Role of excited state solvent fluctuations on time-dependent fluorescence Stokes shift

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Tanping, E-mail: tanping@lsu.edu, E-mail: revatik@lsu.edu; Kumar, Revati, E-mail: tanping@lsu.edu, E-mail: revatik@lsu.edu

2015-11-07

We explore the connection between the solvation dynamics of a chromophore upon photon excitation and equilibrium fluctuations of the solvent. Using molecular dynamics simulations, fluorescence Stokes shift for the tryptophan in Staphylococcus nuclease was examined using both nonequilibrium calculations and linear response theory. When the perturbed and unperturbed surfaces exhibit different solvent equilibrium fluctuations, the linear response approach on the former surface shows agreement with the nonequilibrium process. This agreement is excellent when the perturbed surface exhibits Gaussian statistics and qualitative in the case of an isomerization induced non-Gaussian statistics. However, the linear response theory on the unperturbed surface breaksmore » down even in the presence of Gaussian fluctuations. Experiments also provide evidence of the connection between the excited state solvent fluctuations and the total fluorescence shift. These observations indicate that the equilibrium statistics on the excited state surface characterize the relaxation dynamics of the fluorescence Stokes shift. Our studies specifically analyze the Gaussian fluctuations of the solvent in the complex protein environment and further confirm the role of solvent fluctuations on the excited state surface. The results are consistent with previous investigations, found in the literature, of solutes dissolved in liquids.« less

Diffusion and interactions of interstitials in hard-sphere interstitial solid solutions

NASA Astrophysics Data System (ADS)

van der Meer, Berend; Lathouwers, Emma; Smallenburg, Frank; Filion, Laura

2017-12-01

Using computer simulations, we study the dynamics and interactions of interstitial particles in hard-sphere interstitial solid solutions. We calculate the free-energy barriers associated with their diffusion for a range of size ratios and densities. By applying classical transition state theory to these free-energy barriers, we predict the diffusion coefficients, which we find to be in good agreement with diffusion coefficients as measured using event-driven molecular dynamics simulations. These results highlight that transition state theory can capture the interstitial dynamics in the hard-sphere model system. Additionally, we quantify the interactions between the interstitials. We find that, apart from excluded volume interactions, the interstitial-interstitial interactions are almost ideal in our system. Lastly, we show that the interstitial diffusivity can be inferred from the large-particle fluctuations alone, thus providing an empirical relationship between the large-particle fluctuations and the interstitial diffusivity.

Fluctuation-enhanced electric conductivity in electrolyte solutions.

PubMed

Péraud, Jean-Philippe; Nonaka, Andrew J; Bell, John B; Donev, Aleksandar; Garcia, Alejandro L

2017-10-10

We analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson-Nernst-Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation-anion diffusion coefficient. Specifically, we predict a nonzero cation-anion Maxwell-Stefan coefficient proportional to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye-Huckel-Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Finally, we show that strong applied electric fields result in anisotropically enhanced "giant" velocity fluctuations and reduced fluctuations of salt concentration.

Fluctuation-enhanced electric conductivity in electrolyte solutions

PubMed Central

Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.; Donev, Aleksandar; Garcia, Alejandro L.

2017-01-01

We analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell–Stefan coefficient proportional to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Finally, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration. PMID:28973890

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Shenggao, E-mail: sgzhou@suda.edu.cn, E-mail: bli@math.ucsd.edu; Sun, Hui; Cheng, Li-Tien

Recent years have seen the initial success of a variational implicit-solvent model (VISM), implemented with a robust level-set method, in capturing efficiently different hydration states and providing quantitatively good estimation of solvation free energies of biomolecules. The level-set minimization of the VISM solvation free-energy functional of all possible solute-solvent interfaces or dielectric boundaries predicts an equilibrium biomolecular conformation that is often close to an initial guess. In this work, we develop a theory in the form of Langevin geometrical flow to incorporate solute-solvent interfacial fluctuations into the VISM. Such fluctuations are crucial to biomolecular conformational changes and binding process. Wemore » also develop a stochastic level-set method to numerically implement such a theory. We describe the interfacial fluctuation through the “normal velocity” that is the solute-solvent interfacial force, derive the corresponding stochastic level-set equation in the sense of Stratonovich so that the surface representation is independent of the choice of implicit function, and develop numerical techniques for solving such an equation and processing the numerical data. We apply our computational method to study the dewetting transition in the system of two hydrophobic plates and a hydrophobic cavity of a synthetic host molecule cucurbit[7]uril. Numerical simulations demonstrate that our approach can describe an underlying system jumping out of a local minimum of the free-energy functional and can capture dewetting transitions of hydrophobic systems. In the case of two hydrophobic plates, we find that the wavelength of interfacial fluctuations has a strong influence to the dewetting transition. In addition, we find that the estimated energy barrier of the dewetting transition scales quadratically with the inter-plate distance, agreeing well with existing studies of molecular dynamics simulations. Our work is a first step toward the inclusion of fluctuations into the VISM and understanding the impact of interfacial fluctuations on biomolecular solvation with an implicit-solvent approach.« less

Exact Critical Exponents for the Antiferromagnetic Quantum Critical Metal in Two Dimensions

NASA Astrophysics Data System (ADS)

Schlief, Andres; Lunts, Peter; Lee, Sung-Sik

2017-04-01

Unconventional metallic states which do not support well-defined single-particle excitations can arise near quantum phase transitions as strong quantum fluctuations of incipient order parameters prevent electrons from forming coherent quasiparticles. Although antiferromagnetic phase transitions occur commonly in correlated metals, understanding the nature of the strange metal realized at the critical point in layered systems has been hampered by a lack of reliable theoretical methods that take into account strong quantum fluctuations. We present a nonperturbative solution to the low-energy theory for the antiferromagnetic quantum critical metal in two spatial dimensions. Being a strongly coupled theory, it can still be solved reliably in the low-energy limit as quantum fluctuations are organized by a new control parameter that emerges dynamically. We predict the exact critical exponents that govern the universal scaling of physical observables at low temperatures.

Electrostatic fluctuations in collisional plasmas

NASA Astrophysics Data System (ADS)

Rozmus, W.; Brantov, A.; Fortmann-Grote, C.; Bychenkov, V. Yu.; Glenzer, S.

2017-10-01

We present a theory of electrostatic fluctuations in two-component plasmas where electrons and ions are described by Maxwellian distribution functions at unequal temperatures. Based on the exact solution of the Landau kinetic equation, that includes electron-electron, electron-ion, and ion-ion collision integrals, the dynamic form factor, S (k ⃗,ω ) , is derived for weakly coupled plasmas. The collective plasma responses at ion-acoustic, Langmuir, and entropy mode resonances are described for arbitrary wave numbers and frequencies in the entire range of plasma collisionality. The collisionless limit of S (k ⃗,ω ) and the strong-collision result based on the fluctuation-dissipation theorem and classical transport at Te=Ti are recovered and discussed. Results of several Thomson scattering experiments in the broad range of plasma parameters are described and discussed by means of our theory for S (k ⃗,ω ) .

DNA-DNA interaction beyond the ground state

NASA Astrophysics Data System (ADS)

Lee, D. J.; Wynveen, A.; Kornyshev, A. A.

2004-11-01

The electrostatic interaction potential between DNA duplexes in solution is a basis for the statistical mechanics of columnar DNA assemblies. It may also play an important role in recombination of homologous genes. We develop a theory of this interaction that includes thermal torsional fluctuations of DNA using field-theoretical methods and Monte Carlo simulations. The theory extends and rationalizes the earlier suggested variational approach which was developed in the context of a ground state theory of interaction of nonhomologous duplexes. It shows that the heuristic variational theory is equivalent to the Hartree self-consistent field approximation. By comparison of the Hartree approximation with an exact solution based on the QM analogy of path integrals, as well as Monte Carlo simulations, we show that this easily analytically-tractable approximation works very well in most cases. Thermal fluctuations do not remove the ability of DNA molecules to attract each other at favorable azimuthal conformations, neither do they wash out the possibility of electrostatic “snap-shot” recognition of homologous sequences, considered earlier on the basis of ground state calculations. At short distances DNA molecules undergo a “torsional alignment transition,” which is first order for nonhomologous DNA and weaker order for homologous sequences.

Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Del Razo, Mauricio; Pan, Wenxiao; Qian, Hong

2014-05-30

The currently existing theory of fluorescence correlation spectroscopy (FCS) is based on the linear fluctuation theory originally developed by Einstein, Onsager, Lax, and others as a phenomenological approach to equilibrium fluctuations in bulk solutions. For mesoscopic reaction-diffusion systems with nonlinear chemical reactions among a small number of molecules, a situation often encountered in single-cell biochemistry, it is expected that FCS time correlation functions of a reaction-diffusion system can deviate from the classic results of Elson and Magde [Biopolymers (1974) 13:1-27]. We first discuss this nonlinear effect for reaction systems without diffusion. For nonlinear stochastic reaction-diffusion systems there are no closedmore » solutions; therefore, stochastic Monte-Carlo simulations are carried out. We show that the deviation is small for a simple bimolecular reaction; the most significant deviations occur when the number of molecules is small and of the same order. Extending Delbrück-Gillespie’s theory for stochastic nonlinear reactions with rapidly stirring to reaction-diffusion systems provides a mesoscopic model for chemical and biochemical reactions at nanometric and mesoscopic level such as a single biological cell.« less

Fluctuation-enhanced electric conductivity in electrolyte solutions

DOE PAGES

Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.; ...

2017-09-26

In this work, we analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell– Stefan coefficient proportionalmore » to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Lastly, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration.« less

Fluctuation-enhanced electric conductivity in electrolyte solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.

In this work, we analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell– Stefan coefficient proportionalmore » to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Lastly, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration.« less

Interfacial Ordering and Accompanying Divergent Capacitance at Ionic Liquid-Metal Interfaces.

PubMed

Limmer, David T

2015-12-18

A theory is constructed for dense ionic solutions near charged planar walls that is valid for strong interionic correlations. This theory predicts a fluctuation-induced, first-order transition and spontaneous charge density ordering at the interface, in the presence of an otherwise disordered bulk solution. The surface ordering is driven by applied voltage and results in an anomalous differential capacitance, in agreement with recent simulation results and consistent with experimental observations of a wide array of systems. Explicit forms for the charge density profile and capacitance are given. The theory is compared with numerical results for the charge frustrated Ising model, which is also found to exhibit a voltage driven first-order transition.

Interfacial Ordering and Accompanying Divergent Capacitance at Ionic Liquid-Metal Interfaces

NASA Astrophysics Data System (ADS)

Limmer, David T.

2015-12-01

A theory is constructed for dense ionic solutions near charged planar walls that is valid for strong interionic correlations. This theory predicts a fluctuation-induced, first-order transition and spontaneous charge density ordering at the interface, in the presence of an otherwise disordered bulk solution. The surface ordering is driven by applied voltage and results in an anomalous differential capacitance, in agreement with recent simulation results and consistent with experimental observations of a wide array of systems. Explicit forms for the charge density profile and capacitance are given. The theory is compared with numerical results for the charge frustrated Ising model, which is also found to exhibit a voltage driven first-order transition.

Electrostatic fluctuations in collisional plasmas

DOE PAGES

Rozmus, W.; Brantov, A.; Fortmann-Grote, C.; ...

2017-10-12

Here, we present a theory of electrostatic fluctuations in two-component plasmas where electrons and ions are described by Maxwellian distribution functions at unequal temperatures. Based on the exact solution of the Landau kinetic equation, that includes electron-electron, electron-ion, and ion-ion collision integrals, the dynamic form factor, S( →k,ω), is derived for weakly coupled plasmas. The collective plasma responses at ion-acoustic, Langmuir, and entropy mode resonances are described for arbitrary wave numbers and frequencies in the entire range of plasma collisionality. The collisionless limit of S( →k,ω) and the strong-collision result based on the fluctuation-dissipation theorem and classical transport at Tmore » e = T i are recovered and discussed. Results of several Thomson scattering experiments in the broad range of plasma parameters are described and discussed by means of our theory for S( →k,ω).« less

Electrostatic fluctuations in collisional plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rozmus, W.; Brantov, A.; Fortmann-Grote, C.

Here, we present a theory of electrostatic fluctuations in two-component plasmas where electrons and ions are described by Maxwellian distribution functions at unequal temperatures. Based on the exact solution of the Landau kinetic equation, that includes electron-electron, electron-ion, and ion-ion collision integrals, the dynamic form factor, S( →k,ω), is derived for weakly coupled plasmas. The collective plasma responses at ion-acoustic, Langmuir, and entropy mode resonances are described for arbitrary wave numbers and frequencies in the entire range of plasma collisionality. The collisionless limit of S( →k,ω) and the strong-collision result based on the fluctuation-dissipation theorem and classical transport at Tmore » e = T i are recovered and discussed. Results of several Thomson scattering experiments in the broad range of plasma parameters are described and discussed by means of our theory for S( →k,ω).« less

Electrostatic fluctuations in collisional plasmas.

PubMed

Rozmus, W; Brantov, A; Fortmann-Grote, C; Bychenkov, V Yu; Glenzer, S

2017-10-01

We present a theory of electrostatic fluctuations in two-component plasmas where electrons and ions are described by Maxwellian distribution functions at unequal temperatures. Based on the exact solution of the Landau kinetic equation, that includes electron-electron, electron-ion, and ion-ion collision integrals, the dynamic form factor, S(k[over ⃗],ω), is derived for weakly coupled plasmas. The collective plasma responses at ion-acoustic, Langmuir, and entropy mode resonances are described for arbitrary wave numbers and frequencies in the entire range of plasma collisionality. The collisionless limit of S(k[over ⃗],ω) and the strong-collision result based on the fluctuation-dissipation theorem and classical transport at T_{e}=T_{i} are recovered and discussed. Results of several Thomson scattering experiments in the broad range of plasma parameters are described and discussed by means of our theory for S(k[over ⃗],ω).

Higher derivatives in Type II and M-theory on Calabi-Yau threefolds

NASA Astrophysics Data System (ADS)

Grimm, Thomas W.; Mayer, Kilian; Weissenbacher, Matthias

2018-02-01

The four- and five-dimensional effective actions of Calabi-Yau threefold compactifications are derived with a focus on terms involving up to four space-time derivatives. The starting points for these reductions are the ten- and eleven-dimensional supergravity actions supplemented with the known eight-derivative corrections that have been inferred from Type II string amplitudes. The corrected background solutions are determined and the fluctuations of the Kähler structure of the compact space and the form-field back-ground are discussed. It is concluded that the two-derivative effective actions for these fluctuations only takes the expected supergravity form if certain additional ten- and eleven-dimensional higher-derivative terms for the form-fields are included. The main results on the four-derivative terms include a detailed treatment of higher-derivative gravity coupled to Kähler structure deformations. This is supplemented by a derivation of the vector sector in reductions to five dimensions. While the general result is only given as an expansion in the fluctuations, a complete treatment of the one-Kähler modulus case is presented for both Type II theories and M-theory.

Free-energy analysis of the electron-density fluctuation in the quantum-mechanical/molecular-mechanical simulation combined with the theory of energy representation.

PubMed

Matubayasi, Nobuyuki; Takahashi, Hideaki

2012-01-28

The relationship is investigated for QM/MM (quantum-mechanical/molecular-mechanical) systems between the fluctuations of the electronic state of the QM subsystem and of the solvation effect due to the QM-MM interaction. The free-energy change due to the electron-density fluctuation around its average is highlighted, and is evaluated through an approximate functional formulated in terms of distribution functions of the many-body coupling (pairwise non-additive) part of the QM-MM interaction energy. A set of QM/MM simulations are conducted in MM water solvent for QM water solute in ambient and supercritical conditions and for QM glycine solute in the neutral and zwitterionic forms. The variation of the electronic distortion energy of the QM solute in the course of QM/MM simulation is then shown to be compensated by the corresponding variation of the free energy of solvation. The solvation free energy conditioned by the electronic distortion energy is further analyzed with its components. It is found that the many-body contribution is essentially equal between the free energy and the average sum of solute-solvent interaction energy. © 2012 American Institute of Physics

Stochastic Gravity: Theory and Applications.

PubMed

Hu, Bei Lok; Verdaguer, Enric

2004-01-01

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operatorvalued) stress-energy bi-tensor which describes the fluctuations of quantum matter fields in curved spacetimes. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open systems concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise, and decoherence. We then focus on the properties of the stress-energy bi-tensor. We obtain a general expression for the noise kernel of a quantum field defined at two distinct points in an arbitrary curved spacetime as products of covariant derivatives of the quantum field's Green function. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime. We offer an analytical solution of the Einstein-Langevin equation and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole (enclosed in a box). We derive a fluctuation-dissipation relation between the fluctuations in the radiation and the dissipative dynamics of metric fluctuations.

Competition of mesoscales and crossover to theta-point tricriticality in near-critical polymer solutions.

