMA) hydrogels), on the kinetic solubility profiles of a model poorly soluble drug indomethacin (IND) under nonsink dissolution conditions. The previously established mechanistic model taking into consideration both the crystal growth and ripening processes was extended to predict the evolution of supersaturation resulting from nonlinear rates of supersaturation generation. Our results confirm that excessively high initial supersaturation or a rapid supersaturation generation leads to a surge in maximum supersaturation followed by a rapid decrease in drug concentration owing to supersaturation-induced precipitation; however, an exceedingly low degree of supersaturation or a slow rate of supersaturation generation does not sufficiently raise the supersaturation level, which results in a lower but broader maximum kinetic solubility profile. Our experimental data suggest that an optimal area-under-the-curve of the kinetic solubility profiles exists at an intermediate initial supersaturation level for the amorphous systems studied here, which agrees well with the predicted trend. Our model predictions also support our experimental findings that IND ASD in cross-linked PHEMA exhibits a unique kinetic solubility profile because the resulting supersaturation level is governed by a matrix
Local, global, and nonlinear screening in twisted double-layer graphene
Lu, Chih-Pin; Rodriguez-Vega, Martin; Li, Guohong; Luican-Mayer, Adina; Watanabe, Kenji; Taniguchi, Takashi; Rossi, Enrico; Andrei, Eva Y.
2016-01-01
One-atom-thick crystalline layers and their vertical heterostructures carry the promise of designer electronic materials that are unattainable by standard growth techniques. To realize their potential it is necessary to isolate them from environmental disturbances, in particular those introduced by the substrate. However, finding and characterizing suitable substrates, and minimizing the random potential fluctuations they introduce, has been a persistent challenge in this emerging field. Here we show that Landau-level (LL) spectroscopy offers the unique capability to quantify both the reduction of the quasiparticles’ lifetime and the long-range inhomogeneity due to random potential fluctuations. Harnessing this technique together with direct scanning tunneling microscopy and numerical simulations we demonstrate that the insertion of a graphene buffer layer with a large twist angle is a very effective method to shield a 2D system from substrate interference that has the additional desirable property of preserving the electronic structure of the system under study. We further show that owing to its remarkable nonlinear screening capability a single graphene buffer layer provides better shielding than either increasing the distance to the substrate or doubling the carrier density and reduces the amplitude of the potential fluctuations in graphene to values even lower than the ones in AB-stacked bilayer graphene. PMID:27302949
Lee, Shiu-Hang; Kamae, Tuneyoshi; Ellison, Donald C.
2008-07-02
We present a 3-dimensional model of supernova remnants (SNRs) where the hydrodynamical evolution of the remnant is modeled consistently with nonlinear diffusive shock acceleration occurring at the outer blast wave. The model includes particle escape and diffusion outside of the forward shock, and particle interactions with arbitrary distributions of external ambient material, such as molecular clouds. We include synchrotron emission and cooling, bremsstrahlung radiation, neutral pion production, inverse-Compton (IC), and Coulomb energy-loss. Boardband spectra have been calculated for typical parameters including dense regions of gas external to a 1000 year old SNR. In this paper, we describe the details of our model but do not attempt a detailed fit to any specific remnant. We also do not include magnetic field amplification (MFA), even though this effect may be important in some young remnants. In this first presentation of the model we don't attempt a detailed fit to any specific remnant. Our aim is to develop a flexible platform, which can be generalized to include effects such as MFA, and which can be easily adapted to various SNR environments, including Type Ia SNRs, which explode in a constant density medium, and Type II SNRs, which explode in a pre-supernova wind. When applied to a specific SNR, our model will predict cosmic-ray spectra and multi-wavelength morphology in projected images for instruments with varying spatial and spectral resolutions. We show examples of these spectra and images and emphasize the importance of measurements in the hard X-ray, GeV, and TeV gamma-ray bands for investigating key ingredients in the acceleration mechanism, and for deducing whether or not TeV emission is produced by IC from electrons or pion-decay from protons.
Weeratunga, S K; Kamath, C
2001-12-20
Removing noise from data is often the first step in data analysis. Denoising techniques should not only reduce the noise, but do so without blurring or changing the location of the edges. Many approaches have been proposed to accomplish this; in this paper, they focus on one such approach, namely the use of non-linear diffusion operators. This approach has been studied extensively from a theoretical viewpoint ever since the 1987 work of Perona and Malik showed that non-linear filters outperformed the more traditional linear Canny edge detector. They complement this theoretical work by investigating the performance of several isotropic diffusion operators on test images from scientific domains. They explore the effects of various parameters such as the choice of diffusivity function, explicit and implicit methods for the discretization of the PDE, and approaches for the spatial discretization of the non-linear operator etc. They also compare these schemes with simple spatial filters and the more complex wavelet-based shrinkage techniques. The empirical results show that, with an appropriate choice of parameters, diffusion-based schemes can be as effective as competitive techniques.
A Single Chip Automotive Control LSI Using SOI Bipolar Complimentary MOS Double-Diffused MOS
NASA Astrophysics Data System (ADS)
Kawamoto, Kazunori; Mizuno, Shoji; Abe, Hirofumi; Higuchi, Yasushi; Ishihara, Hideaki; Fukumoto, Harutsugu; Watanabe, Takamoto; Fujino, Seiji; Shirakawa, Isao
2001-04-01
Using the example of an air bag controller, a single chip solution for automotive sub-control systems is investigated, by using a technological combination of improved circuits, bipolar complimentary metal oxide silicon double-diffused metal oxide silicon (BiCDMOS) and thick silicon on insulator (SOI). For circuits, an automotive specific reduced instruction set computer (RISC) center processing unit (CPU), and a novel, all integrated system clock generator, dividing digital phase-locked loop (DDPLL) are proposed. For the device technologies, the authors use SOI-BiCDMOS with trench dielectric-isolation (TD) which enables integration of various devices in an integrated circuit (IC) while avoiding parasitic miss operations by ideal isolation. The structures of the SOI layer and TD, are optimized for obtaining desired device characteristics and high electromagnetic interference (EMI) immunity. While performing all the air bag system functions over a wide range of supply voltage, and ambient temperature, the resulting single chip reduces the electronic parts to about a half of those in the conventional air bags. The combination of single chip oriented circuits and thick SOI-BiCDMOS technologies offered in this work is valuable for size reduction and improved reliability of automotive electronic control units (ECUs).
Rényi entropy and improved equilibration rates to self-similarity for nonlinear diffusion equations
NASA Astrophysics Data System (ADS)
Carrillo, J. A.; Toscani, G.
2014-12-01
We investigate the large-time asymptotics of nonlinear diffusion equations ut = Δup in dimension n ⩾ 1, in the exponent interval p > n/(n + 2), when the initial datum u0 is of bounded second moment. Precise rates of convergence to the Barenblatt profile in terms of the relative Rényi entropy are demonstrated for finite-mass solutions defined in the whole space when they are re-normalized at each time t > 0 with respect to their own second moment, as proposed by Carrillo et al (2006 Arch. Ration. Mech. Anal. 180 127-49) and Toscani (2005 J. Evol. Eqns 5 185-203). The analysis shows that, in the range p > max((n - 1)/n, n/(n + 2)), the relative Rényi entropy exhibits a better decay, for intermediate times, with respect to the standard Ralston-Newman entropy. The result follows by a suitable use of sharp Gagliardo-Nirenberg-Sobolev inequalities considered by Dolbeault and Toscani (2013 Ann. Inst. Henri Poincare (C) Non Linear Anal. 30 917-34), and their information-theoretical proof (Savaré and Toscani 2014 IEEE Trans. Inform. Theory 60 2687-93), known as concavity of Rényi entropy power.
Mustaffa, Izadora; Trenado, Carlos; Schwerdtfeger, Karsten; Strauss, Daniel J
2008-01-01
Recent progress in mathematical image processing shows a remarkable success when applying numerical methods to ill-posed partial differential equations (PDE). In particular, nonlinear diffusion filtering (NDF)process is an approach that belongs to such family of differential equations. It has been successfully applied in many recent methods for image processing and computer vision areas, particularly in denoising, smoothing, segmentation, and restoration. In this paper we focus on a novel NDF application, namely denoising of single-trials of auditory brainstem responses (ABRs) and the analysis of transcranial magnetic stimulation (TMS) responses.We show that by applying NDF on a matrix-form image of single-trials, we were able to denoise the single-trials, resulting in a better extraction of information over the ongoing experiment; morphology, eg. the latency of the single-trials according to different stimuli paradigms at different stimulation intensity levels. It is concluded that NDF represents a novel and useful approach for the analysis of single-trials in brain imaging.
NASA Astrophysics Data System (ADS)
Guner, Ozkan; Bekir, Ahmet; Unsal, Omer; Cevikel, Adem C.
2017-01-01
In this paper, we pay attention to the analytical method named, ansatz method for finding the exact solutions of the variable-coefficient modified KdV equation and variable coefficient diffusion-reaction equation. As a result the singular 1-soliton solution is obtained. These solutions are important for the explanation of some practical physical problems. The obtained results show that these methods provides a powerful mathematical tool for solving nonlinear equations with variable coefficients. This method can be extended to solve other variable coefficient nonlinear partial differential equations.
NASA Astrophysics Data System (ADS)
Zhao, Hongjie; Zhong, Zhi; Fang, Weiwei; Xie, Hong; Zhang, Yabin; Shan, Mingguang
2016-09-01
A double-image encryption method is reported using chaotic maps, nonlinear non-DC joint transform correlator (JTC), and fractional Fourier transform (FrFT). The double images are converted into the amplitude and phase of a synthesized function through the application of chaotic pixel scrambling. The synthesized function bonded with a chaotic random phase mask (CRPM) and another different CRPM serve as the input signal of the JTC architecture in the fractional Fourier domain to obtain a real-valued encrypted image. The nonlinear and non-DC operation is also done to improve the security and decrypted image quality. The parameters in joint FrFT correlator and chaotic map serve as the encrypted keys. Numerical simulations have been done to demonstrate the feasibility and validity of this algorithm.
Brantley, P S
2006-08-08
The double spherical harmonics angular approximation in the lowest order, i.e. double P{sub 0} (DP{sub 0}), is developed for the solution of time-dependent non-equilibrium grey radiative transfer problems in planar geometry. Although the DP{sub 0} diffusion approximation is expected to be less accurate than the P{sub 1} diffusion approximation at and near thermodynamic equilibrium, the DP{sub 0} angular approximation can more accurately capture the complicated angular dependence near a non-equilibrium radiation wave front. In addition, the DP{sub 0} approximation should be more accurate in non-equilibrium optically thin regions where the positive and negative angular domains are largely decoupled. We develop an adaptive angular technique that locally uses either the DP{sub 0} or P{sub 1} flux-limited diffusion approximation depending on the degree to which the radiation and material fields are in thermodynamic equilibrium. Numerical results are presented for two test problems due to Su and Olson and to Ganapol and Pomraning for which semi-analytic transport solutions exist. These numerical results demonstrate that the adaptive P{sub 1}-DP{sub 0} diffusion approximation can yield improvements in accuracy over the standard P{sub 1} diffusion approximation, both without and with flux-limiting, for non-equilibrium grey radiative transfer.
Brantley, P S
2005-12-13
The double spherical harmonics angular approximation in the lowest order, i.e. double P{sub 0} (DP{sub 0}), is developed for the solution of time-dependent non-equilibrium grey radiative transfer problems in planar geometry. Although the DP{sub 0} diffusion approximation is expected to be less accurate than the P{sub 1} diffusion approximation at and near thermodynamic equilibrium, the DP{sub 0} angular approximation can more accurately capture the complicated angular dependence near a non-equilibrium radiation wave front. In addition, the DP{sub 0} approximation should be more accurate in non-equilibrium optically thin regions where the positive and negative angular domains are largely decoupled. We develop an adaptive angular technique that locally uses either the DP{sub 0} or P{sub 1} flux-limited diffusion approximation depending on the degree to which the radiation and material fields are in thermodynamic equilibrium. Numerical results are presented for two test problems due to Su and Olson and to Ganapol and Pomraning for which semi-analytic transport solutions exist. These numerical results demonstrate that the adaptive P{sub 1}-DP{sub 0} diffusion approximation can yield improvements in accuracy over the standard P{sub 1} diffusion approximation, both without and with flux-limiting, for non-equilibrium grey radiative transfer.
Liu, Zhi-Jie; Wang, Wen-Chun; Yang, De-Zheng; Wang, Sen; Zhang, Shuai; Tang, Kai; Jiang, Peng-Chao
2014-01-01
A large-area diffuse air discharge plasma excited by bipolar nanosecond pulse is generated under a double hexagon needle-array electrode at atmospheric pressure. The images of the diffuse discharge, electric characteristics, and the optical emission spectra emitted from the diffuse air discharge plasma are obtained. Based on the waveforms of pulse voltage and current, the power consumption, and the power density of the diffuse air discharge plasma are investigated under different pulse peak voltages. The electron density and the electron temperature of the diffuse plasma are estimated to be approximately 1.42×10(11) cm(-3) and 4.4 eV, respectively. The optical emission spectra are arranged to determine the rotational and vibrational temperatures by comparing experimental with simulated spectra. Meanwhile, the rotational and vibrational temperatures of the diffuse discharge plasma are also discussed under different pulse peak voltages and pulse repetition rates, respectively. In addition, the diffuse air discharge plasma can form an area of about 70×50 mm(2) on the surface of dielectric layer and can be scaled up to the required size.
Liu, Yung-Tien; Fung, Rong-Fong; Wang, Chun-Chao
2007-02-01
In this research, the nonlinear, double-dynamic Taguchi method was used as design and analysis methods for a high-precision positioning device using the combined piezo-voice-coil motor (VCM) actuator. An experimental investigation into the effects of two input signals and three control factors were carried out to determine the optimum parametric configuration of the positioning device. The double-dynamic Taguchi method, which permits optimization of several control factors concurrently, is particularly suitable for optimizing the performance of a positioning device with multiple actuators. In this study, matrix experiments were conducted with L9(3(4)) orthogonal arrays (OAs). The two most critical processes for the optimization of positioning device are the identification of the nonlinear ideal function and the combination of the double-dynamic signal factors for the ideal function's response. The driving voltage of the VCM and the waveform amplitude of the PZT actuator are combined into a single quality characteristic to evaluate the positioning response. The application of the double-dynamic Taguchi method, with dynamic signal-to-noise ratio (SNR) and L9(3(4)) OAs, reduced the number of necessary experiments. The analysis of variance (ANOVA) was applied to set the optimum parameters based on the high-precision positioning process.
NASA Astrophysics Data System (ADS)
Davarpanah Jazi, Shahrzad; Wells, Mathew G.
2016-10-01
The transport rate of particles beneath sediment-laden overflows and interflows in lakes and the ocean can be enhanced by double-diffusive and settling-driven convection. In previous experiments with sediment-laden fluid overlaying a saline layer, visual measurements could only be made in the optically clear lower layer. Hence, there was difficulty distinguishing the two processes, hindering predictions of when enhanced sedimentation occurs. We used an Acoustic Doppler Velocimeter to measure velocities and turbulence above and below the initial sediment/salt interface. The velocity of the sediment fingers in the lower layer were always larger than the Stokes settling velocity of the particles, leading to an asymmetry in the flow field of the two convective layers. Sediment fingers only dominated when there were marginal density differences between the two layers. We conclude that double-diffusive sediment fingers control sedimentation beneath interflows in most lakes, whereas settling-driven convection is dominant in most oceanic overflows.
Bayesian Evolution Models for Jupiter with Helium Rain and Double-diffusive Convection
NASA Astrophysics Data System (ADS)
Mankovich, Christopher; Fortney, Jonathan J.; Moore, Kevin L.
2016-12-01
Hydrogen and helium demix when sufficiently cool, and this bears on the evolution of all giant planets at large separations at or below roughly a Jupiter mass. We model the thermal evolution of Jupiter, including its evolving helium distribution following results of ab initio simulations for helium immiscibility in metallic hydrogen. After 4 Gyr of homogeneous evolution, differentiation establishes a thin helium gradient below 1 Mbar that dynamically stabilizes the fluid to convection. The region undergoes overstable double-diffusive convection (ODDC), whose weak heat transport maintains a superadiabatic temperature gradient. With a generic parameterization for the ODDC efficiency, the models can reconcile Jupiter’s intrinsix flux, atmospheric helium content, and radius at the age of the solar system if the Lorenzen et al. H-He phase diagram is translated to lower temperatures. We cast the evolutionary models in an MCMC framework to explore tens of thousands of evolutionary sequences, retrieving probability distributions for the total heavy-element mass, the superadiabaticity of the temperature gradient due to ODDC, and the phase diagram perturbation. The adopted SCvH-I equation of state (EOS) favors inefficient ODDC such that a thermal boundary layer is formed, allowing the molecular envelope to cool rapidly while the deeper interior actually heats up over time. If the overall cooling time is modulated with an additional free parameter to imitate the effect of a colder or warmer EOS, the models favor those that are colder than SCvH-I. In this case the superadiabaticity is modest and warming and cooling deep interiors are equally likely.
Salinity variations in submarine hydrothermal systems by layered double-diffusive convection
Bischoff, J.L.; Rosenbauer, R.J. )
1989-09-01
Various mechanisms have been proposed to explain the salinity variations in vent fluids of sea floor geothermal systems. New experiments reacting diabase and evolved seawater were carried out to reproduce earlier published observations of Cl depletions attributed to formation of an ephemeral Cl-bearing mineral. The absence of any Cl depletions in the present study suggests that the formation of Cl-bearing minerals is not sufficiently widespread to account for the observed salinity variations in the vent fluids. A re-evaluation of both field and laboratory evidence has led to a new model for subseafloor circulation that accounts for salinity variations as well as other chemical and mineralogic observations. In place of a simple single-pass convection system, the authors propose that the sea floor systems consist of two vertically nested convection cells in which a brine layer at depth heats and drives an overlying seawater cell. Such layering of salinities, a process known in fluid mechanics as double-diffusive convection, is an expected result when convection is induced in saline fluids. The process provides for stable high-temperature heat transfer upward from the cracking front adjacent to the magma, and for limited chemical exchange of the brine with the overlying seawater to explain salinity variations and high metal contents in the vent fluids. The brine also provides an effective medium to produce the secondary mineral assemblages observed in rocks from the mid-ocean ridges and ophiolites unsuccessfully produced in laboratory studies using seawater. The brine originates from the two-phase separation of seawater during magmatic/tectonic events and accumulates and remains relatively stable in the region immediately above the magma chamber.
A numerical study of double-diffusive flow in a long rotating porous channel
NASA Astrophysics Data System (ADS)
Alhusseny, Ahmed; Turan, A.
2015-04-01
The problem of double-diffusive flow in a long rotating porous channel has been analysed numerically. The two opposite vertical walls of the channel are maintained at constant but different temperature and concentration, while both horizontal walls are kept insulated. The generalised model is used to mathematically simulate the momentum equations with employing the Boussinesq approximation for the density variation. Moreover, both the fluid and solid phases are assumed to be at a local thermal equilibrium. The Coriolis effect is considered to be the main effect of rotation, which is induced by means of the combined natural heat and mass transfer within the transverse plane. The governing equations are discretised according to the finite volume method with employing the hybrid differencing scheme to calculate the fluxes across the faces of each control volume. The problem of pressure-velocity coupling is sorted out by relying on PISO algorithm. Computations are performed for a wide range of dimensionless parameters such as Darcy-Rayleigh number (100 ≤ Ra* ≤ 10,000), Darcy number (10-6 ≤ Da ≤ 10-4), the buoyancy ratio (-10 ≤ N ≤ 8), and Ekman number (10-7 ≤ Ek ≤ 10-3), while the values of Prandtl and Schmidt numbers are maintained constant and equal to 1.0. The results reveal that the rotation seems to have a dominant role at high levels of porous medium permeability, where it reduces the strength of the secondary flow, and hence the rates of heat and mass transfer. However, this dominance decreases gradually with lessening the permeability for the same level of rotation, but does not completely vanish.
Non-linear diffusion of cosmic rays escaping from supernova remnants - I. The effect of neutrals
NASA Astrophysics Data System (ADS)
Nava, L.; Gabici, S.; Marcowith, A.; Morlino, G.; Ptuskin, V. S.
2016-10-01
Supernova remnants are believed to be the main sources of galactic cosmic rays (CR). Within this framework, particles are accelerated at supernova remnant shocks and then released in the interstellar medium. The mechanism through which CRs are released and the way in which they propagate still remain open issues. The main difficulty is the high non-linearity of the problem: CRs themselves excite the magnetic turbulence that confines them close to their sources. We solve numerically the coupled differential equations describing the evolution in space and time of the escaping particles and of the waves generated through the CR streaming instability. The warm ionized and warm neutral phases of the interstellar medium are considered. These phases occupy the largest fraction of the disc volume, where most supernovae explode, and are characterized by the significant presence of neutral particles. The friction between those neutrals and ions results in a very effective wave damping mechanism. It is found that streaming instability affects the propagation of CRs even in the presence of ion-neutral friction. The diffusion coefficient can be suppressed by more than a factor of ˜2 over a region of few tens of pc around the remnant. The suppression increases for smaller distances. The propagation of ≈10 GeV particles is affected for several tens of kiloyears after escape, while ≈1 TeV particles are affected for few kiloyears. This might have a great impact on the interpretation of gamma-ray observations of molecular clouds located in the vicinity of supernova remnants.
Zhang, Li; Zhang, Fan; Ruan, Shigui
2017-03-01
We study a diffusive predator-prey model describing the interactions of small fishes and their resource base (small invertebrates) in the fluctuating freshwater marsh landscapes of the Florida Everglades. The spatial model is described by a reaction-diffusion system with Beddington-DeAngelis functional response. Uniform bound, local and global asymptotic stability of the steady state of the PDE model under the no-flux boundary conditions are discussed in details. Sufficient conditions on the Turing (diffusion-driven) instability which induces spatial patterns in the model are derived via linear analysis. Existence of one-dimensional and two-dimensional spatial Turing patterns, including rhombic and hexagonal patterns, are established by weakly nonlinear analyses. These results provide theoretical explanations and numerical simulations of spatial dynamical behaviors of the wetland ecosystems of the Florida Everglades.
Penington, Catherine J; Hughes, Barry D; Landman, Kerry A
2011-10-01
A discrete agent-based model on a periodic lattice of arbitrary dimension is considered. Agents move to nearest-neighbor sites by a motility mechanism accounting for general interactions, which may include volume exclusion. The partial differential equation describing the average occupancy of the agent population is derived systematically. A diffusion equation arises for all types of interactions and is nonlinear except for the simplest interactions. In addition, multiple species of interacting subpopulations give rise to an advection-diffusion equation for each subpopulation. This work extends and generalizes previous specific results, providing a construction method for determining the transport coefficients in terms of a single conditional transition probability, which depends on the occupancy of sites in an influence region. These coefficients characterize the diffusion of agents in a crowded environment in biological and physical processes.
Brantley, P S
2005-06-06
The double spherical harmonics angular approximation in the lowest order, i.e. double P{sub 0} (DP{sub 0}), is developed for the solution of time-dependent non-equilibrium grey radiative transfer problems in planar geometry. The standard P{sub 1} angular approximation represents the angular dependence of the radiation specific intensity using a linear function in the angular domain -1 {le} {mu} {le} 1. In contrast, the DP{sub 0} angular approximation represents the angular dependence as isotropic in each half angular range -1 {le} {mu} < 0 and 0 < {mu} {le} 1. Neglecting the time derivative of the radiation flux, both the P{sub 1} and DP{sub 0} equations can be written as a single diffusion equation for the radiation energy density. Although the DP{sub 0} diffusion approximation is expected to be less accurate than the P{sub 1} diffusion approximation at and near thermodynamic equilibrium, the DP{sub 0} angular approximation can more accurately capture the complicated angular dependence near the non-equilibrium wave front. We develop an adaptive angular technique that locally uses either the DP{sub 0} or the P{sub 1} diffusion approximation depending on the degree to which the radiation and material fields are in thermodynamic equilibrium. Numerical results are presented for a test problem due to Su and Olson for which a semi-analytic transport solution exists. The numerical results demonstrate that the adaptive P{sub 1}-DP{sub 0} diffusion approximation can yield improvements in accuracy over the standard P{sub 1} diffusion approximation for non-equilibrium grey radiative transfer.
NASA Astrophysics Data System (ADS)
Mankovich, Christopher; Fortney, Jonathan J.; Nettelmann, Nadine; Moore, Kevin
2016-10-01
Hydrogen and helium unmix when sufficiently cool, and this bears on the thermal evolution of all cool giant planets at or below one Jupiter mass. Over the past few years, ab initio simulations have put us in the era of quantitative predictions for this H-He immiscibility at megabar pressures. We present models for the thermal evolution of Jupiter, including its evolving helium distribution following one such ab initio H-He phase diagram. After 4 Gyr of homogeneous evolution, differentiation establishes a helium gradient between 1 and 2 Mbar that dynamically stabilizes the fluid to overturning convection. The result is a region undergoing overstable double-diffusive convection (ODDC), whose relatively weak vertical heat transport maintains a superadiabatic temperature gradient. With a general parameterization for the ODDC efficiency, the models can reconcile Jupiter's intrinsic flux, atmospheric helium content, and mean radius at the age of the solar system if the H-He phase diagram is translated to cooler temperatures.We cast our nonadiabatic thermal evolution models in a Markov chain Monte Carlo parameter estimation framework, retrieving the total heavy element mass, the superadiabaticity of the deep temperature gradient, and the phase diagram temperature offset. Models using the interpolated Saumon, Chabrier and van Horn (1995) equation of state (SCvH-I) favor very inefficient ODDC such that the deep temperature gradient is strongly superadiabatic, forming a thermal boundary layer that allows the molecular envelope to cool quickly while the deeper interior (most of the planet's mass) actually heats up over time. If we modulate the overall cooling time with an additional free parameter, mimicking the effect of a colder or warmer EOS, the models favor those that are colder than SCvH-I; this class of EOS is also favored by shock experiments. The models in this scenario have more modest deep superadiabaticities such that the envelope cools more gradually and the deep
Diffusivity of the double negatively charged mono-vacancy in silicon.
Bhoodoo, Chidanand; Vines, Lasse; Monakhov, Edouard; Gunnar Svensson, Bengt
2017-03-27
Lightly-doped silicon (Si) samples of n-type conductivity have been irradiated with 2.0 MeV [Formula: see text] ions at a temperature of 30 K and characterized in situ by deep level transient spectroscopy (DLTS) measurements using an on-line setup. Migration of the Si mono-vacancy in its double negative charge state (V (2-)) starts to occur at temperatures above ∼70 K and is monitored via trapping of V (2-) by interstitial oxygen impurity atoms ([Formula: see text]), leading to the growth of the prominent vacancy-oxygen ([Formula: see text]) center. The [Formula: see text] center gives rise to an acceptor level located at ∼0.17 eV below the conduction band edge (E c ) and is readily detected by DLTS measurements. Post-irradiation isothermal anneals at temperatures in the range of 70 to 90 K reveal first-order kinetics for the reaction [Formula: see text] in both Czochralski-grown and Float-zone samples subjected to low fluences of [Formula: see text] ions, i.e. the irradiation-induced V concentration is dilute ([Formula: see text]10(13) cm(-3)). On the basis of these kinetics data and the content of [Formula: see text], the diffusivity of V (2-) can be determined quantitatively and is found to exhibit an activation energy for migration of ∼0.18 eV with a pre-exponential factor of ∼[Formula: see text] cm(2) s(-1). The latter value evidences a simple jump process without any entropy effects for the motion of V (2-). No deep level in the bandgap to be associated with V (2-) is observed but the results suggest that the level is situated deeper than ∼0.19 eV below E c , corroborating results reported previously in the literature.
Tonkin, J.W.; Balistrieri, L.S.; Murray, J.W.
2004-01-01
Manganese oxides are important scavengers of trace metals and other contaminants in the environment. The inclusion of Mn oxides in predictive models, however, has been difficult due to the lack of a comprehensive set of sorption reactions consistent with a given surface complexation model (SCM), and the discrepancies between published sorption data and predictions using the available models. The authors have compiled a set of surface complexation reactions for synthetic hydrous Mn oxide (HMO) using a two surface site model and the diffuse double layer SCM which complements databases developed for hydrous Fe (III) oxide, goethite and crystalline Al oxide. This compilation encompasses a range of data observed in the literature for the complex HMO surface and provides an error envelope for predictions not well defined by fitting parameters for single or limited data sets. Data describing surface characteristics and cation sorption were compiled from the literature for the synthetic HMO phases birnessite, vernadite and ??-MnO2. A specific surface area of 746 m2g-1 and a surface site density of 2.1 mmol g-1 were determined from crystallographic data and considered fixed parameters in the model. Potentiometric titration data sets were adjusted to a pH1EP value of 2.2. Two site types (???XOH and ???YOH) were used. The fraction of total sites attributed to ???XOH (??) and pKa2 were optimized for each of 7 published potentiometric titration data sets using the computer program FITEQL3.2. pKa2 values of 2.35??0.077 (???XOH) and 6.06??0.040 (???YOH) were determined at the 95% confidence level. The calculated average ?? value was 0.64, with high and low values ranging from 1.0 to 0.24, respectively. pKa2 and ?? values and published cation sorption data were used subsequently to determine equilibrium surface complexation constants for Ba2+, Ca2+, Cd 2+, Co2+, Cu2+, Mg2+, Mn 2+, Ni2+, Pb2+, Sr2+ and Zn 2+. In addition, average model parameters were used to predict additional
NASA Astrophysics Data System (ADS)
Xia, Shaoyan; Huang, Yong; Tan, Xiaodi
2016-03-01
Partial differential equation (PDE)-based nonlinear diffusion processes have been widely used for image denoising. In the traditional nonlinear anisotropic diffusion denoising techniques, behavior of the diffusion depends highly on the gradient of image. However, it is difficult to get a good effect if we use these methods to reduce noise in optical coherence tomography images. Because background has the gradient that is very similar to regions of interest, so background noise will be mistaken for edge information and cannot be reduced. Therefore, nonlinear complex diffusion approaches using texture feature(NCDTF) for noise reduction in phase-resolved optical coherence tomography is proposed here, which uses texture feature in OCT images and structural OCT images to remove noise in phase-resolved OCT. Taking into account the fact that texture between background and signal region is different, which can be linked with diffusion coefficient of nonlinear complex diffusion model, we use NCDTF method to reduce noises of structure and phase images first. Then, we utilize OCT structure images to filter phase image in OCT. Finally, to validate our method, parameters such as image SNR, contrast-to-noise ratio (CNR), equivalent number of looks (ENL), and edge preservation were compared between our approach and median filter, Gaussian filter, wavelet filter, nonlinear complex diffusion filter (NCDF). Preliminary results demonstrate that NCDTF method is more effective than others in keeping edges and denoising for phase-resolved OCT.
Smirnov, Sergey V; Kobtsev, Sergey M; Kukarin, Sergey V
2014-01-13
For the first time we report the results of both numerical simulation and experimental observation of second-harmonic generation as an example of non-linear frequency conversion of pulses generated by passively mode-locked fiber master oscillator in different regimes including conventional (stable) and double-scale (partially coherent and noise-like) ones. We show that non-linear frequency conversion efficiency of double-scale pulses is slightly higher than that of conventional picosecond laser pulses with the same energy and duration despite strong phase fluctuations of double-scale pulses.
NASA Astrophysics Data System (ADS)
Pavelko, V.; Lapsa, K.; Pavlovskis, P.
2016-07-01
The aim of this study is estimation of the effect of large deflections of a double-cantilever beam (DCB) on the accuracy of determination of the mode I interlaminar fracture toughness GIc of layered composites by using the nonlinear theory of bending of beams. The differential equation of the deflection curve of arm of the DCB specimen in the natural form was used to analyze the strain energy of the specimen and its strain energy release rate GI upon propagation of delamination under the action of cleavage forces at the ends of cantilevers. An algorithm for calculating the strain energy and its release rate in the DCB specimens is realized in the form of a MATLAB code. An experimental study was carried out on DCB specimens of a highly flexible carbon/epoxy laminate. The validity of the nonlinear model developed is demonstrated. The standard methods used to determine GIc are refined for the case of highly flexible specimens.
NASA Astrophysics Data System (ADS)
Yesilgul, U.; Sari, H.; Ungan, F.; Martínez-Orozco, J. C.; Restrepo, R. L.; Mora-Ramos, M. E.; Duque, C. A.; Sökmen, I.
2017-03-01
In this study, the effects of electric and magnetic fields on the optical rectification and second and third harmonic generation in asymmetric double quantum well under the intense non-resonant laser field is theoretically investigated. We calculate the optical rectification and second and third harmonic generation within the compact density-matrix approach. The theoretical findings show that the influence of electric, magnetic, and intense laser fields leads to significant changes in the coefficients of nonlinear optical rectification, second and third harmonic generation.
Duarte-Carvajalino, Julio M.; Sapiro, Guillermo; Harel, Noam; Lenglet, Christophe
2013-01-01
Registration of diffusion-weighted magnetic resonance images (DW-MRIs) is a key step for population studies, or construction of brain atlases, among other important tasks. Given the high dimensionality of the data, registration is usually performed by relying on scalar representative images, such as the fractional anisotropy (FA) and non-diffusion-weighted (b0) images, thereby ignoring much of the directional information conveyed by DW-MR datasets itself. Alternatively, model-based registration algorithms have been proposed to exploit information on the preferred fiber orientation(s) at each voxel. Models such as the diffusion tensor or orientation distribution function (ODF) have been used for this purpose. Tensor-based registration methods rely on a model that does not completely capture the information contained in DW-MRIs, and largely depends on the accurate estimation of tensors. ODF-based approaches are more recent and computationally challenging, but also better describe complex fiber configurations thereby potentially improving the accuracy of DW-MRI registration. A new algorithm based on angular interpolation of the diffusion-weighted volumes was proposed for affine registration, and does not rely on any specific local diffusion model. In this work, we first extensively compare the performance of registration algorithms based on (i) angular interpolation, (ii) non-diffusion-weighted scalar volume (b0), and (iii) diffusion tensor image (DTI). Moreover, we generalize the concept of angular interpolation (AI) to non-linear image registration, and implement it in the FMRIB Software Library (FSL). We demonstrate that AI registration of DW-MRIs is a powerful alternative to volume and tensor-based approaches. In particular, we show that AI improves the registration accuracy in many cases over existing state-of-the-art algorithms, while providing registered raw DW-MRI data, which can be used for any subsequent analysis. PMID:23596381
Sun, Wen-Rong; Tian, Bo Jiang, Yan; Zhen, Hui-Ling
2014-04-15
Plasmas are the main constituent of the Universe and the cause of a vast variety of astrophysical, space and terrestrial phenomena. The inhomogeneous nonlinear Schrödinger equation is hereby investigated, which describes the propagation of an electron plasma wave packet with a large wavelength and small amplitude in a medium with a parabolic density and constant interactional damping. By virtue of the double Wronskian identities, the equation is proved to possess the double-Wronskian soliton solutions. Analytic one- and two-soliton solutions are discussed. Amplitude and velocity of the soliton are related to the damping coefficient. Asymptotic analysis is applied for us to investigate the interaction between the two solitons. Overtaking interaction, head-on interaction and bound state of the two solitons are given. From the non-zero potential Lax pair, the first- and second-order rogue-wave solutions are constructed via a generalized Darboux transformation, and influence of the linear and parabolic density profiles on the background density and amplitude of the rogue wave is discussed. -- Highlights: •Double-Wronskian soliton solutions are obtained and proof is finished by virtue of some double Wronskian identities. •Asymptotic analysis is applied for us to investigate the interaction between the two solitons. •First- and second-order rogue-wave solutions are constructed via a generalized Darboux transformation. •Influence of the linear and parabolic density profiles on the background density and amplitude of the rogue wave is discussed.
