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At least 433 records · Page 24

Selection and Assessment of Phenomenological Models of Tumor Growth

We address general approaches to the rational selection and validation of mathematical and computational models of tumor growth using methods of Bayesian inference. The model classes are derived from a general diffuse-interface, continuum mixture theory and focus on mass conservation of mixtures with up to four species. Synthetic data are generated using higher-order base models. We discuss general approaches to model calibration, validation, plausibility, and selection based on Bayesian-based methods, information theory, and maximum information entropy. We also address computational issues and provide numerical experiments based on Markov chain Monte Carlo algorithms and high performance computing implementations.

59 BASIC BIOLOGICAL SCIENCES↗

Modulation of Gravity Waves by Tides as Seen in CRISTA Temperatures

During shuttle missions STS-66 (November, 1994) and STS-85 (August, 1997) the Cryogenic Infrared Spectrometers and Telescopes for the Atmosphere (CRISTA) acquired temperature data with very high spatial resolution. These are analyzed for gravity waves (GW). The altitude range spans the whole middle atmosphere from the tropopause up to the mesopause. In the upper mesosphere tidal amplitudes exceed values of 10 K. Modulation of GW activity by the tides is observed and analyzed using CRISTA temperatures and tidal predictions of the Global Scale Wave Model (GSWM). The modulation process is identified as a tidally-induced change of the background buoyancy frequency. The findings agree well with the expectations for saturated GW and are the first global scale observations of this process.

SHUTTLE MISSIONS↗

Synthesis and magnetic performance of gadolinium powder produced with rotating disk atomization

Spherical powder is key for achieving good heat transfer and maintaining low pressure drop for heat transfer fluid in magnetocaloric regenerator. Obtaining relatively large spherical powder of rare earth metals that are extremely sensitive to oxygen is challenging. Comparing to gas atomization and plasma rotating electrode methods, rotating disk atomization (RDA) method is more robust for obtaining a small amount of powder with a short turn-around time, thereby, more suitable for research and development of new magnetocaloric materials. In this work, commercially bulk gadolinium was successfully atomized to produce spherical powder in the targeted 150–250 μm range. The obtained powder exhibited the expected magnetocaloric performance with a maximum change of magnetic entropy of 12.1 J/kg K and a maximum adiabatic temperature change of 12.8 K with an applied magnetic field of 7 T.

36 MATERIALS SCIENCE↗

Nonequilibrium Entropy in a Shock

In a classic paper, Morduchow and Libby use an analytic solution for the profile of a Navier–Stokes shock to show that the equilibrium thermodynamic entropy has a maximum inside the shock. There is no general nonequilibrium thermodynamic formulation of entropy; the extension of equilibrium theory to nonequililbrium processes is usually made through the assumption of local thermodynamic equilibrium (LTE). However, gas kinetic theory provides a perfectly general formulation of a nonequilibrium entropy in terms of the probability distribution function (PDF) solutions of the Boltzmann equation. In this paper I will evaluate the Boltzmann entropy for the PDF that underlies the Navier–Stokes equations and also for the PDF of the Mott–Smith shock solution. I will show that both monotonically increase in the shock. As a result, I will propose a new nonequilibrium thermodynamic entropy and show that it is also monotone and closely approximates the Boltzmann entropy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

3d-4f spin interaction and field-induced metamagnetism in RCrO{sub 4} (R = Ho, Gd, Lu) compounds

We observe that the zircon-type RCrO{sub 4} (R = Ho, Gd, Lu) compounds exhibit complicated magnetic properties and large magnetic entropy change due to the strong competition between ferromagnetic and antiferromagnetic interactions. For a field change of 7 T, the maximum values of entropy change and refrigerant capacity reach 28 J kg{sup −1} K{sup −1} and 740 J kg{sup −1}, respectively, for GdCrO{sub 4} whereas the corresponding values for HoCrO{sub 4} are 29 J kg{sup −1} K{sup −1} and 550 J kg{sup −1}. For GdCrO{sub 4} compound, the magnetic entropy change is quite large even at low temperatures well below the ferromagnetic transition.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Use and validity of principles of extremum of entropy production in the study of complex systems

It is shown how both the principles of extremum of entropy production, which are often used in the study of complex systems, follow from the maximization of overall system conductivities, under appropriate constraints. In this way, the maximum rate of entropy production (MEP) occurs when all the forces in the system are kept constant. On the other hand, the minimum rate of entropy production (mEP) occurs when all the currents that cross the system are kept constant. A brief discussion on the validity of the application of the mEP and MEP principles in several cases, and in particular to the Earth’s climate is also presented. -- Highlights: •The principles of extremum of entropy production are not first principles. •They result from the maximization of conductivities under appropriate constraints. •The conditions of their validity are set explicitly. •Some long-standing controversies are discussed and clarified.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Magnetic properties of Dy2Ti2O7

