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DOE OSTI2025

Irreversible thermodynamics of curved lipid membranes. II. Permeability and osmosis

We present a theory that combines the framework of irreversible thermodynamics with modified integral theorems to model arbitrarily curved and deforming membranes immersed in bulk fluid solutions. We study the coupling between the mechanics and permeability of a viscous and elastically bendable membrane, and a multicomponent bulk fluid solution. An equation for the internal entropy production for irreversibilities at the membrane is derived, determining the generalized thermodynamic forces and fluxes, from which we identify the deviatoric stress as a novel driving force for permeability. A complete set of equations of motion, constitutive laws, and boundary conditions to model the lipid membrane and bulk fluid system are provided.

Alkadri, Ahmad M↗

DOE OSTI2025

Dual-unitary shadow tomography

We introduce a classical shadow tomography scheme based on dual-unitary brick-wall circuits termed "dual-unitary shadow tomography" (DUST). For this we study operator spreading and Pauli weight dynamics in one-dimensional qubit systems, evolved by random two-local dual-unitary gates arranged in a brick-wall structure, ending with a final measurement layer. We do this by deriving general constraints on the Pauli weight transfer matrix and specializing to the case of dual-unitarity. We first show that dual-unitaries must have a minimal amount of entropy production. Remarkably, we find that operator spreading in these circuits have a rich structure resembling that of relativistic quantum field theories, with massless chiral excitations that can decay or fuse into each other, which we call left- or right-movers. We develop a mean-field description of the Pauli weight in terms of $\rho(x,t)$, which represents the probability of having nontrivial support at site $x$ and depth $t$ starting from a fixed weight distribution. We develop an equation of state for $\rho(x,t)$, and simulate it numerically using Monte Carlo simulations. Lastly, we demonstrate that the fast-thermalizing properties of dual-unitary circuits make them better at predicting large operators than shallow brick-wall Clifford circuits. Our results are robust to finite-size effects due to the chirality of dual-unitary brick-wall circuits.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1965

Investigation to define the propagation characteristics of a finite amplitude acoustic pressure wave, phase 1 final report, 29 jun. 1964 - 29 jul. 1965

The contribution of high entropy production regions to the generation and propagation characteristics of a finite amplitude pressure is considered. Preliminary analysis indicates that, for nozzles where pressure rations are above critical, the predominant contribution may come from the shock layer formation in the exhaust region. Temperature effects indicate high dependence of the forcing function upon the initial temperature of the media.

WAVE PROPAGATION↗

NASA NTRS1983

Anomalous bulk viscosity of two-phase fluids and implications for planetary interiors

The irreversible entropy production is calculated for the imposition of a pressure perturbation on a two-phase medium composed of a dilute suspension of droplets (or snowflakes) and a liquid phase of other materials. An absence of metastability is assumed, allowing the relaxation to be dominated by the solute finite diffusivity. The fluid medium was found to display a behavior suggestive of a bulk viscosity near 10 trillion P, a finding that is significant for studies of dissipation in planetary cores for tidal or seismic disturbances. A minimum quality factor for acoustic or tidal pressure oscillations and the accompanying frequency are calculated. An example is provided in terms of helium rain clouds in the deep interiors of giant planets. Additionally, a tidal quality factor of 10 to the 15th is found necessary to account for Io volcanism and resurfacing on Enceladus.

Stevenson, D. J.↗

NASA NTRS1984

Optimation of cooled shields in insulations

A method to optimize the location, temperature, and heat dissipation rate of each cooled shield inside an insulation layer was developed. The method is based on the minimization of the entropy production rate which is proportional to the heat leak across the insulation. It is shown that the maximum number of shields to be used in most practical applications is three. However, cooled shields are useful only at low values of the overall, cold wall to hot wall absolute temperature ratio. The performance of the insulation system is relatively insensitive to deviations from the optimum values of the temperature and location of the cooling shields. Design curves for rapid estimates of the locations and temperatures of cooling shields in various types of insulations, and an equation for calculating the cooling loads for the shields are presented.

