Entropy Gradient Research Articles

On the Interaction of Jupiter’s Great Red Spot and Zonal Jet Streams

Abstract In this paper, Jupiter’s Great Red Spot (GRS) is used to determine properties of the Jovian atmosphere that cannot otherwise be found. These properties include the potential vorticity of the GRS and its neighboring jet streams, the shear imposed on the GRS by the jet streams, and the vertical entropy gradient (i.e., Rossby deformation radius). The cloud cover of the GRS, which is often used to define the GRS’s area and aspect ratio, is found to differ significantly from the region of the GRS’s potential vorticity anomaly. The westward-going jet stream to the north of the GRS and the eastward-going jet stream to its south are each found to have a large potential vorticity “jump.” The jumps have opposite signs, and as a consequence of their interaction with the GRS, the shear imposed on the GRS is reduced. The aspect ratio of the GRS’s potential vorticity anomaly depends on the ratio of the imposed shear to the strength of the anomaly. The east–west to north–south aspect ratio is found to be ∼2:1, but without the opposing jumps it would be much greater. The GRS’s high-speed collar and quiescent interior require that the potential vorticity in the interior be approximately half that in the collar. No other persistent geophysical vortex has a significant local minimum of potential vorticity in its interior, and laboratory vortices with such a minimum are unstable.

On type I planetary migration in adiabatic disks

AbstractWe investigate type I migration in a two-dimensional adiabatic disk. We find entropy perturbations that are advected in the planet's coorbital region. These entropy perturbations yield an excess of corotation torque that scales with the unperturbed entropy gradient at corotation. This torque excess can be large enough to slow down migration significantly, or even stop it.

Dynamical instability of laminar axisymmetric flows of ideal fluid with stratification

The instability of nonhomentropic axisymmetric flows of ideal fluid with respect to two-dimensional infinitesimal perturbations with the nonconservation of angular momentum is investigated by numerically integrating the differential equations of hydrodynamics. This problem is important in studying the dynamics of astrophysical flows as shear fluid flows around a gravitating center. A complex influence of a nonzero entropy gradient on the instability of sonic and surface gravity modes has been found. In particular, both an increase and a decrease in entropy against the effective gravity g eff causes the growth of surface gravity modes that are stable at the same parameters for a homentropic flow. At the same time, the growth rate of the sonic instability branches either monotonically increases with increasing rate of decrease in entropy against g eff or becomes zero at both negative and positive entropy gradients in the unperturbed flow. Calculations also show that growing internal gravity modes appear in the problem with free boundaries under consideration only if the flow is no longer stable with respect to axisymmetric perturbations. In addition, we show that it is improper to specify the entropy distribution in the main flow by a polytropic law with a polytropic index different from the adiabatic value, since the perturbation field does not satisfy the boundary condition at a free boundary in this case.

Ultrahigh-Resolution 1H−13C HSQC Spectra of Metabolite Mixtures Using Nonlinear Sampling and Forward Maximum Entropy Reconstruction

To obtain a comprehensive assessment of metabolite levels from extracts of leukocytes, we have recorded ultrahigh-resolution 1H-13C HSQC NMR spectra of cell extracts, which exhibit spectral signatures of numerous small molecules. However, conventional acquisition of such spectra is time-consuming and hampers measurements on multiple samples, which would be needed for statistical analysis of metabolite concentrations. Here we show that the measurement time can be dramatically reduced without loss of spectral quality when using nonlinear sampling (NLS) and a new high-fidelity forward maximum-entropy (FM) reconstruction algorithm. This FM reconstruction conserves all measured time-domain data points and guesses the missing data points by an iterative process. This consists of discrete Fourier transformation of the sparse time-domain data set, computation of the spectral entropy, determination of a multidimensional entropy gradient, and calculation of new values for the missing time-domain data points with a conjugate gradient approach. Since this procedure does not alter measured data points, it reproduces signal intensities with high fidelity and does not suffer from a dynamic range problem. As an example we measured a natural abundance 1H-13C HSQC spectrum of metabolites from granulocyte cell extracts. We show that a high-resolution 1H-13C HSQC spectrum with 4k complex increments recorded linearly within 3.7 days can be reconstructed from one-seventh of the increments with nearly identical spectral appearance, indistinguishable signal intensities, and comparable or even lower root-mean-square (rms) and peak noise patterns measured in signal-free areas. Thus, this approach allows recording of ultrahigh resolution 1H-13C HSQC spectra in a fraction of the time needed for recording linearly sampled spectra.