Measurements were made of the magnetization, differential magnetic susceptibility, and magnetic entropy of powered samples of Dy2Ti2O7. The saturation magnetic moment is 4.7 + or - 0.2 Bohr magnetons per Dy ion, instead of 10 as predicted by Hund's rules. A temperature-independent magnetization is observed in the saturation region. Absolute values of magnetic entropy have been obtained for temperatures from 1.25 to 20 K, in applied fields up to 10.4 tesla. The magnetic entropy approaches a maximum value consistent with a ground-state multiplicity of 2. Low field magnetization and differential susceptibility data show a transition to antiferromagnetism near 1.35 K. A construction of the magnetic specific heat from the zero field entropy shows an anomaly near the same temperature.

Flood, D. J.↗

Maximally entangled state and Bell’s inequality in qubits

A maximally entangled state is a quantum state which has maximum von Neumann entropy for each bipartition. Through proposing a new method to classify quantum states by using concurrences of pure states of a region, one can apply Bell’s inequality to study intensity of quantum entanglement of maximally entangled states. We use a class of seven-qubit quantum states to demonstrate the method, in which we express all coefficients of the quantum states in terms of concurrences of pure states of a region. When a critical point of an upper bound of Bell’s inequality occurs in our quantum states, one of the quantum state is a ground state of the toric code model on a disk manifold. Our result also implies that the maximally entangled states do not suggest local maximum quantum entanglement in our quantum states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Continuous electrochemical heat engines

Given the large magnitude of energy in waste heat, its efficient conversion to electrical power offers a significant opportunity to lower greenhouse gas emissions. Furthermore, it has been difficult to optimize the performance of new direct energy conversion approaches because of the coupling between entropy change and thermal and electrical transport in continuously operating devices. With electrochemical cells driving flowing electrolytes in symmetric redox reactions at different temperatures, we demonstrate two continuous electrochemical heat engines that operate at 10–50 °C and at 500–900 °C, respectively. Simulations of kilowatt-scale systems using electrochemical cells stacked in series suggest efficiencies over 30% of the Carnot limit and areal power densities competitive with solid-state thermoelectrics at maximum power. Although entropy change, thermal transport and electrical transport are inherently coupled in solid-state thermoelectrics, they can be somewhat circumvented in electrochemical systems, thus offering new opportunities to engineer efficient energy conversion systems.

30 DIRECT ENERGY CONVERSION↗

Influence of Zn on magnetocaloric effect in (0.95)La{sub 0.7}Sr{sub 0.3}MnO{sub 3}/Ni{sub 1−x}Zn{sub x}Fe{sub 2}O{sub 4} ceramic composites

Highlights: • Synthesis of magnetic ceramic composites. • Magnetization of dual phase ceramics. • Magnetic entropy change in (0.95)La{sub 0.7}Sr{sub 0.3}MnO{sub 3}/(0.05)Ni{sub 1−x}Zn{sub x}Fe{sub 2}O{sub 4} solid solution. - Abstract: We report the magnetic and magnetocaloric properties of (0.95)La{sub 0.7}Sr{sub 0.3}MnO{sub 3}/(0.05)Ni{sub 1−x}Zn{sub x}Fe{sub 2}O{sub 4} (x = 0.0, 0.1, 0.3, and 0.5) ceramic composites. The composite samples with nominal compositions were prepared using the conventional solid-state reaction method. The phase purity and structure were confirmed by using X-ray diffraction. Temperature dependent magnetization measurements and Arrott analysis reveal second order of magnetic phase transition in the composite samples. A maximum in magnetic entropy change of ∼0.75 J/kg K at 1 T has been observed in (0.95)La{sub 0.7}Sr{sub 0.3}MnO{sub 3}/(0.05)NiFe{sub 2}O{sub 4} sample. The values of magnetic entropy change of these composites make them attractive for potential applications. These composite samples may consider as potential material for magnetic refrigeration near room temperature.