NASA Astrophysics Data System (ADS)
Li, Rui; Guo, Chun-Sheng; Feng, Shi-Wei; Shi, Lei; Zhu, Hui; Wang, Lin
2015-07-01
To obtain thermal contact resistance (TCR) between the vertical double-diffused metal-oxide-semiconductor (VDMOS) and the heat sink, we derived the relationship between the total thermal resistance and the contact force imposed on the VDMOS. The total thermal resistance from the chip to the heat sink is measured under different contact forces, and the TCR can be extracted nondestructively from the derived relationship. Finally, the experimental results are compared with the simulation results. Project supported by the National Natural Science Foundation of China (Grant No. 61204081).
Malyarenko, Dariya I; Pang, Yuxi; Senegas, Julien; Ivancevic, Marko K; Ross, Brian D; Chenevert, Thomas L
2015-12-01
Spatially non-uniform diffusion weighting bias due to gradient nonlinearity (GNL) causes substantial errors in apparent diffusion coefficient (ADC) maps for anatomical regions imaged distant from magnet isocenter. Our previously-described approach allowed effective removal of spatial ADC bias from three orthogonal DWI measurements for mono-exponential media of arbitrary anisotropy. The present work evaluates correction feasibility and performance for quantitative diffusion parameters of the two-component IVIM model for well-perfused and nearly isotropic renal tissue. Sagittal kidney DWI scans of a volunteer were performed on a clinical 3T MRI scanner near isocenter and offset superiorly. Spatially non-uniform diffusion weighting due to GNL resulted both in shift and broadening of perfusion-suppressed ADC histograms for off-center DWI relative to unbiased measurements close to isocenter. Direction-average DW-bias correctors were computed based on the known gradient design provided by vendor. The computed bias maps were empirically confirmed by coronal DWI measurements for an isotropic gel-flood phantom. Both phantom and renal tissue ADC bias for off-center measurements was effectively removed by applying pre-computed 3D correction maps. Comparable ADC accuracy was achieved for corrections of both b-maps and DWI intensities in presence of IVIM perfusion. No significant bias impact was observed for IVIM perfusion fraction.
Oxygen nonstoichiometry, defect structure and oxygen diffusion in the double perovskite GdBaCo2O6-δ.
Tsvetkov, D S; Ananjev, M V; Eremin, V A; Zuev, A Yu; Kurumchin, E Kh
2014-11-14
Oxygen nonstoichiometry of GdBaCo2O6-δ was studied by means of the thermogravimetric technique in the temperature range 600-1000 °C. The defect structure model based on the simple cubic perovskite GdCoO3-δ was shown to be valid for GdBaCo2O6-δ up to temperatures as low as 600 °C. Two independent methods, namely dc-polarization with the YSZ microelectrode and (18)O-isotope exchange with gas phase analysis, were used to determine the oxygen self-diffusion coefficient in the double perovskite GdBaCo2O6-δ. All measurements were carried out using ceramic samples identically prepared from the same single phase powder of GdBaCo2O6-δ. The experimental data on oxygen nonstoichiometry of GdBaCo2O6-δ allowed a precise calculation of the oxygen interphase exchange rate and the oxygen tracer diffusion coefficient on the basis of the isotope exchange measurements. The values of the oxygen self-diffusion coefficient measured by the dc-polarization technique were found to be in very good agreement with the ones of the oxygen tracer diffusion coefficient.
NASA Astrophysics Data System (ADS)
Tiguercha, Djlalli; Bennis, Anne-claire; Ezersky, Alexander
2015-04-01
The elliptical motion in surface waves causes an oscillating motion of the sand grains leading to the formation of ripple patterns on the bottom. Investigation how the grains with different properties are distributed inside the ripples is a difficult task because of the segration of particle. The work of Fernandez et al. (2003) was extended from one-dimensional to two-dimensional case. A new numerical model, based on these non-linear diffusion equations, was developed to simulate the grain distribution inside the marine sand ripples. The one and two-dimensional models are validated on several test cases where segregation appears. Starting from an homogeneous mixture of grains, the two-dimensional simulations demonstrate different segregation patterns: a) formation of zones with high concentration of light and heavy particles, b) formation of «cat's eye» patterns, c) appearance of inverse Brazil nut effect. Comparisons of numerical results with the new set of field data and wave flume experiments show that the two-dimensional non-linear diffusion equations allow us to reproduce qualitatively experimental results on particles segregation.
Wang, Y.
2013-07-01
Nonlinear diffusion acceleration (NDA) can improve the performance of a neutron transport solver significantly especially for the multigroup eigenvalue problems. The high-order transport equation and the transport-corrected low-order diffusion equation form a nonlinear system in NDA, which can be solved via a Picard iteration. The consistency of the correction of the low-order equation is important to ensure the stabilization and effectiveness of the iteration. It also makes the low-order equation preserve the scalar flux of the high-order equation. In this paper, the consistent correction for a particular discretization scheme, self-adjoint angular flux (SAAF) formulation with discrete ordinates method (S{sub N}) and continuous finite element method (CFEM) is proposed for the multigroup neutron transport equation. Equations with the anisotropic scatterings and a void treatment are included. The Picard iteration with this scheme has been implemented and tested with RattleS{sub N}ake, a MOOSE-based application at INL. Convergence results are presented. (authors)
Option pricing beyond Black-Scholes based on double-fractional diffusion
NASA Astrophysics Data System (ADS)
Kleinert, H.; Korbel, J.
2016-05-01
We show how the prices of options can be determined with the help of double-fractional differential equation in such a way that their inclusion in a portfolio of stocks provides a more reliable hedge against dramatic price drops than the use of options whose prices were fixed by the Black-Scholes formula.
NASA Astrophysics Data System (ADS)
Rhén, Christin; Isacsson, Andreas
2017-01-01
The harmonic oscillator is one of the most widely used model systems in physics: an indispensable theoretical tool in a variety of fields. It is well known that an otherwise linear oscillator can attain novel and nonlinear features through interaction with another dynamical system. We investigate such an interacting system: a superconducting LC-circuit dispersively coupled to a superconducting quantum interference device (SQUID). We find that the SQUID phase behaves as a classical two-level system, whose two states correspond to one linear and one nonlinear regime for the LC-resonator. As a result, the circuit’s response to forcing can become multistable. The strength of the nonlinearity is tuned by the level of noise in the system, and increases with decreasing noise. This tunable nonlinearity could potentially find application in the field of sensitive detection, whereas increased understanding of the classical harmonic oscillator is relevant for studies of the quantum-to-classical crossover of Jaynes-Cummings systems.
Rhén, Christin; Isacsson, Andreas
2017-01-01
The harmonic oscillator is one of the most widely used model systems in physics: an indispensable theoretical tool in a variety of fields. It is well known that an otherwise linear oscillator can attain novel and nonlinear features through interaction with another dynamical system. We investigate such an interacting system: a superconducting LC-circuit dispersively coupled to a superconducting quantum interference device (SQUID). We find that the SQUID phase behaves as a classical two-level system, whose two states correspond to one linear and one nonlinear regime for the LC-resonator. As a result, the circuit’s response to forcing can become multistable. The strength of the nonlinearity is tuned by the level of noise in the system, and increases with decreasing noise. This tunable nonlinearity could potentially find application in the field of sensitive detection, whereas increased understanding of the classical harmonic oscillator is relevant for studies of the quantum-to-classical crossover of Jaynes-Cummings systems. PMID:28120946
Ziegler, Ronny; Nielsen, Tim; Koehler, Thomas; Grosenick, Dirk; Steinkellner, Oliver; Hagen, Axel; Macdonald, Rainer; Rinneberg, Herbert
2009-08-20
We report on the nonlinear reconstruction of local absorption and fluorescence contrast in tissuelike scattering media from measured time-domain diffuse reflectance and transmittance of laser as well as laser-excited fluorescence radiation. Measurements were taken at selected source-detector offsets using slablike diffusely scattering and fluorescent phantoms containing fluorescent heterogeneities. Such measurements simulate in vivo data that would be obtained employing a scanning, time-domain fluorescence mammograph, where the breast is gently compressed between two parallel glass plates, and source and detector optical fibers scan synchronously at various source-detector offsets, allowing the recording of laser and fluorescence mammograms. The diffusion equations modeling the propagation of the laser and fluorescence radiation were solved in frequency domain by the finite element method simultaneously for several modulation frequencies using Fourier transformation and preprocessed experimental data. To reconstruct the concentration of the fluorescent contrast agent, the Born approximation including higher-order reconstructed photon densities at the excitation wavelength was used. Axial resolution was determined that can be achieved by various detection schemes. We show that remission measurements increase the depth resolution significantly.
NASA Astrophysics Data System (ADS)
Saliba, Daniel; Al-Ghoul, Mazen
2016-11-01
We report the synthesis of magnesium-aluminium layered double hydroxide (LDH) using a reaction-diffusion framework (RDF) that exploits the multiscale coupling of molecular diffusion with chemical reactions, nucleation and growth of crystals. In an RDF, the hydroxide anions are allowed to diffuse into an organic gel matrix containing the salt mixture needed for the precipitation of the LDH. The chemical structure and composition of the synthesized magnesium-aluminium LDHs are determined using powder X-ray diffraction (PXRD), thermo-gravimetric analysis, differential scanning calorimetry, solid-state nuclear magnetic resonance (SSNMR), Fourier transform infrared and energy dispersive X-ray spectroscopy. This novel technique also allows the investigation of the mechanism of intercalation of some fluorescent probes, such as the neutral three-dimensional rhodamine B (RhB) and the negatively charged two-dimensional 8-hydroxypyrene-1,3,6-trisulfonic acid (HPTS), using in situ steady-state fluorescence spectroscopy. The incorporation of these organic dyes inside the interlayer region of the LDH is confirmed via fluorescence microscopy, solid-state lifetime, SSNMR and PXRD. The activation energies of intercalation of the corresponding molecules (RhB and HPTS) are computed and exhibit dependence on the geometry of the involved probe (two or three dimensions), the charge of the fluorescent molecule (anionic, cationic or neutral) and the cationic ratio of the corresponding LDH. This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.
NASA Astrophysics Data System (ADS)
Sheikhzadeh, G. A.; Dastmalchi, M.; Khorasanizadeh, H.
2013-12-01
The effect of wall temperature variations on double diffusive natural convection of Al2O3-water nanofluid in a differentially heated square enclosure with constant temperature hot and cold vertical walls is studied numerically. Transport mechanisms of nanoparticles including Brownian diffusion and thermophoresis that cause heterogeneity are considered in non-homogeneous model. The hot and cold wall temperatures are varied, but the temperature difference between them is always maintained 5 °C. The thermophysical properties such as thermal conductivity, viscosity and density and thermophoresis diffusion and Brownian motion coefficients are considered variable with temperature and volume fraction of nanoparticles. The governing equations are discretized using the control volume method. The results show that nanoparticle transport mechanisms affect buoyancy force and cause formation of small vortexes near the top and bottom walls of the cavity and reduce the heat transfer. By increasing the temperature of the walls the effect of transport mechanisms decreases and due to enhanced convection the heat transfer rate increases.
Noise-adaptive nonlinear diffusion filtering of MR images with spatially varying noise levels.
Samsonov, Alexei A; Johnson, Chris R
2004-10-01
Anisotropic diffusion filtering is widely used for MR image enhancement. However, the anisotropic filter is nonoptimal for MR images with spatially varying noise levels, such as images reconstructed from sensitivity-encoded data and intensity inhomogeneity-corrected images. In this work, a new method for filtering MR images with spatially varying noise levels is presented. In the new method, a priori information regarding the image noise level spatial distribution is utilized for the local adjustment of the anisotropic diffusion filter. Our new method was validated and compared with the standard filter on simulated and real MRI data. The noise-adaptive method was demonstrated to outperform the standard anisotropic diffusion filter in both image error reduction and image signal-to-noise ratio (SNR) improvement. The method was also applied to inhomogeneity-corrected and sensitivity encoding (SENSE) images. The new filter was shown to improve segmentation of MR brain images with spatially varying noise levels.
NASA Astrophysics Data System (ADS)
Sui, Jize; Zhao, Peng; Cheng, Zhengdong; Zheng, Liancun; Zhang, Xinxin
2017-02-01
The rheological and heat-conduction constitutive models of micropolar fluids (MFs), which are important non-Newtonian fluids, have been, until now, characterized by simple linear expressions, and as a consequence, the non-Newtonian performance of such fluids could not be effectively captured. Here, we establish the novel nonlinear constitutive models of a micropolar fluid and apply them to boundary layer flow and heat transfer problems. The nonlinear power law function of angular velocity is represented in the new models by employing generalized "n-diffusion theory," which has successfully described the characteristics of non-Newtonian fluids, such as shear-thinning and shear-thickening fluids. These novel models may offer a new approach to the theoretical understanding of shear-thinning behavior and anomalous heat transfer caused by the collective micro-rotation effects in a MF with shear flow according to recent experiments. The nonlinear similarity equations with a power law form are derived and the approximate analytical solutions are obtained by the homotopy analysis method, which is in good agreement with the numerical solutions. The results indicate that non-Newtonian behaviors involving a MF depend substantially on the power exponent n and the modified material parameter K 0 introduced by us. Furthermore, the relations of the engineering interest parameters, including local boundary layer thickness, local skin friction, and Nusselt number are found to be fitted by a quadratic polynomial to n with high precision, which enables the extraction of the rapid predictions from a complex nonlinear boundary-layer transport system.
Simulation of double layers in a model auroral circuit with nonlinear impedance
NASA Technical Reports Server (NTRS)
Smith, R. A.
1986-01-01
A reduced circuit description of the U-shaped potential structure of a discrete auroral arc, consisting of the flank transmission line plus parallel-electric-field region, is used to provide the boundary condition for one-dimensional simulations of the double-layer evolution. The model yields asymptotic scalings of the double-layer potential, as a function of an anomalous transport coefficient alpha and of the perpendicular length scale l(a) of the arc. The arc potential phi(DL) scales approximately linearly with alpha, and for alpha fixed phi (DL) about l(a) to the z power. Using parameters appropriate to the auroral zone acceleration region, potentials of phi (DPL) 10 kV scale to projected ionospheric dimensions of about 1 km, with power flows of the order of magnitude of substorm dissipation rates.
NASA Astrophysics Data System (ADS)
Hussain, Mirza Zahid; Li, Fuguo; Wang, Jing; Yuan, Zhanwei; Li, Pan; Wu, Tao
2015-07-01
The present study comprises the determination of constitutive relationship for thermo-mechanical processing of INCONEL 718 through double multivariate nonlinear regression, a newly developed approach which not only considers the effect of strain, strain rate, and temperature on flow stress but also explains the interaction effect of these thermo-mechanical parameters on flow behavior of the alloy. Hot isothermal compression experiments were performed on Gleeble-3500 thermo-mechanical testing machine in the temperature range of 1153 to 1333 K within the strain rate range of 0.001 to 10 s-1. The deformation behavior of INCONEL 718 is analyzed and summarized by establishing the high temperature deformation constitutive equation. The calculated correlation coefficient ( R) and average absolute relative error ( AARE) underline the precision of proposed constitutive model.
Double-hump solitary waves in quadratically nonlinear media with loss and gain
NASA Astrophysics Data System (ADS)
Darmanyan, S.; Crasovan, L.; Lederer, F.
2000-03-01
We report the existence of a family of bright chirped localized waves in quadratic media with loss and gain. It is shown that the fundamental field component of the symbiotic solitary wave may exhibit a double-hump shape. The conditions of the solitary wave's existence are identified. Numerical experiments disclose different scenarios of instability as well as domains of rather robust behavior of these objects upon propagation.
A feedback control method for the stabilization of a nonlinear diffusion system on a graph
NASA Astrophysics Data System (ADS)
Yu, Xin; Xu, Chao; Lin, Qun
2014-08-01
In this paper, we consider the internal stabilization problems of FitzHugh-Nagumo (FHN) systems on the locally finite connected weighted graphs, which describe the process of signal transmission across axons in neurobiology. We will establish the proper condition on the weighted Dirichlet-Laplace operator on a graph such that the nonlinear FHN system can be stabilized exponentially and globally only using internal actuation over a sub-domain with a linear feedback form.
NASA Astrophysics Data System (ADS)
Bilal, S.; Rehman, Khalil Ur; Malik, M. Y.; Hussain, Arif; Awais, M.
The current communication is carried to contemplate the unique and novel characteristics of nanofluids by constructing formulation of Prandtl fluid model. The fascinating aspects of thermo diffusion effects are also accounted in this communication. Mathematical modelling is performed by employing boundary layer approach. Afterwards, similarity variables are selected to convert dimensional non-linear system into dimensionless expressions. The solution of governing dimensionless problem is executed by shooting method (SM). Graphical evaluation is displayed to depict the intrinsic behavior of embedded parameters on dimensionless velocity, temperature, solutal concentration and nanoparticle concentration profiles. Furthermore, the numerical variation for skin friction coefficient, local Nusselt number, Sherwood number and nano Sherwood number is scrutinized through tables. The assurance of current analysis is affirmed by developing comparison with previous findings available in literature, which sets a benchmark for implementation of computational approach. It is inferred from the computation that concentration profile increases whereas Sherwood number decreases for progressive values of Dufour solutal number.
Comparison of Nonlinear and Linear Stabilization Schemes for Advection-Diffusion Equations
NASA Astrophysics Data System (ADS)
Grove, R. R.; Heister, T.
2015-12-01
Accurately solving advection-diffusion equations that appear in the finite element discretization of a mantle convection simulation is an important computational issue to the computational geoscience community. This is because it allows for users studying mantle convection to create reliable simulations for something as small and simple as a 2D simulation on their personal laptop to something as complex as a massively parallel 3D simulation on their university supercomputer. Standard finite element discretizations of advection-diffusion equations introduce unphysical oscillations around steep gradients. Therefore, stabilization must be added to the discrete formulation to obtain correct solutions. Using the open source scientific library ASPECT, the SUPG and Entropy Viscosity schemes are compared using stationary and non-stationary test equations. Differences in maximum overshoot and undershoot, smear, and convergence orders are compared to see if improvements can be made to the existing numerical method existing in ASPECT.
NASA Astrophysics Data System (ADS)
Keshavkumar Kamaliya, Parth; Patel, Yashavant Kumar Dashrathlal
2016-01-01
Double arm configuration using parallel manipulator mimic the human arm motions either for planar or spatial space. These configurations are currently lucrative for researchers as it also replaces human workers without major redesign of work-place in industries. Humans' joint ranges limitation of arms can be resolved by replacement of either revolute or spherical joints in manipulator. Hence, the scope of maximum workspace utilization is prevailed. Planar configuration with five revolute joints (5R) is considered to imitate human arm motions in a plane using Double Arm Manipulator (DAM). Position analysis for tool that can be held in end links of configuration is carried out using Pro/mechanism in Creo® as well as SimMechanics. D-H parameters are formulated and its results derived using developed MATLAB programs are compared with mechanism simulation as well as SimMechanics results. Inverse kinematics model is developed for trajectory planning in order to trace tool trajectory in a continuous and smooth sequence. Polynomial functions are derived for position, velocity and acceleration for linear and non-linear curves in joint space. Analytical results obtained for trajectory planning are validated with simulation results of Creo®.
NASA Astrophysics Data System (ADS)
Gupta, R. P.; Banerjee, Malay; Chandra, Peeyush
2014-07-01
The present study investigates a prey predator type model for conservation of ecological resources through taxation with nonlinear harvesting. The model uses the harvesting function as proposed by Agnew (1979) [1] which accounts for the handling time of the catch and also the competition between standard vessels being utilized for harvesting of resources. In this paper we consider a three dimensional dynamic effort prey-predator model with Holling type-II functional response. The conditions for uniform persistence of the model have been derived. The existence and stability of bifurcating periodic solution through Hopf bifurcation have been examined for a particular set of parameter value. Using numerical examples it is shown that the system admits periodic, quasi-periodic and chaotic solutions. It is observed that the system exhibits periodic doubling route to chaos with respect to tax. Many forms of complexities such as chaotic bands (including periodic windows, period-doubling bifurcations, period-halving bifurcations and attractor crisis) and chaotic attractors have been observed. Sensitivity analysis is carried out and it is observed that the solutions are highly dependent to the initial conditions. Pontryagin's Maximum Principle has been used to obtain optimal tax policy to maximize the monetary social benefit as well as conservation of the ecosystem.
A free boundary problem of a diffusive SIRS model with nonlinear incidence
NASA Astrophysics Data System (ADS)
Cao, Jia-Feng; Li, Wan-Tong; Wang, Jie; Yang, Fei-Ying
2017-04-01
This paper is concerned with the spreading (persistence) and vanishing (extinction) of a disease which is characterized by a diffusive SIRS model with a bilinear incidence rate and free boundary. Through discussing the dynamics of a free boundary problem of an SIRS model, the spreading of a disease is described. We get the sufficient conditions which ensure the disease spreading or vanishing. In addition, the estimate of the expanding speed is also given when the free boundaries extend to the whole R.
Reactive-Diffusive-Advective Traveling Waves in a Family of Degenerate Nonlinear Equations.
Sánchez-Garduño, Faustino; Pérez-Velázquez, Judith
This paper deals with the analysis of existence of traveling wave solutions (TWS) for a diffusion-degenerate (at D(0) = 0) and advection-degenerate (at h'(0) = 0) reaction-diffusion-advection (RDA) equation. Diffusion is a strictly increasing function and the reaction term generalizes the kinetic part of the Fisher-KPP equation. We consider different forms of the convection term h(u): (1) h'(u) is constant k, (2) h'(u) = ku with k > 0, and (3) it is a quite general form which guarantees the degeneracy in the advective term. In Case 1, we prove that the task can be reduced to that for the corresponding equation, where k = 0, and then previous results reported from the authors can be extended. For the other two cases, we use both analytical and numerical tools. The analysis we carried out is based on the restatement of searching TWS for the full RDA equation into a two-dimensional dynamical problem. This consists of searching for the conditions on the parameter values for which there exist heteroclinic trajectories of the ordinary differential equations (ODE) system in the traveling wave coordinates. Throughout the paper we obtain the dynamics by using tools coming from qualitative theory of ODE.
Reactive-Diffusive-Advective Traveling Waves in a Family of Degenerate Nonlinear Equations
Sánchez-Garduño, Faustino
2016-01-01
This paper deals with the analysis of existence of traveling wave solutions (TWS) for a diffusion-degenerate (at D(0) = 0) and advection-degenerate (at h′(0) = 0) reaction-diffusion-advection (RDA) equation. Diffusion is a strictly increasing function and the reaction term generalizes the kinetic part of the Fisher-KPP equation. We consider different forms of the convection term h(u): (1) h′(u) is constant k, (2) h′(u) = ku with k > 0, and (3) it is a quite general form which guarantees the degeneracy in the advective term. In Case 1, we prove that the task can be reduced to that for the corresponding equation, where k = 0, and then previous results reported from the authors can be extended. For the other two cases, we use both analytical and numerical tools. The analysis we carried out is based on the restatement of searching TWS for the full RDA equation into a two-dimensional dynamical problem. This consists of searching for the conditions on the parameter values for which there exist heteroclinic trajectories of the ordinary differential equations (ODE) system in the traveling wave coordinates. Throughout the paper we obtain the dynamics by using tools coming from qualitative theory of ODE. PMID:27689131
NASA Astrophysics Data System (ADS)
Mojumder, Satyajit; Saha, Sourav; Saha, Sumon
2016-07-01
Entropy optimization is a major concern for designing modern thermal management system. In the present work, entropy analysis in a square cavity with an isothermal hollow cylinder at the center is carried out for magneto-hydrodynamic (MHD) double diffusive convection. Galerkin weighted residuals method of finite element formulation is adopted for the numerical solution. Entropies due to fluid flow, heat, and mass transfer are computed for wide range of Hartmann (0 ≤ Ha ≤ 50) and Lewis numbers (1 ≤ Le ≤ 15), and buoyancy ratios (-5 ≤ N ≤ 5) at constant Rayleigh and Prandtl numbers. It is found that the influence of buoyancy ratio is prominent on entropy generation, which also depends on both Lewis and Hartmann numbers. The ratio N = -1 shows minimum entropy generation for any combination of Lewis and Hartman numbers. Visualization of isentropic contours and the variation of total entropy with the governing parameters provide remarkable evidences of entropy optimization.
Niculescu, O.; Dimitriu, D. G.
2010-08-04
The periodic current bursts observed in the dynamic current-voltage characteristic of a probe in the presence of a plasma fireball in dynamic state were modeled in the frame of the scale relativity model, based on both the fractal space-time concept and the generalization of Einstein's principle of relativity to scale transformations. The double layer dynamics is described by a set of time-dependent Schroedinger-type equations and the self-structuring is given by means of the negative differential resistance. The obtained experimental and theoretical results are proven to be in very good agreement.
NASA Astrophysics Data System (ADS)
Muriano, Alejandro; Salvador, J.-Pablo; Galve, Roger; Marco, M.-Pilar; Thayil K. N., Anisha; Loza-Alvarez, Pablo; Soria, Silvia
2011-01-01
We report the non linear fluorescence real-time detection of methylboldenone, an androgenic anabolic steroid used illegally as growth promoter based on a resonant sensing chip: a double grating waveguide structure. The limit of detection of this synthetic steroid is two orders of magnitude lower than the Minimum Required Performance Limit required by the World Anti-Doping Agency. The immunoreagents have been have been immobilized onto the surface of the resonant sensor after being activated with phosphonohexanoic acid spacers. The developed immunosensor presents great potential as a robust sensing device for fast and early detection of illegal dopants and food contaminants.
Daly, Edoardo; Porporato, Amilcare
2004-11-01
Similarity solutions of the shallow-water equation with a generalized resistance term are studied for open channel flows when both inertial and gravity forces are negligible. The resulting model encompasses various particular cases that appear, in addition to mathematical hydraulics, in diverse physical phenomena, such as gravity currents, creeping flows of Newtonian and non-Newtonian fluids, thin films, and nonlinear Fokker-Planck equations. Solutions of both source-type and dam-break problems are analyzed. Closed-form solutions are discussed, when possible, along with a qualitative study of two phase-plane formulations based on two different variable transformations.
Nonlinear modifications of photon correlations via controlled single and double Rydberg blockade
NASA Astrophysics Data System (ADS)
Liu, Yi-Mou; Tian, Xue-Dong; Yan, Dong; Zhang, Yan; Cui, Cui-Li; Wu, Jin-Hui
2015-04-01
We study the optical response of cold rubidium atoms driven into the four-level Y configuration exhibiting two high Rydberg levels in the regime of electromagnetically induced transparency (EIT). Atoms excited to either Rydberg level interact with each other just via self-blockade potentials (I) or also via cross blockade potentials (II). Numerical results show a few interesting quantum phenomena on the transmitted properties of a weak probe field owing to controlled single and double Rydberg blockade. In case (I), it is viable to switch between single-photon outputs with vanishing (invariable) two-photon (three-photon) correlation and photon-pair outputs with vanishing (invariable) three-photon (two-photon) correlation. Such output switch can be easily done by modulating frequencies and intensities of two strong coupling fields to create a degenerate EIT window or two separated EIT windows. In case (II), we find that two-photon and three-photon correlations decrease together at a degenerate EIT window center while increasing together between two separated EIT windows. Such consistent changes are observed because both correlations are modified by the identical polarizability degradation though depending on single and double Rydberg blockade, respectively.
Unsteady magnetohydrodynamics mixed convection flow in a rotating medium with double diffusion
Jiann, Lim Yeou; Ismail, Zulkhibri; Khan, Ilyas; Shafie, Sharidan
2015-05-15
Exact solutions of an unsteady Magnetohydrodynamics (MHD) flow over an impulsively started vertical plate in a rotating medium are presented. The effects of thermal radiative and thermal diffusion on the fluid flow are also considered. The governing equations are modelled and solved for velocity, temperature and concentration using Laplace transforms technique. Expressions of velocity, temperature and concentration profiles are obtained and their numerical results are presented graphically. Skin friction, Sherwood number and Nusselt number are also computed and presented in tabular forms. The determined solutions can generate a large class of solutions as special cases corresponding to different motions with technical relevance. The results obtained herein may be used to verify the validation of obtained numerical solutions for more complicated fluid flow problems.
NASA Astrophysics Data System (ADS)
Vlad, Marcel Ovidiu; Moran, Federico; Tsuchiya, Masa; Cavalli-Sforza, L. Luca; Oefner, Peter J.; Ross, John
2002-06-01
We study a general class of nonlinear macroscopic evolution equations with ``transport'' and ``reaction'' terms which describe the dynamics of a species of moving individuals (atoms, molecules, quasiparticles, organisms, etc.). We consider that two types of individuals exist, ``not marked'' and ``marked,'' respectively. We assume that the concentrations of both types of individuals are measurable and that they obey a neutrality condition, that is, the kinetic and transport properties of the ``not marked'' and ``marked'' individuals are identical. We suggest a response experiment, which consists in varying the fraction of ``marked'' individuals with the preservation of total fluxes, and show that the response of the system can be represented by a linear superposition law even though the underlying dynamics of the system is in general highly nonlinear. The linear response law is valid even for large perturbations and is not the result of a linearization procedure but rather a necessary consequence of the neutrality condition. First, we apply the response theorem to chemical kinetics, where the ``marked species'' is a molecule labeled with a radioactive isotope and there is no kinetic isotope effect. The susceptibility function of the response law can be related to the reaction mechanism of the process. Secondly we study the geographical distribution of the nonrecurrent, nonreversible neutral mutations of the nonrecombining portion of the Y chromosome from human populations and show that the fraction of mutants at a given point in space and time obeys a linear response law of the type introduced in this paper. The theory may be used for evaluating the geographic position and the moment in time where and when a mutation originated.
NASA Astrophysics Data System (ADS)
Eskew, Matthew W.; Harrison, Jason; Simoyi, Reuben H.
2016-11-01
Oxidation reactions of thiourea by chlorite in a Hele-Shaw cell are excitable, autocatalytic, exothermic, and generate a lateral instability upon being triggered by the autocatalyst. Reagent concentrations used to develop convective instabilities delivered a temperature jump at the wave front of 2.1 K. The reaction zone was 2 mm and due to normal cooling after the wave front, this generated a spike rather than the standard well-studied front propagation. The reaction front has solutal and thermal contributions to density changes that act in opposite directions due to the existence of a positive isothermal density change in the reaction. The competition between these effects generates thermal plumes. The fascinating feature of this system is the coexistence of plumes and fingering in the same solution which alternate in frequency as the front propagates, generating hot and cold spots within the Hele-Shaw cell, and subsequently spatiotemporal inhomogeneities. The small ΔT at the wave front generated thermocapillary convection which competed effectively with thermogravitational forces at low Eötvös Numbers. A simplified reaction-diffusion-convection model was derived for the system. Plume formation is heavily dependent on boundary effects from the cell dimensions. This work was supported by Grant No. CHE-1056366 from the NSF and a Research Professor Grant from the University of KwaZulu-Natal.
NASA Technical Reports Server (NTRS)
Shaughnessy, J. D.; Groom, N. J.; Nene, V. D.
1973-01-01
The effects of two types of control-system nonlinearities, sensor deadband and actuator breakout torque, on the pointing capability of a Apollo Telescope Mount (ATM) double-gimbal experiment isolation and control system are investigated. A composite structural model of a flexible experiment package connected through frictionless double gimbals to a flexible carrier vehicle is used for this investigation. Contributions of the primary carrier control system to experiment pointing are neglected. Pointing errors onboard the experiment package due to random crew-motion input into the carrier vehicle are computed. A stability investigation is performed to verify control-system stability with nominal nonlinearities and gains. Indications are that there is no stability problem due to the nonlinearities. A nonlinearity sensitivity study is carried out to determine the effects on pointing accuracy. Its results indicate that nominal ATM control system nonlinearities limit the pointing accuracy to approximately 0.4 arc second in the presence of crew motion. Methods of reducing the error to less than 0.1 arc second are discussed.
Malyarenko, Dariya I.; Wilmes, Lisa J.; Arlinghaus, Lori R.; Jacobs, Michael A.; Huang, Wei; Helmer, Karl G.; Taouli, Bachir; Yankeelov, Thomas E.; Newitt, David; Chenevert, Thomas L.
2017-01-01
Previous research has shown that system-dependent gradient nonlinearity (GNL) introduces a significant spatial bias (nonuniformity) in apparent diffusion coefficient (ADC) maps. Here, the feasibility of centralized retrospective system-specific correction of GNL bias for quantitative diffusion-weighted imaging (DWI) in multisite clinical trials is demonstrated across diverse scanners independent of the scanned object. Using corrector maps generated from system characterization by ice-water phantom measurement completed in the previous project phase, GNL bias correction was performed for test ADC measurements from an independent DWI phantom (room temperature agar) at two offset locations in the bore. The precomputed three-dimensional GNL correctors were retrospectively applied to test DWI scans by the central analysis site. The correction was blinded to reference DWI of the agar phantom at magnet isocenter where the GNL bias is negligible. The performance was evaluated from changes in ADC region of interest histogram statistics before and after correction with respect to the unbiased reference ADC values provided by sites. Both absolute error and nonuniformity of the ADC map induced by GNL (median, 12%; range, −35% to +10%) were substantially reduced by correction (7-fold in median and 3-fold in range). The residual ADC nonuniformity errors were attributed to measurement noise and other non-GNL sources. Correction of systematic GNL bias resulted in a 2-fold decrease in technical variability across scanners (down to site temperature range). The described validation of GNL bias correction marks progress toward implementation of this technology in multicenter trials that utilize quantitative DWI. PMID:28105469
Wei, Jingsong; Wang, Rui
2014-03-28
In this work, the resolving limit of maskless direct laser writing is overcome by cooperative manipulation from nonlinear reverse saturation absorption and thermal diffusion, where the nonlinear reverse saturation absorption can induce the formation of below diffraction-limited energy absorption spot, and the thermal diffusion manipulation can make the heat quantity at the central region of energy absorption spot propagate along the thin film thickness direction. The temperature at the central region of energy absorption spot transiently reaches up to melting point and realizes nanolithography. The sample “glass substrate/AgInSbTe” is prepared, where AgInSbTe is taken as nonlinear reverse saturation absorption thin film. The below diffraction-limited energy absorption spot is simulated theoretically and verified experimentally by near-field spot scanning method. The “glass substrate/Al/AgInSbTe” sample is prepared, where the Al is used as thermal conductive layer to manipulate the thermal diffusion channel because the thermal diffusivity coefficient of Al is much larger than that of AgInSbTe. The direct laser writing is conducted by a setup with a laser wavelength of 650 nm and a converging lens of NA=0.85, the lithographic marks with a size of about 100 nm are obtained, and the size is only about 1/10 the incident focused spot. The experimental results indicate that the cooperative manipulation from nonlinear reverse saturation absorption and thermal diffusion is a good method to realize nanolithography in maskless direct laser writing with visible light.