Neutrino‐driven Convection versus Advection in Core‐Collapse Supernovae

A toy model is analyzed in order to evaluate the linear stability of the gain region immediately behind a stalled accretion shock, after core bounce. This model demonstrates that a negative entropy gradient is not sufficient to warrant linear instability. The stability criterion is governed by the ratio \chi of the advection time through the gain region divided by the local timescale of buoyancy. The gain region is linearly stable if \chi 3, perturbations are unstable in a limited range of horizontal wavelengths centered around twice the vertical size H of the gain region. The threshold horizontal wavenumbers k_{min} and k_{max} follow simple scaling laws such that Hk_{min}\propto 1/{\chi} and Hk_{max}\propto \chi. The convective stability of the l=1 mode in spherical accretion is discussed, in relation with the asymmetric explosion of core collapse supernovae. The advective stabilization of long wavelength perturbations weakens the possible influence of convection alone on a global l=1 mode.

Simulation of the Magnetothermal Instability

In many magnetized, dilute astrophysical plasmas, thermal conduction occurs almost exclusively parallel to magnetic field lines. In this case, the usual stability criterion for convective stability, the Schwarzschild criterion, which depends on entropy gradients, is modified. In the magnetized long mean free path regime, instability occurs for small wavenumbers when (dP/dz)(dln T/dz) > 0, which we refer to as the Balbus criterion. We refer to the convective-type instability that results as the magnetothermal instability (MTI). We use the equations of MHD with anisotropic electron heat conduction to numerically simulate the linear growth and nonlinear saturation of the MTI in plane-parallel atmospheres that are unstable according to the Balbus criterion. The linear growth rates measured from the simulations are in excellent agreement with the weak field dispersion relation. The addition of isotropic conduction, e.g. radiation, or strong magnetic fields can damp the growth of the MTI and affect the nonlinear regime. The instability saturates when the atmosphere becomes isothermal as the source of free energy is exhausted. By maintaining a fixed temperature difference between the top and bottom boundaries of the simulation domain, sustained convective turbulence can be driven. MTI-stable layers introduced by isotropic conduction are used to prevent the formation of unresolved, thermal boundary layers. We find that the largest component of the time-averaged heat flux is due to advective motions as opposed to the actual thermal conduction itself. Finally, we explore the implications of this instability for a variety of astrophysical systems, such as neutron stars, the hot intracluster medium of galaxy clusters, and the structure of radiatively inefficient accretion flows.

Sensor band selection for multispectral imaging via average normalized information

The information-rich scene descriptors created by multispectral sensors can act as a bottleneck in further analysis, e.g., real-time scene capturing. Many of the spectral band selection methods treat the two underlying tasks (feature bands selection and redundancy reduction) in isolation. Furthermore, the majority of the work assumes reflectance data. However, the captured surface radiance varies with scene geometry and illumination. We propose a new band selection method, which uses spectral gradient entropy to choose bands that are more stable to such variations. Equally important, our measurement, the average normalized information (ANI) of a set of selected bands, combines feature band selection and band redundancy together. Since feature stability is an important criterion for band selection in ANI, our method favors features whose probability density can be accurately estimated. As a result, our technique selects the most representative feature bands that can be efficiently used in classification. In our experiments, ANI exhibited comparable performance with mutual information on reflectance data but outperformed mutual information when applied on surface radiance data.

