Saturated Entropy Research Articles

A Critical Analysis of the Assumptions Underlying the Formulation of Maximum Potential Intensity for Tropical Cyclones

Abstract Emanuel’s concept of maximum potential intensity (E-PI) estimates the maximum velocity of tropical cyclones from environmental parameters assuming thermal wind (gradient-wind and hydrostatic balances) and slantwise neutrality in the free troposphere. E-PI’s key equation relates proportionally the radial gradients of saturated moist entropy and angular momentum. Here the E-PI derivation is reconsidered to show that the thermal wind and slantwise neutrality imply zero radial gradients of saturation entropy and angular momentum at an altitude where, for a given radius, the tangential wind has a maximum. It is further shown that, while E-PI’s key equation requires that, at the point of maximum tangential wind, the air temperature must increase toward the storm center, the thermal wind equation dictates the opposite. From the analysis of the equations of motion at the altitude of maximum tangential wind in the free troposphere, it is concluded that here the airflow must be supergradient. This implies that the supergradiency factor (a measure of the gradient-wind imbalance) must change in the free troposphere as the airflow tends to restore the balance. It is shown that such a change modifies the derivative of saturation entropy over angular momentum, which cannot therefore remain constant in the free troposphere as E-PI requires. The implications of these findings for the internal coherence of E-PI, including its boundary layer closure, are discussed.

Reduced oxygen saturation entropy is associated with poor prognosis in critically ill patients with sepsis.

Recent studies have found that oxygen saturation (SpO2 ) variability analysis has potential for noninvasive assessment of the functional connectivity of cardiorespiratory control systems during hypoxia. Patients with sepsis have suboptimal tissue oxygenation and impaired organ system connectivity. Our objective with this report was to highlight the potential use for SpO2 variability analysis in predicting intensive care survival in patients with sepsis. MIMIC-III clinical data of 164 adults meeting Sepsis-3 criteria and with 30 min of SpO2 and respiratory rate data were analyzed. The complexity of SpO2 signals was measured through various entropy calculations such as sample entropy and multiscale entropy analysis. The sequential organ failure assessment (SOFA) score was calculated to assess the severity of sepsis and multiorgan failure. While the standard deviation of SpO2 signals was comparable in the non-survivor and survivor groups, non-survivors had significantly lower SpO2 entropy than those who survived their ICU stay (0.107 ± 0.084 vs. 0.070 ± 0.083, p< 0.05). According to Cox regression analysis, higher SpO2 entropy was a predictor of survival in patients with sepsis. Multivariate analysis also showed that the prognostic value of SpO2 entropy was independent of other covariates such as age, SOFA score, mean SpO2 , and ventilation status. When SpO2 entropy was combined with mean SpO2 , the composite had a significantly higher performance in prediction of survival. Analysis of SpO2 entropy can predict patient outcome, and when combined with SpO2 mean, can provide improved prognostic information. The prognostic power is on par with the SOFA score. This analysis can easily be incorporated into current ICU practice and has potential for noninvasive assessment of critically ill patients.

Lilly’s Model for Steady-State Tropical Cyclone Intensity and Structure

AbstractThis study revisits the axisymmetric tropical cyclone (TC) theory from D. K. Lilly’s unpublished manuscript (Lilly model) and compares it to axisymmetric TC simulations from a nonhydrostatic cloud model. Analytic solutions of the Lilly model are presented through simplifying assumptions. Sensitivity experiments varying the sea surface, boundary layer and tropopause temperatures, and the absolute angular momentum (M) at some outer radius in the Lilly model show that these variations influence the radial structure of the tangential wind profile V(r) at the boundary layer top. However, these parameter variations have little effect on the inner-core normalized tangential wind, V(r/rm)/Vm, where Vm is the maximum tangential wind at radius rm. The outflow temperature T∞ as a function of M (or saturation entropy s*) is found to be the only input that changes the normalized tangential wind radial structure in the Lilly model. In contrast with the original assumption of the Lilly model that T∞(s*) is determined by the environment, it is argued here that T∞(s*) is determined by the TC interior flow under the environmental constraint of the tropopause height. The present study shows that the inner-core tangential wind radial structure from the Lilly model generally agrees well with nonhydrostatic cloud model simulations except in the eyewall region where the Lilly model tends to underestimate the tangential winds due to its balanced-dynamics assumptions. The wind structure in temperature–radius coordinates from the Lilly model can largely reproduce the numerical simulation results. Though the Lilly model is based on a number of simplifying assumptions, this paper shows its utility in understanding steady-state TC intensity and structure.