NASA Astrophysics Data System (ADS)
Vincze, Miklos; Borcia, Ion; Harlander, Uwe; Le Gal, Patrice
2016-12-01
A water-filled differentially heated rotating annulus with initially prepared stable vertical salinity profiles is studied in the laboratory. Based on two-dimensional horizontal particle image velocimetry data and infrared camera visualizations, we describe the appearance and the characteristics of the baroclinic instability in this original configuration. First, we show that when the salinity profile is linear and confined between two non-stratified layers at top and bottom, only two separate shallow fluid layers can be destabilized. These unstable layers appear nearby the top and the bottom of the tank with a stratified motionless zone between them. This laboratory arrangement is thus particularly interesting to model geophysical or astrophysical situations where stratified regions are often juxtaposed to convective ones. Then, for more general but stable initial density profiles, statistical measures are introduced to quantify the extent of the baroclinic instability at given depths and to analyze the connections between this depth-dependence and the vertical salinity profiles. We find that, although the presence of stable stratification generally hinders full-depth overturning, double-diffusive convection can lead to development of multicellular sideways convection in shallow layers and subsequently to a multilayered baroclinic instability. Therefore we conclude that by decreasing the characteristic vertical scale of the flow, stratification may even enhance the formation of cyclonic and anticyclonic eddies (and thus, mixing) in a local sense.
Mimouni, N.; Chikh, S.; Rahli, O.; Bennacer, R.
2014-07-15
Two-dimensional (2D) and three-dimensional (3D) numerical simulations of double diffusion natural convection in an elongated enclosure filled with a binary fluid saturating a porous medium are carried out in the present work. The Boussinesq approximation is made in the formulation of the problem, and Neumann boundary conditions for temperature and concentration are adopted, respectively, on vertical and horizontal walls of the cavity. The used numerical method is based on the control volume approach, with the third order quadratic upstream interpolation scheme in approximating the advection terms. A semi implicit method algorithm is used to handle the velocity-pressure coupling. To avoid the excessively high computer time inherent to the solution of 3D natural convection problems, full approximation storage with full multigrid method is used to solve the problem. A wide range of the controlling parameters (Rayleigh-Darcy number Ra, lateral aspect ratio Ay, Lewis number Le, and the buoyancy ration N) is investigated. We clearly show that increasing the depth of the cavity (i.e., the lateral aspect ratio) has an important effect on the flow patterns. The 2D perfect parallel flows obtained for small lateral aspect ratio are drastically destabilized by increasing the cavity lateral dimension. This yields a 3D fluid motion with a much more complex flow pattern and the usually considered 2D parallel flow model cannot be applied.
NASA Astrophysics Data System (ADS)
Goyal, M.; Bhargava, R.
2014-05-01
This paper deals with the double-diffusive boundary layer flow of non-Newtonian nanofluid over a stretching sheet. In this model, where binary nanofluid is used, the Brownian motion and thermophoresis are classified as the main mechanisms which are responsible for the enhancement of the convection features of the nanofluid. The boundary layer equations governed by the partial differential equations are transformed into a set of ordinary differential equations with the help of group theory transformations. The variational finite element method (FEM) is used to solve these ordinary differential equations. We have examined the effects of different controlling parameters, namely, the Brownian motion parameter, the thermophoresis parameter, modified Dufour number, viscoelastic parameter, Prandtl number, regular Lewis number, Dufour Lewis number, and nanofluid Lewis number on the flow field and heat transfer characteristics. Graphical display of the numerical examine are performed to illustrate the influence of various flow parameters on the velocity, temperature, concentration, reduced Nusselt, reduced Sherwood and reduced nanofluid Sherwood number distributions. The present study has many applications in coating and suspensions, movement of biological fluids, cooling of metallic plate, melt-spinning, heat exchangers technology, and oceanography.
Leyre, Sven; Meuret, Youri; Durinck, Guy; Hofkens, Johan; Deconinck, Geert; Hanselaer, Peter
2014-04-01
The accuracy of optical simulations including bulk diffusors is heavily dependent on the accuracy of the bulk scattering properties. If no knowledge on the physical scattering effects is available, an iterative procedure is usually used to obtain the scattering properties, such as the inverse Monte Carlo method or the inverse adding-doubling (AD) method. In these methods, a predefined phase function with one free parameter is usually used to limit the number of free parameters. In this work, three predefined phase functions (Henyey-Greenstein, two-term Henyey-Greenstein, and Gegenbauer kernel (GK) phase function) are implemented in the inverse AD method to determine the optical properties of two strongly diffusing materials: low-density polyethylene and TiO₂ particles. Using the presented approach, an estimation of the effective phase function was made. It was found that the use of the GK phase function resulted in the best agreement between calculated and experimental transmittance, reflectance, and scattered radiant intensity distribution for the LDPE sample. For the TiO₂ sample, a good agreement was obtained with both the two-term Henyey-Greenstein and the GK phase function.
NASA Astrophysics Data System (ADS)
Nourazar, Salman; Nazari-Golshan, Akbar; Yıldırım, Ahmet; Nourazar, Maryam
2012-07-01
The physical science importance of the Cauchy problem of the reaction-diffusion equation appears in the modelling of a wide variety of nonlinear systems in physics, chemistry, ecology, biology, and engineering. A hybrid of Fourier transform and Adomian decomposition method (FTADM) is developed for solving the nonlinear non-homogeneous partial differential equations of the Cauchy problem of reaction-diffusion. The results of the FTADM and the ADM are compared with the exact solution. The comparison reveals that for the same components of the recursive sequences, the errors associated with the FTADM are much lesser than those of the ADM. We show that as time increases the results of the FTADM approaches 1 with only six recursive terms. This is in agreement with the physical property of the density-dependent nonlinear diffusion of the Cauchy problem which is also in agreement with the exact solution. The monotonic and very rapid convergence of the results of the FTADM towards the exact solution is shown to be much faster than that of the ADM
NASA Astrophysics Data System (ADS)
Finsterbusch, Jürgen
2011-01-01
Experiments with two diffusion weightings applied in direct succession in a single acquisition, so-called double- or two-wave-vector diffusion-weighting (DWV) experiments at short mixing times, have been shown to be a promising tool to estimate cell or compartment sizes, e.g. in living tissue. The basic theory for such experiments predicts that the signal decays for parallel and antiparallel wave vector orientations differ by a factor of three for small wave vectors. This seems to be surprising because in standard, single-wave-vector experiments the polarity of the diffusion weighting has no influence on the signal attenuation. Thus, the question how this difference can be understood more pictorially is often raised. In this rather educational manuscript, the phase evolution during a DWV experiment for simple geometries, e.g. diffusion between parallel, impermeable planes oriented perpendicular to the wave vectors, is considered step-by-step and demonstrates how the signal difference develops. Considering the populations of the phase distributions obtained, the factor of three between the signal decays which is predicted by the theory can be reproduced. Furthermore, the intermediate signal decay for orthogonal wave vector orientations can be derived when investigating diffusion in a box. Thus, the presented “phase gymnastics” approach may help to understand the signal modulation observed in DWV experiments at short mixing times.
Asano, Tetsuya; Kaneko, Yukihiro; Omote, Atsushi; Adachi, Hideaki; Fujii, Eiji
2017-02-15
We demonstrated the field-effect conductivity modulation of a gold thin film by all-solid-state electric-double-layer (EDL) gating at room temperature using an epitaxially grown oxide fast lithium conductor, La2/3-xLi3xTiO3 (LLT), as a solid electrolyte. The linearly increasing gold conductivity with increasing gate bias demonstrates that the conductivity modulation is indeed due to carrier injection by EDL gating. The response time becomes exponentially faster with increasing gate bias, a result of the onset of nonlinear ionic transportation. This nonlinear dynamic response indicates that the ionic motion-driven device can be much faster than would be estimated from a linear ionic transport model.
NASA Technical Reports Server (NTRS)
Goldstein, M. L.
1977-01-01
In a study of cosmic ray propagation in interstellar and interplanetary space, a perturbed orbit resonant scattering theory for pitch angle diffusion in a slab model of magnetostatic turbulence is slightly generalized and used to compute the diffusion coefficient for spatial propagation parallel to the mean magnetic field. This diffusion coefficient has been useful for describing the solar modulation of the galactic cosmic rays, and for explaining the diffusive phase in solar flares in which the initial anisotropy of the particle distribution decays to isotropy.
NASA Astrophysics Data System (ADS)
Yasin, Mohd Hafizi Mat; Ishak, Anuar
2016-11-01
The objective of this study is to investigate the effects of mass suction on double diffusive mixed convection boundary layer flow from a vertical flat plate embedded in a porous medium filled by a nanofluid using Buongiorno's model. The appropriate similarity transformation is used to reduce the partial differential equations into a system of ordinary differential equation, which is then solved numerically using a shooting method. The effects of mass suction parameter on the flow field and heat transfer characteristics are presented and discussed.
NASA Astrophysics Data System (ADS)
Afify, A. A.; Uddin, Md. J.
2016-09-01
A numerical study of a steady two-dimensional double-diffusive free convection boundary layer flow over a vertical surface embedded in a porous medium with slip flow and convective boundary conditions, heat generation/absorption, and solar radiation effects is performed. A scaling group of transformations is used to obtain the governing boundary layer equations and the boundary conditions. The transformed equations are then solved by the fourth- and fifth-order Runge-Kutta-Fehlberg numerical method with Maple 13. The results for the velocity, temperature, and concentration profiles, as well as the skin friction coefficient, the Nusselt number, and the Sherwood number are presented and discussed.
NASA Technical Reports Server (NTRS)
Decker, A. J.
1982-01-01
A theory of fringe localization in rapid-double-exposure, diffuse-illumination holographic interferometry was developed. The theory was then applied to compare holographic measurements with laser anemometer measurements of shock locations in a transonic axial-flow compressor rotor. The computed fringe localization error was found to agree well with the measured localization error. It is shown how the view orientation and the curvature and positional variation of the strength of a shock wave are used to determine the localization error and to minimize it. In particular, it is suggested that the view direction not deviate from tangency at the shock surface by more than 30 degrees.
NASA Astrophysics Data System (ADS)
Bois, Pierre-Antoine
2006-11-01
We derive the molecular diffusion equations, and we show how the determination of the molecular diffusion coefficients of passive scalars (pollutants or moisture) in the atmospheric air may be performed, in first approximation, by means of data of pressure, temperature and densities in the medium at the rest. These approximations are sufficient in order to write the equations of shallow convection (Boussinesq equations), whatever be the Brunt-Väisälä frequency of the medium (as well as in the troposphere and in the stratosphere). In the case of deep convection, which is possible in the troposphere only, the weakness of the Brunt-Väisälä frequency modifies the molecular diffusion equations, and these equations also modify the equations of convection. More accurate evaluations of the diffusion coefficients must also be made, using, for instance, static datas associated with several temperature distributions. To cite this article: P.-A. Bois, C. R. Mecanique 334 (2006).
Nonlinear electrochemical relaxation around conductors.
Chu, Kevin T; Bazant, Martin Z
2006-07-01
We analyze the simplest problem of electrochemical relaxation in more than one dimension-the response of an uncharged, ideally polarizable metallic sphere (or cylinder) in a symmetric, binary electrolyte to a uniform electric field. In order to go beyond the circuit approximation for thin double layers, our analysis is based on the Poisson-Nernst-Planck (PNP) equations of dilute solution theory. Unlike most previous studies, however, we focus on the nonlinear regime, where the applied voltage across the conductor is larger than the thermal voltage. In such strong electric fields, the classical model predicts that the double layer adsorbs enough ions to produce bulk concentration gradients and surface conduction. Our analysis begins with a general derivation of surface conservation laws in the thin double-layer limit, which provide effective boundary conditions on the quasineutral bulk. We solve the resulting nonlinear partial differential equations numerically for strong fields and also perform a time-dependent asymptotic analysis for weaker fields, where bulk diffusion and surface conduction arise as first-order corrections. We also derive various dimensionless parameters comparing surface to bulk transport processes, which generalize the Bikerman-Dukhin number. Our results have basic relevance for double-layer charging dynamics and nonlinear electrokinetics in the ubiquitous PNP approximation.
Johnston, Stuart T; Baker, Ruth E; McElwain, D L Sean; Simpson, Matthew J
2017-02-14
Invasion processes are ubiquitous throughout cell biology and ecology. During invasion, individuals can become isolated from the bulk population and behave differently. We present a discrete, exclusion-based description of the birth, death and movement of individuals. The model distinguishes between individuals that are part of, or are isolated from, the bulk population by imposing different rates of birth, death and movement. This enables the simulation of various co-operative or competitive mechanisms, where there is either a positive or negative benefit associated with being part of the bulk population, respectively. The mean-field approximation of the discrete process gives rise to 22 different classes of partial differential equation, which can include Allee kinetics and nonlinear diffusion. Here we examine the ability of each class of partial differential equation to support travelling wave solutions and interpret the long time behaviour in terms of the individual-level parameters. For the first time we show that the strong Allee effect and nonlinear diffusion can result in shock-fronted travelling waves. We also demonstrate how differences in group and individual motility rates can influence the persistence of a population and provide conditions for the successful invasion of a population.
Johnston, Stuart T.; Baker, Ruth E.; McElwain, D. L. Sean; Simpson, Matthew J.
2017-01-01
Invasion processes are ubiquitous throughout cell biology and ecology. During invasion, individuals can become isolated from the bulk population and behave differently. We present a discrete, exclusion-based description of the birth, death and movement of individuals. The model distinguishes between individuals that are part of, or are isolated from, the bulk population by imposing different rates of birth, death and movement. This enables the simulation of various co-operative or competitive mechanisms, where there is either a positive or negative benefit associated with being part of the bulk population, respectively. The mean-field approximation of the discrete process gives rise to 22 different classes of partial differential equation, which can include Allee kinetics and nonlinear diffusion. Here we examine the ability of each class of partial differential equation to support travelling wave solutions and interpret the long time behaviour in terms of the individual-level parameters. For the first time we show that the strong Allee effect and nonlinear diffusion can result in shock-fronted travelling waves. We also demonstrate how differences in group and individual motility rates can influence the persistence of a population and provide conditions for the successful invasion of a population. PMID:28195135
NASA Astrophysics Data System (ADS)
Johnston, Stuart T.; Baker, Ruth E.; McElwain, D. L. Sean; Simpson, Matthew J.
2017-02-01
Invasion processes are ubiquitous throughout cell biology and ecology. During invasion, individuals can become isolated from the bulk population and behave differently. We present a discrete, exclusion-based description of the birth, death and movement of individuals. The model distinguishes between individuals that are part of, or are isolated from, the bulk population by imposing different rates of birth, death and movement. This enables the simulation of various co-operative or competitive mechanisms, where there is either a positive or negative benefit associated with being part of the bulk population, respectively. The mean-field approximation of the discrete process gives rise to 22 different classes of partial differential equation, which can include Allee kinetics and nonlinear diffusion. Here we examine the ability of each class of partial differential equation to support travelling wave solutions and interpret the long time behaviour in terms of the individual-level parameters. For the first time we show that the strong Allee effect and nonlinear diffusion can result in shock-fronted travelling waves. We also demonstrate how differences in group and individual motility rates can influence the persistence of a population and provide conditions for the successful invasion of a population.
NASA Astrophysics Data System (ADS)
Langenbruch, C.
2015-12-01
In August 2014 segmented lateral dyke growth has been observed in a rifting event at Bardarbunga volcanic system, Iceland. The temporal evolution of the magma source and the physical nature of magma flow process during dyke propagation and arrest are unclear. The epidemic-type aftershock sequence model has been used to detect fluid signals in seismicity data. We use the earthquake catalog recorded during the rifting event to reconstruct the magma flow signal at the feeding source of the dyke. We find that the segmentation of dyke growth is caused by a pulsating nature of the magma flow source. We identify two main magma flow pulses, which initiate and propagate the two main segments of the dyke. During phases of dyke arrest magma flow pulses are low and cannot further propagate the dyke. We use the reconstructed magma flow signal to set up a numerical model of non-linear magma pressure diffusion. By using the magma pressure changes resulting from magma flow, we simulate the earthquake catalog caused by the reduction of the effective principal stress. We observe an excellent agreement between the spatio-temporal characteristics of the simulated earthquake catalog and recorded seismicity. Our results suggest that the process of magma pressure relaxation can be described as a non-linear diffusion process. Because the opening of the dyke creates significant new fracture volume, the permeability of the rock is strongly increasing and the diffusion process becomes highly non-linear. Our analysis is based on lessons learned from analysis of seismicity observed during hydraulic fracturing of hydrocarbon reservoirs. Despite large differences in scale, the underlying physical processes are comparable. Finally, we analyze the decay of seismic activity after start of the effusive fissure eruption near the end of the dyke. The magma flow strongly decreases and seismic activity decays according to Omori's law, which describes the decay of aftershock activity after tectonic
NASA Astrophysics Data System (ADS)
Glaus, M. A.; Aertsens, M.; Appelo, C. A. J.; Kupcik, T.; Maes, N.; Van Laer, L.; Van Loon, L. R.
2015-09-01
Enhanced mass transfer rates have been frequently observed in diffusion studies with alkaline and earth alkaline elements in compacted clay minerals and clay rocks. Whether this phenomenon - often termed surface diffusion - is also relevant for more strongly sorbing species is an open question. We therefore investigated the diffusion of Sr2+, Co2+ and Zn2+ in compacted illite with respect to variations of the concentration of the background electrolyte, pH and carbonate. New experimental techniques were developed in order to avoid artefacts stemming from the confinement of the clay sample. A distinct dependence of the effective diffusion coefficients on the concentration of the background electrolyte was observed for all three elements. A similar correlation was found for the sorption distribution ratio (Rd) derived from tracer breakthrough in the case of Sr2+, while this dependence was much weaker for Co2+ and Zn2+. Model calculations using Phreeqc resulted in a good agreement with the experimental data when it was assumed that the cationic species, present in the electrical double layer (EDL) of the charged clay surface, are mobile. Species bound to the specific surface complexation sites at the clay edges were assumed to be immobile. An assessment of the mobility of the type of cationic elements studied here in argillaceous media thus requires an analysis of their distribution among specifically sorbed surface species and species in the EDL. The normal approach of deriving unknown effective diffusion coefficients from reference values of an uncharged water tracer may significantly underestimate the mobility of metal cations in argillaceous media.
Williams, Richard; Grim, Joel; Li, Qi; Ucer, K. B.; Bizarri, G. A.; Kerisit, Sebastien N.; Gao, Fei; Bhattacharya, Pijush; Tupitsyn, Eugene; Rowe, Emmanuel; Buliga, Vladimir M.; Burger, Arnold
2013-10-01
Models of nonproportional response in scintillators have highlighted the importance of parameters such as branching ratios, carrier thermalization times, diffusion, kinetic order of quenching, associated rate constants, and radius of the electron track. For example, the fraction ηeh of excitations that are free carriers versus excitons was shown by Payne and coworkers to have strong correlation with the shape of electron energy response curves from Compton-coincidence studies. Rate constants for nonlinear quenching are implicit in almost all models of nonproportionality, and some assumption about track radius must invariably be made if one is to relate linear energy deposition dE/dx to volume-based excitation density n (eh/cm3) in terms of which the rates are defined. Diffusion, affecting time-dependent track radius and thus density of excitations, has been implicated as an important factor in nonlinear light yield. Several groups have recently highlighted diffusion of hot electrons in addition to thermalized carriers and excitons in scintillators. However, experimental determination of many of these parameters in the insulating crystals used as scintillators has seemed difficult. Subpicosecond laser techniques including interband z scan light yield, fluence-dependent decay time, and transient optical absorption are now yielding experimental values for some of the missing rates and ratios needed for modeling scintillator response. First principles calculations and Monte Carlo simulations can fill in additional parameters still unavailable from experiment. As a result, quantitative modeling of scintillator electron energy response from independently determined material parameters is becoming possible on an increasingly firmer data base. This paper describes recent laser experiments, calculations, and numerical modeling of scintillator response.
Williams, R. T.; Grim, Joel Q.; Li, Qi; Ucer, K. B.; Bizarri, G. A.; Kerisit, S.; Gao, Fei; Bhattacharya, P.; Tupitsyn, E.; Rowe, E.; Buliga, V. M.; Burger, A.
2013-09-26
Models of nonproportional response in scintillators have highlighted the importance of parameters such as branching ratios, carrier thermalization times, diffusion, kinetic order of quenching, associated rate constants, and radius of the electron track. For example, the fraction ηeh of excitations that are free carriers versus excitons was shown by Payne and coworkers to have strong correlation with the shape of electron energy response curves from Compton-coincidence studies. Rate constants for nonlinear quenching are implicit in almost all models of nonproportionality, and some assumption about track radius must invariably be made if one is to relate linear energy deposition dE/dx to volume-based excitation density n (eh/cm^{3}) in terms of which the rates are defined. Diffusion, affecting time-dependent track radius and thus density of excitations, has been implicated as an important factor in nonlinear light yield. Several groups have recently highlighted diffusion of hot electrons in addition to thermalized carriers and excitons in scintillators. However, experimental determination of many of these parameters in the insulating crystals used as scintillators has seemed difficult. Subpicosecond laser techniques including interband z scan light yield, fluence-dependent decay time, and transient optical absorption are now yielding experimental values for some of the missing rates and ratios needed for modeling scintillator response. First principles calculations and Monte Carlo simulations can fill in additional parameters still unavailable from experiment. As a result, quantitative modeling of scintillator electron energy response from independently determined material parameters is becoming possible on an increasingly firmer data base. This study describes recent laser experiments, calculations, and numerical modeling of scintillator response.
Williams, R. T.; Grim, Joel Q.; Li, Qi; ...
2013-09-26
Models of nonproportional response in scintillators have highlighted the importance of parameters such as branching ratios, carrier thermalization times, diffusion, kinetic order of quenching, associated rate constants, and radius of the electron track. For example, the fraction ηeh of excitations that are free carriers versus excitons was shown by Payne and coworkers to have strong correlation with the shape of electron energy response curves from Compton-coincidence studies. Rate constants for nonlinear quenching are implicit in almost all models of nonproportionality, and some assumption about track radius must invariably be made if one is to relate linear energy deposition dE/dx tomore » volume-based excitation density n (eh/cm3) in terms of which the rates are defined. Diffusion, affecting time-dependent track radius and thus density of excitations, has been implicated as an important factor in nonlinear light yield. Several groups have recently highlighted diffusion of hot electrons in addition to thermalized carriers and excitons in scintillators. However, experimental determination of many of these parameters in the insulating crystals used as scintillators has seemed difficult. Subpicosecond laser techniques including interband z scan light yield, fluence-dependent decay time, and transient optical absorption are now yielding experimental values for some of the missing rates and ratios needed for modeling scintillator response. First principles calculations and Monte Carlo simulations can fill in additional parameters still unavailable from experiment. As a result, quantitative modeling of scintillator electron energy response from independently determined material parameters is becoming possible on an increasingly firmer data base. This study describes recent laser experiments, calculations, and numerical modeling of scintillator response.« less
Nonlinear Evolution Equation of a Step with Anisotropy in a Diffusion Field for the Two-Sided Model
NASA Astrophysics Data System (ADS)
Mori, H.; Soma, T.; Okuda, K.; Wada, K.
2004-05-01
The nonlinear evolution equation for the fluctuation of a terrace edge with anisotropy in step stiffness during step flow growth is derived in the two-sided model where adatoms can be incorporated into the step from the upper terrace as well as from the lower terrace. It is shown by reductive perturbation method based on the linear stability analysis that (1) up to ɛ3 order in the smallness parameter of instability the nonlinear evolution equation reduces to the closed Kuramoto-Sivashinsky (KS) equation with extra coefficients compared with the one-sided model and (2) the nonlinear evolution equation up to ɛ5 order is also derived in order to take into account the anisotropy in step stiffness in the lowest order. The nonlinear evolution equation is numerically calculated for various parameters included. It is also shown that the asymmetry of attachment into a step and the Gibbs-Thomson effect with anisotropy in step stiffness bring about various growth patterns of the step from chaotic growth to periodic growth and further to an inclined straight step mode with a single peak.
Rashidi, Mohammad M.; Kavyani, Neda; Abelman, Shirley; Uddin, Mohammed J.; Freidoonimehr, Navid
2014-01-01
In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, , local Nusselt number, , and local Sherwood number are shown and explained through tables. PMID:25343360
Rashidi, Mohammad M; Kavyani, Neda; Abelman, Shirley; Uddin, Mohammed J; Freidoonimehr, Navid
2014-01-01
In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, [Formula: see text], local Nusselt number, [Formula: see text], and local Sherwood number [Formula: see text] are shown and explained through tables.
Amendt, P
2004-02-10
Double-shell ignition is complementary to the baseline approach by virtue of not requiring: (1) cryogenic preparation and fielding, (2) high-contrast pulse-shaping for shock-timing, and (3) demanding x-ray flux symmetry control. The use of simpler low-contrast pulse-shaping potentially allows more benign hohlraum conditions by reducing the risk of laser backscatter. In addition, the associated higher laser fluence threshold for optics damage initiation allows the possibility of more routine high-fluence shots with 2{omega} on the NIF. Based on LDRD-sponsored research in FY01-03 on NIF double-shell ignition target designs, the feasibility of this approach was advanced through both a highly successful implosion campaign on the Omega laser facility and a variety of design improvements for mitigating instability. The double-shell implosion campaign on Omega achieved the important milestone of repeatably demonstrating dominant primary (2.45 MeV) neutron production from the mix-susceptible compressional phase of a double-shell implosion, using fall-line design optimization and exacting fabrication standards. Showing effective control of fuel-pusher mix during final compression is an essential element for achieving ignition. In our studies to control mix by reducing hydrodynamic instability a new pathway for destructive Rayleigh-Taylor growth on the outer surface of the inner shell at ignition scales was identified. However, highly resolved multi-mode simulations showed that with use of a graded dopant in the inner shell and material-matching with an exterior metallic foam, this instability was significantly reduced. In addition, the resulting density-gradient stabilization was seen to quench small-wavelength growth, thereby avoiding the computationally challenging turbulent regime. A major goal of future research for realizing double-shell ignition on the NIF is experimental validation of this instability mitigation approach using the Omega laser facility.
NASA Astrophysics Data System (ADS)
Wang, Tao; Wang, Wei; Du, Pengfei; Geng, Dongxian; Gao, Gan; Gong, Mali
2014-04-01
Atmospheric turbulence affects the transmission of laser pulses through the atmosphere. The effects mean that the peak power of the laser pulses is not stable. For laser pulses reflected by a cooperative target, the peak power instability is greater because of the double-pass propagation of the laser pulses through the same atmosphere. The atmospheric turbulence can be monitored by detecting the peak power instability of echo laser pulses. This paper presents a method for monitoring atmospheric turbulence based on a cooperative target. Comparative experiments are carried out based on using a diffuse whiteboard and a corner-cube retroreflector (CCR) as the cooperative target. The distance between the two terminals of the experimental system is 1550 m. The size of the diffuse whiteboard is 60×60 cm2. The bottom surface of the CCR is a circle with a diameter of 1 in. and the three mirrors of the CCR are coated with silver. Experiment results show that the peak power instability of echo laser pulses retroreflected by the CCR is 28.3%. This is much larger than that diffuse reflected by the whiteboard (11.2%). This indicates that the method based on the CCR has higher atmospheric sensitivity. In addition, the peak power of the echo laser pulses retroreflected by the CCR is also much larger. Therefore, the system based on the CCR is more suitable for monitoring of atmospheric turbulence.
NASA Astrophysics Data System (ADS)
Nourazar, S. S.; Nazari-Golshan, A.
2015-01-01
A hybrid of Fourier transform and new modified homotopy perturbation method based on the Adomian method is developed to solve linear and nonlinear partial differential equations. The Taylor series expansion is used to expand nonlinear term of partial differential equation and the Adomian polynomial incorporated into homotopy perturbation method combined with Fourier transform, is used to solve partial differential equations. Three case study problems, partial differential equations, are handled using homotopy perturbation method and Fourier transform modified homotopy perturbation method (FTMHPM). Results obtained are compared with exact solution. The comparison reveals that for same components of recursive sequences, errors associated with Fourier transform modified method are much less than the other and are valid for a large range of x-axis coordinates.
NASA Astrophysics Data System (ADS)
Kawai, Yusuke; Yamada, Yoshio
2016-07-01
This paper deals with a free boundary problem for diffusion equation with a certain class of bistable nonlinearity which allows two positive stable equilibrium states as an ODE model. This problem models the invasion of a biological species and the free boundary represents the spreading front of its habitat. Our main interest is to study large-time behaviors of solutions for the free boundary problem. We will completely classify asymptotic behaviors of solutions and, in particular, observe two different types of spreading phenomena corresponding to two positive stable equilibrium states. Moreover, it will be proved that, if the free boundary expands to infinity, an asymptotic speed of the moving free boundary for large time can be uniquely determined from the related semi-wave problem.
Keyes, Joseph T.; Simon, Bruce R.; Vande Geest, Jonathan P.
2013-01-01
Purpose Arterial wall mass transport properties dictate local distribution of biomolecules or locally delivered dugs. Knowing how these properties vary between coronary artery locations could provide insight into how therapy efficacy is altered between arterial locations. Methods We introduced an indocarbocyanine drug surrogate to the lumens of left anterior descending and right coronary (LADC; RC) arteries from pigs with or without a pressure gradient. Interstitial fluorescent intensity was measured on live samples with multiphoton microscopy. We also measured binding to porcine coronary SMCs in monoculture. Results Diffusive transport constants peaked in the middle sections of the LADC and RC arteries by 2.09 and 2.04 times, respectively, compared to the proximal and distal segments. There was no statistical difference between the average diffusivity value between LADC and RC arteries. The convection coefficients had an upward trend down each artery, with the RC being higher than the LADC by 3.89 times. Conclusions This study demonstrates that the convective and diffusive transport of lipophilic molecules changes between the LADC and the RC arteries as well as along their length. These results may have important implications in optimizing drug delivery for the treatment of coronary artery disease. PMID:23224981
Yoshida, Kenichiro; Nishidate, Izumi
2014-01-01
To rapidly derive a result for diffuse reflectance from a multilayered model that is equivalent to that of a Monte-Carlo simulation (MCS), we propose a combination of a layered white MCS and the adding-doubling method. For slabs with various scattering coefficients assuming a certain anisotropy factor and without absorption, we calculate the transition matrices for light flow with respect to the incident and exit angles. From this series of precalculated transition matrices, we can calculate the transition matrices for the multilayered model with the specific anisotropy factor. The relative errors of the results of this method compared to a conventional MCS were less than 1%. We successfully used this method to estimate the chromophore concentration from the reflectance spectrum of a numerical model of skin and in vivo human skin tissue. PMID:25426319
Sung, Kunsik; Won, Taeyoung
2011-08-01
In this paper, we discuss on the optimal design of a High-Side n-channel Lateral Double-diffused Metal Oxide Semiconductor Field Effect Transistor (LDMOSFET) whose breakdown voltage is over 100 V with 0.35 microm Bipolar-CMOS-DMOS (BCD) process. The proposed nLDMOSFET has been fabricated and tested in order to confirm the features of a deep N+ sinker and a gap of between the drift region (DEEP N-WELL) and the center of the source. The surface is implanted by the N-layer for high breakdown voltage and simultaneously the low specific on-resistance. The computer simulation of the proposed High-Side LDMOS exhibits BVdss of 115 V and Ron,sp of as low as 2.20 m ohms cm2, which is consistent with the experimental results.
Alexandrov, D V; Nizovtseva, I G; Malygin, A P; Huang, H-N; Lee, D
2008-03-19
A model is presented that describes nonstationary solidification of binary melts or solutions from a cooled boundary maintained at a time-dependent temperature. Heat and mass transfer processes are described on the basis of the principles of a mushy layer, which divides pure solid material and a liquid phase. Nonlinear equations characterizing the dynamics of the phase transition boundaries are deduced. Approximate analytical solutions of the model under consideration are constructed. A method for controlling the external temperature at a cooled wall in order to obtain a required solidification velocity is discussed.
NASA Astrophysics Data System (ADS)
Leconte, Jérémy; Selsis, Franck; Hersant, Franck; Guillot, Tristan
2017-02-01
In an atmosphere, a cloud condensation region is characterized by a strong vertical gradient in the abundance of the related condensing species. On Earth, the ensuing gradient of mean molecular weight has relatively few dynamical consequences because N2 is heavier than water vapor, so that only the release of latent heat significantly impacts convection. On the contrary, in a hydrogen dominated atmosphere (e.g., giant planets), all condensing species are significantly heavier than the background gas. This can stabilize the atmosphere against convection near a cloud deck if the enrichment in the given species exceeds a critical threshold. This raises two questions. What is transporting energy in such a stabilized layer, and how affected can the thermal profile of giant planets be? To answer these questions, we first carry out a linear analysis of the convective and double-diffusive instabilities in a condensable medium showing that an efficient condensation can suppress double-diffusive convection. This suggests that a stable radiative layer can form near a cloud condensation level, leading to an increase in the temperature of the deep adiabat. Then, we investigate the impact of the condensation of the most abundant species (water) with a steady-state atmosphere model. Compared to standard models, the temperature increase can reach several hundred degrees at the quenching depth of key chemical tracers. Overall, this effect could have many implications for our understanding of the dynamical and chemical state of the atmosphere of giant planets, for their future observations (with Juno for example), and for their internal evolution.
NASA Astrophysics Data System (ADS)
Dubovsky, O. A.; Semenov, V. A.; Orlov, A. V.; Sudarev, V. V.