Information Theory in Living Systems, Methods, Applications, and Challenges

Living systems are distinguished in nature by their ability to maintain stable, ordered states far from equilibrium. This is despite constant buffeting by thermodynamic forces that, if unopposed, will inevitably increase disorder. Cells maintain a steep transmembrane entropy gradient by continuous application of information that permits cellular components to carry out highly specific tasks that import energy and export entropy. Thus, the study of information storage, flow and utilization is critical for understanding first principles that govern the dynamics of life. Initial biological applications of information theory (IT) used Shannon's methods to measure the information content in strings of monomers such as genes, RNA, and proteins. Recent work has used bioinformatic and dynamical systems to provide remarkable insights into the topology and dynamics of intracellular information networks. Novel applications of Fisher-, Shannon-, and Kullback-Leibler informations are promoting increased understanding of the mechanisms by which genetic information is converted to work and order. Insights into evolution may be gained by analysis of the the fitness contributions from specific segments of genetic information as well as the optimization process in which the fitness are constrained by the substrate cost for its storage and utilization. Recent IT applications have recognized the possible role of nontraditional information storage structures including lipids and ion gradients as well as information transmission by molecular flux across cell membranes. Many fascinating challenges remain, including defining the intercellular information dynamics of multicellular organisms and the role of disordered information storage and flow in disease.

Standing Accretion Shocks in the Supernova Core: Effects of Convection and Realistic Equations of State

This is a sequel to the previous paper, in which we investigated the structure and stability of the spherically symmetric accretion flows through the standing shock wave onto the proto-neutron star in the postbounce phase of the collapse-driven supernova. Following the prescription in the previous paper, we assume that the accretion flow is in a steady state controlled by the neutrino luminosity and mass accretion rate that are kept constant. We obtain steady solutions for a wide range of neutrino luminosities and mass accretion rates. In so doing, as an extension to the previous models, we employ a realistic EOS and neutrino-heating rate. More importantly, we take into account the effect of convection phenomenologically. For each mass accretion rate, we find the critical neutrino luminosity, above which there exists no steady solution. These critical points are supposed to mark the onset of the shock revival. As the neutrino luminosity increases for a given mass accretion rate, there appears a convectively unstable region at some point before the critical value is reached. We introduce a phenomenological energy flux by convection so that the negative entropy gradient should be canceled out. We find that the convection lowers the critical neutrino luminosity substantially, which is in accord with the results of multidimensional numerical simulations done over the years. We also consider the effect of the self-gravity, which was neglected in the previous paper. It is found that the self-gravity is important only when the neutrino luminosity is high. The critical luminosity, however, is little affected if the energy transport by convection is taken into account.

An artificial nonlinear diffusivity method for supersonic reacting flows with shocks

A computational approach for modeling interactions between shocks waves, contact discontinuities and reactions zones with a high-order compact scheme is investigated. To prevent the formation of spurious oscillations around shocks, artificial nonlinear viscosity [A.W. Cook, W.H. Cabot, A high-wavenumber viscosity for high resolution numerical method, J. Comput. Phys. 195 (2004) 594–601] based on high-order derivative of the strain rate tensor is used. To capture temperature and species discontinuities a nonlinear diffusivity based on the entropy gradient is added. It is shown that the damping of ‘wiggles’ is controlled by the model constants and is largely independent of the mesh size and the shock strength. The same holds for the numerical shock thickness and allows a determination of the L2 error. In the shock tube problem, with fluids of different initial entropy separated by the diaphragm, an artificial diffusivity is required to accurately capture the contact surface. Finally, the method is applied to a shock wave propagating into a medium with non-uniform density/entropy and to a CJ detonation wave. Multi-dimensional formulation of the model is presented and is illustrated by a 2D oblique wave reflection from an inviscid wall, by a 2D supersonic blunt body flow and by a Mach reflection problem.

Infrared properties of boundaries in one-dimensional quantum systems

We present some partial results on the general infrared behaviour of bulk critical 1Dquantum systems with a boundary. We investigate whether the boundary entropy,s(T), is always bounded below as the temperatureT decreasestowards 0, and whether the boundary always becomes critical in the infrared limit. We showthat failure of these properties is equivalent to certain seemingly pathologicalbehaviours far from the boundary. One of our approaches uses real time methods,in which locality at the boundary is expressed by analyticity in the frequency.As a preliminary, we use real time methods to prove again that the boundarybeta function is the gradient of the boundary entropy, which implies thats(T) decreaseswith T. The metric on the space of boundary couplings is interpreted as the renormalizedsusceptibility matrix of the boundary, made finite by a natural subtraction.