PubMed

Anisimov, M A; Kostko, A F; Sengers, J V; Yudin, I K

2005-10-22

The approach to asymptotic critical behavior in polymer solutions is governed by a competition between the correlation length of critical fluctuations diverging at the critical point of phase separation and an additional mesoscopic length scale, the radius of gyration. In this paper we present a theory for crossover between two universal regimes: a regime with Ising (fluctuation-induced) asymptotic critical behavior, where the correlation length prevails, and a mean-field tricritical regime with theta-point behavior controlled by the mesoscopic polymer chain. The theory yields a universal scaled description of existing experimental phase-equilibria data and is in excellent agreement with our light-scattering experiments on polystyrene solutions in cyclohexane with polymer molecular weights ranging from 2 x 10(5) up to 11.4 x 10(6). The experiments demonstrate unambiguously that crossover to theta-point tricriticality is controlled by a competition of the two mesoscales. The critical amplitudes deduced from our experiments depend on the polymer molecular weight as predicted by de Gennes [Phys. Lett. 26A, 313 (1968)]. Experimental evidence for the presence of logarithmic corrections to mean-field tricritical theta-point behavior in the molecular-weight dependence of the critical parameters is also presented.

Holography for Schrödinger backgrounds

NASA Astrophysics Data System (ADS)

Guica, Monica; Skenderis, Kostas; Taylor, Marika; van Rees, Balt C.

2011-02-01

We discuss holography for Schrödinger solutions of both topologically massive gravity in three dimensions and massive vector theories in ( d + 1) dimensions. In both cases the dual field theory can be viewed as a d-dimensional conformal field theory (two dimensional in the case of TMG) deformed by certain operators that respect the Schrödinger symmetry. These operators are irrelevant from the viewpoint of the relativistic conformal group but they are exactly marginal with respect to the non-relativistic conformal group. The spectrum of linear fluctuations around the background solutions corresponds to operators that are labeled by their scaling dimension and the lightcone momentum k v . We set up the holographic dictionary and compute 2-point functions of these operators both holographically and in field theory using conformal perturbation theory and find agreement. The counterterms needed for holographic renormalization are non-local in the v lightcone direction.

On anthropic solutions of the cosmological constant problem

NASA Astrophysics Data System (ADS)

Banks, Tom; Dine, Michael; Motl, Lubos

2001-01-01

Motivated by recent work of Bousso and Polchinski (BP), we study theories which explain the small value of the cosmological constant using the anthropic principle. We argue that simultaneous solution of the gauge hierarchy problem is a strong constraint on any such theory. We exhibit three classes of models which satisfy these constraints. The first is a version of the BP model with precisely two large dimensions. The second involves 6-branes and antibranes wrapped on supersymmetric 3-cycles of Calabi-Yau manifolds, and the third is a version of the irrational axion model. All of them have possible problems in explaining the size of microwave background fluctuations. We also find that most models of this type predict that all constants in the low energy lagrangian, as well as the gauge groups and representation content, are chosen from an ensemble and cannot be uniquely determined from the fundamental theory. In our opinion, this significantly reduces the appeal of this kind of solution of the cosmological constant problem. On the other hand, we argue that the vacuum selection problem of string theory might plausibly have an anthropic, cosmological solution.

A multi-species exchange model for fully fluctuating polymer field theory simulations.

PubMed

Düchs, Dominik; Delaney, Kris T; Fredrickson, Glenn H

2014-11-07

Field-theoretic models have been used extensively to study the phase behavior of inhomogeneous polymer melts and solutions, both in self-consistent mean-field calculations and in numerical simulations of the full theory capturing composition fluctuations. The models commonly used can be grouped into two categories, namely, species models and exchange models. Species models involve integrations of functionals that explicitly depend on fields originating both from species density operators and their conjugate chemical potential fields. In contrast, exchange models retain only linear combinations of the chemical potential fields. In the two-component case, development of exchange models has been instrumental in enabling stable complex Langevin (CL) simulations of the full complex-valued theory. No comparable stable CL approach has yet been established for field theories of the species type. Here, we introduce an extension of the exchange model to an arbitrary number of components, namely, the multi-species exchange (MSE) model, which greatly expands the classes of soft material systems that can be accessed by the complex Langevin simulation technique. We demonstrate the stability and accuracy of the MSE-CL sampling approach using numerical simulations of triblock and tetrablock terpolymer melts, and tetrablock quaterpolymer melts. This method should enable studies of a wide range of fluctuation phenomena in multiblock/multi-species polymer blends and composites.

Fluctuations of a q-deformed fermion gas

NASA Astrophysics Data System (ADS)

Zeng, Qijun; Ge, Jing; Luo, Yongsong

2018-05-01

The theory of q-deformed fermions is one of the theories of q-deformed oscillators. Within the framework of this theory and the traditional fluctuation theory, we investigate fluctuations of q-deformed fermion gas and obtain the expressions of fluctuations of the internal energy U, the particle number N and the correlation of fluctuations of the two physical quantities above. Further numerical calculation reveals that fluctuations of such a system have some interesting and particular features. We consider that this work may provide much insight into the theory of q fermions, and may also be helpful for the theory of q-deformed oscillators.

Stochastic theory of fatigue corrosion

NASA Astrophysics Data System (ADS)

Hu, Haiyun

1999-10-01

A stochastic theory of corrosion has been constructed. The stochastic equations are described giving the transportation corrosion rate and fluctuation corrosion coefficient. In addition the pit diameter distribution function, the average pit diameter and the most probable pit diameter including other related empirical formula have been derived. In order to clarify the effect of stress range on the initiation and growth behaviour of pitting corrosion, round smooth specimen were tested under cyclic loading in 3.5% NaCl solution.

Fluctuating hydrodynamics of multispecies nonreactive mixtures

DOE PAGES

Balakrishnan, Kaushik; Garcia, Alejandro L.; Donev, Aleksandar; ...

2014-01-22

In this study we discuss the formulation of the fluctuating Navier-Stokes equations for multispecies, nonreactive fluids. In particular, we establish a form suitable for numerical solution of the resulting stochastic partial differential equations. An accurate and efficient numerical scheme, based on our previous methods for single species and binary mixtures, is presented and tested at equilibrium as well as for a variety of nonequilibrium problems. These include the study of giant nonequilibrium concentration fluctuations in a ternary mixture in the presence of a diffusion barrier, the triggering of a Rayleigh-Taylor instability by diffusion in a four-species mixture, as well asmore » reverse diffusion in a ternary mixture. Finally, good agreement with theory and experiment demonstrates that the formulation is robust and can serve as a useful tool in the study of thermal fluctuations for multispecies fluids.« less

Nonlocal Galileons and self-acceleration

NASA Astrophysics Data System (ADS)

Gabadadze, Gregory; Yu, Siqing

2017-05-01

A certain class of nonlocal theories eliminates an arbitrary cosmological constant (CC) from a universe that can be perceived as our world. Dark energy then cannot be explained by a CC; it could however be due to massive gravity. We calculate the new corrections, which originate from the nonlocal terms that eliminate the CC, to the decoupling limit Lagrangian of massive gravity. The new nonlocal terms also have internal field space Galilean symmetry and are referred here as ;nonlocal Galileons.; We then study a self-accelerated solution and show that the new nonlocal terms change the perturbative stability analysis. In particular, small fluctuations are now stable and non-superluminal for some simple parameter choices, whereas for the same choices the pure massive gravity fluctuations are unstable. We also study stable spherically symmetric solutions on this background.

Regularizing portfolio optimization

NASA Astrophysics Data System (ADS)

Still, Susanne; Kondor, Imre

2010-07-01

The optimization of large portfolios displays an inherent instability due to estimation error. This poses a fundamental problem, because solutions that are not stable under sample fluctuations may look optimal for a given sample, but are, in effect, very far from optimal with respect to the average risk. In this paper, we approach the problem from the point of view of statistical learning theory. The occurrence of the instability is intimately related to over-fitting, which can be avoided using known regularization methods. We show how regularized portfolio optimization with the expected shortfall as a risk measure is related to support vector regression. The budget constraint dictates a modification. We present the resulting optimization problem and discuss the solution. The L2 norm of the weight vector is used as a regularizer, which corresponds to a diversification 'pressure'. This means that diversification, besides counteracting downward fluctuations in some assets by upward fluctuations in others, is also crucial because it improves the stability of the solution. The approach we provide here allows for the simultaneous treatment of optimization and diversification in one framework that enables the investor to trade off between the two, depending on the size of the available dataset.

A holographic model for the fractional quantum Hall effect

NASA Astrophysics Data System (ADS)

Lippert, Matthew; Meyer, René; Taliotis, Anastasios

2015-01-01

Experimental data for fractional quantum Hall systems can to a large extent be explained by assuming the existence of a Γ0(2) modular symmetry group commuting with the renormalization group flow and hence mapping different phases of two-dimensional electron gases into each other. Based on this insight, we construct a phenomenological holographic model which captures many features of the fractional quantum Hall effect. Using an -invariant Einstein-Maxwell-axio-dilaton theory capturing the important modular transformation properties of quantum Hall physics, we find dyonic diatonic black hole solutions which are gapped and have a Hall conductivity equal to the filling fraction, as expected for quantum Hall states. We also provide several technical results on the general behavior of the gauge field fluctuations around these dyonic dilatonic black hole solutions: we specify a sufficient criterion for IR normalizability of the fluctuations, demonstrate the preservation of the gap under the action, and prove that the singularity of the fluctuation problem in the presence of a magnetic field is an accessory singularity. We finish with a preliminary investigation of the possible IR scaling solutions of our model and some speculations on how they could be important for the observed universality of quantum Hall transitions.