2014-09-01
The microdynamics of large-amplitude nonlinear vibrations of uranium nitride diatomic lattices has been investigated using the computer simulation and neutron scattering methods at temperatures T = 600-2500°C near the thresholds of the dissociation and destruction of the reactor fuel materials. It has been found using the computer simulation that, in the spectral gap between the frequency bands of acoustic and optical phonons in crystals with an open surface, there are resonances of new-type harmonic surface vibrations and a gap-filling band of their genetic successors, i.e., nonlinear surface vibrations. Experimental measurements of the slow neutron scattering spectra of uranium nitride on the DIN-2PI neutron spectrometer have revealed resonances and bands of these surface vibrations in the spectral gap, as well as higher optical vibration overtones. It has been shown that the solitons and bisolitons initiate the formation and collapse of dynamic pores with the generation of surface vibrations at the boundaries of the cavities, evaporation of atoms and atomic clusters, formation of cracks, and destruction of the material. It has been demonstrated that the mass transfer of nitrogen in cracks and along grain boundaries can occur through the revealed microdynamics mechanism of the surfing diffusion of light nitrogen atoms at large-amplitude soliton waves propagating in the stabilizing sublattice of heavy uranium atoms and in the nitrogen sublattice.
Sabelnikov, V A; Lipatnikov, A N
2014-09-01
The problem of traveling wave (TW) speed selection for solutions to a generalized Murray-Burgers-KPP-Fisher parabolic equation with a strictly positive cubic reaction term is considered theoretically and the initial boundary value problem is numerically solved in order to support obtained analytical results. Depending on the magnitude of a parameter inherent in the reaction term (i) the term is either a concave function or a function with the inflection point and (ii) transition from pulled to pushed TW solution occurs due to interplay of two nonlinear terms; the reaction term and the Burgers convection term. Explicit pushed TW solutions are derived. It is shown that physically observable TW solutions, i.e., solutions obtained by solving the initial boundary value problem with a sufficiently steep initial condition, can be determined by seeking the TW solution characterized by the maximum decay rate at its leading edge. In the Appendix, the developed approach is applied to a non-linear diffusion-reaction equation that is widely used to model premixed turbulent combustion.
Zhai, Wu-Chao; Qiao, Tie-Zhu; Cai, Dong-Jin; Wang, Wen-Jie; Chen, Jing-Dong; Chen, Zhi-Hui; Liu, Shao-Ding
2016-11-28
Third-harmonic generation with metallic or dielectric nanoparticles often suffer from, respectively, small modal volumes and weak near-field enhancements. This study propose and demonstrate that a metallic/dielectric hybrid nanostructure composed of a silver double rectangular nanoring and a silicon square nanoplate can be used to overcome these obstacles for enhanced third-harmonic generation. It is shown that the nonradiative anapole mode of the Si plate can be used as a localized source to excite the dark subradiant octupole mode of the Ag ring, and the mode hybridization leads to the formation of an antibonding and a bonding subradiant collective mode, thereby forming anticrossing double Fano resonances. With the strong coupling between individual particles and the effectively suppressed radiative losses of the Fano resonances, several strong hot spots are generated around the Ag ring due to the excitation of the octupole mode, and electromagnetic fields within the Si plate are also strongly amplified, making it possible to confine more incident energy inside the dielectric nanoparticle. Calculation results reveal that the confined energy inside the Si plate and the Ag ring for the hybrid structures can be about, respectively, more than three times and four orders stronger than that of the corresponding isolated nanoparticles, which makes the designed hybrid nanostructure a promising platform for enhanced third-harmonic generation.
Yu, Guang Tao; Chen, Wei; Gu, Feng Long; Aoki, Yuriko
2010-03-01
The static (hyper)polarizabilities of the dimer and trimer with diffuse excess electrons, [Li(+)[calix[4]pyrrole]Li(-)](n), are firstly investigated by the DFT(B3LYP) method in detail. For the dimer and trimer, a Li atom inside each calix[4]pyrrole unit is ionized to form a diffuse excess electron. The results show that the dimer and trimer containing two and three excess electrons, respectively, have very large first hyperpolarizablities as 2.3 x 10(4) and 4.0 x 10(4) au, which are 30 and 40 times larger than that of the corresponding [calix[4]pyrrole](n) (n = 2, 3) without Li atom. Also, beta values of dimer and trimer are twice and four times as large as that of monomer containing one excess electron. Obviously, not only excess electron but also the number of excess electron plays an important role in increasing the first hyperpolarizability. Moreover, the (hyper)polarizabilities of the [Li(+)[calix[4]pyrrole]Li(-)](n) polymer are investigated at ab initio level by using the elongation finite-field (elongation FF) method. All the oligomers of the [Li(+)[calix[4]pyrrole]Li(-)](n) with many excess electrons exhibit very large first hyperpolarizability and large second hyperpolarizability. The present investigation shows that by introducing several and more excess electrons into the nonlinear optical (NLO) materials will be an important strategy for improving their NLO properties, which will be helpful for design of NLO materials.
Bufetova, G A; Gulyamova, E S; Il'ichev, N N; Pashinin, P P; Shapkin, P V; Nasibov, A S
2015-06-30
Transmission spectra of a ZnSe sample diffusion-doped with Fe{sup 2+} ions have been measured in the wavelength range 500 – 7000 nm. A broad absorption band in the range 500 – 1500 nm has been observed in both doped and undoped regions of the sample. This band is possibly due to deviations from stoichiometry in the course of diffusion doping. The transmission of the Fe{sup 2+}:ZnSe sample at a wavelength of 2940 nm has been measured at various dopant concentrations and high peak pulse intensities (up to 8 MW cm{sup -2}). The samples have been shown to be incompletely bleached: during a laser pulse, the transmission first increases, reaches a maximum, and then falls off. Our results suggest that the incomplete bleaching cannot be accounted for by excited-state absorption. The incomplete bleaching (as well as the transmission maximum) is due to the heating of the sample, which leads to a reduction in upper level lifetime and, accordingly, to an increase in absorption saturation intensity. (nonlinear optical phenomena)
Barber, Jared; Tanase, Roxana; Yotov, Ivan
2016-06-01
Several Kalman filter algorithms are presented for data assimilation and parameter estimation for a nonlinear diffusion model of epithelial cell migration. These include the ensemble Kalman filter with Monte Carlo sampling and a stochastic collocation (SC) Kalman filter with structured sampling. Further, two types of noise are considered -uncorrelated noise resulting in one stochastic dimension for each element of the spatial grid and correlated noise parameterized by the Karhunen-Loeve (KL) expansion resulting in one stochastic dimension for each KL term. The efficiency and accuracy of the four methods are investigated for two cases with synthetic data with and without noise, as well as data from a laboratory experiment. While it is observed that all algorithms perform reasonably well in matching the target solution and estimating the diffusion coefficient and the growth rate, it is illustrated that the algorithms that employ SC and KL expansion are computationally more efficient, as they require fewer ensemble members for comparable accuracy. In the case of SC methods, this is due to improved approximation in stochastic space compared to Monte Carlo sampling. In the case of KL methods, the parameterization of the noise results in a stochastic space of smaller dimension. The most efficient method is the one combining SC and KL expansion.
Punga, Anna Rostedt; Eriksson, Annika; Alimohammadi, Mohammad
2015-11-01
Despite the extensive use of botulinum toxin A (BoNTA) in medical and cosmetic treatments, the potential spreading of BoNTA to surrounding tissues remains unknown. A patient with hemifacial paralysis upon blepharospasm treatment with low dose of BoNTA, prompted us to investigate the spreading effect. A randomised, double-blind study was conducted in which 5 healthy women (33-52 years) were treated with different doses of onabotulinum toxin unilaterally in the corrugator muscle. Parameters of efficacy and diffusion (CMAP; EMG and jitter analysis) in both glabellar and frontalis muscles were assessed at baseline, 2 and 4 weeks following BoNTA injection. CMAP of the treated glabellar muscles was reduced to approximately 40% in all dose groups. Additionally, contralateral CMAP reduction was observed in 3 of 5 subjects. These data confirm regional diffusion of BoNTA in facial muscle application, which raises question on the reliability of split-face models in BoNTA studies.
Alhamud, A.; Taylor, Paul A.; van der Kouwe, A.J.W.; Meintjes, E. M.
2015-01-01
Diffusion tensor imaging (DTI) requires a set of diffusion weighted measurements in order to acquire enough information to characterize local structure. The MRI scanner automatically performs a shimming process by acquiring a field map before the start of a DTI scan. Changes in B0, which can occur throughout the DTI acquisition due to several factors (including heating of the iron shim coils or subject motion), cause significant signal distortions that result in warped diffusion tensor (DT) parameter estimates. In this work we introduce a novel technique to simultaneously measure, report and correct in real time subject motion and changes in B0 field homogeneity, both in and through the imaging plane. This is achieved using double volumetric navigators (DvNav), i.e. a pair of 3D EPI acquisitions, interleaved with the DTI pulse sequence. Changes in the B0 field are evaluated in terms of zero-order (frequency) and first-order (linear gradients) shim. The ability of the DvNav to accurately estimate the shim parameters was first validated in a water phantom. Two healthy subjects were scanned both in the presence and absence of motion using standard, motion corrected (single navigator, vNav), and DvNav DTI sequences. The difference in performance between the proposed 3D EPI field maps and the standard 3D gradient echo field maps of the MRI scanner was also evaluated in a phantom and two healthy subjects. The DvNav sequence was shown to accurately measure and correct changes in B0 following manual adjustments of the scanner’s central frequency and the linear shim gradients. Compared to other methods, the DvNav produced DTI results that showed greater spatial overlap with anatomical references, particularly in scans with subject motion. This is largely due to the ability of the DvNav system to correct shim changes and subject motion between each volume acquisition, thus reducing shear distortion. PMID:26584865
NASA Technical Reports Server (NTRS)
Goldstein, M. L.
1976-01-01
The propagation of charged particles through interstellar and interplanetary space has often been described as a random process in which the particles are scattered by ambient electromagnetic turbulence. In general, this changes both the magnitude and direction of the particles' momentum. Some situations for which scattering in direction (pitch angle) is of primary interest were studied. A perturbed orbit, resonant scattering theory for pitch-angle diffusion in magnetostatic turbulence was slightly generalized and then utilized to compute the diffusion coefficient for spatial propagation parallel to the mean magnetic field, Kappa. All divergences inherent in the quasilinear formalism when the power spectrum of the fluctuation field falls off as K to the minus Q power (Q less than 2) were removed. Various methods of computing Kappa were compared and limits on the validity of the theory discussed. For Q less than 1 or 2, the various methods give roughly comparable values of Kappa, but use of perturbed orbits systematically results in a somewhat smaller Kappa than can be obtained from quasilinear theory.
Burger, Karin; Koehler, Thomas; Chabior, Michael; Allner, Sebastian; Marschner, Mathias; Fehringer, Andreas; Willner, Marian; Pfeiffer, Franz; Noël, Peter
2014-12-29
Phase-contrast x-ray computed tomography has a high potential to become clinically implemented because of its complementarity to conventional absorption-contrast.In this study, we investigate noise-reducing but resolution-preserving analytical reconstruction methods to improve differential phase-contrast imaging. We apply the non-linear Perona-Malik filter on phase-contrast data prior or post filtered backprojected reconstruction. Secondly, the Hilbert kernel is replaced by regularized iterative integration followed by ramp filtered backprojection as used for absorption-contrast imaging. Combining the Perona-Malik filter with this integration algorithm allows to successfully reveal relevant sample features, quantitatively confirmed by significantly increased structural similarity indices and contrast-to-noise ratios. With this concept, phase-contrast imaging can be performed at considerably lower dose.
Ginzburg, Irina
2017-01-01
to vanish or attenuate the disparity of the modeled transport coefficients with the equilibrium weights without any modification of the BB rule, we propose to use the two-relaxation-times collision operator with free-tunable product of two eigenfunctions Λ. Two different values Λ_{v} and Λ_{b} are assigned for bulk and boundary nodes, respectively. The rationale behind this is that Λ_{v} is adjustable for stability, accuracy, or other purposes, while the corresponding Λ_{b}(Λ_{v}) controls the primary accommodation effects. Two distinguished but similar functional relations Λ_{b}(Λ_{v}) are constructed analytically: they preserve advection velocity in parabolic profile, exactly in the two-dimensional channel and very accurately in a three-dimensional cylindrical capillary. For any velocity-weight stencil, the (local) double-Λ BB scheme produces quasi-identical solutions with the (nonlocal) specular-forward reflection for first four moments in a channel. In a capillary, this strategy allows for the accurate modeling of the Taylor-dispersion and non-Gaussian effects. As illustrative example, it is shown that in the flow around a circular obstacle, the double-Λ scheme may also vanish the dependency of mean velocity on the velocity weight; the required value for Λ_{b}(Λ_{v}) can be identified in a few bisection iterations in given geometry. A positive solution for Λ_{b}(Λ_{v}) may not exist in pure diffusion, but a sufficiently small value of Λ_{b} significantly reduces the disparity in diffusion coefficient with the mass weight in ducts and in the presence of rectangular obstacles. Although Λ_{b} also controls the effective position of straight or curved boundaries, the double-Λ scheme deals with the lower-order effects. Its idea and construction may help understanding and amelioration of the anomalous, zero- and first-order behavior of the macroscopic solution in the presence of the bulk and boundary or interface discontinuities, commonly found in
NASA Astrophysics Data System (ADS)
Ginzburg, Irina
2017-01-01
to vanish or attenuate the disparity of the modeled transport coefficients with the equilibrium weights without any modification of the BB rule, we propose to use the two-relaxation-times collision operator with free-tunable product of two eigenfunctions Λ . Two different values Λv and Λb are assigned for bulk and boundary nodes, respectively. The rationale behind this is that Λv is adjustable for stability, accuracy, or other purposes, while the corresponding Λb(Λv) controls the primary accommodation effects. Two distinguished but similar functional relations Λb(Λv) are constructed analytically: they preserve advection velocity in parabolic profile, exactly in the two-dimensional channel and very accurately in a three-dimensional cylindrical capillary. For any velocity-weight stencil, the (local) double-Λ BB scheme produces quasi-identical solutions with the (nonlocal) specular-forward reflection for first four moments in a channel. In a capillary, this strategy allows for the accurate modeling of the Taylor-dispersion and non-Gaussian effects. As illustrative example, it is shown that in the flow around a circular obstacle, the double-Λ scheme may also vanish the dependency of mean velocity on the velocity weight; the required value for Λb(Λv) can be identified in a few bisection iterations in given geometry. A positive solution for Λb(Λv) may not exist in pure diffusion, but a sufficiently small value of Λb significantly reduces the disparity in diffusion coefficient with the mass weight in ducts and in the presence of rectangular obstacles. Although Λb also controls the effective position of straight or curved boundaries, the double-Λ scheme deals with the lower-order effects. Its idea and construction may help understanding and amelioration of the anomalous, zero- and first-order behavior of the macroscopic solution in the presence of the bulk and boundary or interface discontinuities, commonly found in multiphase flow and heterogeneous
ERIC Educational Resources Information Center
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…
NASA Astrophysics Data System (ADS)
Kaladhar, K.; Srinivasacharya, D.
2016-12-01
The chemical reaction, Soret and Dufour effects on steady flow of a couple stress fluid between two rotating disks are studied. The lower disc is rotating with angular velocity Ω1 where as the upper disc is rotating with Ω2. The density variation in centrifugal and Coriolis force terms are taken into consideration by invoking a linear density-temperature relation and Boussinesq approximation to account the buoyancy effects. The non-linear governing partial differential equations are transformed into system of ordinary differential equations by using the similarity transformations. Homotopy Analysis Method (HAM) has been used to solve the resulting equations. Graphical illustrations of the dimensionless velocity, concentration and temperature profiles are presented at different values of the emerging parameter of the present study. It has been found that as an increase in couple stresses leads to the decrease in velocity, temperature and increase in concentration of the fluid. Flow velocities, temperature and concentration profiles are decreases with an increase in reaction parameter.
NASA Astrophysics Data System (ADS)
Chakraborty, D.; Nandi, U. N.; Jana, D.; Dasgupta, P.; Poddar, A.
2017-01-01
Scaling analysis of nonOhmic electrical transport in double perovskite (DP) compounds like La2NiMnO6 and Sr2Fe0.3Mn0.7MoO6 is presented over a wide range of electric bias and temperatures. It is shown that the voltage V0(T) at which conductance deviates from its Ohmic value Σ0(T) scales with Σ0(T) as V0(T) ∼Σ0(T) xT , xT being the onset exponent characterizing the onset of nonOhmic conduction. Interestingly, it was found that xT is negative and insensitive to the nature of conduction mechanism in DPs but is related to the characteristic temperature T0 and the mean hopping length Hm. We provide a scaling formalism in terms of the parameters V0(T) and xT in DPs for deeper understanding of the spintronic application and the electrode functioning in solid oxide fuel cells (SOFC). Inelastic multi-step tunneling is found to be the suitable mechanism of electronic transport characterized completely by these two parameters.
Abbes, Ilham Ben; Richard, Pierre-Yves; Lefebvre, Marie-Anne; Guilhem, Isabelle; Poirier, Jean-Yves
2013-01-01
Background Most closed-loop insulin delivery systems rely on model-based controllers to control the blood glucose (BG) level. Simple models of glucose metabolism, which allow easy design of the control law, are limited in their parametric identification from raw data. New control models and controllers issued from them are needed. Methods A proportional integral derivative with double phase lead controller was proposed. Its design was based on a linearization of a new nonlinear control model of the glucose–insulin system in type 1 diabetes mellitus (T1DM) patients validated with the University of Virginia/Padova T1DM metabolic simulator. A 36 h scenario, including six unannounced meals, was tested in nine virtual adults. A previous trial database has been used to compare the performance of our controller with their previous results. The scenario was repeated 25 times for each adult in order to take continuous glucose monitoring noise into account. The primary outcome was the time BG levels were in target (70–180 mg/dl). Results Blood glucose values were in the target range for 77% of the time and below 50 mg/dl and above 250 mg/dl for 0.8% and 0.3% of the time, respectively. The low blood glucose index and high blood glucose index were 1.65 and 3.33, respectively. Conclusion The linear controller presented, based on the linearization of a new easily identifiable nonlinear model, achieves good glucose control with low exposure to hypoglycemia and hyperglycemia. PMID:23759403
Vasil'ev, S A; Stepanova, E Iu; Kutenkov, O P; Belenko, A A; Zharkova, L P; Bol'shakov, M A; Lebedev, I N; Rostov, V V
2012-01-01
Effects of ionizing radiation registered in cells after low dose irradiation are still poorly understood. A pulsed mode of irradiation is even more problematic in terms of predicting the radiation-induced response in cells. Thus, the aim of this paper was to study and analyze the effects of dose and frequency of pulsed X-rays on the frequency of radiation-induced DNA double-strand breaks and their repair kinetics in human peripheral blood lymphocytes in vitro. Analysis of radiation-induced gammaH2AX and 53BP1 repair foci was used to assess the DNA damage in these cells. The dose-response curve of radiation-induced foci of both proteins has shown deviations from linearity to a higher effect in the 12-32 mGy dose range and a lower effect at 72 mGy. The dose-response curve was linear at doses higher than 100 mGy. The number of radiation-induced gammaH2AX and 53BP1 foci depended on the frequency of X-ray pulses: the highest effect was registered at 13 pulses per second. Moreover, slower repair kinetics was observed for those foci induced by very low doses with a nonlinear dose-response relationship.
Ngoko Djiokap, J M; Manakov, N L; Meremianin, A V; Hu, S X; Madsen, L B; Starace, Anthony F
2014-11-28
Control of double ionization of He by means of the polarization and carrier-envelope phase (CEP) of an intense, few-cycle extreme ultraviolet (XUV) pulse is demonstrated numerically by solving the six-dimensional two-electron, time-dependent Schrödinger equation for He interacting with an elliptically polarized XUV pulse. Guided by perturbation theory (PT), we predict the existence of a nonlinear dichroic effect (∝I^{3/2}) that is sensitive to the CEP, ellipticity, peak intensity I, and temporal duration of the pulse. This dichroic effect (i.e., the difference of the two-electron angular distributions for opposite helicities of the ionizing XUV pulse) originates from interference of first- and second-order PT amplitudes, allowing one to probe and control S- and D-wave channels of the two-electron continuum. We show that the back-to-back in-plane geometry with unequal energy sharing is an ideal one for observing this dichroic effect that occurs only for an elliptically polarized, few-cycle attosecond pulse.
Wood, T. S.; Garaud, P.; Stellmach, S.
2013-05-10
Regions of stellar and planetary interiors that are unstable according to the Schwarzschild criterion, but stable according to the Ledoux criterion, are subject to a form of oscillatory double-diffusive (ODD) convection often called ''semi-convection''. In this series of papers, we use an extensive suite of three-dimensional (3D) numerical simulations to quantify the transport of heat and composition by ODD convection, and ultimately propose a new 1D prescription that can be used in stellar and planetary structure and evolution models. The first paper in this series demonstrated that under certain conditions ODD convection spontaneously transitions from an initial homogeneous state of weak wave-breaking turbulence into a staircase of fully convective layers, which results in a substantial increase in the transport of heat and composition. Here, we present simulations of ODD convection in this layered regime, we describe the dynamical behavior of the layers, and we derive empirical scaling laws for the transport through layered convection.
NASA Technical Reports Server (NTRS)
Bune, Andris V.; Gillies, Donald C.; Lehoczky, Sandor L.
1998-01-01
Numerical simulation of the HgCdTe growth by the vertical Bridgman method was performed using FIDAP finite element code. Double-diffusive melt convection is analyzed, as the primary factor at controls inhomogeneity of the solidified material. Temperature and concentration fields in the model are also coupled via material properties, such as thermal and solutal expansion coefficients with the dependence on both temperature and concentration, and melting temperature evaluation from pseudobinary CdTe-HgTe phase diagram. Experimental measurements were used to obtain temperature boundary conditions. Parametric study of the melt convection dependence on the gravity conditions was undertaken. It was found, that the maximum convection velocity in the melt can be reduced under certain conditions. Optimal conditions to obtain a near flat solidified interface are discussed. The predicted interface shape is in agreement with one obtained experimentally by quenching. The results of 3-D calculations are compared with previous 2- D findings. A video film featuring 3-D melt convection will be presented.
Farhadi, Rozita; Farhadi, Bita
2014-01-01
Power transistors, such as the vertical, double-diffused, metal-oxide semiconductor (VDMOS), are used extensively in the amplifier circuits of medical devices. The aim of this research was to construct a VDMOS power transistor with an optimized structure to enhance the operation of medical devices. First, boron was implanted in silicon by implanting unclamped inductive switching (UIS) and a Faraday shield. The Faraday shield was implanted in order to replace the gate-field parasitic capacitor on the entry part of the device. Also, implanting the UIS was used in order to decrease the effect of parasitic bipolar junction transistor (BJT) of the VDMOS power transistor. The research tool used in this study was Silvaco software. By decreasing the transistor entry resistance in the optimized VDMOS structure, power losses and noise at the entry of the transistor were decreased, and, by increasing the breakdown voltage, the lifetime of the VDMOS transistor lifetime was increased, which resulted in increasing drain flow and decreasing Ron. This consequently resulted in enhancing the operation of high-frequency medical devices that use transistors, such as Radio Frequency (RF) and electrocardiograph machines. PMID:25763152
Farhadi, Rozita; Farhadi, Bita
2014-01-01
Power transistors, such as the vertical, double-diffused, metal-oxide semiconductor (VDMOS), are used extensively in the amplifier circuits of medical devices. The aim of this research was to construct a VDMOS power transistor with an optimized structure to enhance the operation of medical devices. First, boron was implanted in silicon by implanting unclamped inductive switching (UIS) and a Faraday shield. The Faraday shield was implanted in order to replace the gate-field parasitic capacitor on the entry part of the device. Also, implanting the UIS was used in order to decrease the effect of parasitic bipolar junction transistor (BJT) of the VDMOS power transistor. The research tool used in this study was Silvaco software. By decreasing the transistor entry resistance in the optimized VDMOS structure, power losses and noise at the entry of the transistor were decreased, and, by increasing the breakdown voltage, the lifetime of the VDMOS transistor lifetime was increased, which resulted in increasing drain flow and decreasing Ron. This consequently resulted in enhancing the operation of high-frequency medical devices that use transistors, such as Radio Frequency (RF) and electrocardiograph machines.
NASA Astrophysics Data System (ADS)
Na, Kyoung-Il; Kah, Dong-Ha; Kim, Sang-Gi; Koo, Jin-Gun; Kim, Jongdae; Yang, Yil-Suk; Lee, Jin-Ho
2012-05-01
The vertical power metal-oxide semiconductor field-effect transistors (MOSFETs) with deep trench structures are the most promising candidates to overcome the trade-off relationship between the ON-resistance (R ON ) and the blocking voltage (BV DS ). Especially, 100 V/100 A rated trench power MOSFETs are used in components of many power systems, such as motors and LED lighting drive ICs, DC-DC converters in electric vehicles, and so on. In this work, we studied variations of the electrical characteristics, such as threshold voltage (V TH ), BV DS , and drain current drivability, with p-well doping concentration via the SILVACO simulator. From simulation results, we found the BV DS and the drain current (I D ) as functions of the p-well doping concentration at an ion implantation energy of 80 keV. With increasing of p-well doping concentration in the guard ring region, both V TH and BV DS slowly increased, but I D decreased, because the boron lateral diffusion during the fabrication process below gate trench region affected the doping concentration of the p-body at the active region. Additionally, 100 V/100 A rated trench double-diffused MOSFETs (TDMOSFETs) with meshes and stripes were successfully developed by using a silicon deep etching process. The variations in the electrical properties, such as V TH , BV DS , and drain current drivability, of the two different kinds of fabricated devices, with cell design and density in TDMOSFETs were also studied. The BV DS and the V TH in the stripe-type TDMOSFET were 110 and 3 V, respectively. However, the V TH of mesh-type device was smaller 0.5 V than that of stripe-type because of corner effect. The BV DS improved about 20 V compared to stripe-type TDMOSFET due to edge termination, and the maximum drain current (I D.MAX ) was improved by about 10% due to an increase in the gate width at the same chip size. These effects were reflected in devices with different cell densities. When the cell density was increased, however
Aydogan, Ebru; Comoglu, Tansel; Pehlivanoglu, Bilge; Dogan, Murat; Comoglu, Selcuk; Dogan, Aysegul; Basci, Nursabah
2015-01-01
Pregabalin is an anticonvulsant drug used for neuropathic pain and as an adjunct therapy for partial seizures with or without secondary generalization in adults. In conventional therapy recommended dose for pregabalin is 75 mg twice daily or 50 mg three times a day, with maximum dosage of 600 mg/d. To achieve maximum therapeutic effect with a low risk of adverse effects and to reduce often drug dosing, modified release preparations; such as microspheres might be helpful. However, most of the microencapsulation techniques have been used for lipophilic drugs, since hydrophilic drugs like pregabalin, showed low-loading efficiency and rapid dissolution of compounds into the aqueous continous phase. The purpose of this study was to improve loading efficiency of a water-soluble drug and modulate release profiles, and to test the efficiency of the prepared microspheres with the help of animal modeling studies. Pregabalin is a water soluble drug, and it was encapsulated within anionic acrylic resin (Eudragit S 100) microspheres by water in oil in oil (w/o/o) double emulsion solvent diffusion method. Dichloromethane and corn oil were chosen primary and secondary oil phases, respectively. The presence of internal water phase was necessary to form stable emulsion droplets and it accelerated the hardening of microspheres. Tween 80 and Span 80 were used as surfactants to stabilize the water and corn oil phases, respectively. The optimum concentration of Tween 80 was 0.25% (v/v) and Span 80 was 0.02% (v/v). The volume of the continous phase was affected the size of the microspheres. As the volume of the continous phase increased, the size of microspheres decreased. All microsphere formulations were evaluated with the help of in vitro characterization parameters. Microsphere formulations (P1-P5) exhibited entrapment efficiency ranged between 57.00 ± 0.72 and 69.70 ± 0.49%; yield ranged between 80.95 ± 1.21 and 93.05 ± 1.42%; and mean particle size were
NASA Astrophysics Data System (ADS)
Da, Ma; Xiao-Rong, Luo; Jie, Wei; Qiao, Tan; Kun, Zhou; Jun-Feng, Wu
2016-04-01
A new ultra-low specific on-resistance (R on,sp) vertical double diffusion metal-oxide-semiconductor field-effect transistor (VDMOS) with continuous electron accumulation (CEA) layer, denoted as CEA-VDMOS, is proposed and its new current transport mechanism is investigated. It features a trench gate directly extended to the drain, which includes two PN junctions. In on-state, the electron accumulation layers are formed along the sides of the extended gate and introduce two continuous low-resistance current paths from the source to the drain in a cell pitch. This mechanism not only dramatically reduces the R on,sp but also makes the R on,sp almost independent of the n-pillar doping concentration (N n). In off-state, the depletion between the n-pillar and p-pillar within the extended trench gate increases the N n, and further reduces the R on,sp. Especially, the two PN junctions within the trench gate support a high gate-drain voltage in the off-state and on-state, respectively. However, the extended gate increases the gate capacitance and thus weakens the dynamic performance to some extent. Therefore, the CEA-VDMOS is more suitable for low and medium frequencies application. Simulation indicates that the CEA-VDMOS reduces the R on,sp by 80% compared with the conventional super-junction VDMOS (CSJ-VDMOS) at the same high breakdown voltage (BV). Project supported by the National Natural Science Foundation of China (Grant Nos. 61176069 and 61376079) and the Fundamental Research Funds for the Central Universities, China (Grant No. ZYGX2014Z006).
Ambipolar diffusion in complex plasma.
Losseva, T V; Popel, S I; Yu, M Y; Ma, J X
2007-04-01
A self-consistent model of the ambipolar diffusion of electrons and ions in complex (dusty) plasmas accounting for the local electric fields, the dust grain charging process, and the interaction of the plasma particles with the dust grains and neutrals is presented. The dependence of the diffusion coefficient on the interaction of the electrons and ions with the dust grains as well as with the neutrals are investigated. It is shown that increase of the dust density leads to a reduction of the diffusion scale length, and this effect is enhanced at higher electron densities. The dependence of the diffusion scale length on the neutral gas pressure is found to be given by a power law, where the absolute value of the power exponent decreases with increase of the dust density. The electric field gradient and its effects are shown to be significant and should thus be taken into account in studies of complex plasmas with not very small dust densities. The possibility of observing localized coherent dissipative nonlinear dust ion-acoustic structures in an asymmetrically discharged double plasma is discussed.
Testo, Natalia; Olson, Luke C; Subramaniyam, Shivakumar; Hanson, Ty; Magro, Cynthia M
2016-10-01
Aggressive extracutaneous B-cell lymphomas span the various stages of B-cell ontogeny and include B-cell lymphoblastic lymphoma, Burkitt lymphoma, mantle cell lymphoma, and diffuse large B-cell lymphoma. Diffuse large B-cell lymphomas represent the most common histologic subtype of non-Hodgkin lymphomas, comprising 30% of adult non-Hodgkin lymphomas in the United States. A distinctive form of diffuse large B-cell lymphoma is the double-hit lymphoma, with most cases exhibiting a combined MYC and BCL2 rearrangement, leading some hematopathologists to propose the term MYC/BCL2 lymphoma. More recently, MYC rearrangement with multiple copies/gain of BCL2 or multiple copies/gain of MYC with a BCL2 rearrangement have been described and exhibit a very similar clinical course to conventional double-hit lymphomas. We report the seventh case of diffuse large B-cell lymphoma exhibiting this distinct cytogenetic abnormality and the first reported case in the skin. The patient's clinical course was aggressive, succumbing to disease 18 months after his initial presentation.
Annan, Kodwo
2012-01-01
The efficiency of a high-flux dialyzer in terms of buffering and toxic solute removal largely depends on the ability to use convection-diffusion mechanism inside the membrane. A two-dimensional transient convection-diffusion model coupled with acid-base correction term was developed. A finite volume technique was used to discretize the model and to numerically simulate it using MATLAB software tool. We observed that small solute concentration gradients peaked and were large enough to activate solute diffusion process in the membrane. While CO(2) concentration gradients diminished from their maxima and shifted toward the end of the membrane, HCO(3)(-) concentration gradients peaked at the same position. Also, CO(2) concentration decreased rapidly within the first 47 minutes while optimal HCO(3)(-) concentration was achieved within 30 minutes of the therapy. Abnormally high diffusion fluxes were observed near the blood-membrane interface that increased diffusion driving force and enhanced the overall diffusive process. While convective flux dominated total flux during the dialysis session, there was a continuous interference between convection and diffusion fluxes that call for the need to seek minimal interference between these two mechanisms. This is critical for the effective design and operation of high-flux dialyzers.
Annan, Kodwo
2012-01-01
The efficiency of a high-flux dialyzer in terms of buffering and toxic solute removal largely depends on the ability to use convection-diffusion mechanism inside the membrane. A two-dimensional transient convection-diffusion model coupled with acid-base correction term was developed. A finite volume technique was used to discretize the model and to numerically simulate it using MATLAB software tool. We observed that small solute concentration gradients peaked and were large enough to activate solute diffusion process in the membrane. While CO2 concentration gradients diminished from their maxima and shifted toward the end of the membrane, HCO3 − concentration gradients peaked at the same position. Also, CO2 concentration decreased rapidly within the first 47 minutes while optimal HCO3 − concentration was achieved within 30 minutes of the therapy. Abnormally high diffusion fluxes were observed near the blood-membrane interface that increased diffusion driving force and enhanced the overall diffusive process. While convective flux dominated total flux during the dialysis session, there was a continuous interference between convection and diffusion fluxes that call for the need to seek minimal interference between these two mechanisms. This is critical for the effective design and operation of high-flux dialyzers. PMID:23197994
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.
Lee, Jaehoon; Wilczek, Frank
2013-11-27
Motivated by the problem of identifying Majorana mode operators at junctions, we analyze a basic algebraic structure leading to a doubled spectrum. For general (nonlinear) interactions the emergent mode creation operator is highly nonlinear in the original effective mode operators, and therefore also in the underlying electron creation and destruction operators. This phenomenon could open up new possibilities for controlled dynamical manipulation of the modes. We briefly compare and contrast related issues in the Pfaffian quantum Hall state.
Strongly nonlinear dynamics of electrolytes in large ac voltages
NASA Astrophysics Data System (ADS)
Højgaard Olesen, Laurits; Bazant, Martin Z.; Bruus, Henrik
2010-07-01
We study the response of a model microelectrochemical cell to a large ac voltage of frequency comparable to the inverse cell relaxation time. To bring out the basic physics, we consider the simplest possible model of a symmetric binary electrolyte confined between parallel-plate blocking electrodes, ignoring any transverse instability or fluid flow. We analyze the resulting one-dimensional problem by matched asymptotic expansions in the limit of thin double layers and extend previous work into the strongly nonlinear regime, which is characterized by two features—significant salt depletion in the electrolyte near the electrodes and, at very large voltage, the breakdown of the quasiequilibrium structure of the double layers. The former leads to the prediction of “ac capacitive desalination” since there is a time-averaged transfer of salt from the bulk to the double layers, via oscillating diffusion layers. The latter is associated with transient diffusion limitation, which drives the formation and collapse of space-charge layers, even in the absence of any net Faradaic current through the cell. We also predict that steric effects of finite ion sizes (going beyond dilute-solution theory) act to suppress the strongly nonlinear regime in the limit of concentrated electrolytes, ionic liquids, and molten salts. Beyond the model problem, our reduced equations for thin double layers, based on uniformly valid matched asymptotic expansions, provide a useful mathematical framework to describe additional nonlinear responses to large ac voltages, such as Faradaic reactions, electro-osmotic instabilities, and induced-charge electrokinetic phenomena.
