Free Energy Flux Research Articles

Incorporating graphene nanosheets in PDMS membrane: Effects of filler functionalization on pervaporation performance

Graphenic materials including Graphene oxide (GO) functionalized with butylamine/octadecylamine (GOButA, GOODA) and their chemically-reduced derivatives (rGO, rGOButA, rGOODA) were used in polydimethylsiloxane/polyethersulfone membranes to increase the enrichment factor for pervaporative removal of toluene from water. The characteristics of synthesized nanosheets assessed by FTIR, XPS, XRD, RAMAN, SEM, and TGA showed that the graphenic materials were properly synthesized, functionalized, and reduced. The membrane-filler interactions were assessed by the contact angle, solvent uptake, and pervaporation. The pervaporation showed incorporating GO or GOButA resulted in deterioration of enrichment factors down to 51% and 34% (comparing to the neat PDMS membrane) due to increase the membrane's hydrophilicity and affinity to water by oxygen functional groups while GOODA increased the enrichment factor by 12%. Using chemically-reduced derivatives of rGO, rGOButA, and rGOODA, the enrichment factors were increased by 110, 130, and 449%, respectively. Increasing the alkyl chain length of functionalizing groups on the nanosheets causes their higher hydrophobicity and better dispersion, which result in decrease of free energy and water flux and ultimately enhancement in the membrane's enrichment factor. The improvement in performance by incorporating the nanosheets was verified by comparing the results of present research with those in literature based on a developed boundary.

Generalized hydrodynamics of the KdV soliton gas

We establish the explicit correspondence between the theory of soliton gases in classical integrable dispersive hydrodynamics, and generalized hydrodynamics (GHD), the hydrodynamic theory for many-body quantum and classical integrable systems. This is done by constructing the GHD description of the soliton gas for the Korteweg–de Vries equation. We further predict the exact form of the free energy density and flux, and of the static correlation matrices of conserved charges and currents, for the soliton gas. For this purpose, we identify the solitons’ statistics with that of classical particles, and confirm the resulting GHD static correlation matrices by numerical simulations of the soliton gas. Finally, we express conjectured dynamical correlation functions for the soliton gas by simply borrowing the GHD results. In principle, other conjectures are also immediately available, such as diffusion and large-deviation functions for fluctuations of soliton transport.

Sub-grid-scale effects in magnetised plasma turbulence

In the present paper, we use a coarse-graining approach to investigate the nonlinear redistribution of free energy in both position and scale space for weakly collisional magnetised plasma turbulence. For this purpose, we use high-resolution numerical simulations of gyrokinetic (GK) turbulence that span the proton–electron range of scales, in a straight magnetic guide field geometry. Accounting for the averaged effect of the particles’ fast gyro-motion on the slow plasma fluctuations, the GK approximation captures the dominant energy redistribution mechanisms in strongly magnetised plasma turbulence. Here, the GK system is coarse grained with respect to a cut-off scale, separating in real space the contributions to the nonlinear interactions from the coarse-grid scales and the sub-grid scales (SGS). We concentrate on the analysis of nonlinear SGS effects. Not only does this allow us to investigate the flux of free energy across the scales, but also to now analyse its spatial density. We find that the net value of scale flux is an order of magnitude smaller than both the positive and negative flux density contributions. The dependence of the results on the filter type is also analysed. Moreover, we investigate the advection of energy in position space. This rather novel approach for GK turbulence can help in the development of SGS models that account for advective unstable structures for space and fusion plasmas, and with the analysis of the turbulent transport saturation.

A solvable model of Vlasov-kinetic plasma turbulence in Fourier–Hermite phase space

A class of simple kinetic systems is considered, described by the one-dimensional Vlasov–Landau equation with Poisson or Boltzmann electrostatic response and an energy source. Assuming a stochastic electric field, a solvable model is constructed for the phase-space turbulence of the particle distribution. The model is a kinetic analogue of the Kraichnan–Batchelor model of chaotic advection. The solution of the model is found in Fourier–Hermite space and shows that the free-energy flux from low to high Hermite moments is suppressed, with phase mixing cancelled on average by anti-phase-mixing (stochastic plasma echo). This implies that Landau damping is an ineffective route to dissipation (i.e. to thermalisation of electric energy via velocity space). The full Fourier–Hermite spectrum is derived. Its asymptotics are $m^{-3/2}$ at low wavenumbers and high Hermite moments ($m$) and $m^{-1/2}k^{-2}$ at low Hermite moments and high wavenumbers ($k$). These conclusions hold at wavenumbers below a certain cutoff (analogue of Kolmogorov scale), which increases with the amplitude of the stochastic electric field and scales as inverse square of the collision rate. The energy distribution and flows in phase space are a simple and, therefore, useful example of competition between phase mixing and nonlinear dynamics in kinetic turbulence, reminiscent of more realistic but more complicated multi-dimensional systems that have not so far been amenable to complete analytical solution.