D-bound and Bekenstein bound for McVittie solution surrounded by dark energy cosmological fields

The cosmological candidate fields for dark energy as quintessence, phantom and cosmological constant, are studied in terms of an entropic hypothesis imposed on the McVittie solution surrounded by dark energy. We certify this hypothesis as "$D$-bound-Bekenstein bound identification" for dilute systems and use it as a criterion to determine which candidate of dark energy can satisfy this criterion for a dilute McVittie solution. It turns out that only the cosmological constant can pass this criterion successfully while the quintessence and phantom fields fail, as non-viable dark energy fields for this particular black hole solution. Moreover, assuming this black hole to possess the saturated entropy, the entropy-area law and the holographic principle can put two constraints on the radius $R$ of the cosmological horizon. The first one shows that the Hubble radius is discrete such that for any arbitrary value of the black hole mass $m_{0}$, the value of $R$ is determined up to an integer number. The latter one shows that when a black hole is immersed in a cosmological background, the radius of the cosmological horizon is constrained as $R<\frac{1}{H}$.

Evolution of an Axisymmetric Tropical Cyclone before Reaching Slantwise Moist Neutrality

Abstract In a previous study, the authors showed that the intensification process of a numerically simulated axisymmetric tropical cyclone (TC) can be divided into two periods denoted by “phase I” and “phase II.” The intensification process in phase II can be qualitatively described by Emanuel’s intensification theory in which the angular momentum (M) and saturated entropy (s*) surfaces are congruent in the TC interior. During phase I, however, the M and s* surfaces evolve from nearly orthogonal to almost congruent, and thus, the intensifying simulated TC has a different physical character as compared to that found in phase II. The present work uses a numerical simulation to investigate the evolution of an axisymmetric TC during phase I. The present results show that sporadic, deep convective annular rings play an important role in the simulated axisymmetric TC evolution in phase I. The convergence in low-level radial (Ekman) inflow in the boundary layer of the TC vortex, together with the increase of near-surface s* produced by sea surface fluxes, leads to episodes of convective rings around the TC center. These convective rings transport larger values of s* and M from the lower troposphere upward to the tropopause; the locally large values of M associated with the convective rings cause a radially outward bias in the upper-level radial velocity and an inward bias in the low-level radial velocity. Through a repetition of this process, the pattern (i.e., phase II) gradually emerges. The role of internal gravity waves related to the episodes of convection and the TC intensification process during phase I is also discussed.

Evaluation of a Time-Dependent Model for the Intensification of Tropical Cyclones

Abstract Axisymmetric and three-dimensional simulations are used to evaluate the theory of tropical cyclone (TC) intensification proposed by K. A. Emanuel, which is based on gradient wind balance and moist-neutral ascent along angular momentum (M) surfaces. According to the numerical model results, the intensification of the TC can be divided into two periods, phase I and phase II. During phase I, the TC intensifies while the M and saturation entropy (s*) surfaces evolve from nearly orthogonal to almost congruent. During phase II, the M and s* surfaces in the eyewall and outflow are congruent as the TC intensifies, which is consistent with Emanuel’s study. Therefore, the condition of moist slantwise neutrality in Emanuel’s study is sufficiently satisfied throughout the intensification in phase II. It is also found that the sensitivity of the intensification rates to the surface exchange coefficient for entropy Ck matches Emanuel’s theoretical result, which is that the intensification rate is proportional to Ck. However, the intensification rate varies in proportion to the surface exchange coefficient for momentum Cd, while the Emanuel model growth rate is insensitive to Cd. Furthermore, although the tendency diagnosed by Emanuel is qualitatively similar to the numerical model result during phase II, it is not quantitatively similar. The present analysis finds the inclusion of non–gradient wind effects in the theoretical framework of Emanuel’s study produces an intensification rate that is quantitatively similar to the numerical model results. The neglect of non–gradient wind effects in Emanuel’s study may be the reason for the different dependence of its intensification rate on Cd compared to that of the numerical model. Other aspects of Emanuel’s study in the context of recent research on TC intensification are discussed.