NASA Astrophysics Data System (ADS)
Losse, F.
2005-09-01
This paper presents 262 measurements of visual binaries. They essentially come from a three years evaluation period of cheap CCD sensors coupled with either off the shelves or modified webcam electronics. The evaluation cycle and results are largely described in Bulletin n°40 de la Commission des Etoiles Doubles (Sept. 2002 - Société Astronomique de France). These devices can produce measurements as consistent as those obtained with a filar micrometer on the same 8" telescope. The most recent measurements (epoch 2004+) were obtained with an "Audine" camera shipped with a KAF400. Besides the stars visited for evaluation purpose, we present some systems of interest : 17 orbital binaries, 35 neglected systems, 15 confirmations and 2 discoveries of a third component in already known systems.
NASA Astrophysics Data System (ADS)
Phillipson-Nichols, Rebecca A.; Boyd, Patricia T.; Smale, Alan P.
2015-01-01
4U 1705-44 is a bright low mass x-ray binary (LMXB) containing a neutron star and a close, low mass companion. The Rossi X-ray Timing Explorer (RXTE) All-Sky Monitor obtained approximately 14 years of daily monitoring on 4U 1705-44 in the 2-20 keV energy range. Understanding the x-ray variability of 4U1705-44 is critical to the study of all low mass x-ray binaries because they share many of the same global characteristics in their high-amplitude transitions and non-periodic variability. After comparing the longterm light curve and phase space trajectories of 4U1705-44 to various nonlinear oscillators, the Duffing Oscillator was revealed to be a strong candidate to describe these systems. The parameters of the Duffing equation were optimized and six solutions sharing the same characteristics as 4U1705-44 were found. Striking commonalities were revealed via a phase-space analysis of both 4U1705-44 and the six Duffing solutions: the low-order driving period is no less than 87 days and spans up to 180 days, which is seenand highlighted in the power spectra, zero-crossings and close returns analysis of4U1705-44. Furthermore, the driving frequency of all six Duffing solutions tend toconverge to a range of 3.6 - 4.5, corresponding to driving periods in the range from 130 to 175 days, in agreement with that found in 4U1705-44. Nonlinear analysis methods such as close returns and zero-crossings of the Duffing solutions also show the same trends. This strongly suggests that 4U1705-44 shares the same topological characteristics as the Duffing equation. With further analysis, we hope to develop a model to explain why 4U1705-44 shares the unique topology of the Duffing Oscillator specifically, rather than those of other families of nonlinear differential equations.
Nonlinear Ultrasonic Phased Array Imaging
NASA Astrophysics Data System (ADS)
Potter, J. N.; Croxford, A. J.; Wilcox, P. D.
2014-10-01
This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging through depth.
Nonlinear ultrasonic phased array imaging.
Potter, J N; Croxford, A J; Wilcox, P D
2014-10-03
This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging through depth.
Nilsen, Gøran. J.; Thompson, Corey M.; Ehlers, Georg; Marjerrison, Casey A.; Greedan, John E.
2015-02-23
Here we investigated diffuse magnetic scattering in the highly frustrated double perovskite Ba_{2}YRuO_{6} using polarized neutrons. Consistent with previous reports, the material shows two apparent transitions at 47 and 36 K to an eventual type I face-centered-cubic magnetic ground state. The (100) magnetic reflection shows different behavior from the five other observed reflections upon heating from 1.8 K, with the former broadening well beyond the resolution limit near 36 K. Closer examination of the latter group reveals a small, but clear, increase in peak widths between 36 and 47 K, indicating that this regime is dominated by short-range spin correlations. Diffuse magnetic scattering persists above 47 K near the position of (100) to at least 200 K, consistent with strong frustration. Reverse Monte Carlo (RMC) modeling of the diffuse scattering from 45 to 200 K finds that the spin-spin correlations between nearest and next-nearest neighbors are antiferromagnetic and ferromagnetic, respectively, at temperatures near the upper ordering temperature, but both become antiferromagnetic and of similar magnitude above 100 K. The significance of this unusual crossover is discussed in light of the super-superexchange interactions between nearest and next-nearest neighbors in this material and the demands of type I order. The dimensionality of the correlations is addressed by reconstructing the scattering in the (hk0) plane using the RMC spin configurations. This indicates that one-dimensional spin correlations dominate at temperatures close to the first transition. In addition, a comparison between mean-field calculations and (hk0) scattering implies that further neighbor couplings play a significant role in the selection of the ground state. Finally, the results and interpretation are compared with those recently published for monoclinic Sr_{2}YRuO_{6}, and similarities and differences are emphasized.
Quantum Diffusion Monte Carlo Method for strong field time dependent problems
NASA Astrophysics Data System (ADS)
Kalinski, Matt
2006-05-01
We formulate the Quantum Diffusion Quantum Monte Carlo (QDMC) method for the solution of the time-dependent Schr"odinger equation for atoms in strong laser fields. Unlike for the normal diffusion Monte Carlo the wave function is represented by walkers with two kinds or colors which solve two coupled and nonlinear diffusion equations. Those diffusion equations are coupled by the potentials similar to those introduced by Shay which must be added to Schr"odingers equation to obtain classical dynamics equivalent to the quantum mechanics [1]. The potentials are calculated semi-analytically similarly to smoothing methods of smooth particle electrodynamics (SPD) with Gaussian smoothing kernels. We apply this method to strong field two electron ionization of Helium. We calculate two electron double ionization rate in full six-dimensional configuration space quantum mechanically. Comparison with classical mechanics and the low dimensional grid models is also provided. 1cm [1] D. Shay, Phys. Rev A 13, 2261 (1976)
Nonlinear phased array imaging
NASA Astrophysics Data System (ADS)
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.
Nonlinear Image Denoising Methodologies
2002-05-01
53 5.3 A Multiscale Approach to Scale-Space Analysis . . . . . . . . . . . . . . . . 53 5.4...etc. In this thesis, Our approach to denoising is first based on a controlled nonlinear stochastic random walk to achieve a scale space analysis ( as in... stochastic treatment or interpretation of the diffusion. In addition, unless a specific stopping time is known to be adequate, the resulting evolution
Nonlinear optical Galton board
Navarrete-Benlloch, C.; Perez, A.; Roldan, Eugenio
2007-06-15
We generalize the concept of optical Galton board (OGB), first proposed by Bouwmeester et al. [Phys. Rev. A 61, 013410 (2000)], by introducing the possibility of nonlinear self-phase modulation on the wave function during the walker evolution. If the original Galton board illustrates classical diffusion, the OGB, which can be understood as a grid of Landau-Zener crossings, illustrates the influence of interference on diffusion, and is closely connected with the quantum walk. Our nonlinear generalization of the OGB shows new phenomena, the most striking of which is the formation of nondispersive pulses in the field distribution (solitonlike structures). These exhibit a variety of dynamical behaviors, including ballistic motion, dynamical localization, nonelastic collisions, and chaotic behavior, in the sense that the dynamics is very sensitive to the nonlinearity strength.
Cosmic ray diffusion: Report of the Workshop in Cosmic Ray Diffusion Theory
NASA Technical Reports Server (NTRS)
Birmingham, T. J.; Jones, F. C.
1975-01-01
A workshop in cosmic ray diffusion theory was held at Goddard Space Flight Center on May 16-17, 1974. Topics discussed and summarized are: (1) cosmic ray measurements as related to diffusion theory; (2) quasi-linear theory, nonlinear theory, and computer simulation of cosmic ray pitch-angle diffusion; and (3) magnetic field fluctuation measurements as related to diffusion theory.
Gureghian, A.B.
1990-08-01
Analytical solutions based on the Laplace transforms are presented for the one-dimensional, transient, advective-dispersive transport of a reacting radionuclide through a discrete planar fracture with constant aperture subject to diffusion in the surrounding rock matrix where both regions of solute migration display residual concentrations. The dispersion-free solutions, which are of closed form, are also reported. The solution assumes that the ground-water flow regime is under steady-state and isothermal conditions and that the rock matrix is homogeneous, isotropic, and saturated with stagnant water. The verification of the solution was performed by means of related analytical solutions dealing with particular aspects of the transport problem under investigation on the one hand, and a numerical solution capable of handling the complete problem on the other. The integrals encountered in the general solution are evaluated by means of a composite Gauss-Legendre quadrature scheme. 9 refs., 8 figs., 32 tabs.
Dakhlaoui, Hassen
2015-04-07
In the present paper, the linear and nonlinear optical absorption coefficients and refractive index changes between the ground and the first excited states in double GaN/Al{sub x}Ga{sub (1−x)}N quantum wells are studied theoretically. The electronic energy levels and their corresponding wave functions are obtained by solving Schrödinger-Poisson equations self-consistently within the effective mass approximation. The obtained results show that the optical absorption coefficients and refractive index changes can be red- and blue-shifted through varying the left quantum well width and the aluminum concentration x{sub b2} of the central barrier, respectively. These structural parameters are found to present optimum values for carrying out the transition of 0.8 eV (1.55 μm). Furthermore, we show that the desired transition can also be achieved by replacing the GaN in the left quantum well with Al{sub y}Ga{sub (1−y)}N and by varying the aluminum concentration y{sub Al}. The obtained results give a new degree of freedom in optoelectronic device applications such as optical fiber telecommunications operating at (1.55 μm)
Sköldenberg, Olof; Rysinska, Agata; Chammout, Ghazi; Salemyr, Mats; Muren, Olle; Bodén, Henrik; Eisler, Thomas
2016-01-01
Introduction In vitro, Vitamin-E-diffused, highly cross-linked polyethylene (PE) has been shown to have superior wear resistance and improved mechanical properties when compared to those of standard highly cross-linked PE liners used in total hip arthroplasty (THA). The aim of the study is to evaluate the safety of a new cemented acetabular cup with Vitamin-E-doped PE regarding migration, head penetration and clinical results. Methods and analysis In this single-centre, double-blinded, randomised controlled trial, we will include 50 patients with primary hip osteoarthritis scheduled for THA and randomise them in a 1:1 ratio to a cemented cup with either argon gas-sterilised PE (control group) or Vitamin-E-diffused PE (vitamin-e group). All patients and the assessor of the primary outcome will be blinded and the same uncemented stem will be used for all participants. The primary end point will be proximal migration of the cup at 2 years after surgery measured with radiostereometry. Secondary end points include proximal migration at other follow-ups, total migration, femoral head penetration, clinical outcome scores and hip-related complications. Patients will be followed up at 3 months and at 1, 2, 5 and 10 years postoperatively. Results Results will be analysed using 95% CIs for the effect size. A regression model will also be used to adjust for stratification factors. Ethics and dissemination The ethical committee at Karolinska Institutet has approved the study. The first results from the study will be disseminated to the medical community via presentations and publications in relevant medical journals when the last patient included has been followed up for 2 years. Trial registration number NCT02254980. PMID:27388352
Zhou, Xin; Qiao, Ming; He, Yitao; Li, Zhaoji; Zhang, Bo
2015-11-16
Hot-carrier-induced linear drain current (I{sub dlin}) and threshold voltage (V{sub th}) degradations for the thin layer SOI field p-channel lateral double-diffused MOS (pLDMOS) are investigated. Two competition degradation mechanisms are revealed and the hot-carrier conductance modulation model is proposed. In the channel, hot-hole injection induced positive oxide trapped charge and interface trap gives rise to the V{sub th} increasing and the channel conductance (G{sub ch}) decreasing, then reduces I{sub dlin}. In the p-drift region, hot-electron injection induced negative oxide trapped charge enhances the conductance of drift doping resistance (G{sub d}), and then increases I{sub dlin}. Consequently, the eventual I{sub dlin} degradation is controlled by the competition of the two mechanisms due to conductance modulation in the both regions. Based on the model, it is explained that the measured I{sub dlin} anomalously increases while the V{sub th} is increasing with power law. The thin layer field pLDMOS exhibits more severe V{sub th} instability compared with thick SOI layer structure; as a result, it should be seriously evaluated in actual application in switching circuit.
Fayad, Luis; Ansell, Stephen M; Advani, Ranjana; Coiffier, Bertrand; Stuart, Robert; Bartlett, Nancy L; Forero-Torres, Andres; Kuliczkowski, Kazimierz; Belada, David; Ng, Edmund; Drachman, Jonathan G
2015-01-01
Single-agent dacetuzumab has demonstrated antitumor activity in relapsed/refractory diffuse large B-cell lymphoma (DLBCL). Preclinical data demonstrated improved dacetuzumab antitumor activity in combination with rituximab, ± chemotherapy. We designed a phase 2b, double-blind, placebo-controlled trial to compare rituximab, ifosfamide, carboplatin and etoposide (R-ICE) + dacetuzumab with R-ICE + placebo in patients with DLBCL who relapsed after rituximab, cyclophosphamide, doxorubicin, vincristine and prednisolone (R-CHOP) (ClinicalTrials.gov #NCT00529503). The primary endpoint was complete response (CR); additional endpoints included failure-free survival and overall survival (OS). Overall, 151 patients were randomized (75 dacetuzumab, 76 placebo). No notable differences between arms in demographics or subsequent treatment parameters were observed. Cytopenias, cough and infection were more frequent with dacetuzumab. Futility analysis failed to demonstrate higher CR rates with dacetuzumab (36% dacetuzumab, 42% placebo); consequently, enrollment was stopped. Unplanned post hoc analysis showed that patients who underwent subsequent autologous stem cell transplant experienced improvement in OS (hazard ratio = 0.195, p = 0.004), which may be explained by potential immunomodulatory effects of dacetuzumab on antigen-presenting cells.
Diffusion Influenced Adsorption Kinetics.
Miura, Toshiaki; Seki, Kazuhiko
2015-08-27
When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir-Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the Langmuir-Hinshelwood adsorption equation leads to the nonlinear integro-differential equation for the surface coverage. In this paper, we solved the nonlinear integro-differential equation using the Grünwald-Letnikov formula developed to solve fractional kinetics. Guided by the numerical results, analytical expressions for the upper and lower bounds of the exact numerical results were obtained. The upper and lower bounds were close to the exact numerical results in the diffusion- and reaction-controlled limits, respectively. We examined the validity of the two simple analytical expressions obtained in the diffusion-controlled limit. The results were generalized to include the effect of dispersive diffusion. We also investigated the effect of molecular rearrangement of anisotropic molecules on surface coverage.
Nonlinear Landau damping in the ionosphere
NASA Technical Reports Server (NTRS)
Kiwamoto, Y.; Benson, R. F.
1978-01-01
A model is presented to explain the non-resonant waves which give rise to the diffuse resonance observed near 3/2 f sub H by the Alouette and ISIS topside sounders, where f sub H is the ambient electron cyclotron frequency. In a strictly linear analysis, these instability driven waves will decay due to Landau damping on a time scale much shorter than the observed time duration of the diffuse resonance. Calculations of the nonlinear wave particle coupling coefficients, however, indicate that the diffuse resonance wave can be maintained by the nonlinear Landau damping of the sounder stimulated 2f sub H wave. The time duration of the diffuse resonance is determined by the transit time of the instability generated and nonlinearly maintained diffuse resonance wave from the remote short lived hot region back to the antenna. The model is consistent with the Alouette/ISIS observations, and clearly demonstrates the existence of nonlinear wave-particle interactions in the ionosphere.
Double layers and double wells in arbitrary degenerate plasmas
NASA Astrophysics Data System (ADS)
Akbari-Moghanjoughi, M.
2016-06-01
Using the generalized hydrodynamic model, the possibility of variety of large amplitude nonlinear excitations is examined in electron-ion plasma with arbitrary electron degeneracy considering also the ion temperature effect. A new energy-density relation is proposed for plasmas with arbitrary electron degeneracy which reduces to the classical Boltzmann and quantum Thomas-Fermi counterparts in the extreme limits. The pseudopotential method is employed to find the criteria for existence of nonlinear structures such as solitons, periodic nonlinear structures, and double-layers for different cases of adiabatic and isothermal ion fluids for a whole range of normalized electron chemical potential, η0, ranging from dilute classical to completely degenerate electron fluids. It is observed that there is a Mach-speed gap in which no large amplitude localized or periodic nonlinear excitations can propagate in the plasma under consideration. It is further revealed that the plasma under investigation supports propagation of double-wells and double-layers the chemical potential and Mach number ranges of which are studied in terms of other plasma parameters. The Mach number criteria for nonlinear waves are shown to significantly differ for cases of classical with η0 < 0 and quantum with η0 > 0 regimes. It is also shown that the localized structure propagation criteria possess significant dissimilarities for plasmas with adiabatic and isothermal ions. Current research may be generalized to study the nonlinear structures in plasma containing positrons, multiple ions with different charge states, and charged dust grains.
1989-06-15
following surprising situation. Namely associated with the integrable nonlinear Schrodinger equations are standard numerical schemes which exhibit at...36. An Initial Boundary Value Problem for the Nonlinear Schrodinger Equations , A.S. Fokas, Physica D March 1989. 37. Evolution Theory, Periodic... gravity waves and wave excitation phenomena related to moving pressure distributions; numerical approximation and computation; nonlinear optics; and
Equilibrium Transport in Double-Diffusive Convection
2011-06-01
continue to make the U.S. Navy my career . I love you all! To Arabella and Kerrigan, Daddy loves you both with all his heart. Thank you for being... astrophysical fluid systems, from magmatic melts (Tait and Jaupart 1989) to the interiors of giant planets and stars (Guillot 1999; Vauclair 2004...Chapter V, we also explore a broader parameter range, including the low Prandtl number regime, relevant for astrophysical applications, and high
Fluid dynamics of double diffusive systems
Koseff, J.R.
1990-04-03
The major accomplishments of our initial research period (August 1, 1987, to March 1, 1990) are as follows; we completed construction of the experimental facility. Originally, it had been our intent to modify an existing facility in our laboratory. When this became impractical we constructed a new stand-alone facility. Modified an existing three-dimensional numerical code developed in our laboratory, SEAFLOS1, by incorporating a salinity transport equation. Developed experimental and analytical techniques, and performed both physical and numerical experiments for a wide range of initial and boundary conditions. Focused our overall research effort to answer the following four questions pertaining to the formation of convective intrusions due to lateral temperature gradients established by sidewall heating. (1) What is the internal structure of the convective intrusions as a function of the initial stratification and sidewall heating rates (2) What is the correct scaling for the initial vertical dimension of the intrusions (3) How does the merging process vary as a function of initial stratification and sidewall heating rate (4) Is the sidewall heating critical for continued propagation of the intrusions, or is it merely a trigger which releases the internal instability in the fluid
NASA Astrophysics Data System (ADS)
Geniet, F.; Leon, J.
2003-05-01
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.
Anomalous Diffusion Mediated by Atom Deposition into a Porous Substrate
Brault, Pascal; Bauchire, Jean-Marc; Josserand, Christophe; Caillard, Amaeel; Charles, Christine; Boswell, Rod W.
2009-01-30
Constant flux atom deposition into a porous medium is shown to generate a dense overlayer and a diffusion profile. Scaling analysis shows that the overlayer acts as a dynamic control for atomic diffusion in the porous substrate. This is modeled by generalizing the porous diffusion equation with a time-dependent diffusion coefficient equivalent to a nonlinear rescaling of time.
NASA Astrophysics Data System (ADS)
Fukuyama, Hidenao
Recent advances of magnetic resonance imaging have been described, especially stressed on the diffusion sequences. We have recently applied the diffusion sequence to functional brain imaging, and found the appropriate results. In addition to the neurosciences fields, diffusion weighted images have improved the accuracies of clinical diagnosis depending upon magnetic resonance images in stroke as well as inflammations.
Chang, Y T; Huang, Y P; Su, K W; Chen, Y F
2008-12-08
The effective focal lengths of thermal lens in diode-end-pumped continuous-wave Nd:YVO(4) lasers for the (4)F(3/2)-->(4)I(11/2) and (4)F(3/2)-->(4)I(13/2) transitions were determined. The experimental results revealed that the thermal lensing effect for the (4)F(3/2)-->(4)I(11/2) transition can be sufficiently improved by employing a single-end diffusion-bonded Nd:YVO(4) crystal replacing a conventional Nd:YVO(4) crystal. However, using a double-end diffusion-bonded Nd:YVO(4) crystal was a great improvement over a single-end diffusion-bonded Nd:YVO(4) crystal for the (4)F(3/2)-->(4)I(13/2) transition with stronger thermal lensing effect.
Advanced manufacturing: Technology diffusion
Tesar, A.
1995-12-01
In this paper we examine how manufacturing technology diffuses rom the developers of technology across national borders to those who do not have the capability or resources to develop advanced technology on their own. None of the wide variety of technology diffusion mechanisms discussed in this paper are new, yet the opportunities to apply these mechanisms are growing. A dramatic increase in technology diffusion occurred over the last decade. The two major trends which probably drive this increase are a worldwide inclination towards ``freer`` markets and diminishing isolation. Technology is most rapidly diffusing from the US In fact, the US is supplying technology for the rest of the world. The value of the technology supplied by the US more than doubled from 1985 to 1992 (see the Introduction for details). History shows us that technology diffusion is inevitable. It is the rates at which technologies diffuse to other countries which can vary considerably. Manufacturers in these countries are increasingly able to absorb technology. Their manufacturing efficiency is expected to progress as technology becomes increasingly available and utilized.
Theory of nonmonotonic double layers
Kim, K.Y.
1987-12-01
A simple graphic method of solving the Vlasov--Poisson system associated with nonlinear eigenvalue conditions for arbitrary potential structures is presented. A general analytic formulation for nonmonotonic double layers is presented and illustrated with some particular closed form solutions. This class of double layers satisfies the time stationary Vlasov--Poisson system while requiring a Sagdeev potential, which is a double-valued function of the physical potential. It follows that any distribution function having a density representation as any integer or noninteger power series of potential can never satisfy the nonmonotonic double-layer boundary conditions. A Korteweg--de Vries-like equation is found showing a relationship among the speed of the nonmonotonic double layer, its scale length, and its degree of asymmetry.
NASA Technical Reports Server (NTRS)
Yang, T.-T.; Nelson, C. D.
1979-01-01
Contoured wall diffusers are designed by using an inverse method. The prescribed wall velocity distribution(s) was taken from the high lift airfoil designed by A. A. Griffith in 1938; therefore, such diffusers are named Griffith diffusers. First the formulation of the inverse problem and the method of solution are outlined. Then the typical contour of a two-dimensional diffuser and velocity distributions across the flow channel at various stations are presented. For a Griffith diffuser to operate as it is designed, boundary layer suction is necessary. Discussion of the percentage of through-flow required to be removed for the purpose of boundary layer control is given. Finally, reference is made to the latest version of a computer program for a two-dimensional diffuser requiring only area ratio, nondimensional length and suction percentage as inputs.
NASA Astrophysics Data System (ADS)
Horne, Richard B.; Kersten, Tobias; Glauert, Sarah A.; Meredith, Nigel P.; Boscher, Daniel; Sicard, Angelica; Maget, Vincent
2013-04-01
Whistler mode chorus waves play a major role in the loss and acceleration of electrons in the Earth's radiation belts. While high time resolution satellite data show that these waves are highly structured in frequency and time, at present their effects on the electron distribution can only be assessed on a global scale by using quasi-linear diffusion theory. Here we present new quasi-linear diffusion coefficients for upper and lower band chorus waves for use in global radiation belt models. Using data from DE 1 CRRES, Cluster 1, Double Star TC1 and THEMIS, we have constructed a database of wave properties and used this to construct new diffusion coefficients for L* = 1.5 to 10 in steps of 0.5, 10 latitude bins between 0o and 60o ,8 bins in MLT and 5 levels of geomagnetic activity as measured by Kp. We find that the peak frequency of lower band chorus is close to 0.2 fce, which is lower than that used in previous models. The combined upper and lower band chorus diffusion shows structure that should result in an energy dependent pitch angle anisotropy, particularly between 1 keV and 100 keV. The diffusion rates suggest that wave-particle interactions should still be very important outside geostationary orbit, out to at least L* = 8. We find significant energy diffusion near 1 keV near the loss cone, consistent with wave growth. By including the new chorus diffusion matrix into the BAS radiation belt (BRB) model we compare the effects on the evolution of the radiation belts against previous models.
Nonlinear differential equations
Dresner, L.
1988-01-01
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.
Ammonia diffusion through Nalophan™ bags.
Sironi, Selena; Eusebio, Lidia; Dentoni, Licinia; Capelli, Laura; Del Rosso, Renato
2014-01-01
The aim of the work is to verify the diffusion rate of ammonia through the Nalophan™ film that constitutes the sampling bag, considering storage times ranging from 1 to 26 h. The ammonia decay over time was evaluated using gas-chromatography for the quantification of ammonia concentration inside the bag. The research assesses the roles of both of ammonia and water concentration gradients at the polymeric film interface on the diffusion process. The results show that both the ammonia concentration gradient and, in a less pronounced way, the water concentration gradient are the main 'engines' of ammonia diffusion. Double bags seem to represent a simple solution for preventing ammonia losses during storage. Another interesting result concerns the role of the bag surface on the ammonia diffusion rate: the higher the surface/volume (S/V) ratio, the higher the ammonia diffusion rate through the polymeric film.
Tunable infrared generation with diffusion-bonded-stacked gallium arsenide
NASA Astrophysics Data System (ADS)
Zheng, Dong
Mid-infrared (MIR) radiation finds increasing applications in remote sensing, spectroscopy and military counter-measures. Nonlinear optical interactions provide one approach to tunable MIR sources generation. The development of MIR nonlinear optical crystals with excellent performance at a reasonable cost is essential for applications. Diffusion-bonded-stacked (DBS) GaAs periodic structures are a new family of quasi-phasematched (QPM) nonlinear optical crystals. The bonding process preserves the optical and mechanical properties of the bulk material, while the periodic modulation of the nonlinear coefficient permits QPM interactions. DBS GaAs bonding requirements, such as number of bonded layers and tolerable optical loss, are discussed. Nonlinear optical properties like mixing gain, wavelength, temperature and angular acceptance of the bonded structure, are predicted. DBS GaAs devices with up to 50 layers were bonded and characterized. Optical loss from interfacial voids and gaps at shorter wavelengths, from processing induced p- type free carrier absorption at longer wavelengths was characterized. 'Lithographic dicing' was invented and demonstrated as a replacement for mechanical dicing, resulting in the capability to handle thin wafers and cleaner interfaces for better bonding. Absorption due to semi-insulating-to-p-type conversion, a bulk crystal loss mechanism, was found to be induced by high bonding temperatures, and dependent on wafer sources and materials in contact with the stack. Optimized bonding parameters reduced the optical loss of 36-layer DBS GaAs to less than 0.2 cm-1 at long wavelengths. Tunable 15.6 to 17.6 μm coherent radiation at 90-ps pulse width was generated by difference frequency mixing in a 24-layer DBS GaAs device. The wavelength tuning curve agreed with theoretical predictions demonstrating that the bonding process maintained nonlinear optical phasematching over the 6 mm interaction length. Maximum mixing gain of 0.7%, or 5% internal
Nonlinear waves: Dynamics and evolution
NASA Astrophysics Data System (ADS)
Gaponov-Grekhov, A. V.; Rabinovich, M. I.
Papers on nonlinear waves are presented, covering topics such as the history of studies on nonlinear dynamics since Poincare, attractors, pattern formation and the dynamics of two-dimensional structures in nonequilibirum dissipative media, the onset of spatial chaos in one-dimensional systems, and self-organization phenomena in laser thermochemistry. Additional topics include criteria for the existence of moving structures in two-component reaction-diffusion systems, space-time structures in optoelectronic devices, stimulated scattering and surface structures, and distributed wave collapse in the nonlinear Schroedinger equation. Consideration is also given to dimensions and entropies in multidimensional systems, measurement methods for correlation dimensions, quantum localization and dynamic chaos, self-organization in bacterial cells and populations, nonlinear phenomena in condensed matter, and the origin and evolutionary dynamics of Uranian rings.
The Non-linear Saturation of the Goldreich-Schubert-Fricke Instability
NASA Astrophysics Data System (ADS)
Oishi, Jeffrey; Burns, Keaton; Brown, Ben; Lecoanet, Daniel; Vasil, Geoffrey
2015-11-01
The Goldreich-Schubert-Fricke (GSF) instability is an important process in stellar interiors and possibly in exoplanetary atmospheres. While the linear phase of the instability has been explored for nearly fifty years, its non-linear saturation has not been explored in detail. The GSF is a double-diffusive instability in which Rayleigh unstable perturbations are robbed of buoyant stability by thermal diffusion. Here, we will present results from a suite of direct numerical simulations using the Spiegel-Veronis Boussinesq equations in the Dedalus framework. These DNS are designed to explore the behavior of the GSF over a range of Prandtl numbers. In stellar interiors, Pr ~=10-6 , but we are limited by computational resources to much higher values, so instead we will discuss the Pr scaling of transport and mixing. We will also discuss the impact of the Boussinesq approximation in the case where large aspect ration perturbations exceed a scale height.
Nonlinear optical protection against frequency agile lasers
McDowell, V.P.
1988-08-04
An eye-protection or equipment-filter device for protection from laser energy is disclosed. The device may be in the form of a telescope, binoculars, goggles, constructed as part of equipment such as image intensifiers or range designators. Optical elements focus the waist of the beam within a nonlinear frequency-doubling crystal or nonlinear optical element or fiber. The nonlinear elements produce a harmonic outside the visible spectrum in the case of crystals, or absorb the laser energy in the case of nonlinear fibers. Embodiments include protectors for the human eye as well as filters for sensitive machinery such as TV cameras, FLIR systems or other imaging equipment.
NASA Technical Reports Server (NTRS)
Nicolet, M. A.
1983-01-01
The choice of the metallic film for the contact to a semiconductor device is discussed. One way to try to stabilize a contact is by interposing a thin film of a material that has low diffusivity for the atoms in question. This thin film application is known as a diffusion barrier. Three types of barriers can be distinguished. The stuffed barrier derives its low atomic diffusivity to impurities that concentrate along the extended defects of a polycrystalline layer. Sacrificial barriers exploit the fact that some (elemental) thin films react in a laterally uniform and reproducible fashion. Sacrificial barriers have the advantage that the point of their failure is predictable. Passive barriers are those most closely approximating an ideal barrier. The most-studied case is that of sputtered TiN films. Stuffed barriers may be viewed as passive barriers whose low diffusivity material extends along the defects of the polycrystalline host.
NASA Technical Reports Server (NTRS)
1981-01-01
A diffuse celestial radiation which is isotropic at least on a course scale were measured from the soft X-ray region to about 150 MeV, at which energy the intensity falls below that of the galactic emission for most galactic latitudes. The spectral shape, the intensity, and the established degree of isotropy of this diffuse radiation already place severe constraints on the possible explanations for this radiation. Among the extragalactic theories, the more promising explanations of the isotropic diffuse emission appear to be radiation from exceptional galaxies from matter antimatter annihilation at the boundaries of superclusters of galaxies of matter and antimatter in baryon symmetric big bang models. Other possible sources for extragalactic diffuse gamma radiation are discussed and include normal galaxies, clusters of galaxies, primordial cosmic rays interacting with intergalactic matter, primordial black holes, and cosmic ray leakage from galaxies.
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.
Motté, G; Dinanian, S; Sebag, C; Drieu, L; Slama, M
1995-12-01
Double response is a rare electrocardiographic phenomenon requiring two atrioventricular conduction pathways with very different electrophysiological properties. Double ventricular responses are the usual manifestation: an atrial depolarisation (spontaneous or provoked, anticipated or not) is followed by a first ventricular response dependent on an accessory pathway or a rapid nodal pathway and then a second response resulting from sufficiently delayed transmission through a nodal pathway for the ventricles to have recovered their excitability when the second wave of activation reaches them. A simple curiosity when isolated and occurring under unusual conditions, particularly during electrophysiological investigation of the Wolff-Parkinson-White syndrome, the double response may initiate symptomatic non-reentrant junctional tachycardia when associated with nodal duality and repeating from atria in sinus rhythm. The functional incapacity and resistance to antiarrhythmic therapy may require referral for ablation of the slow pathway.
NASA Astrophysics Data System (ADS)
Pan, Shoukui; Okano, Y.; Tsunekawa, S.; Fukuda, T.
1993-03-01
The Kyropoulus method was used to grow nonlinear optical organic crystals ABP (4-aminobenzophenone). The crystals were characterized by nonlinear optical measurements and had a large effect of frequency doubling.
Weakly nonlinear electrophoresis of a highly charged colloidal particle
NASA Astrophysics Data System (ADS)
Schnitzer, Ory; Zeyde, Roman; Yavneh, Irad; Yariv, Ehud
2013-05-01
At large zeta potentials, surface conduction becomes appreciable in thin-double-layer electrokinetic transport. In the linear weak-field regime, where this effect is quantified by the Dukhin number, it is manifested in non-Smoluchowski electrophoretic mobilities. In this paper we go beyond linear response, employing the recently derived macroscale model of Schnitzer and Yariv ["Macroscale description of electrokinetic flows at large zeta potentials: Nonlinear surface conduction," Phys. Rev. E 86, 021503 (2012), 10.1103/PhysRevE.86.021503] as the infrastructure for a weakly nonlinear analysis of spherical-particle electrophoresis. A straightforward perturbation in the field strength is frustrated by the failure to satisfy the far-field conditions, representing a non-uniformity of the weak-field approximation at large distances away from the particle, where salt advection becomes comparable to diffusion. This is remedied using inner-outer asymptotic expansions in the spirit of Acrivos and Taylor ["Heat and mass transfer from single spheres in Stokes flow," Phys. Fluids 5, 387 (1962), 10.1063/1.1706630], with the inner region representing the particle neighborhood and the outer region corresponding to distances scaling inversely with the field magnitude. This singular scheme furnishes an asymptotic correction to the electrophoretic velocity, proportional to the applied field cubed, which embodies a host of nonlinear mechanisms unfamiliar from linear electrokinetic theories. These include the effect of induced zeta-potential inhomogeneity, animated by concentration polarization, on electro-osmosis and diffuso-osmosis; bulk advection of salt; nonuniform bulk conductivity; Coulomb body forces acting on bulk volumetric charge; and the nonzero electrostatic force exerted upon the otherwise screened particle-layer system. A numerical solution of the macroscale model validates our weakly nonlinear analysis.