Chromatin Hydrodynamics

PubMed Central

Bruinsma, Robijn; Grosberg, Alexander Y.; Rabin, Yitzhak; Zidovska, Alexandra

2014-01-01

Following recent observations of large scale correlated motion of chromatin inside the nuclei of live differentiated cells, we present a hydrodynamic theory—the two-fluid model—in which the content of a nucleus is described as a chromatin solution with the nucleoplasm playing the role of the solvent and the chromatin fiber that of a solute. This system is subject to both passive thermal fluctuations and active scalar and vector events that are associated with free energy consumption, such as ATP hydrolysis. Scalar events drive the longitudinal viscoelastic modes (where the chromatin fiber moves relative to the solvent) while vector events generate the transverse modes (where the chromatin fiber moves together with the solvent). Using linear response methods, we derive explicit expressions for the response functions that connect the chromatin density and velocity correlation functions to the corresponding correlation functions of the active sources and the complex viscoelastic moduli of the chromatin solution. We then derive general expressions for the flow spectral density of the chromatin velocity field. We use the theory to analyze experimental results recently obtained by one of the present authors and her co-workers. We find that the time dependence of the experimental data for both native and ATP-depleted chromatin can be well-fitted using a simple model—the Maxwell fluid—for the complex modulus, although there is some discrepancy in terms of the wavevector dependence. Thermal fluctuations of ATP-depleted cells are predominantly longitudinal. ATP-active cells exhibit intense transverse long wavelength velocity fluctuations driven by force dipoles. Fluctuations with wavenumbers larger than a few inverse microns are dominated by concentration fluctuations with the same spectrum as thermal fluctuations but with increased intensity. PMID:24806919

[Kinetic theory and boundary conditions for highly inelastic spheres]. Quarterly progress report, April 1, 1993--June 30, 1993

DOE Office of Scientific and Technical Information (OSTI.GOV)

Richman, M.

1993-12-31

In this quarter, a kinetic theory was employed to set up the boundary value problem for steady, fully developed, gravity-driven flows of identical, smooth, highly inelastic spheres down bumpy inclines. The solid fraction, mean velocity, and components of the full second moment of fluctuation velocity were treated as mean fields. In addition to the balance equations for mass and momentum, the balance of the full second moment of fluctuation velocity was treated as an equation that must be satisfied by the mean fields. However, in order to simplify the resulting boundary value problem, fluxes of second moments in its isotropicmore » piece only were retained. The constitutive relations for the stresses and collisional source of second moment depend explicitly on the second moment of fluctuation velocity, and the constitutive relation for the energy flux depends on gradients of granular temperature, solid fraction, and components of the second moment. The boundary conditions require that the flows are free of stress and energy flux at their tops, and that momentum and energy are balanced at the bumpy base. The details of the boundary value problem are provided. In the next quarter, a solution procedure will be developed, and it will be employed to obtain sample numerical solutions to the boundary value problem described here.« less

Nominal vs. actual supersaturation of solutions

NASA Astrophysics Data System (ADS)

Borisenko, Alexander

2018-03-01

Following the formalism of the Classical Nucleation Theory beyond the dilute solution approximation, this paper considers a difference between the actual solute supersaturation (given by the present-to-saturated solute activity ratio) and the nominal supersaturation (given by the present-to-saturated solute concentration ratio) due to formation of subcritical transient solute clusters, called heterophase fluctuations. Based on their distribution function, we introduce an algebraic equation of supersaturation that couples the nominal supersaturation of a binary metastable solution with its actual supersaturation and a function of the specific interface energy and temperature. The applicability of this approach is validated by comparison to simulation data [(Clouet et al., Phys. Rev. B 69, 064109 (2004)] on nucleation of Al3Zr and Al3Sc in model binary Al alloys.

Terahertz absorption of lysozyme in solution

NASA Astrophysics Data System (ADS)

Martin, Daniel R.; Matyushov, Dmitry V.

2017-08-01

Absorption of radiation by solution is described by its frequency-dependent dielectric function and can be viewed as a specific application of the dielectric theory of solutions. For ideal solutions, the dielectric boundary-value problem separates the polar response into the polarization of the void in the liquid, created by the solute, and the response of the solute dipole. In the case of a protein as a solute, protein nuclear dynamics do not project on significant fluctuations of the dipole moment in the terahertz domain of frequencies and the protein dipole can be viewed as dynamically frozen. Absorption of radiation then reflects the interfacial polarization. Here we apply an analytical theory and computer simulations to absorption of radiation by an ideal solution of lysozyme. Comparison with the experiment shows that Maxwell electrostatics fails to describe the polarization of the protein-water interface and the "Lorentz void," which does not anticipate polarization of the interface by the external field (no surface charges), better represents the data. An analytical theory for the slope of the solution absorption against the volume fraction of the solute is formulated in terms of the cavity field response function. It is calculated from molecular dynamics simulations in good agreement with the experiment. The protein hydration shell emerges as a separate sub-ensemble, which, collectively, is not described by the standard electrostatics of dielectrics.

Second quantization in bit-string physics

NASA Technical Reports Server (NTRS)

Noyes, H. Pierre

1993-01-01

Using a new fundamental theory based on bit-strings, a finite and discrete version of the solutions of the free one particle Dirac equation as segmented trajectories with steps of length h/mc along the forward and backward light cones executed at velocity +/- c are derived. Interpreting the statistical fluctuations which cause the bends in these segmented trajectories as emission and absorption of radiation, these solutions are analogous to a fermion propagator in a second quantized theory. This allows us to interpret the mass parameter in the step length as the physical mass of the free particle. The radiation in interaction with it has the usual harmonic oscillator structure of a second quantized theory. How these free particle masses can be generated gravitationally using the combinatorial hierarchy sequence (3,10,137,2(sup 127) + 136), and some of the predictive consequences are sketched.

Quantum-like dynamics of decision-making

NASA Astrophysics Data System (ADS)

Asano, Masanari; Basieva, Irina; Khrennikov, Andrei; Ohya, Masanori; Tanaka, Yoshiharu

2012-03-01

In cognitive psychology, some experiments for games were reported, and they demonstrated that real players did not use the “rational strategy” provided by classical game theory and based on the notion of the Nasch equilibrium. This psychological phenomenon was called the disjunction effect. Recently, we proposed a model of decision making which can explain this effect (“irrationality” of players) Asano et al. (2010, 2011) [23,24]. Our model is based on the mathematical formalism of quantum mechanics, because psychological fluctuations inducing the irrationality are formally represented as quantum fluctuations Asano et al. (2011) [55]. In this paper, we reconsider the process of quantum-like decision-making more closely and redefine it as a well-defined quantum dynamics by using the concept of lifting channel, which is an important concept in quantum information theory. We also present numerical simulation for this quantum-like mental dynamics. It is non-Markovian by its nature. Stabilization to the steady state solution (determining subjective probabilities for decision making) is based on the collective effect of mental fluctuations collected in the working memory of a decision maker.

Electroosmotic flow in a rectangular channel with variable wall zeta-potential: comparison of numerical simulation with asymptotic theory.

PubMed

Datta, Subhra; Ghosal, Sandip; Patankar, Neelesh A

2006-02-01

Electroosmotic flow in a straight micro-channel of rectangular cross-section is computed numerically for several situations where the wall zeta-potential is not constant but has a specified spatial variation. The results of the computation are compared with an earlier published asymptotic theory based on the lubrication approximation: the assumption that any axial variations take place on a long length scale compared to a characteristic channel width. The computational results are found to be in excellent agreement with the theory even when the scale of axial variations is comparable to the channel width. In the opposite limit when the wavelength of fluctuations is much shorter than the channel width, the lubrication theory fails to describe the solution either qualitatively or quantitatively. In this short wave limit the solution is well described by Ajdari's theory for electroosmotic flow between infinite parallel plates (Ajdari, A., Phys. Rev. E 1996, 53, 4996-5005.) The infinitely thin electric double layer limit is assumed in the theory as well as in the simulation.