Application of alternative synthetic kernel approximation to radiative transfer in regular and irregular two-dimensional media

Alternative synthetic kernel (ASKN) approximation, just as the standard SKN method, is derived from the radiative integral transfer equations in full 3D generality. The direct and diffuse terms of thermal radiation appear explicitly in the radiative integral transfer equations as surface and volume integrals, respectively. In standard SKN method, the approximation is employed to the diffuse terms while direct terms are evaluated analytically. The alternative formulation differs from the standard one in that the direct radiation wall contributions are also approximated with the same spirit of the synthetic kernel approximation. This alternative formulation also yields a set of coupled partial differential-the ASKN–equations which could be solved using finite volume methods. This approximation is applied to radiative transfer calculations in regular and irregular two-dimensional absorbing, emitting and isotropically scattering media. Four benchmark problems-one rectangular and three irregular media-are considered, and the net radiative flux and/or incident energy solutions along the boundaries are compared with available exact, standard discrete ordinates S4 and S12, modified discrete ordinates S4, Monte Carlo and collocation spectral method to assess the accuracy of the method. The ASKN approximation yields ray effect free incident energy and radiative flux distributions, and low order ASKN solutions are generally better than those of the high order standard discrete ordinates method.

The anisotropic redistribution of free energy for gyrokinetic plasma turbulence in a Z-pinch

For a Z-pinch geometry, we report on the nonlinear redistribution of free energy across scales perpendicular to the magnetic guide field, for a turbulent plasma described in the framework of gyrokinetics. The analysis is performed using a local flux-surface approximation, in a regime dominated by electrostatic fluctuations driven by the entropy mode, with both ion and electron species being treated kinetically. To explore the anisotropic nature of the free energy redistribution caused by the emergence of zonal flows, we use a polar coordinate representation for the field-perpendicular directions and define an angular density for the scale flux. Positive values for the classically defined (angle integrated) scale flux, which denote a direct energy cascade, are shown to be also composed of negative angular sections, a fact that impacts our understanding of the backscatter of energy and the way in which it enters the modeling of sub-grid scales for turbulence. A definition for the flux of free energy across each perpendicular direction is introduced as well, which shows that the redistribution of energy in the presence of zonal flows is highly anisotropic.

Fluctuation-dissipation relations for a plasma-kinetic Langevin equation

A linearised kinetic equation describing electrostatic perturbations of a Maxwellian equilibrium in a weakly collisional plasma forced by a random source is considered. The problem is treated as a kinetic analogue of the Langevin equation and the corresponding fluctuation-dissipation relations are derived. The kinetic fluctuation-dissipation relation reduces to the standard “fluid” one in the regime where the Landau damping rate is small and the system has no real frequency; in this case the simplest possible Landau-fluid closure of the kinetic equation coincides with the standard Langevin equation. Phase mixing of density fluctuations and emergence of fine scales in velocity space is diagnosed as a constant flux of free energy in Hermite space; the fluctuation-dissipation relations for the perturbations of the distribution function are derived, in the form of a universal expression for the Hermite spectrum of the free energy. Finite-collisionality effects are included. This work is aimed at establishing the simplest fluctuation-dissipation relations for a kinetic plasma, clarifying the connection between Landau and Hermite-space formalisms, and setting a benchmark case for a study of phase mixing in turbulent plasmas.

Dynamic procedure for filtered gyrokinetic simulations

Large Eddy Simulations (LES) of gyrokinetic plasma turbulence are investigated as interesting candidates to decrease the computational cost. A dynamic procedure is implemented in the GENE code, allowing for dynamic optimization of the free parameters of the LES models (setting the amplitudes of dissipative terms). Employing such LES methods, one recovers the free energy and heat flux spectra obtained from highly resolved Direct Numerical Simulations (DNS). Systematic comparisons are performed for different values of the temperature gradient and magnetic shear, parameters which are of prime importance in Ion Temperature Gradient (ITG) driven turbulence. Moreover, the degree of anisotropy of the problem, that can vary with parameters, can be adapted dynamically by the method that shows Gyrokinetic Large Eddy Simulation (GyroLES) to be a serious candidate to reduce numerical cost of gyrokinetic solvers.