Diffusion of Ellipsoids in Bacterial Suspensions
NASA Astrophysics Data System (ADS)
Peng, Yi; Lai, Lipeng; Tai, Yi-Shu; Zhang, Kechun; Xu, Xinliang; Cheng, Xiang
2016-02-01
Active fluids such as swarming bacteria and motile colloids exhibit exotic properties different from conventional equilibrium materials. As a peculiar example, a spherical tracer immersed inside active fluids shows an enhanced translational diffusion, orders of magnitude stronger than its intrinsic Brownian motion. Here, rather than spherical tracers, we investigate the diffusion of isolated ellipsoids in a quasi-two-dimensional bacterial bath. Our study shows a nonlinear enhancement of both translational and rotational diffusions of ellipsoids. More importantly, we uncover an anomalous coupling between particles' translation and rotation that is strictly prohibited in Brownian diffusion. The coupling reveals a counterintuitive anisotropic particle diffusion, where an ellipsoid diffuses fastest along its minor axis in its body frame. Combining experiments with theoretical modeling, we show that such an anomalous diffusive behavior arises from the generic straining flow of swimming bacteria. Our work illustrates an unexpected feature of active fluids and deepens our understanding of transport processes in microbiological systems.
Quantum well nonlinear microcavities
NASA Astrophysics Data System (ADS)
Oudar, J. L.; Kuszelewicz, R.; Sfez, B.; Pellat, D.; Azoulay, R.
We report on recent progress in reducing the power threshold of all-optical bistable quantum well vertical microcavities. Significant improvements are achieved through an increase of the cavity finesse, together with a reduction of the device active layer thickness. A critical intensity of 5 μW/μm 2 has been observed on a microcavity of finesse 250, with a nonlinear medium of only 18 GaAs quantum wells of 10 nm thickness. Further improvements of the Bragg mirror quality resulted in a finesse of 700 and a power-lifetime product of 15 fJ/μm 2. Microresonator pixellation allows to obtain 2-dimensional arrays. A thermally-induced alloy-mixing technique is described, which produced a 110 meV carrier confinement energy, together with a refractive index change of -.012, averaged over the 2.6 μm nonlinear medium thickness. The resulting electrical and optical confinement is shown to improve the nonlinear characteristics, by limiting lateral carrier diffusion and light diffraction.
2010-05-27
microstructure measurements were collected by Jim Mourn with a profiling microstructure instrument, Chameleon . The contribution to scattering from...measurements were performed by Jim Mourn using the turbulence profiler Chameleon (Mourn et al., 1995). The broadband acoustic system was fully operational...community animals with implications for spinner dolphin foraging," The Journal of the Acoustical Society of America 123: 2884-2894. Au, W.W.L
1974-02-14
Wester- velt. [60] Streaming. In 1831, Michael Faraday [61] noted that currents of air were set up in the neighborhood of vibrating plates-the first... ducei in the case of a paramettc amy (from Berktay an Leahy 141). C’ "". k•, SEC 10.1 NONLINEAR ACOUSTICS 345 The principal results of their analysis
NASA Astrophysics Data System (ADS)
Kevorkian, J.
This report discusses research in the area of slowly varying nonlinear oscillatory systems. Some of the topics discussed are as follows: adiabatic invariants and transient resonance in very slowly varying Hamiltonian systems; sustained resonance in very slowly varying Hamiltonian systems; free-electron lasers with very slow wiggler taper; and bursting oscillators.
Nonlinear dynamics in cardiac conduction
NASA Technical Reports Server (NTRS)
Kaplan, D. T.; Smith, J. M.; Saxberg, B. E.; Cohen, R. J.
1988-01-01
Electrical conduction in the heart shows many phenomena familiar from nonlinear dynamics. Among these phenomena are multiple basins of attraction, phase locking, and perhaps period-doubling bifurcations and chaos. We describe a simple cellular-automation model of electrical conduction which simulates normal conduction patterns in the heart as well as a wide range of disturbances of heart rhythm. In addition, we review the application of percolation theory to the analysis of the development of complex, self-sustaining conduction patterns.
Nonlinear dynamics experiments
Fischer, W.
2011-01-01
The goal of nonlinear dynamics experiments is to improve the understanding of single particle effects that increase the particle amplitude and lead to loss. Particle motion in storage rings is nearly conservative and for transverse dynamics the Hamiltonian in action angle variables (I{sub x},I{sub y},{phi}{sub x},{phi}{sub y}) near an isolated resonance k{nu}{sub x} + l{nu}{sub y} {approx} p is H = I{sub x}{nu}{sub x0} + I{sub y}{nu}{sub y0} + g(I{sub x}, I{sub y}) + h(I{sub x}, I{sub y})cos(k{phi}{sub x} + l{phi}{sub y} - p{theta}), (1) where k, l, p are integers, {theta} = 2{pi}s/L is the azimuth, and s and L are the path length and circumference respectively. The amplitude dependent tunes are given by {nu}{sub x,y}(I{sub x},I{sub y}) = {nu}{sub x0,y0} + {partial_derivative}g(I{sub x},I{sub y})/{partial_derivative}I{sub x,y} (2) and h(I{sub x},I{sub y}) is the resonance driving term (RDT). If the motion is governed by multiple resonances, h(I{sub x},I{sub y}) has to be replace by a series of terms. The particle motion is completely determined by the terms g and h, which can be calculated from higher order multipoles (Sec. ??), or obtained from simulations. Deviations from pure Hamiltonian motion occur due to synchrotron radiation damping (Sec. ??) in lepton or very high energy hadron rings, parameter variations, and diffusion processes such as residual gas and intrabeam scattering. The time scale of the non-Hamiltonian process determines the applicability of the Hamiltonian analysis. Transverse nonlinearities are introduced through sextupoles or higher order multipoles and magnetic field errors in dipoles and quadrupoles. Sextupoles can already drive all resonances. The beam-beam interaction and space charge also introduce nonlinear fields. Intentionally introduced nonlinearities are used to extract beam on a resonance or through capture in stable islands. Localization and minimization of nonlinearities in a ring is a general strategy to decrease emittance growth
New double soft emission theorems
NASA Astrophysics Data System (ADS)
Cachazo, Freddy; He, Song; Yuan, Ellis Ye
2015-09-01
We study the behavior of the tree-level S-matrix of a variety of theories as two particles become soft. By analogy with the recently found subleading soft theorems for gravitons and gluons, we explore subleading terms in double soft emissions. We first consider double soft scalar emissions and find subleading terms that are controlled by the angular momentum operator acting on hard particles. The order of the subleading theorems depends on the presence or not of color structures. Next we obtain a compact formula for the leading term in a double soft photon emission. The theories studied are a special Galileon, Dirac-Born-Infeld, Einstein-Maxwell-Scalar, nonlinear sigma model and Yang-Mills-Scalar. We use the recently found Cachazo-He-Yuan representation of these theories in order to give a simple proof of the leading order part of all these theorems.
NASA Technical Reports Server (NTRS)
Williams, Alton C. (Editor); Moorehead, Tauna W. (Editor)
1987-01-01
Topics addressed include: laboratory double layers; ion-acoustic double layers; pumping potential wells; ion phase-space vortices; weak double layers; electric fields and double layers in plasmas; auroral double layers; double layer formation in a plasma; beamed emission from gamma-ray burst source; double layers and extragalactic jets; and electric potential between plasma sheet clouds.
Wavelength-doubling optical parametric oscillator
Armstrong, Darrell J.; Smith, Arlee V.
2007-07-24
A wavelength-doubling optical parametric oscillator (OPO) comprising a type II nonlinear optical medium for generating a pair of degenerate waves at twice a pump wavelength and a plurality of mirrors for rotating the polarization of one wave by 90 degrees to produce a wavelength-doubled beam with an increased output energy by coupling both of the degenerate waves out of the OPO cavity through the same output coupler following polarization rotation of one of the degenerate waves.
Nonlinear Optics in Negative Index Metamaterials
2012-06-05
analytical model and solutions for nonlinear wave propagation in waveguide couplers with opposite signs of the linear refractive index, non-zero phase... couplers based on either double-negative or strongly anisotropic metamaterials that are likely to enable ultra-compact optical strorage and memory...Venugopal, Zhaxylyk Kudyshev, Natalia Litchinitser. Asymmetric Positive-Negative IndexNonlinear Waveguide Couplers , IEEE Journal of Selected Topics in
Gratia, Pierre; Hu, Wayne; Joyce, Austin; Ribeiro, Raquel H.
2016-06-15
Attempts to modify gravity in the infrared typically require a screening mechanism to ensure consistency with local tests of gravity. These screening mechanisms fit into three broad classes; we investigate theories which are capable of exhibiting more than one type of screening. Specifically, we focus on a simple model which exhibits both Vainshtein and kinetic screening. We point out that due to the two characteristic length scales in the problem, the type of screening that dominates depends on the mass of the sourcing object, allowing for different phenomenology at different scales. We consider embedding this double screening phenomenology in a broader cosmological scenario and show that the simplest examples that exhibit double screening are radiatively stable.
ERIC Educational Resources Information Center
Dou, Remy; Hogan, DaNel; Kossover, Mark; Spuck, Timothy; Young, Sarah
2013-01-01
Diffusion has often been taught in science courses as one of the primary ways by which molecules travel, particularly within organisms. For years, classroom teachers have used the same common demonstrations to illustrate this concept (e.g., placing drops of food coloring in a beaker of water). Most of the time, the main contributor to the motion…
ERIC Educational Resources Information Center
Foy, Barry G.
1977-01-01
Two demonstrations are described. Materials and instructions for demonstrating movement of molecules into cytoplasm using agar blocks, phenolphthalein, and sodium hydroxide are given. A simple method for demonstrating that the rate of diffusion of a gas is inversely proportional to its molecular weight is also presented. (AJ)
Chiriac, S.; Dimitriu, D. G.; Sanduloviciu, M.
2007-07-15
Anodic double layer instabilities occur in low-temperature diffusion filament-type discharge plasma by applying a certain positive bias with respect to the plasma potential to an additional electrode. Periodic nonlinear regimes, characterized by proper dynamics of double layers, are sustained if excitation and ionization rates in front of the electrode reach the value for which current limitation effects appear in the static current-voltage characteristic. It was experimentally shown that under specific experimental conditions these ordered spatiotemporal phenomena can evolve into chaotic states by type I intermittency. This transition was verified by the evolution of time series, fast Fourier transform amplitude plots, three-dimensional reconstructed state spaces, power laws, and flickering phenomena spectrum, as well as by the return map and tangent bifurcation.
The Design and its Verification of the Double Rotor Double Cage Induction Motor
NASA Astrophysics Data System (ADS)
Sinha, Sumita; Deb, Nirmal K.; Biswas, Sujit K.
2017-02-01
The concept of a double rotor motor presented earlier and its equivalent circuit has been developed, showing a non-linear parameter content. The two rotors (which are recommended to be double cage type for development of high starting torque) can run with equal or unequal speed independently, depending on their individual loading. This paper presents the elaborate design procedure, step-by-step, for the double rotor double cage motor and verifies the designed data with that obtained from three separate tests (compared to two for conventional motor) on a prototype, such that optimum performance can be obtained from the motor.
Self-Frequency-Doubling Glass-Fiber Laser
NASA Technical Reports Server (NTRS)
Selker, Mark D.; Dallas, Joseph L.
1993-01-01
Specially prepared germanium and phosphorous-doped glass optical fiber doped with neodymium shown to act as self-frequency-doubling laser. Self-frequency-doubling fiber laser with further refinements, eliminates need for expensive, easily damaged, nonlinear crystals currently used. Enables one to avoid loss and damage mechanisms associated with interfaces of nonlinear crystals as well as to eliminate angle/temperature phase-matching tuning.
Diffusion, Viscosity and Crystal Growth in Microgravity
NASA Technical Reports Server (NTRS)
Myerson, Allan S.
1996-01-01
The diffusivity of TriGlycine Sulfate (TGS), Potassium Dihydrogen Phosphate (KDP), Ammonium Dihydrogen Phosphate (ADF) and other compounds of interest to microgravity crystal growth, in supersaturated solutions as a function of solution concentration, 'age' and 'history was studied experimentally. The factors that affect the growth of crystals from water solutions in microgravity have been examined. Three non-linear optical materials have been studied, potassium dihydrogen phosphate (KDP), ammonium dihydrogen phosphate (ADP) and triglycine sulfate (TGC). The diffusion coefficient and viscosity of supersaturated water solutions were measured. Also theoretical model of diffusivity and viscosity in a metastable state, model of crystal growth from solution including non-linear time dependent diffusivity and viscosity effect and computer simulation of the crystal growth process which allows simulation of the microgravity crystal growth were developed.
Scaling of chaos in strongly nonlinear lattices
Mulansky, Mario
2014-06-15
Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic observations still remain mostly in the dark. In this work, we numerically analyze the probability of chaos in strongly nonlinear Hamiltonian systems and find different scaling properties depending on the nonlinear structure of the model. We argue that these different scaling laws of chaos have definite consequences for the macroscopic diffusive behavior, as chaos is the microscopic mechanism of diffusion. This is compared with previous results on chaotic diffusion [M. Mulansky and A. Pikovsky, New J. Phys. 15, 053015 (2013)], and a relation between microscopic chaos and macroscopic diffusion is established.
Nonlinear Landau damping in the ionosphere
NASA Technical Reports Server (NTRS)
Kiwamoto, Y.; Benson, R. F.
1979-01-01
A model which explains the nonresonant waves which produce the diffuse resonance observed near 3/2 f(H) by the Alouette and Isis topside sounders, where f(H) is the ambient electron cyclotron frequency, is presented. These waves are the result of plasma wave instabilities driven by anisotropic electron velocity distributions initiated by the high-power short-duration sounder pulse. Calculations of the nonlinear wave-particle coupling coefficients show that the diffuse resonance wave can be maintained by nonlinear Landau damping of the sounder-stimulated 2f(H) wave which is observed with a time duration longer than that of the diffuse resonance wave. The time duration of the diffuse resonance is determined by the transit time of the instability-generated and nonlinearly maintained diffuse resonance wave from the remote short-lived hot region back to the antenna. The model is consistent with the Alouette/Isis observations and it demonstrates the existence of nonlinear wave-particle interactions in the ionosphere.
Nonlinear integrable ion traps
Nagaitsev, S.; Danilov, V.; /SNS Project, Oak Ridge
2011-10-01
Quadrupole ion traps can be transformed into nonlinear traps with integrable motion by adding special electrostatic potentials. This can be done with both stationary potentials (electrostatic plus a uniform magnetic field) and with time-dependent electric potentials. These potentials are chosen such that the single particle Hamilton-Jacobi equations of motion are separable in some coordinate systems. The electrostatic potentials have several free adjustable parameters allowing for a quadrupole trap to be transformed into, for example, a double-well or a toroidal-well system. The particle motion remains regular, non-chaotic, integrable in quadratures, and stable for a wide range of parameters. We present two examples of how to realize such a system in case of a time-independent (the Penning trap) as well as a time-dependent (the Paul trap) configuration.
Anderson, Robert C.
1976-06-22
1. A method for joining beryllium to beryllium by diffusion bonding, comprising the steps of coating at least one surface portion of at least two beryllium pieces with nickel, positioning a coated surface portion in a contiguous relationship with an other surface portion, subjecting the contiguously disposed surface portions to an environment having an atmosphere at a pressure lower than ambient pressure, applying a force upon the beryllium pieces for causing the contiguous surface portions to abut against each other, heating the contiguous surface portions to a maximum temperature less than the melting temperature of the beryllium, substantially uniformly decreasing the applied force while increasing the temperature after attaining a temperature substantially above room temperature, and maintaining a portion of the applied force at a temperature corresponding to about maximum temperature for a duration sufficient to effect the diffusion bond between the contiguous surface portions.
Coupled nonlinear dynamical systems
NASA Astrophysics Data System (ADS)
Sun, Hongyan
In this dissertation, we study coupled nonlinear dynamical systems that exhibit new types of complex behavior. We numerically and analytically examine a variety of dynamical models, ranging from systems of ordinary differential equations (ODE) with novel elements of feedback to systems of partial differential equations (PDE) that model chemical pattern formation. Chaos, dynamical uncertainty, synchronization, and spatiotemporal pattern formation constitute the primary topics of the dissertation. Following the introduction in Chapter 1, we study chaos and dynamical uncertainty in Chapter 2 with coupled Lorenz systems and demonstrate the existence of extreme complexity in high-dimensional ODE systems. In Chapter 3, we demonstrate that chaos synchronization can be achieved by mutual and multiplicative coupling of dynamical systems. Chapter 4 and 5 focus on pattern formation in reaction-diffusion systems, and we investigate segregation and integration behavior of populations in competitive and cooperative environments, respectively.
Diffusion of finite-size particles in confined geometries.
Bruna, Maria; Chapman, S Jonathan
2014-04-01
The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear diffusion equation for the one-particle probability density function, with an overall collective diffusion that depends on both the excluded-volume and the narrow confinement. By including both these effects, the equation is able to interpolate between severe confinement (for example, single-file diffusion) and unconfined diffusion. Numerical solutions of both the effective nonlinear diffusion equation and the stochastic particle system are presented and compared. As an application, the case of diffusion under a ratchet potential is considered, and the change in transport properties due to excluded-volume and confinement effects is examined.
Nonlinear lattice waves in heterogeneous media
NASA Astrophysics Data System (ADS)
Laptyeva, T. V.; Ivanchenko, M. V.; Flach, S.
2014-12-01
We discuss recent advances in the understanding of the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry-André localization for quasiperiodic potentials. Additional nonlinear terms in the wave equations can either preserve the phase-coherent localization of waves, or destroy it through nonintegrability and deterministic chaos. Spreading wave packets are observed to show universal features in their dynamics which are related to properties of nonlinear diffusion equations.
Minimizing radiation damage in nonlinear optical crystals
Cooke, D.W.; Bennett, B.L.; Cockroft, N.J.
1998-09-08
Methods are disclosed for minimizing laser induced damage to nonlinear crystals, such as KTP crystals, involving various means for electrically grounding the crystals in order to diffuse electrical discharges within the crystals caused by the incident laser beam. In certain embodiments, electrically conductive material is deposited onto or into surfaces of the nonlinear crystals and the electrically conductive surfaces are connected to an electrical ground. To minimize electrical discharges on crystal surfaces that are not covered by the grounded electrically conductive material, a vacuum may be created around the nonlinear crystal. 5 figs.
Minimizing radiation damage in nonlinear optical crystals
Cooke, D. Wayne; Bennett, Bryan L.; Cockroft, Nigel J.
1998-01-01
Methods are disclosed for minimizing laser induced damage to nonlinear crystals, such as KTP crystals, involving various means for electrically grounding the crystals in order to diffuse electrical discharges within the crystals caused by the incident laser beam. In certain embodiments, electrically conductive material is deposited onto or into surfaces of the nonlinear crystals and the electrically conductive surfaces are connected to an electrical ground. To minimize electrical discharges on crystal surfaces that are not covered by the grounded electrically conductive material, a vacuum may be created around the nonlinear crystal.
Nonlinear Wave-Packet Dynamics in a Disordered Medium
Schwiete, G.; Finkel'stein, A. M.
2010-03-12
We develop an effective theory of pulse propagation in a nonlinear and disordered medium in two dimensions. The theory is formulated in terms of a nonlinear diffusion equation. Despite its apparent simplicity this equation describes novel phenomena which we refer to as 'locked explosion' and diffusive collapse. The equation can be applied to such distinct physical systems as laser beams propagating in disordered photonic crystals or Bose-Einstein condensates expanding in a disordered environment.
Levenson, L.
1963-09-01
A high-vacuum diffusion pump is described, featuring a novel housing geometry for enhancing pumping speed. An upright, cylindrical lower housing portion is surmounted by a concentric, upright, cylindrical upper housing portion of substantially larger diameter; an uppermost nozzle, disposed concentrically within the upper portion, is adapted to eject downwardly a conical sheet of liquid outwardly to impinge upon the uppermost extremity of the interior wall of the lower portion. Preferably this nozzle is mounted upon a pedestal rising coaxially from within the lower portion and projecting up into said upper portion. (AEC)
NASA Astrophysics Data System (ADS)
Aitova, E. V.; Bratsun, D. A.; Kostarev, K. G.; Mizev, A. I.; Mosheva, E. A.
2016-12-01
The development of convective instability in a two-layer system of miscible fluids placed in a narrow vertical gap has been studied theoretically and experimentally. The upper and lower layers are formed with aqueous solutions of acid and base, respectively. When the layers are brought into contact, the frontal neutralization reaction begins. We have found experimentally a new type of convective instability, which is characterized by the spatial localization and the periodicity of the structure observed for the first time in the miscible systems. We have tested a number of different acid-base systems and have found a similar patterning there. In our opinion, it may indicate that the discovered effect is of a general nature and should be taken into account in reaction-diffusion-convection problems as another tool with which the reaction can govern the movement of the reacting fluids. We have shown that, at least in one case (aqueous solutions of nitric acid and sodium hydroxide), a new type of instability called as the concentration-dependent diffusion convection is responsible for the onset of the fluid flow. It arises when the diffusion coefficients of species are different and depend on their concentrations. This type of instability can be attributed to a variety of double-diffusion convection. A mathematical model of the new phenomenon has been developed using the system of reaction-diffusion-convection equations written in the Hele-Shaw approximation. It is shown that the instability can be reproduced in the numerical experiment if only one takes into account the concentration dependence of the diffusion coefficients of the reagents. The dynamics of the base state, its linear stability and nonlinear development of the instability are presented. It is also shown that by varying the concentration of acid in the upper layer one can achieve the occurrence of chemo-convective solitary cell in the bulk of an almost immobile fluid. Good agreement between the
Model of a nonlinear directional coupler in gallium arsenide
NASA Astrophysics Data System (ADS)
Gibbons, Wayne M.; Sarid, Dror
1987-08-01
We have calculated the response of a nonlinear directional coupler fabricated in an AlGaAs/GaAs structure using a realistic model for the optical nonlinearities. The model takes into account carrier-density-dependent index of refraction and absorption, and lateral carrier diffusion in each of the two coupled channel waveguides. Our results differ considerably from those obtained using a Kerr model for the optical nonlinearities.
A multigrid Newton-Krylov method for flux-limited radiation diffusion
Rider, W.J.; Knoll, D.A.; Olson, G.L.
1998-09-01
The authors focus on the integration of radiation diffusion including flux-limited diffusion coefficients. The nonlinear integration is accomplished with a Newton-Krylov method preconditioned with a multigrid Picard linearization of the governing equations. They investigate the efficiency of the linear and nonlinear iterative techniques.
Analysis of Coupled Reaction-Diffusion Equations for RNA Interactions.
Hohn, Maryann E; Li, Bo; Yang, Weihua
2015-05-01
We consider a system of coupled reaction-diffusion equations that models the interaction between multiple types of chemical species, particularly the interaction between one messenger RNA and different types of non-coding microRNAs in biological cells. We construct various modeling systems with different levels of complexity for the reaction, nonlinear diffusion, and coupled reaction and diffusion of the RNA interactions, respectively, with the most complex one being the full coupled reaction-diffusion equations. The simplest system consists of ordinary differential equations (ODE) modeling the chemical reaction. We present a derivation of this system using the chemical master equation and the mean-field approximation, and prove the existence, uniqueness, and linear stability of equilibrium solution of the ODE system. Next, we consider a single, nonlinear diffusion equation for one species that results from the slow diffusion of the others. Using variational techniques, we prove the existence and uniqueness of solution to a boundary-value problem of this nonlinear diffusion equation. Finally, we consider the full system of reaction-diffusion equations, both steady-state and time-dependent. We use the monotone method to construct iteratively upper and lower solutions and show that their respective limits are solutions to the reaction-diffusion system. For the time-dependent system of reaction-diffusion equations, we obtain the existence and uniqueness of global solutions. We also obtain some asymptotic properties of such solutions.
Analysis of Coupled Reaction-Diffusion Equations for RNA Interactions
Hohn, Maryann E.; Li, Bo; Yang, Weihua
2015-01-01
We consider a system of coupled reaction-diffusion equations that models the interaction between multiple types of chemical species, particularly the interaction between one messenger RNA and different types of non-coding microRNAs in biological cells. We construct various modeling systems with different levels of complexity for the reaction, nonlinear diffusion, and coupled reaction and diffusion of the RNA interactions, respectively, with the most complex one being the full coupled reaction-diffusion equations. The simplest system consists of ordinary differential equations (ODE) modeling the chemical reaction. We present a derivation of this system using the chemical master equation and the mean-field approximation, and prove the existence, uniqueness, and linear stability of equilibrium solution of the ODE system. Next, we consider a single, nonlinear diffusion equation for one species that results from the slow diffusion of the others. Using variational techniques, we prove the existence and uniqueness of solution to a boundary-value problem of this nonlinear diffusion equation. Finally, we consider the full system of reaction-diffusion equations, both steady-state and time-dependent. We use the monotone method to construct iteratively upper and lower solutions and show that their respective limits are solutions to the reaction-diffusion system. For the time-dependent system of reaction-diffusion equations, we obtain the existence and uniqueness of global solutions. We also obtain some asymptotic properties of such solutions. PMID:25601722
Double-discrete solitons in fishnet arrays of optical fibers.
Staliunas, Kestutis; Malomed, Boris
2013-08-01
We demonstrate that crossed arrays of optical fibers support the double-discrete linear and nonlinear propagation of light beams, in which not only the transverse coordinate (the fiber's number) is discrete, but also the longitudinal (propagation) coordinate, i.e., the number of the fiber-crossing site, is effectively discrete too. In the linear limit, this transmission regime features double-discrete self-collimation. The nonlinear fishnet arrays with both focusing and defocusing nonlinearities give rise to double-discrete spatial solitons. Solitons bifurcating from two different branches of the linear dispersion relation feature strong interactions and form composite states. In the continuum limit, the model of the nonlinear fishnet reduces to a system of coupled-mode equations similar to those describing Bragg gratings, but without the cross-phase-modulation terms.
Nonlinear vibration and radiation from a panel with transition to chaos induced by acoustic waves
NASA Technical Reports Server (NTRS)
Maestrello, Lucio; Frendi, Abdelkader; Brown, Donald E.
1992-01-01
The dynamic response of an aircraft panel forced at resonance and off-resonance by plane acoustic waves at normal incidence is investigated experimentally and numerically. Linear, nonlinear (period doubling) and chaotic responses are obtained by increasing the sound pressure level of the excitation. The response time history is sensitive to the input level and to the frequency of excitation. The change in response behavior is due to a change in input conditions, triggered either naturally or by modulation of the bandwidth of the incident waves. Off-resonance, bifurcation is diffused and difficult to maintain, thus the panel response drifts into a linear behavior. The acoustic pressure emanated by the panel is either linear or nonlinear as is the vibration response. The nonlinear effects accumulate during the propagation with distance. Results are also obtained on the control of the panel response using damping tape on aluminum panel and using a graphite epoxy panel having the same size and weight. Good agreement is obtained between the experimental and numerical results.
Nonlinear vibration and radiation from a panel with transition to chaos
NASA Technical Reports Server (NTRS)
Maestrello, Lucio; Frendi, Abdelkader; Brown, Donald E.
1992-01-01
The dynamic response of an aircraft panel forced at resonance and off-resonance by plane acoustic waves at normal incidence is investigated experimentally and numerically. Linear, nonlinear (period doubling), and chaotic responses are obtained by increasing the sound pressure level of the excitation. The response time history is sensitive to the input level and to the frequency of excitation. The change in response behavior is due to a change in input conditions, triggered either naturally or by modulation of the bandwidth of the incident waves. Off-resonance bifurcation is diffused and difficult to maintain; thus the panel response drifts into a linear behavior. The acoustic pressure emanated by the panel is either linear or nonlinear as is the vibration response. The nonlinear effects accumulate during the propagation with distance. Results are also obtained on the control of the panel response using damping tape on an aluminum panel and a graphite epoxy panel having the same size and weight. Good agreement is obtained betwen the experimental and numerical results.
New Nonlinear Multigrid Analysis
NASA Technical Reports Server (NTRS)
Xie, Dexuan
1996-01-01
The nonlinear multigrid is an efficient algorithm for solving the system of nonlinear equations arising from the numerical discretization of nonlinear elliptic boundary problems. In this paper, we present a new nonlinear multigrid analysis as an extension of the linear multigrid theory presented by Bramble. In particular, we prove the convergence of the nonlinear V-cycle method for a class of mildly nonlinear second order elliptic boundary value problems which do not have full elliptic regularity.
Exact solutions for logistic reaction-diffusion equations in biology
NASA Astrophysics Data System (ADS)
Broadbridge, P.; Bradshaw-Hajek, B. H.
2016-08-01
Reaction-diffusion equations with a nonlinear source have been widely used to model various systems, with particular application to biology. Here, we provide a solution technique for these types of equations in N-dimensions. The nonclassical symmetry method leads to a single relationship between the nonlinear diffusion coefficient and the nonlinear reaction term; the subsequent solutions for the Kirchhoff variable are exponential in time (either growth or decay) and satisfy the linear Helmholtz equation in space. Example solutions are given in two dimensions for particular parameter sets for both quadratic and cubic reaction terms.
Vertical diffusion processes in the Eastern Mediterranean - Black Sea System
NASA Astrophysics Data System (ADS)
Kioroglou, Sotiris; Tragou, Elina; Zervakis, Vassilis; Georgopoulos, Dimitris; Herut, Barak; Gertman, Isaak; Kovacevic, Vedrana; Özsoy, Emin; Tutsak, Ersin
2014-07-01
The identification and examination of ‘complete' potential density overturns in CTD profiles, within the framework of SESAME project, are employed to assess vertical eddy diffusivities, mostly in the top 100 m of the water column, for a broad area covering the East Mediterranean, the Turkish Straits and the Black Sea. The implementation of this method shows that, mixing induced by mechanical turbulence is enhanced in frontal areas, in the proximity of straits and inside anticyclones; furthermore, that mechanical turbulence is insignificant, down to the scale of CTD resolution, within areas of double diffusive staircases, encountered in deep layers of the water column. Consequently, only laminar theories about double diffusion are applied for assessing diffusivities therein. Susceptibility to different types of double diffusion seems to be related to the interaction of different types of water masses.
Numerical evaluation of lateral diffusion inside diffusive gradients in thin films samplers.
Santner, Jakob; Kreuzeder, Andreas; Schnepf, Andrea; Wenzel, Walter W
2015-05-19
Using numerical simulation of diffusion inside diffusive gradients in thin films (DGT) samplers, we show that the effect of lateral diffusion inside the sampler on the solute flux into the sampler is a nonlinear function of the diffusion layer thickness and the physical sampling window size. In contrast, earlier work concluded that this effect was constant irrespective of parameters of the sampler geometry. The flux increase caused by lateral diffusion inside the sampler was determined to be ∼8.8% for standard samplers, which is considerably lower than the previous estimate of ∼20%. Lateral diffusion is also propagated to the diffusive boundary layer (DBL), where it leads to a slightly stronger decrease in the mass uptake than suggested by the common 1D diffusion model that is applied for evaluating DGT results. We introduce a simple correction procedure for lateral diffusion and demonstrate how the effect of lateral diffusion on diffusion in the DBL can be accounted for. These corrections often result in better estimates of the DBL thickness (δ) and the DGT-measured concentration than earlier approaches and will contribute to more accurate concentration measurements in solute monitoring in waters.
Numerical Evaluation of Lateral Diffusion Inside Diffusive Gradients in Thin Films Samplers
2015-01-01
Using numerical simulation of diffusion inside diffusive gradients in thin films (DGT) samplers, we show that the effect of lateral diffusion inside the sampler on the solute flux into the sampler is a nonlinear function of the diffusion layer thickness and the physical sampling window size. In contrast, earlier work concluded that this effect was constant irrespective of parameters of the sampler geometry. The flux increase caused by lateral diffusion inside the sampler was determined to be ∼8.8% for standard samplers, which is considerably lower than the previous estimate of ∼20%. Lateral diffusion is also propagated to the diffusive boundary layer (DBL), where it leads to a slightly stronger decrease in the mass uptake than suggested by the common 1D diffusion model that is applied for evaluating DGT results. We introduce a simple correction procedure for lateral diffusion and demonstrate how the effect of lateral diffusion on diffusion in the DBL can be accounted for. These corrections often result in better estimates of the DBL thickness (δ) and the DGT-measured concentration than earlier approaches and will contribute to more accurate concentration measurements in solute monitoring in waters. PMID:25877251
Nonlinear equations of 'variable type'
NASA Astrophysics Data System (ADS)
Larkin, N. A.; Novikov, V. A.; Ianenko, N. N.
In this monograph, new scientific results related to the theory of equations of 'variable type' are presented. Equations of 'variable type' are equations for which the original type is not preserved within the entire domain of coefficient definition. This part of the theory of differential equations with partial derivatives has been developed intensively in connection with the requirements of mechanics. The relations between equations of the considered type and the problems of mathematical physics are explored, taking into account quasi-linear equations, and models of mathematical physics which lead to equations of 'variable type'. Such models are related to transonic flows, problems involving a separation of the boundary layer, gasdynamics and the van der Waals equation, shock wave phenomena, and a combustion model with a turbulent diffusion flame. Attention is also given to nonlinear parabolic equations, and nonlinear partial differential equations of the third order.
NASA Astrophysics Data System (ADS)
Pesic, Peter
2003-10-01
The separateness and connection of individuals is perhaps the central question of human life: What, exactly, is my individuality? To what degree is it unique? To what degree can it be shared, and how? To the many philosophical and literary speculations about these topics over time, modern science has added the curious twist of quantum theory, which requires that the elementary particles of which everything consists have no individuality at all. All aspects of chemistry depend on this lack of individuality, as do many branches of physics. From where, then, does our individuality come? In Seeing Double, Peter Pesic invites readers to explore this intriguing set of questions. He draws on literary and historical examples that open the mind (from Homer to Martin Guerre to Kafka), philosophical analyses that have helped to make our thinking and speech more precise, and scientific work that has enabled us to characterize the phenomena of nature. Though he does not try to be all-inclusive, Pesic presents a broad range of ideas, building toward a specific point of view: that the crux of modern quantum theory is its clash with our ordinary concept of individuality. This represents a departure from the usual understanding of quantum theory. Pesic argues that what is bizarre about quantum theory becomes more intelligible as we reconsider what we mean by individuality and identity in ordinary experience. In turn, quantum identity opens a new perspective on us. Peter Pesic is a Tutor and Musician-in-Residence at St. John's College, Santa Fe, New Mexico. He has a Ph.D. in physics from Stanford University.