Cosmic acceleration and the helicity-0 graviton

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rham, Claudia de; Heisenberg, Lavinia; Gabadadze, Gregory

2011-05-15

We explore cosmology in the decoupling limit of a nonlinear covariant extension of Fierz-Pauli massive gravity obtained recently in arXiv:1007.0443. In this limit the theory is a scalar-tensor model of a unique form defined by symmetries. We find that it admits a self-accelerated solution, with the Hubble parameter set by the graviton mass. The negative pressure causing the acceleration is due to a condensate of the helicity-0 component of the massive graviton, and the background evolution, in the approximation used, is indistinguishable from the {Lambda}CDM model. Fluctuations about the self-accelerated background are stable for a certain range of parameters involved.more » Most surprisingly, the fluctuation of the helicity-0 field above its background decouples from an arbitrary source in the linearized theory. We also show how massive gravity can remarkably screen an arbitrarily large cosmological constant in the decoupling limit, while evading issues with ghosts. The obtained static solution is stable against small perturbations, suggesting that the degravitation of the vacuum energy is possible in the full theory. Interestingly, however, this mechanism postpones the Vainshtein effect to shorter distance scales. Hence, fifth force measurements severely constrain the value of the cosmological constant that can be neutralized, making this scheme phenomenologically not viable for solving the old cosmological constant problem. We briefly speculate on a possible way out of this issue.« less

Molecular-dynamics simulations of urea nucleation from aqueous solution

PubMed Central

Salvalaglio, Matteo; Perego, Claudio; Giberti, Federico; Mazzotti, Marco; Parrinello, Michele

2015-01-01

Despite its ubiquitous character and relevance in many branches of science and engineering, nucleation from solution remains elusive. In this framework, molecular simulations represent a powerful tool to provide insight into nucleation at the molecular scale. In this work, we combine theory and molecular simulations to describe urea nucleation from aqueous solution. Taking advantage of well-tempered metadynamics, we compute the free-energy change associated to the phase transition. We find that such a free-energy profile is characterized by significant finite-size effects that can, however, be accounted for. The description of the nucleation process emerging from our analysis differs from classical nucleation theory. Nucleation of crystal-like clusters is in fact preceded by large concentration fluctuations, indicating a predominant two-step process, whereby embryonic crystal nuclei emerge from dense, disordered urea clusters. Furthermore, in the early stages of nucleation, two different polymorphs are seen to compete. PMID:25492932

Molecular-dynamics simulations of urea nucleation from aqueous solution.

PubMed

Salvalaglio, Matteo; Perego, Claudio; Giberti, Federico; Mazzotti, Marco; Parrinello, Michele

2015-01-06

Despite its ubiquitous character and relevance in many branches of science and engineering, nucleation from solution remains elusive. In this framework, molecular simulations represent a powerful tool to provide insight into nucleation at the molecular scale. In this work, we combine theory and molecular simulations to describe urea nucleation from aqueous solution. Taking advantage of well-tempered metadynamics, we compute the free-energy change associated to the phase transition. We find that such a free-energy profile is characterized by significant finite-size effects that can, however, be accounted for. The description of the nucleation process emerging from our analysis differs from classical nucleation theory. Nucleation of crystal-like clusters is in fact preceded by large concentration fluctuations, indicating a predominant two-step process, whereby embryonic crystal nuclei emerge from dense, disordered urea clusters. Furthermore, in the early stages of nucleation, two different polymorphs are seen to compete.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sasakura, Naoki

The tensor model is discussed as theory of dynamical fuzzy spaces in order to formulate gravity on fuzzy spaces. The numerical analyses of the tensor models possessing Gaussian background solutions have shown that the low-lying long-wavelength fluctuations around the backgrounds are in remarkable agreement with the geometric fluctuations on flat spaces in the general relativity. It has also been shown that part of the orthogonal symmetry of the tensor model spontaneously broken by the backgrounds agrees with the local translation symmetry of the general relativity. Thus the tensor model provides an interesting model of simultaneous emergence of space, the generalmore » relativity, and its local translation symmetry.« less

Electrode redox reactions with polarizable molecules.

PubMed

Matyushov, Dmitry V

2018-04-21

A theory of redox reactions involving electron transfer between a metal electrode and a polarizable molecule in solution is formulated. Both the existence of molecular polarizability and its ability to change due to electron transfer distinguish this problem from classical theories of interfacial electrochemistry. When the polarizability is different between the oxidized and reduced states, the statistics of thermal fluctuations driving the reactant over the activation barrier becomes non-Gaussian. The problem of electron transfer is formulated as crossing of two non-parabolic free energy surfaces. An analytical solution for these free energy surfaces is provided and the activation barrier of electrode electron transfer is given in terms of two reorganization energies corresponding to the oxidized and reduced states of the molecule in solution. The new non-Gaussian theory is, therefore, based on two theory parameters in contrast to one-parameter Marcus formulation for electrode reactions. The theory, which is consistent with the Nernst equation, predicts asymmetry between the cathodic and anodic branches of the electrode current. They show different slopes at small electrode overpotentials and become curved at larger overpotentials. However, the curvature of the Tafel plot is reduced compared to the Marcus-Hush model and approaches the empirical Butler-Volmer form with different transfer coefficients for the anodic and cathodic currents.

Electrode redox reactions with polarizable molecules

NASA Astrophysics Data System (ADS)

Matyushov, Dmitry V.

2018-04-01

A theory of redox reactions involving electron transfer between a metal electrode and a polarizable molecule in solution is formulated. Both the existence of molecular polarizability and its ability to change due to electron transfer distinguish this problem from classical theories of interfacial electrochemistry. When the polarizability is different between the oxidized and reduced states, the statistics of thermal fluctuations driving the reactant over the activation barrier becomes non-Gaussian. The problem of electron transfer is formulated as crossing of two non-parabolic free energy surfaces. An analytical solution for these free energy surfaces is provided and the activation barrier of electrode electron transfer is given in terms of two reorganization energies corresponding to the oxidized and reduced states of the molecule in solution. The new non-Gaussian theory is, therefore, based on two theory parameters in contrast to one-parameter Marcus formulation for electrode reactions. The theory, which is consistent with the Nernst equation, predicts asymmetry between the cathodic and anodic branches of the electrode current. They show different slopes at small electrode overpotentials and become curved at larger overpotentials. However, the curvature of the Tafel plot is reduced compared to the Marcus-Hush model and approaches the empirical Butler-Volmer form with different transfer coefficients for the anodic and cathodic currents.

On the fluctuations that drive small ions toward, and away from, interfaces between polar liquids and their vapors

PubMed Central

Noah-Vanhoucke, Joyce; Geissler, Phillip L.

2009-01-01

Contrary to the expectations from classic theories of ion solvation, spectroscopy and computer simulations of the liquid–vapor interface of aqueous electrolyte solutions suggest that ions little larger than a water molecule can prefer to reside near the liquid's surface. Here we advance the view that such affinity originates in a competition between strong opposing forces, primarily due to volume exclusion and dielectric polarization, that are common to all dense polar liquids. We present evidence for this generic mechanism from computer simulations of (i) water and (ii) a Stockmayer fluid near its triple point. In both cases, we show that strong surface enhancement of small ions, obtained by tuning solutes' size and charge, can be accentuated or suppressed by modest changes in either of those parameters. Statistics of solvent polarization, when the ion is held at and above the Gibbs dividing surface, highlight a basic deficiency in conventional models of dielectric response, namely, the neglect of interfacial flexibility. By distorting the solution's boundary, an ion experiences fluctuations in electrostatic potential and in electric field whose magnitudes attenuate much more gradually (as the ion is removed from the liquid phase) than for a quiescent planar interface. As one consequence, the collective responses that determine free energies of solvation can resolve very differently in nonuniform environments than in bulk. We show that this persistence of electric-field fluctuations additionally shapes the sensitivity of solute distributions to ion polarizability. PMID:19720991

Prediction of global vapor-liquid equilibria for mixtures containing polar and associating components with improved renormalization group theory.

PubMed

Mi, Jianguo; Tang, Yiping; Zhong, Chongli; Li, Yi-Gui

2005-11-03

Our recently improved renormalization group (RG) theory is further reformulated within the context of density functional theory. To improve the theory for polar and associating fluids, an explicit and complete expression of the theory is derived in which the density fluctuation is expanded up to the third-order term instead of the original second-order term. A new predictive equation of state based on the first-order mean spherical approximation statistical associating fluid theory (FMSA-SAFT) and the newly improved RG theory is proposed for systems containing polar and associating fluids. The calculated results for both pure fluids and mixtures are in good agreement with experimental data both inside and outside the critical region. This work demonstrates that the RG theory incorporated with the solution of FMSA is a promising route for accurately describing the global phase behavior of complex fluids and mixtures.