Feasibility of tropical cyclone intensity estimation using satellite‐borne radiometer measurements: An observing system simulation experiment

AbstractThis study evaluates the potential of a proposed technique in using satellite‐borne radiometer measurements and weather analyses to estimate the intensity of tropical cyclones. This theory shows that intensity is essentially directly related to the temperature deficit of cloud top versus sea surface, and the surplus in saturation entropy in the eyewall versus its surroundings. The eyewall entropy estimate comes from measurements of cloud top temperature and pressure, and the analysis provides the environmental saturation entropy. An Observing Systems Simulation Experiment was conducted, and the results were compared to those from previous studies using cloud‐profiling radar altimetry measurements. The use of cloud top pressure measurements may produce more accurate results. Inherent challenges still require caution in considering operational implementation.

Using Bi-level Multi-Objective Programming in Passenger Structure Optimization for Comprehensive Transportation Channel

The economic structure is the lifeblood of national economic development. Passenger structure within comprehensive transportation channel (CTC) is the key to play a higher efficiency and to operate normally of an integrated transport system. This paper analyzes the ideas of PTS optimization within CTC using bi-level planning strategies. And then a bi-level multi-objective programming model is established in this paper, in which the upper level takes the builders and government’s concern into account, such as system efficiency, transport capacity, capital investment. The lower level is a network equilibrium model based on a generalized cost function, while Channel saturation entropy index is introduced in the response function. A particle swarm optimization algorithm is designed to efficiently solve this NP-hard model. Finally, numerical implementations based on Beijing-Shanghai Channel are carried out to account for the performance of our model and algorithm.

Entanglement entropy in quantum spin chains with broken reflection symmetry

We investigate the entanglement entropy of a block of L sites in quasifree translation-invariant spin chains concentrating on the effect of reflection symmetry breaking. The majorana two-point functions corresponding to the Jordan-Wigner transformed fermionic modes are determined in the most general case; from these it follows that reflection symmetry in the ground state can only be broken if the model is quantum critical. The large L asymptotics of the entropy is calculated analytically for general gauge-invariant models, which has, until now, been done only for the reflection symmetric sector. Analytical results are also derived for certain non-gauge-invariant models, e.g., for the Ising model with Dzyaloshinskii-Moriya interaction. We also study numerically finite chains of length N with a non-reflection-symmetric Hamiltonian and report that the reflection symmetry of the entropy of the first L spins is violated but the reflection-symmetric Calabrese-Cardy formula is recovered asymptotically. Furthermore, for non-critical reflection-symmetry-breaking Hamiltonians, we find an anomaly in the behavior of the "saturation entropy" as we approach the critical line. The paper also provides a concise but extensive review of the block entropy asymptotics in translation invariant quasifree spin chains with an analysis of the nearest neighbor case and the enumeration of the yet unsolved parts of the quasifree landscape.

A Climatology of the Tropospheric Thermal Stratification Using Saturation Potential Vorticity

AbstractThe condition of convective neutrality is assessed in the troposphere by calculating the saturation potential vorticity P* from reanalysis data. Regions of the atmosphere in which saturation entropy is constant along isosurfaces of absolute angular momentum, a state indicative of slantwise-convective neutrality, have values of P* equal to zero. In a global reanalysis dataset spanning the years 1970–2004, tropospheric regions are identified in which P* is near zero, implying that vertical convection or slantwise convection may be important in determining the local thermal stratification. Convectively neutral air masses are common not only in the Tropics but also in higher latitudes, for example, over midlatitude continents in summer and in storm tracks over oceans in winter. Large-scale eddies appear to stabilize parts of the lower troposphere, particularly in winter.