Integrals of the Vorticity Equation. Part I: General Three- and Two-Dimensional Flows

AbstractThe integral of the vector vorticity equation for the vorticity of a moving parcel in 3D baroclinic flow with friction is cast in a new form. This integral of the vorticity equation applies to synoptic-scale or mesoscale flows and to deep compressible or shallow Boussinesq motions of perfectly clear or universally saturated air. The present integral is equivalent to that of Epifanio and Durran in the Boussinesq limit, but its simpler form reduces easily to Dutton’s integral when the flow is assumed to be isentropic and frictionless.The integral for vorticity has the following physical interpretation. The vorticity of a parcel is composed of barotropic vorticity; baroclinic vorticity, which originates from solenoidal generation; and vorticity stemming from frictional generation. Its barotropic vorticity is the result of freezing into the fluid the w field (specific volume times vorticity) that is present at the initial time. Its baroclinic vorticity is the vector sum of contributions from small subintervals of time that partition the interval between initial and current times. In each subinterval, the baroclinic torque generates a small vector element of vorticity and hence w. The contribution to the current baroclinic vorticity is the result of freezing this element of w into the fluid immediately after its formation. The physical interpretation of vorticity owing to frictional generation is identical except the torque is frictional rather than solenoidal.The baroclinic vorticity is decomposed into a part that would occur if the current entropy of the flow were conserved materially backward in time to the initial time and an adjustment term that accounts for production of entropy gradients in material coordinates during this interval. A method for computing all the vorticity parts in an Eulerian framework within a 3D numerical model is outlined.The usefulness of the 3D vorticity integral is demonstrated further by deriving Eckart’s, Bjerknes’s, and Kelvin’s circulation theorems from it in relatively few steps, and by showing that the associated expression for potental vorticity is an integral of the potential vorticity equation and implies conservation of potential vorticity for isentropic frictionless motion of clear air (Ertel’s theorem). Last, a formula for the helicity density of a parcel is obtained from the vorticity integral and an expression for the parcel’s velocity, and is verified by proving that it is an integral of the equation for helicity density.

Analysis of the linkages between rainfall and land surface conditions in the West African monsoon through CMAP, ERS‐WSC, and NOAA‐AVHRR data

The European Remote Sensing Wind Scatterometer (ERS‐WSC) backscattering coefficient, NOAA Advanced Very High Resolution Radiometer (NOAA‐AVHRR) Normalized Difference Vegetation Index (NDVI), and Climate Prediction Center Merged Analysis Precipitation (CMAP) precipitation data sets are studied over the period August 1991 to December 2000 to document (1) the interannual and intra‐annual evolutions of vegetation photosynthetic activity and soil‐vegetation water content over West Africa and (2) their two‐way links with precipitation. Over the Sahel, at interannual timescales the strongest relationships between vegetation, soil moisture, and precipitation are observed from July to October and when 1‐month lag is considered between the parameters. This delay reflects the vegetation response time to the moisture pulses that follow precipitation events. The high correlation between NDVI and sigma_0 at interannual timescales confirms the importance of vegetation in the backscattering coefficient. However, sigma_0 shows stronger statistical links with precipitation, suggesting that this product contains additional useful information related in particular to upper soil moisture. Over Guinea, large differences are observed between the two remote sensing products, and their relationship with precipitation at interannual timescales is weaker. Sigma_0 is significantly linked to precipitation from July to November, whereas NDVI does not show any significant relationship with precipitation. NDVI and sigma_0 serial correlations over the Sahel and Guinea suggest that a 2‐month memory usually characterizes vegetation photosynthetic activity and soil‐vegetation water content anomalies. However, anomalies disappearance in winter then reappearance in the following spring also suggests an interseason memory held by deep soil moisture reservoirs and deep‐rooted plants. A composite analysis reveals that the wettest Sahelian rainy seasons were preceded by positive anomalies of soil‐vegetation water content over Guinea from winter to spring. Cross correlations and Granger causality analyses partly relate these winter to spring land surface anomalies to those recorded in precipitation during the previous autumn. Spring soil‐vegetation water content anomalies strengthen the meridional gradient of soil‐vegetation water content over the subcontinent. This gradient is thought to contribute to the gradient of entropy that drives the West African monsoon.