Turbulent Equilibria for Charged Particles in Space

NASA Astrophysics Data System (ADS)

Yoon, Peter

2017-04-01

The solar wind electron distribution function is apparently composed of several components including non-thermal tail population. The electron distribution that contains energetic tail feature is well fitted with the kappa distribution function. The solar wind protons also possess quasi power-law tail distribution function that is well fitted with an inverse power law model. The present paper discusses the latest theoretical development regarding the dynamical steady-state solution of electrons and Langmuir turbulence that are in turbulent equilibrium. According to such a theory, the Maxwellian and kappa distribution functions for the electrons emerge as the only two possible solution that satisfy the steady-state weak turbulence plasma kinetic equation. For the proton inverse power-law tail problem, a similar turbulent equilibrium solution can be conceived of, but instead of high-frequency Langmuir fluctuation, the theory involves low-frequency kinetic Alfvenic turbulence. The steady-state solution of the self-consistent proton kinetic equation and wave kinetic equation for Alfvenic waves can be found in order to obtain a self-consistent solution for the inverse power law tail distribution function.

Quasi-linear theory via the cumulant expansion approach

NASA Technical Reports Server (NTRS)

Jones, F. C.; Birmingham, T. J.

1974-01-01

The cumulant expansion technique of Kubo was used to derive an intergro-differential equation for f , the average one particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the f equation degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory for this limited class of fluctuations. For more physically realistic fluctuations, however, quasi-linear theory is at best approximate.

Nonstationary stochastic charge fluctuations of a dust particle in plasmas.

PubMed

Shotorban, B

2011-06-01

Stochastic charge fluctuations of a dust particle that are due to discreteness of electrons and ions in plasmas can be described by a one-step process master equation [T. Matsoukas and M. Russell, J. Appl. Phys. 77, 4285 (1995)] with no exact solution. In the present work, using the system size expansion method of Van Kampen along with the linear noise approximation, a Fokker-Planck equation with an exact Gaussian solution is developed by expanding the master equation. The Gaussian solution has time-dependent mean and variance governed by two ordinary differential equations modeling the nonstationary process of dust particle charging. The model is tested via the comparison of its results to the results obtained by solving the master equation numerically. The electron and ion currents are calculated through the orbital motion limited theory. At various times of the nonstationary process of charging, the model results are in a very good agreement with the master equation results. The deviation is more significant when the standard deviation of the charge is comparable to the mean charge in magnitude.

On the initial conditions of scalar and tensor fluctuations in f(R,φ ) gravity

NASA Astrophysics Data System (ADS)

Cheraghchi, S.; Shojai, F.

2018-05-01

We have considered the perturbation equations governing the growth of fluctuations during inflation in generalized scalar tensor theory f(R,φ ). We have found that the scalar metric perturbations at very early times are negligible compared to the scalar field perturbation, just like general relativity. At sufficiently early times, when the physical momentum of perturbation mode, q / a is much larger than the Hubble parameter H, i.e. q/a≫ H, we have obtained the metric and scalar field perturbation in the form of WKB solutions up to an undetermined coefficient. Then we have quantized the scalar fluctuations and expanded the metric and the scalar field perturbations with the help of annihilation and creation operators of the scalar field perturbation. The standard commutation relations of annihilation and creation operators fix the unknown coefficient. Going over to the gauge invariant quantities which are conserved beyond the horizon, we have obtained the initial condition of the generalized Mukhanov-Sasaki equation. Then a similar procedure is performed for the case of tensor metric perturbation. As an example of the generalized Mukhanov-Sasaki equation and its initial condition, we have proposed a power-law functional form as f(R,φ )=f_0 R^m φ ^n and obtained an exact inflationary solution. In this background, then we have discussed how the scalar and tensor fluctuations grow.

Using Grand Canonical Monte Carlo Simulations to Understand the Role of Interfacial Fluctuations on Solvation at the Water-Vapor Interface.

PubMed

Rane, Kaustubh; van der Vegt, Nico F A

2016-09-15

The present work investigates the effect of interfacial fluctuations (predominantly capillary wave-like fluctuations) on the solvation free energy (Δμ) of a monatomic solute at the water-vapor interface. We introduce a grand-canonical-ensemble-based simulation approach that quantifies the contribution of interfacial fluctuations to Δμ. This approach is used to understand how the above contribution depends on the strength of dispersive and electrostatic solute-water interactions at the temperature of 400 K. At this temperature, we observe that interfacial fluctuations do play a role in the variation of Δμ with the strength of the electrostatic solute-water interaction. We also use grand canonical simulations to further investigate how interfacial fluctuations affect the propensity of the solute toward the water-vapor interface. To this end, we track a quantity called the interface potential (surface excess free energy) with the number of water molecules. With increasing number of water molecules, the liquid-vapor interface moves across a solute, which is kept at a fixed position in the simulation. Hence, the dependence of the interface potential on the number of waters models the process of moving the solute through the water-vapor interface. We analyze the change of the interface potential with the number of water molecules to explain that solute-induced changes in the interfacial fluctuations, like the pinning of capillary-wave-like undulations, do not play any role in the propensity of solutes toward water-vapor interfaces. The above analysis also shows that the dampening of interfacial fluctuations accompanies the adsorption of any solute at the liquid-vapor interface, irrespective of the chemical nature of the solute and solvent. However, such a correlation does not imply that dampening of fluctuations causes adsorption.

Inorganic and Protein Crystal Assembly in Solutions

NASA Technical Reports Server (NTRS)

Chernov, A. A.

2005-01-01

The basic kinetic and thermodynamic concepts of crystal growth will be revisited in view of recent AFM and interferometric findings. These concepts are as follows: 1) The Kossel crystal model that allows only one kink type on the crystal surface. The modern theory is developed overwhelmingly for the Kessel model; 2) Presumption that intensive step fluctuations maintain kink density sufficiently high to allow applicability of Gibbs-Thomson law; 3) Common experience that unlimited step bunching (morphological instability) during layer growth from solutions and supercooled melts always takes place if the step flow direction coincides with that of the fluid.

A quasi-one-dimensional theory of sound propagation in lined ducts with mean flow

NASA Astrophysics Data System (ADS)

Dokumaci, Erkan

2018-04-01

Sound propagation in ducts with locally-reacting liners has received the attention of many authors proposing two- and three-dimensional solutions of the convected wave equation and of the Pridmore-Brown equation. One-dimensional lined duct models appear to have received less attention. The present paper proposes a quasi-one-dimensional theory for lined uniform ducts with parallel sheared mean flow. The basic assumption of the theory is that the effects of refraction and wall compliance on the fundamental mode remain within ranges in which the acoustic fluctuations are essentially uniform over a duct section. This restricts the model to subsonic low Mach numbers and Helmholtz numbers of less than about unity. The axial propagation constants and the wave transfer matrix of the duct are given by simple explicit expressions and can be applied with no-slip, full-slip or partial slip boundary conditions. The limitations of the theory are discussed and its predictions are compared with the fundamental mode solutions of the convected wave equation, the Pridmore-Brown equation and measurements where available.

Polarons and Mobile Impurities Near a Quantum Phase Transition

NASA Astrophysics Data System (ADS)