Chato, J. C.↗

NASA NTRS1985

Lorentz-covariant dissipative Lagrangian systems

The concept of dissipative Hamiltonian system is converted to Lorentz-covariant form, with evolution generated jointly by two scalar functionals, the Lagrangian action and the global entropy. A bracket formulation yields the local covariant laws of energy-momentum conservation and of entropy production. The formalism is illustrated by a derivation of the covariant Landau kinetic equation.

Kaufman, A. N.↗

NASA NTRS1987

Vortex shedding in compressor blade wakes

The wakes of highly loaded axial compressor blades were often considered to be turbulent, unstructured flows. Recent work has suggested that the blade wakes are in fact dominated by a vortex street-like structure. The work on the wake structure at MIT is reviewed, the results of a viscous numerical simulation are presented, the blade wake vortices are compared to those shed from a cylinder, and the implications of the wake structure on compressor performance are discussed. In particular, a two-dimensional, time accurate, viscous calculation shows both a periodic wake structure and time variations in the passage shock strength. The numerical calculations are compared to laser anemometer and high frequency response probe data. The effect of the wake structure on the entropy production and apparent adiabatic efficiency of the compressor rotor is discussed.

Epstein, A. H.↗

NASA NTRS1986

Transonic flow solutions using a composite velocity procedure for potential, Euler and RNS equations

Solutions for transonic viscous and inviscid flows using a composite velocity procedure are presented. The velocity components of the compressible flow equations are written in terms of a multiplicative composite consisting of a viscous or rotational velocity and an inviscid, irrotational, potential-like function. This provides for an efficient solution procedure that is locally representative of both asymptotic inviscid and boundary layer theories. A modified conservative form of the axial momentum equation that is required to obtain rotational solutions in the inviscid region is presented and a combined conservation/nonconservation form is applied for evaluation of the reduced Navier-Stokes (RNS), Euler and potential equations. A variety of results is presented and the effects of the approximations on entropy production, shock capturing, and viscous interaction are discussed.

Gordnier, R. E.↗

NASA NTRS1988

Semi-discrete approximations to nonlinear systems of conservation laws; consistency and L(infinity)-stability imply convergence

A convergence theory for semi-discrete approximations to nonlinear systems of conservation laws is developed. It is shown, by a series of scalar counter-examples, that consistency with the conservation law alone does not guarantee convergence. Instead, a notion of consistency which takes into account both the conservation law and its augmenting entropy condition is introduced. In this context it is concluded that consistency and L(infinity)-stability guarantee for a relevant class of admissible entropy functions, that their entropy production rate belongs to a compact subset of H(loc)sup -1 (x,t). One can now use compensated compactness arguments in order to turn this conclusion into a convergence proof. The current state of the art for these arguments includes the scalar and a wide class of 2 x 2 systems of conservation laws. The general framework of the vanishing viscosity method is studied as an effective way to meet the consistency and L(infinity)-stability requirements. How this method is utilized to enforce consistency and stability for scalar conservation laws is shown. In this context we prove, under the appropriate assumptions, the convergence of finite difference approximations (e.g., the high resolution TVD and UNO methods), finite element approximations (e.g., the Streamline-Diffusion methods) and spectral and pseudospectral approximations (e.g., the Spectral Viscosity methods).

Tadmor, Eitan↗

NASA NTRS1988

Decomposition of hydrazine by high frequency glow electrical discharges

Originally, de Groot et al. examined electrical conductivity phenomena in terms of the thermodynamics of irreversible processes. They considered the system to be discontinuous and calculated only the differences between the opposing ends of the process. Thus these theories are phenomenological. In the present work, thermodynamics is developed as a continuous system based on hydrodynamics and the entropy production for a thin capillary. It is shown that electroconductivity can be interpreted without difficulty. For the electric double layer, the effects of electrolytes and surface conductivity and the gap width were calculated for the Gouy model.