Turbulence Model Studies to Investigate the Aerodynamic Performance of a NASA Dual Control Missile at Supersonic Mach Numbers

This paper contains an investigation of the ability of some of the current turbulence models to predict viscous effects in supersonic Mach number regimes. In most cases, these turbulence models have been derived and validated in traditional subsonic to transonic Mach number regimes and their application to supersonic and hypersonic regimes is assumed valid without a proper recourse to understanding the wider implications of the viscous flow field at high Mach numbers. In such flow regimes, such characteristics as the strong shock interactions with control surfaces and evolving vortices present in the flow, or other large entropy gradient effects brought about by the forebody or other fin surfaces, produce non-trivial challenges for the turbulence models. This study was aimed at interrogating the strength of the turbulence models to model such physics. The Applied Vehicle Technology Panel Group 082 of the Research Technology Organisation selected a dual control NASA missile to investigate the capabilities of Computational Fluid Dynamics (CFD) to predict the flow field and performance characteristics of complex-shaped projectiles at high Mach numbers. There are two types of difficulties that are encountered when computing such problems. The first type are geometry based, and are related to the shape of the nose and forebody, number and types of strakes or forward control mechanisms, fin geometry deployment, and shape and design of the cowls and intakes. The second type of difficulty deals with flow complexities such as the heat transfer (M > 4) implications; the vortices shed from the forebody and other control surfaces; the interaction of these vortices with the body structures, the free stream, and with each other; the base flow interaction with the free stream; the boundary-layer development; and, in the case of supersonic flows, the shock boundary-layer interactions. Air-breathing missiles with intakes or missiles with jet-controlled guidance systems add to the flow complexities. Various turbulence models employed in current CFD codes are tested for their ability to address these viscous issues.

Effect of mean entropy on unsteady disturbance propagation in a slowly varying duct with mean swirling flow

The propagation of acoustic disturbances in a slowly-varying duct with mean swirling flow and non-uniform mean entropy is considered. This is representative of the region of swirling flow downstream of the rotor in aeroengine applications where variations in mean entropy can be significant. The duct is assumed to vary slowly in axial cross section and a consistent multiple-scales solution is derived. The variation in axial wavenumber and amplitude of the duct modes is determined as part of the solution. Comparisons are made between the cases of isentropic and non-isentropic flow. The cut-on/cut-off characteristics of a given mode are altered by any form of non-uniform mean entropy, with modes pushed closer to cut-off resulting in larger variations in amplitude. The greatest departure from the baseline isentropic result occurs for a positive entropy gradient. Increasing the swirl velocity at the duct inlet leads to increasing levels of mean entropy.

Cooperative multi-robot systems:: A study of vision-based 3-D mapping using information theory

Building cooperatively 3-D maps of unknown environments is one of the application fields of multi-robot systems. This article addresses that problem through a probabilistic approach based on information theory. A distributed cooperative architecture model is formulated whereby robots exhibit cooperation through efficient information sharing. A probabilistic model of a 3-D map and a statistical sensor model are used to update the map upon range measurements, with an explicit representation of uncertainty through the definition of the map’s entropy. Each robot is able to build a 3-D map upon measurements from its own range sensor and is committed to cooperate with other robots by sharing useful measurements. An entropy-based measure of information utility is used to define a cooperation strategy for sharing useful information, without overwhelming communication resources with redundant or unnecessary information. Each robot reduces the map’s uncertainty by exploring maximum information viewpoints, by using its current map to drive its sensor to frontier regions having maximum entropy gradient. The proposed framework is validated through experiments with mobile robots equipped with stereo-vision sensors.