Shadkhoo, Shahriar

This dissertation aims at improving the current understanding of the physics of mobile impurities in highly correlated liquid-like phases of matter. Impurity problems pose challenging and intricate questions in different realms of many-body physics. For instance, the problem of ''solvation'' of charged solutes in polar solvents, has been the subject of longstanding debates among chemical physicists. The significant role of quantum fluctuations of the solvent, as well as the break down of linear response theory, render the ordinary treatments intractable. Inspired by this complicated problem, we first attempt to understand the role of non-specific quantum fluctuations in the solvation process. To this end, we calculate the dynamic structure factor of a model polar liquid, using the classical Molecular Dynamics (MD) simulations. We verify the failure of linear response approximation in the vicinity of a hydrated electron, by comparing the outcomes of MD simulations with the predictions of linear response theory. This nonlinear behavior is associated with the pronounced peaks of the structure factor, which reflect the strong fluctuations of the local modes. A cavity picture is constructed based on heuristic arguments, which suggests that the electron, along with the surrounding polarization cloud, behave like a frozen sphere, for which the linear response theory is broken inside and valid outside. The inverse radius of the spherical region serves as a UV momentum cutoff for the linear response approximation to be applicable. The problem of mobile impurities in polar liquids can be also addressed in the framework of the ''polaron'' problem. Polaron is a quasiparticle that typically acquires an extended state at weak couplings, and crossovers to a self-trapped state at strong couplings. Using the analytical fits to the numerically obtained charge-charge structure factor, a phenomenological approach is proposed within the Leggett's influence functional formalism, which derives the effective Euclidean action from the classical equation of motion. We calculate the effective mass of the polaron in the model polar liquid at zero and finite temperatures. The self-trapping transition of this polaron turns out to be discontinuous in certain regions of the phase diagram. In order to systematically investigate the role of quantum fluctuations on the polaron properties, we adopt a quantum field theory which supports nearly-critical local modes: the quantum Landau-Brazovskii (QLB) model, which exhibits fluctuation-induced first order transition (weak crystallization). In the vicinity of the phase transition, the quantum fluctuations are strongly correlated; one can in principle tune the strength of these fluctuations, by adjusting the parameters close to or away from the transition point. Furthermore, sufficiently close to the transition, the theory accommodates "soliton'' solutions, signaling the nonlinear response of the system. Therefore, the model seems to be a promising candidate for studying the effects of strong quantum fluctuations and also failure of linear response theory, in the polaron problem. We observe that at zero temperature, and away from the Brazovskii transition where the linear response approximation is valid, the localization transition of the polaron is discontinuous. Upon enhancing fluctuations---of either thermal or quantum nature---the gap of the effective mass closes at distinct second-order critical points. Sufficiently close to the Brazovskii transition where the nonlinear contributions of the field are significantly large, a new state appears in addition to extended and self-trapped polarons: an impurity-induced soliton. We interpret this as the break-down of linear response, reminiscent of what we observe in a polar liquid. Quantum LB model has been proposed to be realizable in ultracold Bose gases in cavities. We thus discuss the experimental feasibility, and propose a setup which is believed to exhibit the aforementioned polaronic and solitonic states. We eventually generalize the polaron formalism to the case of impurities that couple quadratically to a nearly-critical field; hence called the ''quadratic polaron''. The Hertz-Millis field theory and its generalization to the case of magnetic transition in helimagnets, is taken as a toy model. The phase diagram of the bare model contains both second-order and fluctuation-induced first-order quantum phase transitions. We propose a semi-classical scenario in which the impurity and the field couple quadratically. The polaron properties in the vicinity of these transitions are calculated in different dimensions. We observe that the quadratic coupling in three dimensions, even in the absence of the critical modes with finite wavelength, leads to a jump-like localization of the polaron. In lower dimensions, the transition behavior remains qualitatively similar to those in the case of linear coupling, namely the critical modes must have a finite wavelength to localize the particle.

The role of the attractive and the repulsive interactions in the nonpolar solvation dynamics in simple fluids from the gas-like to the liquid-like densities

NASA Astrophysics Data System (ADS)

Yamaguchi, T.; Kimura, Y.; Hirota, N.

1999-09-01

We have performed molecular dynamics (MD) simulations of the nonpolar solvation dynamics in simple fluids composed of particles interacting through the Lennard-Jones (LJ) 12-6 potential or its repulsive part. The attractive or the repulsive part of the solute-solvent interaction is assumed to change on the excitation of a solute. We have followed the transition energy fluctuation of the solute by the equilibrium simulation. The division of the LJ potential followed the method of WCA [J. W. Weeks, D. Chandler, and H. C. Andersen, J. Chem. Phys. 54, 5237 (1971)]. We have surveyed over a wide solvent density region from gas-like to liquid-like densities at the constant temperature. When the attractive part changes, the relaxation becomes faster with an increase of the solvent density. This result contradicts with previous theories that treat the nonpolar solvation dynamics in terms of the diffusion of solvent particles. The time scale of the initial part of the relaxation is well correlated with the static fluctuation divided by the static average, which suggests the importance of the curvature of the free energy surface in the initial part of the solvation. When the repulsive part changes, the initial part of the relaxation is almost density independent, determined by the binary motion between solute and solvent. It is consistent with the result that the static fluctuation is almost proportional to the static average, which indicates the absence of the static correlation between solvent particles. On the other hand, the solvation correlation function shows rather complicated density dependence at the longer time scale. In the case of the binary mixture solvent, the relaxation time is inversely proportional to the diffusion coefficient. On the basis of the nonpolar solvation dynamics, the validity of the isolated binary collision model for the vibrational energy relaxation is also discussed, and the recent hydrodynamic theory on the vibrational energy relaxation [B. J. Cherayil and M. D. Feyer, J. Chem. Phys. 107, 7642 (1997)] is critically examined.

Bed load transport over a broad range of timescales: Determination of three regimes of fluctuations

NASA Astrophysics Data System (ADS)

Ma, Hongbo; Heyman, Joris; Fu, Xudong; Mettra, Francois; Ancey, Christophe; Parker, Gary

2014-12-01

This paper describes the relationship between the statistics of bed load transport flux and the timescale over which it is sampled. A stochastic formulation is developed for the probability distribution function of bed load transport flux, based on the Ancey et al. (2008) theory. An analytical solution for the variance of bed load transport flux over differing sampling timescales is presented. The solution demonstrates that the timescale dependence of the variance of bed load transport flux reduces to a three-regime relation demarcated by an intermittency timescale (tI) and a memory timescale (tc). As the sampling timescale increases, this variance passes through an intermittent stage (≪tI), an invariant stage (tI < t < tc), and a memoryless stage (≫ tc). We propose a dimensionless number (Ra) to represent the relative strength of fluctuation, which provides a common ground for comparison of fluctuation strength among different experiments, as well as different sampling timescales for each experiment. Our analysis indicates that correlated motion and the discrete nature of bed load particles are responsible for this three-regime behavior. We use the data from three experiments with high temporal resolution of bed load transport flux to validate the proposed three-regime behavior. The theoretical solution for the variance agrees well with all three sets of experimental data. Our findings contribute to the understanding of the observed fluctuations of bed load transport flux over monosize/multiple-size grain beds, to the characterization of an inherent connection between short-term measurements and long-term statistics, and to the design of appropriate sampling strategies for bed load transport flux.

Long-range correlations, geometrical structure, and transport properties of macromolecular solutions. The equivalence of configurational statistics and geometrodynamics of large molecules.

PubMed

Mezzasalma, Stefano A

2007-12-04

A special theory of Brownian relativity was previously proposed to describe the universal picture arising in ideal polymer solutions. In brief, it redefines a Gaussian macromolecule in a 4-dimensional diffusive spacetime, establishing a (weak) Lorentz-Poincaré invariance between liquid and polymer Einstein's laws for Brownian movement. Here, aimed at inquiring into the effect of correlations, we deepen the extension of the special theory to a general formulation. The previous statistical equivalence, for dynamic trajectories of liquid molecules and static configurations of macromolecules, and rather obvious in uncorrelated systems, is enlarged by a more general principle of equivalence, for configurational statistics and geometrodynamics. Accordingly, the three geodesic motion, continuity, and field equations could be rewritten, and a number of scaling behaviors were recovered in a spacetime endowed with general static isotropic metric (i.e., for equilibrium polymer solutions). We also dealt with universality in the volume fraction and, unexpectedly, found that a hyperscaling relation of the form, (average size) x (diffusivity) x (viscosity)1/2 ~f(N0, phi0) is fulfilled in several regimes, both in the chain monomer number (N) and polymer volume fraction (phi). Entangled macromolecular dynamics was treated as a geodesic light deflection, entaglements acting in close analogy to the field generated by a spherically symmetric mass source, where length fluctuations of the chain primitive path behave as azimuth fluctuations of its shape. Finally, the general transformation rule for translational and diffusive frames gives a coordinate gauge invariance, suggesting a widened Lorentz-Poincaré symmetry for Brownian statistics. We expect this approach to find effective applications to solutions of arbitrarily large molecules displaying a variety of structures, where the effect of geometry is more explicit and significant in itself (e.g., surfactants, lipids, proteins).

Theoretical study on the sound absorption of electrolytic solutions. II. Assignments of relaxations.

PubMed

Yamaguchi, T; Matsuoka, T; Koda, S

2007-08-14

The theory on the ultrasonic absorption spectrum of electrolytic solutions recently proposed by us is applied to the model system that resembles to the aqueous solution of MgSO4. The charges on ions are reduced to +/-1.5e in order to obtain the equilibrium structure by the integral equation theory. The theory reproduces the existence of two relaxations around 100 kHz and 1 GHz. The physical origin of the relaxation is analyzed based on the theoretical expression. The slower relaxation is shown to originate in the formation of contact ion pair, in harmony with the conventional assignment. The amplitude of this relaxation agrees with the experimental one fairly well. The absorption cross section is a weakly increasing function of the concentration of the salt in theory, whereas it depends little on the concentration in experiment, which is ascribed to the weaker association of the pair in the theory. The deviation from the Debye relaxation is found for the faster process, and the concentration dependence is small. The analysis shows that this relaxation stems from the coupling between the pressure and the long-range concentration fluctuation, and the concentration independence and the non-Debye relaxation are explained based on the theoretical analysis. In particular, the theory demonstrates that this process has the t(-3/2) tail in the time domain, which is confirmed by numerical calculation. The deviation of the theoretical relaxation amplitude from the experimental one is elucidated in terms of the theoretical expression of the coefficient.