Capture of Planktonic Microbial Diversity in Fractures by Long-Term Monitoring of Flowing Boreholes, Evander Basin, South Africa

The diversity of planktonic microorganisms in fluids from a group of flowing subterranean boreholes was monitored from the day they were drilled to as long as three and a half months after drilling as they drained into Evander Au mine. Geochemical analyses of the water, characterization of microbial communities by phospholipids fatty acid (PLFA) and DNA sequence analyses, and calculations of free energy flux indicated that mine-introduced microbial contaminants, dominated by β and γ Proteobacteria, Cenarchaeaceae and Candidatus Nitrososphaera, were flushed from the boreholes and replaced by fracture water derived microbial communities dominated by Firmicutes, Methanosarcinalesand Thermoproteaceaea. The fracture water was a mixture of paleometeoric water and 2.0 Ga old, diagenetically altered, hydrothermal fluid. The C and H isotopic data for C1−4 indicated that the CH4 was primarily abiogenic in origin although ∼35–50% of it might have originated from microbial methanogenesis. Noble gas analyses yielded estimated residence times of some 10 million years for the fracture water, which is estimated to represent a capture cross-section of 0.25–0.50 km2. The 16S rRNA and dsrAB gene sequences indicated that the indigenous bacterial communities were predominantly comprised of sulfate reducers belonging to the genera Desulfotomaculum, Candiditus Desulforudis and Desulfofustis. The sulfur isotopic analyses of sulfate and sulfide yielded fractionation Δ34S values ranging from 16 to 22% consistent with microbial sulfate reduction. Thermodynamic analyses indicate that methanogenic reactions are inhibited by the high partial pressure of abiogenic CH4 and that sulfate-reducing reactions are more favorable, which is consistent with the abundance of 16S rRNA genes belonging to known sulfate reducing bacteria. Supplemental materials are available for this article. Go to the publisher's online edition of Geomicrobiology Journal to view the free supplemental files.

A Constitutive Formulation for the Linear Thermoelastic Behavior of Arbitrary Fiber-Reinforced Composites

The linear thermoelastic behavior of a composite material reinforced by two independent and inextensible fiber families has been analyzed theoretically. The composite material is assumed to be anisotropic, compressible, dependent on temperature gradient, and showing linear elastic behavior. Basic principles and axioms of modern continuum mechanics and equations belonging to kinematics and deformation geometries of fibers have provided guidance and have been determining in the process of this study. The matrix material is supposed to be made of elastic material involving an artificial anisotropy due to fibers reinforcing by arbitrary distributions. As a result of thermodynamic constraints, it has been determined that the free energy function is dependent on a symmetric tensor and two vectors whereas the heat flux vector function is dependent on a symmetric tensor and three vectors. The free energy and heat flux vector functions have been represented by a power series expansion, and the type and the number of terms taken into consideration in this series expansion have determined the linearity of the medium. The linear constitutive equations of the stress and heat flux vector are substituted in the Cauchy equation of motion and in the equation of conservation of energy to obtain the field equations.

Radial propagation of geodesic acoustic modes

The GAM group velocity is estimated from the ratio of the radial free energy flux to the total free energy applying gyrokinetic and two-fluid theory. This method is much more robust than approaches that calculate the group velocity directly and can be generalized to include additional physics, e.g., magnetic geometry. The results are verified with the gyrokinetic code GYRO [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)], the two-fluid code NLET [K. Hallatschek and A. Zeiler, Phys. Plasmas 7, 2554 (2000)], and analytical calculations. GAM propagation must be kept in mind when discussing the windows of GAM activity observed experimentally and the match between linear theory and experimental GAM frequencies.

Solar conversion efficiency of photovoltaic and photoelectrolysis cells with carrier multiplication absorbers

We calculate the maximum power conversion efficiency for conversion of solar radiation to electrical power or to a flux of chemical free energy for the case of hydrogen production from water photoelectrolysis. We consider several types of ideal absorbers where absorption of one photon can produce more than one electron-hole pair that are based on semiconductor quantum dots with efficient multiple exciton generation (MEG) or molecules that undergo efficient singlet fission (SF). Using a detailed balance model with 1 sun AM1.5G illumination, we find that for single gap photovoltaic (PV) devices the maximum efficiency increases from 33.7% for cells with no carrier multiplication to 44.4% for cells with carrier multiplication. We also find that the maximum efficiency of an ideal two gap tandem PV device increases from 45.7% to 47.7% when carrier multiplication absorbers are used in the top and bottom cells. For an ideal water electrolysis two gap tandem device, the maximum conversion efficiency is 46.0% using a SF top cell and a MEG bottom cell versus 40.0% for top and bottom cell absorbers with no carrier multiplication. We also consider absorbers with less than ideal MEG quantum yields as are observed experimentally.