Use of transformed correlations to help screen and populate properties within databanks

In-house thermophysical property databanks are often sparsely populated with properties and contain legacy correlations which impede using database information in other simulation or database tools. As part of their flatfile origin, they often contain errors which eluded earlier detection. While many organizations, such as DIPPRs 801 database consortium, employ quality checks to help eliminate defects within their databanks, what is proposed here is a more systematic use of “transformed” correlations that automatically “fit” properties to desired equation forms used within a database. This approach is most applicable to properties that can be estimated by relatively simple group contribution (GC) or corresponding states principle (CSP) methods. Dow Corning (DC) is applying this approach to help find errors and to convert non-standard correlation forms to more widely accepted DIPPR equation forms. Three transforms of tabular correlations are presented in this paper: (1) Halm and Stiel's [R.L. Halm, L.I. Stiel, A fourth parameter for the vapor pressure and entropy of vaporization of polar fluids, AIChE J. 13 (2) (1967) 351–355] four-parameter ( T c, P c, w , x) CSP vapor pressure (VP) correlation to DIPPR equation 101 (Riedel); (2) Pitzer's [K.S. Pitzer, D.Z. Lippman, R.F. Curl Jr., C.M. Huggins, D.E. Petersen, The volumetric and thermodynamic properties of fluids. I. Theoretical basis and virial coefficients. II. Compressibility factor, vapor pressure and entropy of vaporization, J. Am. Chem. Soc. 77 (1955) 3427–3440] saturated entropy of vaporization tables to DIPPR equation 106 for heat of vaporization ( H v); (3) Harrison and Seaton's [B.K. Harrison, W.H. Seaton, Solution to missing group problem for estimation of ideal gas heat capacities, Ind. Eng. Chem. Res. 27 (8) (1988) 1536–1540] ideal gas heat capacity (ICP) GC method with Si, B, and Al group updates from Myers and Danner [K.H. Myers, R.P. Danner, Prediction of properties of silicon, boron, and aluminum compounds, J. Chem. Eng. Data 38 (2) (1993) 175–200] to DIPPR equation 107 (Aly and Lee). Statistical measures of the VP re-correlation in the ranges, 0.44 ≤ T r ≤ 1, 0 ≤ w ≤ 1.2 , | x| ≤ 0.25 are S.D. = 4.2%, AAD = 2.6%, and maximum deviation = 27.5%. The VP transform represents Pitzer's original VP correlation from which the Halm and Stiel method is derived with RMS = 0.66% and AAD = 0.37%. The H v transform was fitted in the 0.56 ≤ T r ≤ 1 and 0 ≤ w ≤ 1.2 ranges with S.D. = 0.26%. The ICP transform reproduces the original Harrison and Seaton method with a S.D. = 0.7%, and AAD = 0.3%. It has been used to identify problems within DC databanks, with a literature ICP evaluation, and with siloxane ICP data in the DIPPR database which were estimated by ab initio methods.

A mean-field study on the thermo-magnetic properties of Gd xCo 1− x amorphous alloys (0.16⩽ x⩽0.25)

We present a mean-field study on the thermo-magnetic properties of Gd x Co 1− x amorphous alloys in the 0.16⩽ x⩽0.25 composition range. A single set of exchange integrals and fixed values of the angular momenta of Gd and Co fairly describe the temperature dependence of magnetization. The magnetic specific heat and magnetic entropy show field and composition dependence. Both the specific heat anomaly and the saturated entropy, at the temperature of the magnetic phase transition, increase with increasing Co concentration. The two magnetic subnetworks and their cross-interactions contribute differently to the specific heat.

The equation of state of liquid uranium monocarbide: An application of the significant structure theory

A new equation of state has been derived for liquid uranium monocarbide by an application of the Significant Structure Theory of liquids which accounts for seventeen different “gas-like” molecules. Critical parameters have been calculated together with various thermodynamic quantities such as the vapour pressure, the saturated entropy, the isobaric thermal expansion, the isothermal compressibility, the standard free energy function and heat content. A graphical representation of the relationship between internal energy and pressure is also reported. In order to obtain a self consistent set of input data, a critical assessment of literature data for UC n ( n = 1−6) molecules was made. New thermal functions of these molecules as well as of neutral and first ionized uranium were calculated and are given together with the reevaluated atomization energies.