Feng, Xia; Ma, Jun-Wu; Sun, Shi-Qi; Guo, Hui-Chen; Yang, Ya-Min; Jin, Ye; Zhou, Guang-Qing; He, Ji-Jun; Guo, Jian-Hong; Qi, Shu-yun; Lin, Mi; Cai, Hu; Liu, Xiang-Tao
2016-01-01
The efficacy of an inactivated foot-and-mouth disease (FMD) vaccine is mainly dependent on the integrity of the foot-and-mouth disease virus (FMDV) particles. At present, the standard method to quantify the active component, the 146S antigen, of FMD vaccines is sucrose density gradient (SDG) analysis. However, this method is highly operator dependent and difficult to automate. In contrast, the enzyme-linked immunosorbent assay (ELISA) is a time-saving technique that provides greater simplicity and sensitivity. To establish a valid method to detect and quantify the 146S antigen of a serotype O FMD vaccine, a double-antibody sandwich (DAS) ELISA was compared with an SDG analysis. The DAS ELISA was highly correlated with the SDG method (R2 = 0.9215, P<0.01). In contrast to the SDG method, the DAS ELISA was rapid, robust, repeatable and highly sensitive, with a minimum quantification limit of 0.06 μg/mL. This method can be used to determine the effective antigen yields in inactivated vaccines and thus represents an alternative for assessing the potency of FMD vaccines in vitro. But it still needs to be prospectively validated by analyzing a new vaccine preparation and determining the proper protective dose followed by an in vivo vaccination-challenge study to confirm the ELISA findings.
Piezoelectric monolayers as nonlinear energy harvesters.
López-Suárez, Miquel; Pruneda, Miguel; Abadal, Gabriel; Rurali, Riccardo
2014-05-02
We study the dynamics of h-BN monolayers by first performing ab-initio calculations of the deformation potential energy and then solving numerically a Langevine-type equation to explore their use in nonlinear vibration energy harvesting devices. An applied compressive strain is used to drive the system into a nonlinear bistable regime, where quasi-harmonic vibrations are combined with low-frequency swings between the minima of a double-well potential. Due to its intrinsic piezoelectric response, the nonlinear mechanical harvester naturally provides an electrical power that is readily available or can be stored by simply contacting the monolayer at its ends. Engineering the induced nonlinearity, a 20 nm2 device is predicted to harvest an electrical power of up to 0.18 pW for a noisy vibration of 5 pN.
Parabolic Perturbation of a Nonlinear Hyperbolic Problem Arising in Physiology
NASA Astrophysics Data System (ADS)
Colli, P.; Grasselli, M.
We study a transport-diffusion initial value problem where the diffusion codlicient is "small" and the transport coefficient is a time function depending on the solution in a nonlinear and nonlocal way. We show the existence and the uniqueness of a weak solution of this problem. Moreover we discuss its asymptotic behaviour as the diffusion coefficient goes to zero, obtaining a well-posed first-order nonlinear hyperbolic problem. These problems arise from mathematical models of muscle contraction in the framework of the sliding filament theory.
Double Your Major, Double Your Return?
ERIC Educational Resources Information Center
Del Rossi, Alison F.; Hersch, Joni
2008-01-01
We use the 2003 National Survey of College Graduates to provide the first estimates of the effect on earnings of having a double major. Overall, double majoring increases earnings by 2.3% relative to having a single major among college graduates without graduate degrees. Most of the gains from having a double major come from choosing fields across…
A new hydrodynamic analysis of double layers
NASA Technical Reports Server (NTRS)
Hora, Heinrich
1987-01-01
A genuine two-fluid model of plasmas with collisions permits the calculation of dynamic (not necessarily static) electric fields and double layers inside of plasmas including oscillations and damping. For the first time a macroscopic model for coupling of electromagnetic and Langmuir waves was achieved with realistic damping. Starting points were laser-produced plasmas showing very high dynamic electric fields in nonlinear force-produced cavitous and inverted double layers in agreement with experiments. Applications for any inhomogeneous plasma as in laboratory or in astrophysical plasmas can then be followed up by a transparent hydrodynamic description. Results are the rotation of plasmas in magnetic fields and a new second harmonic resonance, explanation of the measured inverted double layers, explanation of the observed density-independent, second harmonics emission from laser-produced plasmas, and a laser acceleration scheme by the very high fields of the double layers.
Frequency Doubling Broadband Light in Multiple Crystals
ALFORD,WILLIAM J.; SMITH,ARLEE V.
2000-07-26
The authors compare frequency doubling of broadband light in a single nonlinear crystal with doubling in five crystals with intercrystal temporal walk off compensation, and with doubling in five crystals adjusted for offset phase matching frequencies. Using a plane-wave, dispersive numerical model of frequency doubling they study the bandwidth of the second harmonic and the conversion efficiency as functions of crystal length and fundamental irradiance. For low irradiance the offset phase matching arrangement has lower efficiency than a single crystal of the same total length but gives a broader second harmonic bandwidth. The walk off compensated arrangement gives both higher conversion efficiency and broader bandwidth than a single crystal. At high irradiance, both multicrystal arrangements improve on the single crystal efficiency while maintaining broad bandwidth.
High power double-scale pulses from a gain-guided double-clad fiber laser
NASA Astrophysics Data System (ADS)
Zhang, Haitao; Gao, Gan; Li, Qinghua; Gong, Mali
2017-03-01
Generation of high power double-scale pulses from a gain-guided double-clad fiber laser is experimentally demonstrated. By employing the Yb-doped 10/130 double-clad fiber as the gain medium, the laser realizes an output power of 5.1 W and pulse energy of 0.175 µJ at repetition rate of 29.14 MHz. To the best of our knowledge, this average output power is the highest among the reported double-scale pulse oscillators. The autocorrelation trace of pulses contains the short (98 fs) and long (29.5 ps) components, and the spectral bandwidth of the pulse is 27.3 nm. Such double-scale pulses are well suited for seeding the high power MOPA (master oscillator power amplifier) systems, nonlinear frequency conversion and optical coherence tomography.
Dynamic optical nonlinearities in di-furfuryl ether solution
NASA Astrophysics Data System (ADS)
Mendonça, C. R.; Barbosa Neto, N. M.; Batista, P. S.; de Souza, M. F.; Zilio, S. C.
2002-08-01
Dynamic nonlinear refraction and absorption of di-furfuryl ether dissolved in dichloro-methane are investigated with a frequency-doubled Q-switched and mode-locked Nd:YAG laser. The nonlinear absorption presents a strong reverse saturation that seems promising for use in optical limiting devices. Three contributions are observed for the nonlinear refraction: one fast process related to the singlet population, and two slow accumulative contributions arising from the triplet population and thermal lensing. The time evolution of the optical nonlinearities, modeled by means of a five-energy-level diagram, allows the determination of excited state cross-sections as well as the intersystem crossing lifetime.
Nonlinear Chemical Dynamics and Synchronization
NASA Astrophysics Data System (ADS)
Li, Ning
Alan Turing's work on morphogenesis, more than half a century ago, continues to motivate and inspire theoretical and experimental biologists even today. That said, there are very few experimental systems for which Turing's theory is applicable. In this thesis we present an experimental reaction-diffusion system ideally suited for testing Turing's ideas in synthetic "cells" consisting of microfluidically produced surfactant-stabilized emulsions in which droplets containing the Belousov-Zhabotinsky (BZ) oscillatory chemical reactants are dispersed in oil. The BZ reaction has become the prototype of nonlinear dynamics in chemistry and a preferred system for exploring the behavior of coupled nonlinear oscillators. Our system consists of a surfactant stabilized monodisperse emulsion of drops of aqueous BZ solution dispersed in a continuous phase of oil. In contrast to biology, here the chemistry is understood, rate constants are measured and interdrop coupling is purely diffusive. We explore a large set of parameters through control of rate constants, drop size, spacing, and spatial arrangement of the drops in lines and rings in one-dimension (1D) and hexagonal arrays in two-dimensions (2D). The Turing model is regarded as a metaphor for morphogenesis in biology but not for prediction. Here, we develop a quantitative and falsifiable reaction-diffusion model that we experimentally test with synthetic cells. We quantitatively establish the extent to which the Turing model in 1D describes both stationary pattern formation and temporal synchronization of chemical oscillators via reaction-diffusion and in 2D demonstrate that chemical morphogenesis drives physical differentiation in synthetic cells.
Diffusion archeology for diffusion progression history reconstruction.
Sefer, Emre; Kingsford, Carl
2016-11-01
Diffusion through graphs can be used to model many real-world processes, such as the spread of diseases, social network memes, computer viruses, or water contaminants. Often, a real-world diffusion cannot be directly observed while it is occurring - perhaps it is not noticed until some time has passed, continuous monitoring is too costly, or privacy concerns limit data access. This leads to the need to reconstruct how the present state of the diffusion came to be from partial diffusion data. Here, we tackle the problem of reconstructing a diffusion history from one or more snapshots of the diffusion state. This ability can be invaluable to learn when certain computer nodes are infected or which people are the initial disease spreaders to control future diffusions. We formulate this problem over discrete-time SEIRS-type diffusion models in terms of maximum likelihood. We design methods that are based on submodularity and a novel prize-collecting dominating-set vertex cover (PCDSVC) relaxation that can identify likely diffusion steps with some provable performance guarantees. Our methods are the first to be able to reconstruct complete diffusion histories accurately in real and simulated situations. As a special case, they can also identify the initial spreaders better than the existing methods for that problem. Our results for both meme and contaminant diffusion show that the partial diffusion data problem can be overcome with proper modeling and methods, and that hidden temporal characteristics of diffusion can be predicted from limited data.
Filtering by nonlinear systems.
Campos Cantón, E; González Salas, J S; Urías, J
2008-12-01
Synchronization of nonlinear systems forced by external signals is formalized as the response of a nonlinear filter. Sufficient conditions for a nonlinear system to behave as a filter are given. Some examples of generalized chaos synchronization are shown to actually be special cases of nonlinear filtering.
Wang, Chi-Jen
2013-01-01
In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.
A Huygens principle for diffusion and anomalous diffusion in spatially extended systems
Gottwald, Georg A.; Melbourne, Ian
2013-01-01
We present a universal view on diffusive behavior in chaotic spatially extended systems for anisotropic and isotropic media. For anisotropic systems, strong chaos leads to diffusive behavior (Brownian motion with drift) and weak chaos leads to superdiffusive behavior (Lévy processes with drift). For isotropic systems, the drift term vanishes and strong chaos again leads to Brownian motion. We establish the existence of a nonlinear Huygens principle for weakly chaotic systems in isotropic media whereby the dynamics behaves diffusively in even space dimension and exhibits superdiffusive behavior in odd space dimensions. PMID:23653481
Analysis of tilt by modulated speckles generated with a double aperture pupil mask
NASA Astrophysics Data System (ADS)
Molina Prado, Martha Lucía; Bolognini, Néstor; Tebaldi, Myrian
2015-03-01
We present a method based on modulated speckles to detect tilt movement of a diffusing surface. In our proposal a speckle image of the speckle produced by a reflective diffusing surface is formed by a lens having a double aperture. The double aperture yields to an interference process so that the resulting speckle distribution is fringe modulated. The tilting of the diffusing surface is mapped as a shifting of the speckle. Then, the double aperture pupil lens system maps the speckle shifting into a fringes shifting. We study the system performance in terms of the diffuser tilt. Experimental results that confirm our proposal are presented.
National Institute of Standards and Technology Data Gateway
NIST Diffusion Data Center (Web, free access) The NIST Diffusion Data Center is a collection of over 14,100 international papers, theses, and government reports on diffusion published before 1980.
Parallel flow diffusion battery
Yeh, Hsu-Chi; Cheng, Yung-Sung
1984-08-07
A parallel flow diffusion battery for determining the mass distribution of an aerosol has a plurality of diffusion cells mounted in parallel to an aerosol stream, each diffusion cell including a stack of mesh wire screens of different density.
Parallel flow diffusion battery
Yeh, H.C.; Cheng, Y.S.
1984-01-01
A parallel flow diffusion battery for determining the mass distribution of an aerosol has a plurality of diffusion cells mounted in parallel to an aerosol stream, each diffusion cell including a stack of mesh wire screens of different density.
FRACTIONAL PEARSON DIFFUSIONS.
Leonenko, Nikolai N; Meerschaert, Mark M; Sikorskii, Alla
2013-07-15
Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also presents stochastic solutions, using a non-Markovian inverse stable time change.
Leonenko, Nikolai N.; Meerschaert, Mark M.
2013-01-01
Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also presents stochastic solutions, using a non-Markovian inverse stable time change. PMID:23626377
How a Nanodroplet Diffuses on Smooth Surfaces
NASA Astrophysics Data System (ADS)
Li, Chu; Huang, Jizu; Li, Zhigang
2016-11-01
In this study, we investigate how nanodroplets diffuse on smooth surfaces through molecular dynamics (MD) simulations and theoretical analyses. The simulations results show that the surface diffusion of nanodroplet is different from that of single molecules and solid nanoparticles. The dependence of nanodroplet diffusion coefficient on temperature is surface wettability dependent, which undergoes a transition from linear to nonlinear as the surface wettability is weakened due to the coupling of temperature and surface energy. We also develop a simple relation for the diffusion coefficient by using the contact angle and contact radius of the droplet. It works well for different surface wettabilities and sized nanodroplets, as confirmed by MD simulations. This work was supported by the Research Grants Council of the Hong Kong Special Administrative Region under Grant No. 615312.
Vorticity Transport in a Two Layer, Double Gyre Ocean Basin
NASA Astrophysics Data System (ADS)
Kaiser, Bryan; Clayson, Carol Anne; Jayne, Steve
2016-11-01
The double gyre ocean circulations predicted by strongly frictional, barotropic, linearized ocean models qualitatively agree with the patterns of large scale gyres in the world ocean. However, nonlinear ocean models featuring less intense eddy diffusion parameterization can converge to an infinite number of statistically stationary circulations, depending on the parameterization of dissipation of energy and vorticity. Patterns of vorticity flux and dissipation in a barotropic ocean have been examined previous studies; in this work the inclusion of the first baroclinic mode is examined. The first vertical mode permits the model to be split into two layers, the top approximating the thermocline and the bottom approximating the abyssal circulation. The separation into two layers not only adds realism and but also removes the nonphysical direct restraint of the upper ocean by bottom friction. Steady state circulations for various boundary conditions, sources and sinks of vorticity, and Reynolds numbers are simulated using a parallel pseudo-spectral quasi-geostrophic flow solver and mechanisms of vorticity flux and dissipation are discussed.
Generating Second Harmonics In Nonlinear Resonant Cavities
NASA Technical Reports Server (NTRS)
Kozlovsky, William J.; Nabors, C. David; Byer, Robert L.
1990-01-01
Single-axial-mode lasers pump very-low-loss doubling crystals. Important advance in making resonant generation of second harmonics possible for diode-laser-pumped solid-state lasers is recent development of monolithic nonplanar ring geometries in neodymium:yttrium aluminum garnet (Nd:YAG) lasers that produce frequency-stable single-mode outputs. Other advance is development of high-quality MgO:LiNbO3 as electro-optically nonlinear material. Series of experiments devised to improve doubling efficiency of low-power lasers, and particularly of diode-laser-pumped continuous-wave Nd:YAG lasers.
Yu, X.; Hsu, T.-J.; Hanes, D.M.
2010-01-01
Sediment transport under nonlinear waves in a predominately sheet flow condition is investigated using a two-phase model. Specifically, we study the relative importance between the nonlinear waveshape and nonlinear boundary layer streaming on cross-shore sand transport. Terms in the governing equations because of the nonlinear boundary layer process are included in this one-dimensional vertical (1DV) model by simplifying the two-dimensional vertical (2DV) ensemble-averaged two-phase equations with the assumption that waves propagate without changing their form. The model is first driven by measured time series of near-bed flow velocity because of a wave group during the SISTEX99 large wave flume experiment and validated with the measured sand concentration in the sheet flow layer. Additional studies are then carried out by including and excluding the nonlinear boundary layer terms. It is found that for the grain diameter (0.24 mm) and high-velocity skewness wave condition considered here, nonlinear waveshape (e.g., skewness) is the dominant mechanism causing net onshore transport and nonlinear boundary layer streaming effect only causes an additional 36% onshore transport. However, for conditions of relatively low-wave skewness and a stronger offshore directed current, nonlinear boundary layer streaming plays a more critical role in determining the net transport. Numerical experiments further suggest that the nonlinear boundary layer streaming effect becomes increasingly important for finer grain. When the numerical model is driven by measured near-bed flow velocity in a more realistic surf zone setting, model results suggest nonlinear boundary layer processes may nearly double the onshore transport purely because of nonlinear waveshape. Copyright 2010 by the American Geophysical Union.
NASA Astrophysics Data System (ADS)
Huang, Yi; Zhang, Xingyi; Zhou, You-He
2016-07-01
The vibration of a permanent magnet (PM) levitated upon a high temperature superconductor (HTS) shows anomalous motion under external disturbance. In this paper we construct a cantilevered beam experimental setup composed of a bulk PM and a thermally insulated cylindrical YBa2Cu3O x superconductor. When the levitation system is disturbed by vertical excitation, the thermal character of the superconductor surface could be measured directly. Our experiments on a clean and large single-domain superconductor show that a giant temperature spike appears once the levitated PM experiences period doubling oscillation. We develop a numerical simulation for the analysis of the nonlinear vibration of the levitated PM coupled with the nonlinear electromagnetic force between the PM and HTS, taking into account heat diffusion. Using this procedure, we explore the electromagnetic and thermal properties at the thermally insulated HTS surface when the levitated PM shows a period doubling vibration. We find a remarkable difference between the experimental results and simulation. In order to interpret this temperature difference, we suggest a type of flux motion triggered by the electromagnetic force when it is far larger than the pinning force of the superconductor. The quantitative approach is based on the analysis process of the partial flux jump as a result of the flux creep. Finally, the calculated result is shown to be very close to the experimental result.
When Linear Stability Does Not Exclude Nonlinear Instability
NASA Astrophysics Data System (ADS)
Kevrekidis, P. G.; Pelinovsky, D. E.; Saxena, A.
2015-05-01
We describe a mechanism that results in the nonlinear instability of stationary states even in the case where the stationary states are linearly stable. This instability is due to the nonlinearity-induced coupling of the linearization's internal modes of negative energy with the continuous spectrum. In a broad class of nonlinear Schrödinger equations considered, the presence of such internal modes guarantees the nonlinear instability of the stationary states in the evolution dynamics. To corroborate this idea, we explore three prototypical case examples: (a) an antisymmetric soliton in a double-well potential, (b) a twisted localized mode in a one-dimensional lattice with cubic nonlinearity, and (c) a discrete vortex in a two-dimensional saturable lattice. In all cases, we observe a weak nonlinear instability, despite the linear stability of the respective states.
When linear stability does not exclude nonlinear instability
Kevrekidis, P. G.; Pelinovsky, D. E.; Saxena, A.
2015-05-29
We describe a mechanism that results in the nonlinear instability of stationary states even in the case where the stationary states are linearly stable. In this study, this instability is due to the nonlinearity-induced coupling of the linearization’s internal modes of negative energy with the continuous spectrum. In a broad class of nonlinear Schrödinger equations considered, the presence of such internal modes guarantees the nonlinear instability of the stationary states in the evolution dynamics. To corroborate this idea, we explore three prototypical case examples: (a) an antisymmetric soliton in a double-well potential, (b) a twisted localized mode in a one-dimensionalmore » lattice with cubic nonlinearity, and (c) a discrete vortex in a two-dimensional saturable lattice. In all cases, we observe a weak nonlinear instability, despite the linear stability of the respective states.« less
When linear stability does not exclude nonlinear instability
Kevrekidis, P. G.; Pelinovsky, D. E.; Saxena, A.
2015-05-29
We describe a mechanism that results in the nonlinear instability of stationary states even in the case where the stationary states are linearly stable. In this study, this instability is due to the nonlinearity-induced coupling of the linearization’s internal modes of negative energy with the continuous spectrum. In a broad class of nonlinear Schrödinger equations considered, the presence of such internal modes guarantees the nonlinear instability of the stationary states in the evolution dynamics. To corroborate this idea, we explore three prototypical case examples: (a) an antisymmetric soliton in a double-well potential, (b) a twisted localized mode in a one-dimensional lattice with cubic nonlinearity, and (c) a discrete vortex in a two-dimensional saturable lattice. In all cases, we observe a weak nonlinear instability, despite the linear stability of the respective states.
A Relation for Nanodroplet Diffusion on Smooth Surfaces
Li, Chu; Huang, Jizu; Li, Zhigang
2016-01-01
In this work, we study the diffusion of nanodroplets on smooth surfaces through molecular dynamics (MD) simulations and theoretical analyses. Molecular dynamics simulations show that nanodroplet surface diffusion is different from that of single molecules and solid particles. The dependence of nanodroplet diffusion coefficient on temperature undergoes a transition from linear to nonlinear as the surface wettability is weakened due to the coupling of temperature and surface energy. We also develop a simple relation for the diffusion coefficient by using the contact angle and contact radius of the droplet. It works well for a wide range of surface wettabilities and different sized nanodroplets, as confirmed by MD simulations. PMID:27215471
Nonlinear Hysteretic Torsional Waves
NASA Astrophysics Data System (ADS)
Cabaret, J.; Béquin, P.; Theocharis, G.; Andreev, V.; Gusev, V. E.; Tournat, V.
2015-07-01
We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.
Nonlinear Hysteretic Torsional Waves.
Cabaret, J; Béquin, P; Theocharis, G; Andreev, V; Gusev, V E; Tournat, V
2015-07-31
We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.
Electron dynamics with radiation and nonlinear wigglers
Jowett, J.M.
1986-06-01
The physics of electron motion in storage rings is described by supplementing the Hamiltonian equations of motion with fluctuating radiation reaction forces to describe the effects of synchrotron radiation. This leads to a description of radiation damping and quantum diffusion in single-particle phase-space by means of Fokker-Planck equations. For practical purposes, most storage rings remain in the regime of linear damping and diffusion; this is discussed in some detail with examples, concentrating on longitudinal phase space. However special devices such as nonlinear wigglers may permit the new generation of very large rings to go beyond this into regimes of nonlinear damping. It is shown how a special combined-function wiggler can be used to modify the energy distribution and current profile of electron bunches.
An ion diffusion model in semi-permeable clay materials.
Liu, Chongxuan
2007-08-01
Clay materials typically contain negative surface charges that induce electrostatic fields (or diffuse double layers) in electrolytes. During ion diffusion in a porous medium of clay materials, ions dynamically interact with the electrostatic fields associated with individual clay grains by depressing or expanding the electrostatic double layers, which subsequently affects ionic fluxes. Current theory of ion transport in porous media, however, cannot explicitly account for the dynamic interactions. Here we proposed a model by coupling electrodynamics and nonequilibrium thermodynamics (EDNT) to describe ion diffusion in clay materials as a complex function of factors including clay surface charge density, tortuosity, porosity, chemicoosmotic coefficient, and ion self-diffusivity. The model was validated by comparing the calculated and measured apparent ion diffusion coefficients in clay materials as a function of ionic strength. At transitional states, ion diffusive fluxes are dynamically related to the electrostatic fields, which shrink or expand as ion diffusion occurs. At steady states, the electrostatic fields are time-invariant and ion diffusive fluxes conform to flux and concentration gradient relationships; and apparent diffusivity can be approximated by the ion diffusivity in bulk electrolytes corrected by a tortuosity factor and macroscopic concentration discontinuities at the interfaces between clay materials and bulk solutions.
Shaping wave patterns in reaction-diffusion systems
NASA Astrophysics Data System (ADS)
Löber, Jakob; Martens, Steffen; Engel, Harald
2014-12-01
We present a method to control the two-dimensional shape of traveling wave solutions to reaction-diffusion systems, such as, interfaces and excitation pulses. Control signals that realize a pregiven wave shape are determined analytically from nonlinear evolution equation for isoconcentration lines as the perturbed nonlinear phase diffusion equation or the perturbed linear eikonal equation. While the control enforces a desired wave shape perpendicular to the local propagation direction, the wave profile along the propagation direction itself remains almost unaffected. Provided that the one-dimensional wave profile of all state variables and its propagation velocity can be measured experimentally, and the diffusion coefficients of the reacting species are given, the new approach can be applied even if the underlying nonlinear reaction kinetics are unknown.
Nonlinear femtosecond laser induced scanning tunneling microscopy.
Dey, Shirshendu; Mirell, Daniel; Perez, Alejandro Rodriguez; Lee, Joonhee; Apkarian, V Ara
2013-04-21
We demonstrate ultrafast laser driven nonlinear scanning tunneling microscopy (STM), under ambient conditions. The design is an adaptation of the recently introduced cross-polarized double beat method, whereby z-polarized phase modulated fields are tightly focused at a tunneling junction consisting of a sharp tungsten tip and an optically transparent gold film as substrate. We demonstrate the prerequisites for ultrafast time-resolved STM through an operative mechanism of nonlinear laser field-driven tunneling. The spatial resolution of the nonlinear laser driven STM is determined by the local field intensity. Resolution of 0.3 nm-10 nm is demonstrated for the intensity dependent, exponential tunneling range. The demonstration is carried out on a junction consisting of tungsten tip and gold substrate. Nano-structured gold is used for imaging purposes, to highlight junction plasmon controlled tunneling in the conductivity limit.
Spatial frequency doubling - Retinal or central. [visual illusion
NASA Technical Reports Server (NTRS)
Richards, W.; Felton, T. B.
1973-01-01
When a wide field is sinusoidally modulated both in space and in time, the spatial frequency of the pattern will appear doubled at high rates of modulation. Kelly (1966) proposed that this illusion is due to temporal integration of the nonlinear brightness response of the visual system. The anatomical locus of this temporal integrator is uncertain, and could be subcortical. Results indicate that spatial frequency doubling follows binocular disparity detection and is thus a cortical phenomenon.
Mink van der Molen, A B; Salu, M K
1991-04-06
A 59-year-old woman is described with symptomatic cholelithiasis. A double gallbladder was incidentally found during abdominal surgery. The literature on a double gallbladder is reviewed with respect to incidence, anatomy, diagnosis and therapy.
Supersymmetric pairing of kinks for polynomial nonlinearities
Rosu, H.C.; Cornejo-Perez, O.
2005-04-01
We show how one can obtain kink solutions of ordinary differential equations with polynomial nonlinearities by an efficient factorization procedure directly related to the factorization of their nonlinear polynomial part. We focus on reaction-diffusion equations in the traveling frame and damped-anharmonic-oscillator equations. We also report an interesting pairing of the kink solutions, a result obtained by reversing the factorization brackets in the supersymmetric quantum-mechanical style. In this way, one gets ordinary differential equations with a different polynomial nonlinearity possessing kink solutions of different width but propagating at the same velocity as the kinks of the original equation. This pairing of kinks could have many applications. We illustrate the mathematical procedure with several important cases, among which are the generalized Fisher equation, the FitzHugh-Nagumo equation, and the polymerization fronts of microtubules.
Kato, Akio
2006-11-14
The invention provides methods for chromosome doubling in plants. The technique overcomes the low yields of doubled progeny associated with the use of prior techniques for doubling chromosomes in plants such as grasses. The technique can be used in large scale applications and has been demonstrated to be highly effective in maize. Following treatment in accordance with the invention, plants remain amenable to self fertilization, thereby allowing the efficient isolation of doubled progeny plants.
Efficient gradient calibration based on diffusion MRI
Teh, Irvin; Maguire, Mahon L.
2016-01-01
Purpose To propose a method for calibrating gradient systems and correcting gradient nonlinearities based on diffusion MRI measurements. Methods The gradient scaling in x, y, and z were first offset by up to 5% from precalibrated values to simulate a poorly calibrated system. Diffusion MRI data were acquired in a phantom filled with cyclooctane, and corrections for gradient scaling errors and nonlinearity were determined. The calibration was assessed with diffusion tensor imaging and independently validated with high resolution anatomical MRI of a second structured phantom. Results The errors in apparent diffusion coefficients along orthogonal axes ranged from −9.2% ± 0.4% to + 8.8% ± 0.7% before calibration and −0.5% ± 0.4% to + 0.8% ± 0.3% after calibration. Concurrently, fractional anisotropy decreased from 0.14 ± 0.03 to 0.03 ± 0.01. Errors in geometric measurements in x, y and z ranged from −5.5% to + 4.5% precalibration and were likewise reduced to −0.97% to + 0.23% postcalibration. Image distortions from gradient nonlinearity were markedly reduced. Conclusion Periodic gradient calibration is an integral part of quality assurance in MRI. The proposed approach is both accurate and efficient, can be setup with readily available materials, and improves accuracy in both anatomical and diffusion MRI to within ±1%. Magn Reson Med 77:170–179, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. PMID:26749277
The double identity of linguistic doubling.
Berent, Iris; Bat-El, Outi; Brentari, Diane; Dupuis, Amanda; Vaknin-Nusbaum, Vered
2016-11-29
Does knowledge of language consist of abstract principles, or is it fully embodied in the sensorimotor system? To address this question, we investigate the double identity of doubling (e.g., slaflaf, or generally, XX; where X stands for a phonological constituent). Across languages, doubling is known to elicit conflicting preferences at different levels of linguistic analysis (phonology vs. morphology). Here, we show that these preferences are active in the brains of individual speakers, and they are demonstrably distinct from sensorimotor pressures. We first demonstrate that doubling in novel English words elicits divergent percepts: Viewed as meaningless (phonological) forms, doubling is disliked (e.g., slaflaf < slafmak), but once doubling in form is systematically linked to meaning (e.g., slaf = ball, slaflaf = balls), the doubling aversion shifts into a reliable (morphological) preference. We next show that sign-naive speakers spontaneously project these principles to novel signs in American Sign Language, and their capacity to do so depends on the structure of their spoken language (English vs. Hebrew). These results demonstrate that linguistic preferences doubly dissociate from sensorimotor demands: A single stimulus can elicit diverse percepts, yet these percepts are invariant across stimulus modality--for speech and signs. These conclusions are in line with the possibility that some linguistic principles are abstract, and they apply broadly across language modality.
Tiny Molybdenites Tell Diffusion Tales
NASA Astrophysics Data System (ADS)
Stein, H. J.; Hannah, J. L.
2014-12-01
Diffusion invokes micron-scale exchange during crystal growth and dissolution in magma chambers on short time-scales. Fundamental to interpreting such data are assumptions on magma-fluid dynamics at all scales. Nevertheless, elemental diffusion profiles are used to estimate time scales for magma storage, eruption, and recharge. An underutilized timepiece to evaluate diffusion and 3D mobility of magmatic fluids is high-precision Re-Os dating of molybdenite. With spatially unique molybdenite samples from a young ore system (e.g., 1 Ma) and a double Os spike, analytical errors of 1-3 ka unambiguously separate events in time. Re-Os ages show that hydrous shallow magma chambers locally recharge and expel Cu-Mo-Au-silica as superimposed stockwork vein networks at time scales less than a few thousand years [1]. Re-Os ages provide diffusion rates controlled by a dynamic crystal mush, accumulation and expulsion of metalliferous fluid, and magma reorganization after explosive crystallization events. Importantly, this approach has broad application far from ore deposits. Here, we use Re-Os dating of molybdenite to assess time scales for generating and diffusing metals through the deep crust. To maximize opportunity for chemical diffusion, we use a continental-scale Sveconorwegian mylonite zone for the study area. A geologically constrained suite of molybdenite samples was acquired from quarry exposures. Molybdenite, previously unreported, is extremely scarce. Tiny but telling molybdenites include samples from like occurrences to assure geologic accuracy in Re-Os ages. Ages range from mid-Mesoproterozoic to mid-Neoproterozoic, and correspond to early metamorphic dehydration of a regionally widespread biotite-rich gneiss, localized melting of gneiss to form cm-m-scale K-feldspar ± quartz pods, development of vapor-rich, vuggy mm stringers that serve as volatile collection surfaces in felsic leucosomes, and low-angle (relative to foliation) cross-cutting cm-scale quartz veins
Microfabricated diffusion source
Oborny, Michael C.; Frye-Mason, Gregory C.; Manginell, Ronald P.
2008-07-15
A microfabricated diffusion source to provide for a controlled diffusion rate of a vapor comprises a porous reservoir formed in a substrate that can be filled with a liquid, a headspace cavity for evaporation of the vapor therein, a diffusion channel to provide a controlled diffusion of the vapor, and an outlet to release the vapor into a gas stream. The microfabricated diffusion source can provide a calibration standard for a microanalytical system. The microanalytical system with an integral diffusion source can be fabricated with microelectromechanical systems technologies.
Biktashev, V. N.; Tsyganov, M. A.
2016-01-01
Solitons, defined as nonlinear waves which can reflect from boundaries or transmit through each other, are found in conservative, fully integrable systems. Similar phenomena, dubbed quasi-solitons, have been observed also in dissipative, “excitable” systems, either at finely tuned parameters (near a bifurcation) or in systems with cross-diffusion. Here we demonstrate that quasi-solitons can be robustly observed in excitable systems with excitable kinetics and with self-diffusion only. This includes quasi-solitons of fixed shape (like KdV solitons) or envelope quasi-solitons (like NLS solitons). This can happen in systems with more than two components, and can be explained by effective cross-diffusion, which emerges via adiabatic elimination of a fast but diffusing component. We describe here a reduction procedure can be used for the search of complicated wave regimes in multi-component, stiff systems by studying simplified, soft systems. PMID:27491430
Perpendicular diffusion of energetic particles in noisy reduced magnetohydrodynamic turbulence
Shalchi, A.; Hussein, M. E-mail: m_hussein@physics.umanitoba.ca
2014-10-10
A model for noisy reduced magnetohydrodynamic turbulence was recently proposed. This model was already used to study the random walk of magnetic field lines. In the current article we use the same model to investigate the diffusion of energetic particles across the mean magnetic field. To compute the perpendicular diffusion coefficient, two analytical theories are used, namely, the Non-Linear Guiding Center theory and the Unified Non-Linear Transport (UNLT) theory. It is shown that the two theories provide different results for the perpendicular diffusion coefficient. We also perform test-particle simulations for the aforementioned turbulence model. We show that only the UNLT theory describes perpendicular transport accurately, confirming that this is a powerful tool in diffusion theory.
Purging of multilayer insulation by gas diffusion
NASA Technical Reports Server (NTRS)
Sumner, I. E.; Spuckler, C. M.
1976-01-01
An experimental investigation was conducted to determine the time required to purge a multilayer insulation (MLI) panel with gaseous helium by means of gas diffusion to obtain a condensable (nitrogen) gas concentration of less than 1 percent within the panel. Two flat, rectangular MLI panel configurations, one incorporating a butt joint, were tested. The insulation panels consisted of 15 double-aluminized Mylar radiation shields separated by double silk net spacers. The test results indicated that the rate which the condensable gas concentration at the edge or at the butt joint of an MLI panel was reduced was a significant factor in the total time required to reduce the condensable gas concentration within the panel to less than 1 percent. The experimental data agreed well with analytical predictions made by using a simple, one-dimensional gas diffusion model in which the boundary conditions at the edge of the MLI panel were time dependent.