36 MATERIALS SCIENCE↗

Structural Analysis, Magnetocaloric Effect, and Critical Exponents for La{sub 0.6}Sr{sub 0.2}Na{sub 0.2}MnO{sub 3} Manganite

This work focuses on the structural, magnetocaloric effect, and critical exponent investigations of La{sub 0.6}Sr{sub 0.2}Na{sub 0.2}MnO{sub 3} manganite prepared via sol–gel method. XRD analysis confirms the rhombohedral structure with R 3-bar c symmetry for this sample, and Rietveld method was used to estimate its different structural parameters. The sample presents FM-PM phase transition of second-order type at T{sub C} = 309 K. The maximum of magnetic entropy change (−ΔS{sub M}{sup max}) and relative cooling power (RCP) reach values of about 3.57 J kg{sup −1} K{sup −1} and 214.46 J kg{sup −1}, respectively (at μ{sub 0}H = 5 T). These values indicate that La{sub 0.6}Sr{sub 0.2}Na{sub 0.2}MnO{sub 3} sample can be used as active magnetic refrigerator. Critical exponents (β, γ, and δ) of the sample have studied by analyzing the M(μ{sub 0}H, T) isotherms using different techniques. The estimated values of these critical exponents are found to be different to those predicted for standard theoretical models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Augmented Adam-Gibbs model for glass melt viscosity and configuration entropy as functions of temperature and composition

As the temperature of glass melt increases, its structure approaches the state of a simple liquid while the configuration entropy approaches a maximum value. We describe this gradual change using a power law function of inverse temperature. The Adam-Gibbs model for glass viscosity as a function of temperature and glass composition augmented in this way is greatly simplified when applied to common glass families occupying moderate composition regions, such as float glass or nuclear waste glasses, on which properties can be approximated as linear functions of composition. The parsimonious model thus obtained is preferable for use in optimizing glass formulation and mathematical modeling of glass melting and forming. For multicomponent glasses with N viscosity-affecting components, the augmented Adam-Gibbs model requires 2N + 3 adjustable parameters. The model efficacy is demonstrated by fitting the model to a viscosity-temperature-composition dataset for low-activity nuclear waste glasses.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Y-doped La{sub 0.7}Ca{sub 0.3}MnO{sub 3} manganites exhibiting a large magnetocaloric effect and the crossover of first-order and second-order phase transitions

We prepared orthorhombic La{sub 0.7−x}Y{sub x}Ca{sub 0.3}MnO{sub 3} samples (x = 0, 0.04, 0.06, and 0.08) by conventional solid-state reaction and then studied their magnetic properties and magnetocaloric (MC) effect based on magnetization versus temperature and magnetic-field measurements, M(T, H). The experimental results revealed that an x increase in La{sub 0.7−x}Y{sub x}Ca{sub 0.3}MnO{sub 3} reduced the ferromagnetic-paramagnetic transition temperature (T{sub C}) from 260 K (for x = 0) to ∼126 K (for x = 0.08). Around the T{sub C}, maximum magnetic-entropy changes for a magnetic-field variation interval H = 50 kOe are about 10.7, 8.5, 7.4, and 5.8 J·kg{sup −1}·K{sup −1} for x = 0, 0.04, 0.06, and 0.08, respectively, corresponding to refrigerant capacities RC = 250–280 J·kg{sup −1}. These values are comparable to those of some conventional MC materials, revealing the applicability of La{sub 0.7−x}Y{sub x}Ca{sub 0.3}MnO{sub 3} in magnetic refrigeration. Using the Arrott method and scaling hypothesis as analyzing high-field M(H, T) data, and the universal-curve construction of the magnetic entropy change, we found a magnetic-phase separation. While the samples x = 0−0.06 exhibit a first-order magnetic phase transition, x = 0.08 exhibits the crossover of the first-to-second-order phase transformation (with its critical-exponent values close to those expected for the tricritical mean-field theory) and has the presence of ferromagnetic clusters even above the T{sub C}. Such the variations in the magnetism and MC effect are related to the changes in structural parameters caused by the Y substitution for La because Y doping does not change the concentration ratio of Mn{sup 3+}/Mn{sup 4+}.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Incommensurate spin density wave and magnetocaloric effect in the metallic triangular lattice HoAl 2 Ge 2