Nonlinear Evolution of the Magnetothermal Instability in Two Dimensions

In weakly magnetized, dilute plasmas in which thermal conduction along magnetic field lines is important, the usual convective stability criterion is modified. Instead of depending on entropy gradients, instability occurs for small wavenumbers when (∂P/∂z)(∂ ln T/∂z) > 0, which we refer to as the Balbus criterion. We refer to the convective instability that results in this regime as the magnetothermal instability (MTI). We use numerical MHD simulations that include anisotropic electron heat conduction to follow the growth and saturation of the MTI in two-dimensional, plane-parallel atmospheres that are unstable according to the Balbus criterion. The linear growth rates measured in the simulations agree with the weak-field dispersion relation. We investigate the effect of strong fields and isotropic conduction on the linear properties and nonlinear regime of the MTI. In the nonlinear regime, the instability saturates and convection decays away when the atmosphere becomes isothermal. Sustained convective turbulence can be driven if there is a fixed temperature difference between the top and bottom edges of the simulation domain, and if isotropic conduction is used to create convectively stable layers that prevent the formation of unresolved, thermal boundary layers. The largest component of the time-averaged heat flux is due to advective motions. These results have implications for a variety of astrophysical systems, such as the temperature profile of hot gas in galaxy clusters and the structure of radiatively inefficient accretion flows.

3D localization of clustered microcalcifications using cranio-caudal and medio-lateral oblique views

This paper presents a 3D localization method to register clustered microcalcifications on mammograms from cranio-caudal (CC) and medio-lateral oblique (MLO) views. The method consists of three major components: registration of clustered microcalcifications in CC and MLO views, 3D localization of clustered microcalcifications and 3D visualization of clustered microcalcifications. The registration is performed based on three features, gradient, energy and local entropy codes that are independent of spatial locations of microcalcifications in two different views and are prioritized by discriminability in a binary decision tree. The 3D localization is determined by a sequence of coordinate corrections of calcified pixels using the breast nipple as a controlling point. Finally, the 3D visualization implements a virtual reality modeling language viewer (VRMLV) to view the exact location of the lesion as a guide for needle biopsy. In order to validate our proposed 3D localization system, a set of breast lesions, which appear both in mammograms and in MR Images is used for experiments where the depth of clustered microcalcifications can be verified by the MR images.

Relativistic shock formation in the presence of radial entropy gradients

The nonlinear steepening of relativistic acoustic waves is investigated. The nonlinear evolution of a planar wave in a homentropic flow field is understood well through relativistic simple waves. However, in situations where the wave is nonplanar and the flow field is nonhomentropic, the concept of simple waves cannot be used. In the present paper, effect of entropy gradients on the nonlinear distortion of a spherical wave is analyzed using the wave front expansion technique. It is shown that the behavior of a relativistic wave in nonhomentropic environment is slightly different from the nonrelativistic wave. A closed form solution is obtained for the slope at the wave front. A general criterion for a compression wave to steepen into a shock is obtained. The distortion of compression and rarefaction waves is examined for some well known equations of state. However, the method used in this paper is general and can be easily extended to analyze shock formation in any fluid. Also, expressions for time and location of shock formation are obtained. The effects of gravity or self-gravity are not taken into account in this paper.

Mixture of fluids involving entropy gradients and acceleration waves in interfacial layers

Through an Hamiltonian action we write down the system of equations of motions for a mixture of thermocapillary fluids under the assumption that the internal energy is a function not only of the gradient of the densities but also of the gradient of the entropies of each component. A Lagrangian associated with the kinetic energy and the internal energy allows to obtain the equations of momentum for each component and for the barycentric motion of the mixture. We obtain also the balance of energy and we prove that the equations are compatible with the second law of thermodynamics. Though the system is of parabolic type, we prove that there exist two tangential acceleration waves that characterize the interfacial motion. The dependence of the internal energy of the entropy gradients is mandatory for the existence of this kind of waves. The differential system is non-linear but the waves propagate without distortion due to the fact that they are linearly degenerate (exceptional waves).