Semi-monolithic cavity for external resonant frequency doubling and method of performing the same
NASA Technical Reports Server (NTRS)
Hemmati, Hamid (Inventor)
1999-01-01
The fabrication of an optical cavity for use in a laser, in a frequency doubling external cavity, or any other type of nonlinear optical device, can be simplified by providing the nonlinear crystal in combination with a surrounding glass having an index of refraction substantially equal to that of the nonlinear crystal. The closed optical path in this cavity is formed in the surrounding glass and through the nonlinear crystal which lies in one of the optical segments of the light path. The light is transmitted through interfaces between the surrounding glass in the nonlinear crystal through interfaces which are formed at the Brewster-angle to minimize or eliminate reflection.
Restoration of rhythmicity in diffusively coupled dynamical networks.
Zou, Wei; Senthilkumar, D V; Nagao, Raphael; Kiss, István Z; Tang, Yang; Koseska, Aneta; Duan, Jinqiao; Kurths, Jürgen
2015-07-15
Oscillatory behaviour is essential for proper functioning of various physical and biological processes. However, diffusive coupling is capable of suppressing intrinsic oscillations due to the manifestation of the phenomena of amplitude and oscillation deaths. Here we present a scheme to revoke these quenching states in diffusively coupled dynamical networks, and demonstrate the approach in experiments with an oscillatory chemical reaction. By introducing a simple feedback factor in the diffusive coupling, we show that the stable (in)homogeneous steady states can be effectively destabilized to restore dynamic behaviours of coupled systems. Even a feeble deviation from the normal diffusive coupling drastically shrinks the death regions in the parameter space. The generality of our method is corroborated in diverse non-linear systems of diffusively coupled paradigmatic models with various death scenarios. Our study provides a general framework to strengthen the robustness of dynamic activity in diffusively coupled dynamical networks.
Vector Diffusion Maps and the Connection Laplacian
Singer, A.; Wu, H.-T.
2013-01-01
We introduce vector diffusion maps (VDM), a new mathematical framework for organizing and analyzing massive high-dimensional data sets, images, and shapes. VDM is a mathematical and algorithmic generalization of diffusion maps and other nonlinear dimensionality reduction methods, such as LLE, ISOMAP, and Laplacian eigenmaps. While existing methods are either directly or indirectly related to the heat kernel for functions over the data, VDM is based on the heat kernel for vector fields. VDM provides tools for organizing complex data sets, embedding them in a low-dimensional space, and interpolating and regressing vector fields over the data. In particular, it equips the data with a metric, which we refer to as the vector diffusion distance. In the manifold learning setup, where the data set is distributed on a low-dimensional manifold ℳd embedded in ℝp, we prove the relation between VDM and the connection Laplacian operator for vector fields over the manifold. PMID:24415793
Galactic civilizations: Population dynamics and interstellar diffusion
NASA Technical Reports Server (NTRS)
Newman, W. I.; Sagan, C.
1978-01-01
The interstellar diffusion of galactic civilizations is reexamined by potential theory; both numerical and analytical solutions are derived for the nonlinear partial differential equations which specify a range of relevant models, drawn from blast wave physics, soil science, and, especially, population biology. An essential feature of these models is that, for all civilizations, population growth must be limited by the carrying capacity of the environment. Dispersal is fundamentally a diffusion process; a density-dependent diffusivity describes interstellar emigration. Two models are considered: the first describing zero population growth (ZPG), and the second which also includes local growth and saturation of a planetary population, and for which an asymptotic traveling wave solution is found.
Propagation of nonlinearly generated harmonic spin waves in microscopic stripes
Rousseau, O.; Yamada, M.; Miura, K.; Ogawa, S.; Otani, Y.
2014-02-07
We report on the experimental study of the propagation of nonlinearly generated harmonic spin waves in microscopic CoFeB stripes. Using an all electrical technique with coplanar waveguides, we find that two kinds of spin waves can be generated by nonlinear frequency multiplication. One has a non-uniform spatial geometry and thus requires appropriate detector geometry to be identified. The other corresponds to the resonant fundamental propagative spin waves and can be efficiently excited by double- or triple-frequency harmonics with any geometry. Nonlinear excited spin waves are particularly efficient in providing an electrical signal arising from spin wave propagation.
NONLINEAR ASTEROSEISMOLOGY OF RR LYRAE
Molnar, L.; Kollath, Z.; Szabo, R.; Bryson, S.; Mullally, F.; Thompson, S. E.; Kolenberg, K.
2012-09-20
The observations of the Kepler Space Telescope revealed that fundamental-mode RR Lyrae stars may show various radial overtones. The presence of multiple radial modes may allow us to conduct nonlinear asteroseismology: comparison of mode amplitudes and frequency shifts between observations and models. Here we report the detection of three radial modes in the star RR Lyr, the eponym of the class, using the Kepler short cadence data: besides the fundamental mode, both the first and the ninth overtones can be derived from the data set. RR Lyrae shows period doubling, but switches occasionally to a state where a pattern of six pulsation cycles repeats instead of two. We found hydrodynamic models that show the same three modes and the period-six state, allowing for comparison with the observations.
Shaping the nonlinear near field
Wolf, Daniela; Schumacher, Thorsten; Lippitz, Markus
2016-01-01
Light scattering at plasmonic nanoparticles and their assemblies has led to a wealth of applications in metamaterials and nano-optics. Although shaping of fields around nanostructures is widely studied, the influence of the field inside the nanostructures is often overlooked. The linear field distribution inside the structure taken to the third power causes third-harmonic generation, a nonlinear optical response of matter. Here we demonstrate by a far field Fourier imaging method how this simple fact can be used to shape complex fields around a single particle alone. We employ this scheme to switch the third-harmonic emission from a single point source to two spatially separated but coherent sources, as in Young's double-slit assembly. We envision applications as diverse as coherently feeding antenna arrays and optical spectroscopy of spatially extended electronic states. PMID:26762487
Analysis of Nonlinear Problems in Hydrodynamics and Reaction-Diffusion.
1986-10-01
evidence concerning chemotactic response in aggregating Dictyostelium discoideum." Journal of Cell Science 25, 191-204 (1977). L. A. Segel, I. Chet, and Y...34Unified mechanism for relay and oscillation of cyclic AMP in Dictyostelium discoideum." Proceedings National Academy of Sciences (U.S.A.) 4, 1543-1547 (1977...190 (1978). 4 v -~~~~. 17 -77 . - -- - - U. Parnas and L. A. Segel, "A computer simulation of pulsatile aggregation in Dictyostelium discoideum
Diffusion Geometry Based Nonlinear Methods for Hyperspectral Change Detection
2010-05-12
Schaum and A. Stocker, “Hyperspectral change detection and supervised matched filtering based on covariance equalization,” Proceedings of the SPIE, vol...5425, pp. 77- 90 (2004). 10. A. Schaum and A. Stocker, “Linear chromodynamics models for hyperspectral target detection,” Proceedings of the IEEE...Aerospace Conference (February 2003). 11. A. Schaum and A. Stocker, “Linear chromodynamics models for hyperspectral target detection
DEVELOPMENT OF SPLIT-OPERATOR, PETROV-GALERKIN METHODS TO SIMULATE TRANSPORT AND DIFFUSION PROBLEMS
The rate at which contaminants in groundwater undergo sorption and desorption is routinely described using diffusion models. Such approaches, when incorporated into transport models, lead to large systems of coupled equations, often nonlinear. This has restricted applications of ...
Instability of turing patterns in reaction-diffusion-ODE systems.
Marciniak-Czochra, Anna; Karch, Grzegorz; Suzuki, Kanako
2017-02-01
The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of interactions between cellular processes such as cell growth, differentiation or transformation and diffusing signaling factors. We focus on stability analysis of solutions of a prototype model consisting of a single reaction-diffusion equation coupled to an ordinary differential equation. We show that such systems are very different from classical reaction-diffusion models. They exhibit diffusion-driven instability (turing instability) under a condition of autocatalysis of non-diffusing component. However, the same mechanism which destabilizes constant solutions of such models, destabilizes also all continuous spatially heterogeneous stationary solutions, and consequently, there exist no stable Turing patterns in such reaction-diffusion-ODE systems. We provide a rigorous result on the nonlinear instability, which involves the analysis of a continuous spectrum of a linear operator induced by the lack of diffusion in the destabilizing equation. These results are extended to discontinuous patterns for a class of nonlinearities.
Generalized Sagdeev approach to nonlinear plasma excitations
NASA Astrophysics Data System (ADS)
Akbari-Moghanjoughi, M.
2017-02-01
In this work, we extend the Sagdeev pseudopotential approach by introducing the generalized potential, which is used for the investigation of nonlinear periodic, solitary, as well as double layer excitations in plasmas. Particularly in the framework of the generalized potential, the nonlinear excitations are investigated based on their total Sagdeev pseudoenergy. In this framework, conventional solitons are categorized as species with zero Sagdeev energy. A new type of positive energy solitons with subsonic Mach numbers is found. It is remarked that positive energy solitons do not obey the standard behavior of KdV solitons. Different types of nonlinear excitations are characterized in terms of their Sagdeev energy, and the parametric regions in which they exist are studied in detail. The nonlinear periodic waves are found to be either negative or positive energy type, characteristics of which are found to be quite different. A small amplitude theory of Sagdeev cnoidal waves is developed, which can be used to investigate the low energy waves with Mach numbers close to the critical one. Using the new concept of Sagdeev energy, we study different properties of large amplitude positive and negative energy nonlinear periodic waves in a plasma with arbitrary degree of electron degeneracy ranging from dilute classical up to the completely degenerate plasmas.
Diffusion bonding aeroengine components
NASA Astrophysics Data System (ADS)
Fitzpatrick, G. A.; Broughton, T.
1988-10-01
The use of diffusion bonding processes at Rolls-Royce for the manufacture of titanium-alloy aircraft engine components and structures is described. A liquid-phase diffusion bonding process called activated diffusion bonding has been developed for the manufacture of the hollow titanium wide chord fan blade. In addition, solid-state diffusion bonding is being used in the manufacture of hollow vane/blade airfoil constructions mainly in conjunction with superplastic forming and hot forming techniques.
Steric effects in the dynamics of electrolytes at large applied voltages. I. Double-layer charging
NASA Astrophysics Data System (ADS)
Kilic, Mustafa Sabri; Bazant, Martin Z.; Ajdari, Armand
2007-02-01
The classical Poisson-Boltzmann (PB) theory of electrolytes assumes a dilute solution of point charges with mean-field electrostatic forces. Even for very dilute solutions, however, it predicts absurdly large ion concentrations (exceeding close packing) for surface potentials of only a few tenths of a volt, which are often exceeded, e.g., in microfluidic pumps and electrochemical sensors. Since the 1950s, several modifications of the PB equation have been proposed to account for the finite size of ions in equilibrium, but in this two-part series, we consider steric effects on diffuse charge dynamics (in the absence of electro-osmotic flow). In this first part, we review the literature and analyze two simple models for the charging of a thin double layer, which must form a condensed layer of close-packed ions near the surface at high voltage. A surprising prediction is that the differential capacitance typically varies nonmonotonically with the applied voltage, and thus so does the response time of an electrolytic system. In PB theory, the differential capacitance blows up exponentially with voltage, but steric effects actually cause it to decrease while remaining positive above a threshold voltage where ions become crowded near the surface. Other nonlinear effects in PB theory are also strongly suppressed by steric effects: The net salt adsorption by the double layers in response to the applied voltage is greatly reduced, and so is the tangential “surface conduction” in the diffuse layer, to the point that it can often be neglected compared to bulk conduction (small Dukhin number).
Diffusion of tungsten hexafluoride
NASA Astrophysics Data System (ADS)
Winkelmann, J.
This document is part of Subvolume A `Gases in Gases, Liquids and their Mixtures' of Volume 15 `Diffusion in Gases, Liquids and Electrolytes' of Landolt-Börnstein Group IV `Physical Chemistry'. It is part of the chapter of the chapter `Diffusion in Pure Gases' and contains data on diffusion of tungsten hexafluoride
Reduce Confusion about Diffusion.
ERIC Educational Resources Information Center
Hebrank, Mary R.
1997-01-01
Presents activities that allow students to explore the fundamental but poorly understood concept of diffusion by appealing to their kinesthetic senses first, then challenging their analytical skills as they try to deduce the mathematical principle involved. Presents a computer simulation of diffusion and discusses diffusion's limitations and…
ERIC Educational Resources Information Center
McCutcheon, James R.; Sanders, John R.
A methodology is presented for planning and managing the spread of educational innovations. The first portion of the guide develops a theoretical framework for diffusion which summarizes and capitalizes on the latest marketing and on the latest marketing and diffusion research findings. Major stages in the diffusion paradigm discussed include…
NASA Astrophysics Data System (ADS)
Kutzner, Mickey; Pearson, Bryan
2017-02-01
Diffusion is a truly interdisciplinary topic bridging all areas of STEM education. When biomolecules are not being moved through the body by fluid flow through the circulatory system or by molecular motors, diffusion is the primary mode of transport over short distances. The direction of the diffusive flow of particles is from high concentration toward low concentration.
Handbook on atmospheric diffusion
Hanna, S.R.; Briggs, G.A.; Hosker, R.P. Jr.
1982-01-01
Basic meteorological concepts are covered as well as plume rise, source effects, and diffusion models. Chapters are included on cooling tower plumes and urban diffusion. Suggestions are given for calculating diffusion in special situations, such as for instantaneous releases over complex terrain, over long distances, and during times when chemical reactions or dry or wet deposition are important. (PSB)
Nonlinear inversion schemes for fluorescence optical tomography.
Freiberger, Manuel; Egger, Herbert; Scharfetter, Hermann
2010-11-01
Fluorescence optical tomography is a non-invasive imaging modality that employs the absorption and re-emission of light by fluorescent dyes. The aim is to reconstruct the fluorophore distribution in a body from measurements of light intensities at the boundary. Due to the diffusive nature of light propagation in tissue, fluorescence tomography is a nonlinear and severely ill-posed problem, and some sort of regularization is required for a stable solution. In this paper we investigate reconstruction methods based on Tikhonov regularization with nonlinear penalty terms, namely total-variation regularization and a levelset-type method using a nonlinear parameterization of the unknown function. Moreover, we use the full threedimensional nonlinear forward model, which arises from the governing system of partial differential equations. We discuss the numerical realization of the regularization schemes by Newtontype iterations, present some details of the discretization by finite element methods, and outline the efficient implementation of sensitivity systems via adjoint methods. As we will demonstrate in numerical tests, the proposed nonlinear methods provide better reconstructions than standard methods based on linearized forward models and linear penalty terms. We will additionally illustrate, that the careful discretization of the methods derived on the continuous level allows to obtain reliable, mesh independent reconstruction algorithms.
Parametric Identification of Nonlinear Dynamical Systems
NASA Technical Reports Server (NTRS)
Feeny, Brian
2002-01-01
In this project, we looked at the application of harmonic balancing as a tool for identifying parameters (HBID) in a nonlinear dynamical systems with chaotic responses. The main idea is to balance the harmonics of periodic orbits extracted from measurements of each coordinate during a chaotic response. The periodic orbits are taken to be approximate solutions to the differential equations that model the system, the form of the differential equations being known, but with unknown parameters to be identified. Below we summarize the main points addressed in this work. The details of the work are attached as drafts of papers, and a thesis, in the appendix. Our study involved the following three parts: (1) Application of the harmonic balance to a simulation case in which the differential equation model has known form for its nonlinear terms, in contrast to a differential equation model which has either power series or interpolating functions to represent the nonlinear terms. We chose a pendulum, which has sinusoidal nonlinearities; (2) Application of the harmonic balance to an experimental system with known nonlinear forms. We chose a double pendulum, for which chaotic response were easily generated. Thus we confronted a two-degree-of-freedom system, which brought forth challenging issues; (3) A study of alternative reconstruction methods. The reconstruction of the phase space is necessary for the extraction of periodic orbits from the chaotic responses, which is needed in this work. Also, characterization of a nonlinear system is done in the reconstructed phase space. Such characterizations are needed to compare models with experiments. Finally, some nonlinear prediction methods can be applied in the reconstructed phase space. We developed two reconstruction methods that may be considered if the common method (method of delays) is not applicable.
1992-02-13
Self-diffusion studies of Se in CdSe and chemical interdiffusion studies of Se in CdTe, on the other hand, revealed diffusivities on the order of 107...pp. 922-933 (1990). - 23 - 10. R. S. Fiegelson and R. S. Route, "Improved yield of Bridgman grown AgGaSe 2 crystals using shaped crucibles," J. Cryst...and F. G. Storz, "Linear and nonlinear optical properties of ZnGeP2 and CdSe ," Appl. Phys. Lett. 18, pp. 301-303 (1971). 50. K. L. Vodopyanov, L. A
NASA Astrophysics Data System (ADS)
Roling, Bernhard
2002-07-01
The potential of nonlinear conductivity spectroscopy for obtaining new information on the hopping dynamics of mobile charge carriers in disordered materials is analyzed from a theoretical as well as from an experimental point of view. The nonlinear conductivity spectra of simple hopping models are calculated by means of analytical methods and Monte Carlo simulations. It is shown that the nonlinearity of the high-frequency conductivity is strongly influenced by the local asymmetry of the potential landscape, while the nonlinearity of the low-frequency conductivity is sensitive to the structure of the long-range diffusion pathways. Furthermore, experimental results for the nonlinear conductivity of ion conducting glasses and polymers are reviewed.
Z-scan: A simple technique for determination of third-order optical nonlinearity
Singh, Vijender; Aghamkar, Praveen
2015-08-28
Z-scan is a simple experimental technique to measure intensity dependent nonlinear susceptibilities of third-order nonlinear optical materials. This technique is used to measure the sign and magnitude of both real and imaginary part of the third order nonlinear susceptibility (χ{sup (3)}) of nonlinear optical materials. In this paper, we investigate third-order nonlinear optical properties of Ag-polymer composite film by using single beam z-scan technique with Q-switched, frequency doubled Nd: YAG laser (λ=532 nm) at 5 ns pulse. The values of nonlinear absorption coefficient (β), nonlinear refractive index (n{sub 2}) and third-order nonlinear optical susceptibility (χ{sup (3)}) of permethylazine were found to be 9.64 × 10{sup −7} cm/W, 8.55 × 10{sup −12} cm{sup 2}/W and 5.48 × 10{sup −10} esu, respectively.
Transmission performance of the double-sideband SCM optical label
NASA Astrophysics Data System (ADS)
Chen, Minghua; Zhou, Weiqing; Jia, Zhensheng; Xie, Shizhong
2002-09-01
Transmission performance of the optical label with the double-sideband subcarrier multiplexing is investigated using Volterra transfer function approach. It is shown that the phase shifts of the two sideband signal is induced jointly by the interaction between SCM component and payload component due to fiber dispersion and nonlinearity. This will cause the SCM label fading, and then harm to system performance.
Nonlinear rotordynamics analysis
NASA Technical Reports Server (NTRS)
Day, W. B.
1985-01-01
The special nonlinearities of the Jeffcott equations in rotordynamics are examined. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot firing ground testing. Deadband, side force and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency is defined and used to develop the solutions of the nonlinear Jeffcott equations as asympotic expansions. This nonlinear natural frequency which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies. Numerical solutions are included for comparison with the analysis. Also, nonlinear frequency-response tables are made for a typical range of values.
A self-consistent theory of localization in nonlinear random media
NASA Astrophysics Data System (ADS)
Cherroret, Nicolas
2017-01-01
The self-consistent theory of localization is generalized to account for a weak quadratic nonlinear potential in the wave equation. For spreading wave packets, the theory predicts the destruction of Anderson localization by the nonlinearity and its replacement by algebraic subdiffusion, while classical diffusion remains unaffected. In 3D, this leads to the emergence of a subdiffusion-diffusion transition in place of the Anderson transition. The accuracy and the limitations of the theory are discussed.
Nonlinear Dynamics of Single Bunch Instability
Stupakov, G.V.; Breizman, B.N.; Pekker, M.S.; /Texas U.
2011-09-09
A nonlinear equation is derived that governs the evolution of the amplitude of unstable oscillations with account of quantum diffusion effects due to the synchrotron radiation. Numerical solutions to this equation predict a variety of possible scenarios of nonlinear evolution of the instability some of which are in good qualitative agreement with experimental observations. Microwave single bunch instability in circular accelerators has been observed in many machines. The instability usually arises when the number of particles in the bunch exceeds some critical value, Nc, which varies depending on the parameters of the accelerating regime. Recent observations on the SLC damping rings at SLAC with a new low-impedance vacuum chamber revealed new interesting features of the instability. In some cases, after initial exponential growth, the instability eventually saturated at a level that remained constant through the accumulation cycle. In other regimes, relaxation-type oscillations were measured in nonlinear phase of the instability. In many cases, the instability was characterized by a frequency close to the second harmonic of the synchrotron oscillations. Several attempts have been made to address the nonlinear stage of the instability based on either computer simulations or some specific assumptions regarding the structure of the unstable mode. An attempt of a more general consideration of the problem is carried out in this paper. We adopt an approach recently developed in plasma physics for analysis of nonlinear behavior of weakly unstable modes in dynamic systems. Assuming that the growth rate of the instability is much smaller than its frequency, we find a time dependent solution to Vlasov equation and derive an equation for the complex amplitude of the oscillations valid in the nonlinear regime. Numerical solutions to this equation predict a variety of possible scenarios of nonlinear evolution of the instability some of which are in good qualitative agreement
Principles of Nonlinear Optics
1989-11-01
Holography 74 6.2 Semiclassical Analysis 77 7. The Nonlinear Schrodinger Equation and Soliton Propagation 81 8. Conclusion Ancession For 86 ETis -GRA...is analyzed through the nonlinear Schrodinger equation , which is first heuristically derived. The distortionless pulses arising out of a balance...Eq. (71) has the same form as the nonlinear Schrodinger equation (2], (4], [17], (20], which is used to explain soliton propagation through fibers (21
1992-07-07
mrtegrating the original governing differential equation. 2. A. H. Nayfeh, " Parametric Identification of Nonlinear Dynamic Systems," Computers...Structures, Vol. 20. No. 1-3. 1985, pp. 487-493. A parametric identification technique that exploits nonlinear resonances and comparisons of the behavior of...617-631. Presentations 1. A. H. Vn’.yfeh, " Parametric Identification of Nonlinear Dynamic Systems," Symposium on Advances and Trends in Structures
Correia, Teresa; Aguirre, Juan; Sisniega, Alejandro; Chamorro-Servent, Judit; Abascal, Juan; Vaquero, Juan J.; Desco, Manuel; Kolehmainen, Ville; Arridge, Simon
2011-01-01
Fluorescence diffuse optical tomography (fDOT) is an imaging modality that provides images of the fluorochrome distribution within the object of study. The image reconstruction problem is ill-posed and highly underdetermined and, therefore, regularisation techniques need to be used. In this paper we use a nonlinear anisotropic diffusion regularisation term that incorporates anatomical prior information. We introduce a split operator method that reduces the nonlinear inverse problem to two simpler problems, allowing fast and efficient solution of the fDOT problem. We tested our method using simulated, phantom and ex-vivo mouse data, and found that it provides reconstructions with better spatial localisation and size of fluorochrome inclusions than using the standard Tikhonov penalty term. PMID:22091447
Eddy diffusivity in the ocean surface
NASA Astrophysics Data System (ADS)
Redondo, Jose M.; Castilla, Robert; Platonov, Alexei
2010-05-01
., Vortical structures in stratified turbulent flows, in Turbulent Diffusion in the Environment, eds. Redondo J. M. and Babiano A. (FRAGMA, Madrid)(2000), 113. [4] Castilla R., Redondo J. M., Gamez-Monterol P. J. and Babiano A., Nonlinear Processes Geophys., 14 (2007) 139. [5] Fung J. and Vassilicos J. C., Phys. Rev. E, 52 (1998) 1677. [6] Redondo J. M. and Platonov, Environ. Res. Lett., 4 (2009) 14008.
Nonlinearity-reduced interferometer
NASA Astrophysics Data System (ADS)
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.
Coherent propagation of waves in dilute random media with weak nonlinearity
Wellens, Thomas; Gremaud, Benoit
2009-12-15
We develop a diagrammatic theory for transport of waves in dilute disordered media with weak nonlinearity. We first represent the solution of the nonlinear wave equation as a nonlinear Born series. From this, we construct nonlinear ladder and crossed diagrams for the average wave intensity. Then, we sum up the diagrammatic series completely, i.e., nonperturbatively in the strength of the nonlinearity, and thereby obtain integral equations describing both nonlinear diffusive transport and coherent backscattering of the average intensity. As main result, we find that the nonlinearity significantly influences the magnitude of the coherent backscattering effect. Depending on the type of nonlinearity, coherent backscattering is either enhanced or suppressed, as compared to the linear case.
Origin of soft limits from nonlinear supersymmetry in Volkov-Akulov theory
NASA Astrophysics Data System (ADS)
Kallosh, Renata; Karlsson, Anna; Murli, Divyanshu
2017-03-01
We apply the background field technique, recently developed for a general class of nonlinear symmetries, at tree level, to the Volkov-Akulov theory with spontaneously broken N=1 supersymmetry. We find that the background field expansion in terms of the free fields to the lowest order reproduces the nonlinear supersymmetry transformation rules. The double soft limit of the background field is, in agreement with the new general identities, defined by the algebra of the nonlinear symmetries.
Controlled synthesis of double-wall a-FePO4 nanotubes and their LIB cathode properties.
Cai, Ren; Liu, Hai; Zhang, Wenyu; Tan, Huiteng; Yang, Dan; Huang, Yizhong; Hng, Huey Hoon; Lim, Tuti Mariana; Yan, Qingyu
2013-04-08
Double-wall amorphous FePO4 nanotubes are prepared by an oil-phase chemical route. The inward diffusion of vacancies and outward diffusion of ions through passivation layers result in double-wall nanotubes with thin walls. Such a process can be extended to prepare hollow polydedral nanocrystals and hollow ellipsoids. The double-wall FePO4 nanotubes show interesting cathode performance in Li ion batteries.
Tunneling control using classical non-linear oscillator
Kar, Susmita; Bhattacharyya, S. P.
2014-04-24
A quantum particle is placed in symmetric double well potential which is coupled to a classical non-linear oscillator via a coupling function. With different spatial symmetry of the coupling and under various controlling fashions, the tunneling of the quantum particle can be enhanced or suppressed, or totally destroyed.
Nonlinear Landau-Zener tunneling in coupled waveguide arrays
Khomeriki, Ramaz
2010-07-15
The possibility of direct observation of the nonlinear Landau-Zener tunneling effect with a device consisting of two waveguide arrays connected to a tilted reduced refractive index barrier is discussed. Numerical simulations on this realistic setup are interpreted via a simplified double-well system and different asymmetric tunneling scenarios are predicted varying just the injected beam intensity.
NASA Astrophysics Data System (ADS)
Genet, Russell M.; Fulton, B. J.; Bianco, Federica B.; Martinez, John; Baxter, John; Brewer, Mark; Carro, Joseph; Collins, Sarah; Estrada, Chris; Johnson, Jolyon; Salam, Akash; Wallen, Vera; Warren, Naomi; Smith, Thomas C.; Armstrong, James D.; McGaughey, Steve; Pye, John; Mohanan, Kakkala; Church, Rebecca
2012-05-01
Double stars have been systematically observed since William Herschel initiated his program in 1779. In 1803 he reported that, to his surprise, many of the systems he had been observing for a quarter century were gravitationally bound binary stars. In 1830 the first binary orbital solution was obtained, leading eventually to the determination of stellar masses. Double star observations have been a prolific field, with observations and discoveries - often made by students and amateurs - routinely published in a number of specialized journals such as the Journal of Double Star Observations. All published double star observations from Herschel's to the present have been incorporated in the Washington Double Star Catalog. In addition to reviewing the history of visual double stars, we discuss four observational technologies and illustrate these with our own observational results from both California and Hawaii on telescopes ranging from small SCTs to the 2-meter Faulkes Telescope North on Haleakala. Two of these technologies are visual observations aimed primarily at published "hands-on" student science education, and CCD observations of both bright and very faint doubles. The other two are recent technologies that have launched a double star renaissance. These are lucky imaging and speckle interferometry, both of which can use electron-multiplying CCD cameras to allow short (30 ms or less) exposures that are read out at high speed with very low noise. Analysis of thousands of high speed exposures allows normal seeing limitations to be overcome so very close doubles can be accurately measured.
NASA Astrophysics Data System (ADS)
Sahadevan, R.; Prakash, P.
2017-01-01
We show how invariant subspace method can be extended to time fractional coupled nonlinear partial differential equations and construct their exact solutions. Effectiveness of the method has been illustrated through time fractional Hunter-Saxton equation, time fractional coupled nonlinear diffusion system, time fractional coupled Boussinesq equation and time fractional Whitman-Broer-Kaup system. Also we explain how maximal dimension of the time fractional coupled nonlinear partial differential equations can be estimated.
Pullback attractors for nonclassical diffusion equations with delays
NASA Astrophysics Data System (ADS)
Zhu, Kaixuan; Sun, Chunyou
2015-09-01
In this paper, we prove the existence of pullback attractors in C H0 1 ( Ω ) for a nonclassical diffusion equation with delay term g(t, ut) which contains some hereditary characteristics. We consider two types of nonlinearity f: one is the case of critical growth and the other one is the polynomial growth of arbitrary order p - 1(p ≥ 2).
Restabilizing Forcing for a Diffusive Prey-Predator Model
NASA Astrophysics Data System (ADS)
Buonomo, Bruno; Rionero, Salvatore
2008-04-01
We consider a diffusive prey-predator model and find conditions under which a relevant non trivial equilibrium undergoes to Turing bifurcation. Then, a forcing is applied to the model and values of forcing able to regain the (nonlinear) stability are detected. A maximal restabilizing region is derived.
Collisional diffusion in toroidal plasmas with elongation and triangularity
Martin, P.; Castro, E.; Haines, M. G.
2007-05-15
Collisional diffusion is analyzed for plasma tokamaks with different ellipticities and triangularities. Improved nonlinear equations for the families of magnetic surfaces are used here. Dimensionless average velocities are calculated as a function of the inductive electric field, elongation, triangularity, and Shafranov shift. Confinement has been found to depend significantly on triangularity.
Kulkarni, Nagraj S.; Bruce Warmack, Robert J.; Radhakrishnan, Bala; Hunter, Jerry L.; Sohn, Yongho; Coffey, Kevin R.; Murch, Graeme E.; Belova, Irina V.
2014-09-23
Tracer diffusivities provide the most fundamental information on diffusion in materials and are the foundation of robust diffusion databases. Compared to traditional radiotracer techniques that utilize radioactive isotopes, the secondary ion mass spectrometry (SIMS) based thin-film technique for tracer diffusion is based on the use of enriched stable isotopes that can be accurately profiled using SIMS. Experimental procedures & techniques that are utilized for the measurement of tracer diffusion coefficients are presented for pure magnesium, which presents some unique challenges due to the ease of oxidation. The development of a modified Shewmon-Rhines diffusion capsule for annealing Mg and an ultra-high vacuum (UHV) system for sputter deposition of Mg isotopes are discussed. Optimized conditions for accurate SIMS depth profiling in polycrystalline Mg are provided. An automated procedure for the correction of heat-up and cool-down times during tracer diffusion annealing is discussed. The non-linear fitting of a SIMS depth profile data using the thin film Gaussian solution to obtain the tracer diffusivity along with the background tracer concentration and tracer film thickness is discussed. An Arrhenius fit of the Mg self-diffusion data obtained using the low-temperature SIMS measurements from this study and the high-temperature radiotracer measurements of Shewmon and Rhines (1954) was found to be a good representation of both types of diffusion data that cover a broad range of temperatures between 250 - 627° C (523 900 K).
Kulkarni, Nagraj S.; Bruce Warmack, Robert J.; Radhakrishnan, Bala; ...
2014-09-23
Tracer diffusivities provide the most fundamental information on diffusion in materials and are the foundation of robust diffusion databases. Compared to traditional radiotracer techniques that utilize radioactive isotopes, the secondary ion mass spectrometry (SIMS) based thin-film technique for tracer diffusion is based on the use of enriched stable isotopes that can be accurately profiled using SIMS. Experimental procedures & techniques that are utilized for the measurement of tracer diffusion coefficients are presented for pure magnesium, which presents some unique challenges due to the ease of oxidation. The development of a modified Shewmon-Rhines diffusion capsule for annealing Mg and an ultra-highmore » vacuum (UHV) system for sputter deposition of Mg isotopes are discussed. Optimized conditions for accurate SIMS depth profiling in polycrystalline Mg are provided. An automated procedure for the correction of heat-up and cool-down times during tracer diffusion annealing is discussed. The non-linear fitting of a SIMS depth profile data using the thin film Gaussian solution to obtain the tracer diffusivity along with the background tracer concentration and tracer film thickness is discussed. An Arrhenius fit of the Mg self-diffusion data obtained using the low-temperature SIMS measurements from this study and the high-temperature radiotracer measurements of Shewmon and Rhines (1954) was found to be a good representation of both types of diffusion data that cover a broad range of temperatures between 250 - 627° C (523 900 K).« less
Nonlinear Analysis of Surface EMG Time Series of Back Muscles
NASA Astrophysics Data System (ADS)
Dolton, Donald C.; Zurcher, Ulrich; Kaufman, Miron; Sung, Paul
2004-10-01
A nonlinear analysis of surface electromyography time series of subjects with and without low back pain is presented. The mean-square displacement and entropy shows anomalous diffusive behavior on intermediate time range 10 ms < t < 1 s. This behavior implies the presence of correlations in the signal. We discuss the shape of the power spectrum of the signal.
NASA Technical Reports Server (NTRS)
Sheen, Jyh-Jong; Bishop, Robert H.
1992-01-01
The feedback linearization technique is applied to the problem of spacecraft attitude control and momentum management with control moment gyros (CMGs). The feedback linearization consists of a coordinate transformation, which transforms the system to a companion form, and a nonlinear feedback control law to cancel the nonlinear dynamics resulting in a linear equivalent model. Pole placement techniques are then used to place the closed-loop poles. The coordinate transformation proposed here evolves from three output functions of relative degree four, three, and two, respectively. The nonlinear feedback control law is presented. Stability in a neighborhood of a controllable torque equilibrium attitude (TEA) is guaranteed and this fact is demonstrated by the simulation results. An investigation of the nonlinear control law shows that singularities exist in the state space outside the neighborhood of the controllable TEA. The nonlinear control law is simplified by a standard linearization technique and it is shown that the linearized nonlinear controller provides a natural way to select control gains for the multiple-input, multiple-output system. Simulation results using the linearized nonlinear controller show good performance relative to the nonlinear controller in the neighborhood of the TEA.
Optically Nonlinear Polymeric Materials.
1983-01-01
optical chromophores into the hydrophobic portions of the polymer, second order . ,nonlinear optical effects may be obtained. Experimental 01 0...8217V cinnamaldehyde , giving the polymer shown in Figure 3. This chromophore should have greater optical nonlinearity because of its better electron