The Origin and Age of Biogeochemical Trends in Deep Fracture Water of the Witwatersrand Basin, South Africa

Water residing within crustal fractures encountered during mining at depths greater than 500 meters in the Witwatersrand basin of South Africa represents a mixture of paleo-meteoric water and 2.0–2.3 Ga hydrothermal fluid. The hydrothermal fluid is highly saline, contains abiogenic CH 4 and hydrocarbon, occasionally N 2 , originally formed at ∼ 250–300°C and during cooling isotopically exchanged O and H with minerals and accrued H 2 , 4 He and other radiogenic gases. The paleo-meteoric water ranges in age from ∼ 10 Ka to > 1.5 Ma, is of low salinity, falls along the global meteoric water line (GMWL) and is CO 2 and atmospheric noble gas-rich. The hydrothermal fluid, which should be completely sterile, has probably been mixing with paleo-meteoric water for at least the past ∼100 Myr, a process which inoculates previously sterile environments at depths > 2.0 to 2.5 km. Free energy flux calculations suggest that sulfate reduction is the dominant electron acceptor microbial process for the high salinity fracture water and that it is 10 7 times that normally required for cell maintenance in lab cultures. Flux calculations also indicate that the potential bioavailable chemical energy increases with salinity, but because the fluence of bioavailable C, N and P also increase with salinity, the environment remains energy-limited. The 4 He concentrations and theoretical calculations indicate that the H 2 that is sustaining the subsurface microbial communities (e.g. H 2 -utilizing SRB and methanogens) is produced by water radiolysis at a rate of ∼1 nM yr −1 . Microbial CH 4 mixes with abiogenic CH 4 to produce the observed isotopic signatures and indicates that the rate of methanogenesis diminishes with depth from ∼ 100 at < 1 kmbls, to < 0.01 nM yr −1 at > 3 kmbls. Microbial Fe(III) reduction is limited due to the elevated pH. The δ13C of dissolved inorganic carbon is consistent with heterotrophy rather than autotrophy dominating the deeper, more saline environments. One potential source of the organic carbon may be microfilms present on the mineral surfaces.

Free Magnetic Energy Changes in AR 8210

Fourier local correlation tracking (FLCT) was applied to time series of the normal magnetic field in vector magnetograms of NOAA AR 8210, from 17:13–21:29 UT on 1998 May 1, to derive photospheric flows. These flows, combined with both the observed horizontal magnetic field and an inferred horizontal potential magnetic field, can be used to derive the flux of free magnetic energy across the photosphere. Here, we present the formalism used, as well as a map of the time-averaged free energy flux. Over the time interval covered by the magnetograms, erg of free magnetic energy flowed upward across the photosphere, a significant fraction of the energy typically released in large flares coronal mass ejections (CMEs). A flare and coronal mass ejection began at 22:30 UT. We acknowledge the kind support of AFOSR's MURI program.

Magnetic Flux Cancellation and Coronal Magnetic Energy

I investigate the processes at work in the cancellation of normal magnetic flux in solar magnetograms and study the relationships between cancellation and the budget of free magnetic energy in the coronal magnetic field that can power solar flares and CMEs. After defining cancellation mathematically, I derive equations that quantify the evolution of free magnetic energy in response to arbitrary plasma flows on the boundary, including flows consistent with cancellation. While cancellation can reduce the magnetic energy in both the actual coronal field and the potential field matching the same normal field boundary condition, cancellation can, in the process, increase the difference between the two; i.e., cancellation can increase the free magnetic energy in the corona. By making simple assumptions based upon typical observed field configurations in filament channels, I show that cancellation tends to add free energy to these fields. Finally, I discuss the implications of this fact, as well as wider applications of the free energy flux formalism developed here. I also briefly address related issues, including the relationship of cancellation to Taylor's hypothesis.