Here, we report the magnetic structure and the magnetocaloric effect (MCE) of the ternary compound HoAl 2 Ge 2 with a trigonal CaAl 2 Si 2 -type crystal structure. A neutron powder diffraction experiment reveals that HoAl 2 Ge 2 exhibits an incommensurate spin density wave (SDW) with a propagation vector k=(0.23,0,0.06). The special arrangement of magnetic moments in HoAl 2 Ge 2 induces interesting physical phenomena and large magnetocaloric effects. The rise in resistivity at low temperatures indicates the effect of the SDW state in the electronic transport. The maximum magnetic-entropy change is –16.1J/kg K under a magnetic field change of 0–70 kOe for an isotropic HoAl 2 Ge 2 powder and it increases to –17.9J/kg K for a single crystal when the magnetic field (H) is applied parallel to the ab plane. A large rotating magnetic-entropy change of –5.1J/kg K for H=20 kOe in a HoAl 2 Ge 2 single crystal is obtained, which is closely associated to the magnetic anisotropy of the SDW order and its response to the external magnetic field. We discuss the large MCE in terms of the field-induced metamagnetic transition from the incommensurate SDW order to the ferromagnetic order. Our study establishes the triangular lattice R Al 2 Ge 2 (R=rare-earth elements) as a unique family of compounds to explore the existence of the incommensurate spin density waves and the correlated physical properties.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Space from Hilbert space: Recovering geometry from bulk entanglement

We examine here how to construct a spatial manifold and its geometry from the entanglement structure of an abstract quantum state in Hilbert space. Given a decomposition of Hilbert space H into a tensor product of factors, we consider a class of “redundancy-constrained states” in H that generalize the area-law behavior for entanglement entropy usually found in condensed-matter systems with gapped local Hamiltonians. Using mutual information to define a distance measure on the graph, we employ classical multidimensional scaling to extract the best-fit spatial dimensionality of the emergent geometry. We then show that entanglement perturbations on such emergent geometries naturally give rise to local modifications of spatial curvature which obey a (spatial) analog of Einstein’s equation. The Hilbert space corresponding to a region of flat space is finite-dimensional and scales as the volume, yet the entropy (and the maximum change thereof) scales like the area of the boundary. A version of the ER = EPR conjecture is recovered, in that perturbations that entangle distant parts of the emergent geometry generate a configuration that may be considered as a highly quantum wormhole.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Dendritic growth in a supercooled alloy melt

A simple model which describes the growth of an 'array' of dendrites into a supercooled, binary, alloy melt is presented. Solute diffusion is calculated by superposing the solutions given by Flemings and Zener, and also, by superposing the solutions given by Ivantsov and Flemings. A general expression for the transport solution is suggested from which all other dendrite growth models presented earlier may be obtained as special cases. It is shown that both 'free' and 'constrained' growth may be described by a single transport solution, which indicates that (1) both thermal and solutal effects will be important during 'free' growth in dilute alloys, (2) only solutal effects are predominant during 'free' growth in concentrated alloys and during 'constrained' growth. An examination of the relevant dimensionless parameters also suggests that all dendrite growth models, regardless of the assumptions used to determine the tip radius (marginal stability, minimum undercooling, maximum velocity, minimum entropy production) should predict the experimentally observed extrema in tip radius and growth velocity in dilute alloys, during 'free' dendritic growth. Experimental data in binary H2O-NaCl and succinonitrile-acetone solutions are shown to be in good agreement with the model.

Laxmanan, V.↗

Time dependence of Hawking radiation entropy

If a black hole starts in a pure quantum state and evaporates completely by a unitary process, the von Neumann entropy of the Hawking radiation initially increases and then decreases back to zero when the black hole has disappeared. Here numerical results are given for an approximation to the time dependence of the radiation entropy under an assumption of fast scrambling, for large nonrotating black holes that emit essentially only photons and gravitons. The maximum of the von Neumann entropy then occurs after about 53.81% of the evaporation time, when the black hole has lost about 40.25% of its original Bekenstein-Hawking (BH) entropy (an upper bound for its von Neumann entropy) and then has a BH entropy that equals the entropy in the radiation, which is about 59.75% of the original BH entropy 4πM{sub 0}{sup 2}, or about 7.509M{sub 0}{sup 2} ≈ 6.268 × 10{sup 76}(M{sub 0}/M{sub s}un){sup 2}, using my 1976 calculations that the photon and graviton emission process into empty space gives about 1.4847 times the BH entropy loss of the black hole. Results are also given for black holes in initially impure states. If the black hole starts in a maximally mixed state, the von Neumann entropy of the Hawking radiation increases from zero up to a maximum of about 119.51% of the original BH entropy, or about 15.018M{sub 0}{sup 2} ≈ 1.254 × 10{sup 77}(M{sub 0}/M{sub s}un){sup 2}, and then decreases back down to 4πM{sub 0}{sup 2} = 1.049 × 10{sup 77}(M{sub 0}/M{sub s}un){sup 2}.

79 ASTRONOMY AND ASTROPHYSICS↗