Suzuki, M.↗

NASA NTRS1987

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.↗

NASA NTRS1988

Viscous induced drag

A fundamentally new approach to the aircraft minimum induced drag problem is presented. The method, a 'viscous lifting line', is based on the minimum entropy production principle and does not require the planar wake assumption. An approximate, closed form solution is obtained and compared with several classical results. In addition, the problem of optimizing in-plane wing sweep with constant wing root bending moment is considered. Like the classical lifting line theory, this theory predicts that induced drag is proportional to the square of the lift coefficient and inversely proportional to the wing aspect ratio. Unlike the classical theory, it predicts that in-plane wing sweep may significantly reduce induced drag, that induced drag is Reynolds number dependent, and that the optimum spanwise circulation distribution is non-elliptic.

Greene, George C.↗

NASA NTRS1988

Solutions of one-dimensional steady nozzle flow revisited

A formulation is presented by which any iteration process for obtaining the entropy increase in the flow of a one-dimensional steady nozzle is eliminated, and the simple solution of a quadratic equation is obtained. The proper parameters are then explicitly seen in the equation, and their effects on the solution are easily determined. Since only one root of the equation is physically admissible, entropy production, and therefore the shock wave, are uniquely determined by this set of parameters.

Liou, Meng-Sing↗

NASA NTRS1988

Effects of ordinary and superconducting cosmic strings on primordial nucleosynthesis

A precise calculation is done of the primordial nucleosynthesis constraint on the energy per length of ordinary and superconducting cosmic strings. A general formula is provided for the constraint on the string tension for ordinary strings. Using the current values for the various parameters that describe the evolution of loops, the constraint for ordinary strings is G mu less than 2.2 x 10 to the minus 5 power. Our constraint is weaker than previously quoted limits by a factor of approximately 5. For superconducting loops, with currents generated by primordial magnetic fields, the constraint can be less or more stringent than this limit, depending on the strength of the magnetic field. It is also found in this case that there is a negligible amount of entropy production if the electromagnetic radiation from strings thermalizes with the radiation background.

Hodges, Hardy M.↗

NASA NTRS1989

Transonic flow solutions using a composite velocity procedure for potential, Euler and RNS equations

Gordnier, R. E.↗

NASA NTRS1989

Towards a rigorous approach to artificial dissipation

Artificial dissipation in modern computational fluid dynamics is something of an art. In spite of the dramatic strides made over the last decade, dissipation continues to lack a quantitative theory with predictive power. Such a theory, based on entropy production, is presented. An important side-effect is nonlinear stability for schemes which satisfy certain conditions.

Merriam, Marshal L.↗

NASA NTRS1989

An Entropy-Based Approach to Nonlinear Stability

Many numerical methods used in computational fluid dynamics (CFD) incorporate an artificial dissipation term to suppress spurious oscillations and control nonlinear instabilities. The same effect can be accomplished by using upwind techniques, sometimes augmented with limiters to form Total Variation Diminishing (TVD) schemes. An analysis based on numerical satisfaction of the second law of thermodynamics allows many such methods to be compared and improved upon. A nonlinear stability proof is given for discrete scalar equations arising from a conservation law. Solutions to such equations are bounded in the L sub 2 norm if the second law of thermodynamics is satisfied in a global sense over a periodic domain. It is conjectured that an analogous statement is true for discrete equations arising from systems of conservation laws. Analysis and numerical experiments suggest that a more restrictive condition, a positive entropy production rate in each cell, is sufficient to exclude unphysical phenomena such as oscillations and expansion shocks. Construction of schemes which satisfy this condition is demonstrated for linear and nonlinear wave equations and for the one-dimensional Euler equations.

Merriam, Marshal L.↗

NASA NTRS1989

An entropy method for induced drag minimization

A fundamentally new approach to the aircraft minimum induced drag problem is presented. The method, a 'viscous lifting line', is based on the minimum entropy production principle and does not require the planar wake assumption. An approximate, closed form solution is obtained for several wing configurations including a comparison of wing extension, winglets, and in-plane wing sweep, with and without a constraint on wing-root bending moment. Like the classical lifting-line theory, this theory predicts that induced drag is proportional to the square of the lift coefficient and inversely proportioinal to the wing aspect ratio. Unlike the classical theory, it predicts that induced drag is Reynolds number dependent and that the optimum spanwise circulation distribution is non-elliptic.

Greene, George C.↗