System analysis of links interactions and development of ecosystems of different types

The anthropogenic impact on the Earth's ecosystems are leading to dramatic changes in ecosystem functioning and even to destruction of them. System analysis and the use of heuristic modeling can be an effective means to determine the main biological interactions and key factors that are of high importance for understanding the development of ecosystems. Cycling of limiting substances, induced by the external free energy flux, and trophic links interaction is the basis of the mathematical modeling studies presented in this paper. Mathematical models describe the dynamics of simplified ecosystems having different characteristics: 1) different degrees of biotic turnover closure (from open to completely closed); 2) different numbers. of trophic links (including both “top-down”, “bottom-up” regulation types); 3) different intensities of input - output flows of the limiting nutrient and its total amount in the system. Adaptive values of the changes of lower hierarchical levels (populational, trophic chain level) are to be estimated by integrity indices for total system functioning (e.g. NPP, total photosynthesis). The approach developed can be used for evaluating the contributions of lower hierarchical levels to the functioning of the higher hierarchical levels of the system. This approach may have value for determining biomanipulation management and their assessment.

High-temperature corrections for the classical expressions of radiative losses from a black body

The contribution from thermally generated electron-positron pairs to the radiative losses from a black body is considered near the temperature corresponding to the electron's rest mass energy Tc = mec2/k. The correction factors are defined as the ratio of corrected expressions (which also include the contribution from thermal pairs) to the classical expressions (which include merely photons). The correction factors for energy, free energy, and entropy fluxes have different values about 0.5Tc, while they have the same value at T « Tc and T » Tc. The Stephan-Boltzmann's constant becomes temperature dependent due to the contribution of thermal pairs. According to the classical expressions of radiative losses, the ratio of energy flux to the absolute value of free energy flux is a constant and it is equal to 3. On the contrary, it is shown that it is a function of temperature about Tc and it has a maximum about 0.38Tc. The correction factor for mean energy per emitted thermal particle has also a maximum about T = 0.42Tc. PACS No.: 4440

Soliton-like waves in a low-temperature nonlinear rigid heat conductor

A nonlinear rigid heat conductor whose free energy and heat flux depend not only on the absolute temperature but also on the elastic heat flow that satisfies an evolution equation is considered. First, nonlinear field equations coupling the temperature T and elastic heat flow B are scaled to the dimensionless form involving a low temperature parameter ϵ, and the associated nonlinear initial-boundary value problem is formulated. Next, a nonlinear coupled (T; B) problem in which B = ▽Φ, where Φ is a scalar potential, is replaced by a nonlinear Φ-problem alone. Finally, the Φ-problem is used to obtain a number of new properties of one-dimensional soliton-like thermal waves propagating in an infinite rigid heat conductor. In particular, it is shown that (i) a thermal wave propagates with the velocity c = 1/√ϵ along the conductor, (ii) its internal energy is a convex function of scaled temperature, (iii) the associated elastic heat flow is a linear decreasing function of scaled temperature that passes through a zero at which the absolute temperature attains a reference value, and (iv) in a neighborhood of thermodynamical equilibrium the thermal wave can be approximated by a singular soliton with singularities on a plane wave front propagating with velocity c = 1/√ϵ. Graphs illustrating the propagation of a thermal wave along the conductor are presented.

Control theory of metabolic channelling.

Various factors appear to control muscle energetics, often in conjunction. This calls for a quantitative approach of the type provided by Metabolic Control Analysis for intermediary metabolism and mitochondrial oxidative phosphorylation. To the extent that direct transfer of high energy phosphates and spatial organization plays a role in muscle energetics however, the standard Metabolic Control Theory does not apply, neither do its theorems regarding control. This paper develops the Control Theory that does apply to the muscle system. It shows that direct transfer of high energy phosphates bestows a system with enhanced control: the sum of the control exerted by the participating enzymes on the flux of free energy from the mitochondrial matrix to the actinomyosin may well exceed the 100% mandatory for ideal metabolic pathways. It is also shown how sequestration of high energy phosphates may allow for negative control on pathway flux. The new control theory gives method functionally to diagnose the extent to which channelling and metabolite sequestration occur.

Control theory of metabolic channelling.

Various factors appear to control muscle energetics, often in conjunction. This calls for a quantitative approach of the type provided by Metabolic Control Analysis for intermediary metabolism and mitochondrial oxidative phosphorylation. To the extent that direct transfer of high energy phosphates and spatial organization plays a role in muscle energetics however, the standard Metabolic Control Theory does not apply, neither do its theorems regarding control. This chapter develops the Control Theory that does apply to the muscle system. It shows that direct transfer of high energy phosphates bestows a system with enhanced control: the sum of the control exerted by the participating enzymes on the flux of free energy form the mitochondrial matrix to the actinomyosin may well exceed the 100% mandatory for ideal metabolic pathways. It is also shown how sequestration of high energy phosphates may allow for negative control on pathway flux. The new control theory gives methods functionally to diagnose the extent to which channelling and metabolite sequestration occur.