Theoretical modeling of the effect of Casimir attraction on the electrostatic instability of nanowire-fabricated actuators

NASA Astrophysics Data System (ADS)

Mokhtari, J.; Farrokhabadi, A.; Rach, R.; Abadyan, M.

2015-04-01

The presence of the quantum vacuum fluctuations, i.e. the Casimir attraction, can strongly affect the performance of ultra-small actuators. The strength of the Casimir force is significantly influenced by the geometries of interacting bodies. Previous research has exclusively studied the impact of the vacuum fluctuations on the instability of nanoactuators with planar geometries. However, no work has yet considered this phenomenon in actuators fabricated from nanowires/nanotubes with cylindrical geometries. In our present work, the influence of the Casimir attraction on the electrostatic stability of nanoactuators fabricated from cylindrical conductive nanowire/nanotube is investigated. The Dirichlet mode is considered and an asymptotic solution, based on scattering theory, is applied to consider the effect of vacuum fluctuations in the theoretical model. The size-dependent modified couple stress theory is employed to derive the constitutive equation of the actuator. The governing nonlinear equations are solved by two different approaches, i.e. the finite difference method and modified Adomian-Padé method. Various aspects of the problem, i.e. comparison with the van der Waals force regime, the variation of instability parameters, effect of geometry and coupling between the Casimir force and size dependency are discussed. This work is beneficial to determine the impact of Casimir force on nanowire/nanotube-fabricated actuators.

Coherent states field theory in supramolecular polymer physics

NASA Astrophysics Data System (ADS)

Fredrickson, Glenn H.; Delaney, Kris T.

2018-05-01

In 1970, Edwards and Freed presented an elegant representation of interacting branched polymers that resembles the coherent states (CS) formulation of second-quantized field theory. This CS polymer field theory has been largely overlooked during the intervening period in favor of more conventional "auxiliary field" (AF) interacting polymer representations that form the basis of modern self-consistent field theory (SCFT) and field-theoretic simulation approaches. Here we argue that the CS representation provides a simpler and computationally more efficient framework than the AF approach for broad classes of reversibly bonding polymers encountered in supramolecular polymer science. The CS formalism is reviewed, initially for a simple homopolymer solution, and then extended to supramolecular polymers capable of forming reversible linkages and networks. In the context of the Edwards model of a non-reacting homopolymer solution and one and two-component models of telechelic reacting polymers, we discuss the structure of CS mean-field theory, including the equivalence to SCFT, and show how weak-amplitude expansions (random phase approximations) can be readily developed without explicit enumeration of all reaction products in a mixture. We further illustrate how to analyze CS field theories beyond SCFT at the level of Gaussian field fluctuations and provide a perspective on direct numerical simulations using a recently developed complex Langevin technique.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dechant, Lawrence J.

Wave packet analysis provides a connection between linear small disturbance theory and subsequent nonlinear turbulent spot flow behavior. The traditional association between linear stability analysis and nonlinear wave form is developed via the method of stationary phase whereby asymptotic (simplified) mean flow solutions are used to estimate dispersion behavior and stationary phase approximation are used to invert the associated Fourier transform. The resulting process typically requires nonlinear algebraic equations inversions that can be best performed numerically, which partially mitigates the value of the approximation as compared to a more complete, e.g. DNS or linear/nonlinear adjoint methods. To obtain a simpler,more » closed-form analytical result, the complete packet solution is modeled via approximate amplitude (linear convected kinematic wave initial value problem) and local sinusoidal (wave equation) expressions. Significantly, the initial value for the kinematic wave transport expression follows from a separable variable coefficient approximation to the linearized pressure fluctuation Poisson expression. The resulting amplitude solution, while approximate in nature, nonetheless, appears to mimic many of the global features, e.g. transitional flow intermittency and pressure fluctuation magnitude behavior. A low wave number wave packet models also recover meaningful auto-correlation and low frequency spectral behaviors.« less

Transition between Two Regimes Describing Internal Fluctuation of DNA in a Nanochannel

PubMed Central

Su, Tianxiang; Das, Somes K.; Xiao, Ming; Purohit, Prashant K.

2011-01-01

We measure the thermal fluctuation of the internal segments of a piece of DNA confined in a nanochannel about 50100 nm wide. This local thermodynamic property is key to accurate measurement of distances in genomic analysis. For DNA in 100 nm channels, we observe a critical length scale 10 m for the mean extension of internal segments, below which the de Gennes' theory describes the fluctuations with no fitting parameters, and above which the fluctuation data falls into Odijk's deflection theory regime. By analyzing the probability distributions of the extensions of the internal segments, we infer that folded structures of length 150250 nm, separated by 10 m exist in the confined DNA during the transition between the two regimes. For 50 nm channels we find that the fluctuation is significantly reduced since the Odijk regime appears earlier. This is critical for genomic analysis. We further propose a more detailed theory based on small fluctuations and incorporating the effects of confinement to explicitly calculate the statistical properties of the internal fluctuations. Our theory is applicable to polymers with heterogeneous mechanical properties confined in non-uniform channels. We show that existing theories for the end-to-end extension/fluctuation of polymers can be used to study the internal fluctuations only when the contour length of the polymer is many times larger than its persistence length. Finally, our results suggest that introducing nicks in the DNA will not change its fluctuation behavior when the nick density is below 1 nick per kbp DNA. PMID:21423606

Cosmology for quadratic gravity in generalized Weyl geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiménez, Jose Beltrán; Heisenberg, Lavinia; Koivisto, Tomi S.

A class of vector-tensor theories arises naturally in the framework of quadratic gravity in spacetimes with linear vector distortion. Requiring the absence of ghosts for the vector field imposes an interesting condition on the allowed connections with vector distortion: the resulting one-parameter family of connections generalises the usual Weyl geometry with polar torsion. The cosmology of this class of theories is studied, focusing on isotropic solutions wherein the vector field is dominated by the temporal component. De Sitter attractors are found and inhomogeneous perturbations around such backgrounds are analysed. In particular, further constraints on the models are imposed by excludingmore » pathologies in the scalar, vector and tensor fluctuations. Various exact background solutions are presented, describing a constant and an evolving dark energy, a bounce and a self-tuning de Sitter phase. However, the latter two scenarios are not viable under a closer scrutiny.« less

Simple and exact approach to the electronic polarization effect on the solvation free energy: formulation for quantum-mechanical/molecular-mechanical system and its applications to aqueous solutions.

PubMed

Takahashi, Hideaki; Omi, Atsushi; Morita, Akihiro; Matubayasi, Nobuyuki

2012-06-07

We present a simple and exact numerical approach to compute the free energy contribution δμ in solvation due to the electron density polarization and fluctuation of a quantum-mechanical solute in the quantum-mechanical/molecular-mechanical (QM/MM) simulation combined with the theory of the energy representation (QM/MM-ER). Since the electron density fluctuation is responsible for the many-body QM-MM interactions, the standard version of the energy representation method cannot be applied directly. Instead of decomposing the QM-MM polarization energy into the pairwise additive and non-additive contributions, we take sum of the polarization energies in the QM-MM interaction and adopt it as a new energy coordinate for the method of energy representation. Then, it is demonstrated that the free energy δμ can be exactly formulated in terms of the energy distribution functions for the solution and reference systems with respect to this energy coordinate. The benchmark tests were performed to examine the numerical efficiency of the method with respect to the changes in the individual properties of the solvent and the solute. Explicitly, we computed the solvation free energy of a QM water molecule in ambient and supercritical water, and also the free-energy change associated with the isomerization reaction of glycine from neutral to zwitterionic structure in aqueous solution. In all the systems examined, it was demonstrated that the computed free energy δμ agrees with the experimental value, irrespective of the choice of the reference electron density of the QM solute. The present method was also applied to a prototype reaction of adenosine 5'-triphosphate hydrolysis where the effect of the electron density fluctuation is substantial due to the excess charge. It was demonstrated that the experimental free energy of the reaction has been accurately reproduced with the present approach.

On the interaction between turbulence and a planar rarefaction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnson, Bryan M.

2014-04-01

The modeling of turbulence, whether it be numerical or analytical, is a difficult challenge. Turbulence is amenable to analysis with linear theory if it is subject to rapid distortions, i.e., motions occurring on a timescale that is short compared to the timescale for nonlinear interactions. Such an approach (referred to as rapid distortion theory) could prove useful for understanding aspects of astrophysical turbulence, which is often subject to rapid distortions, such as supernova explosions or the free-fall associated with gravitational instability. As a proof of principle, a particularly simple problem is considered here: the evolution of vorticity due to amore » planar rarefaction in an ideal gas. Analytical solutions are obtained for incompressive modes having a wave vector perpendicular to the distortion; as in the case of gradient-driven instabilities, these are the modes that couple most strongly to the mean flow. Vorticity can either grow or decay in the wake of a rarefaction front, and there are two competing effects that determine which outcome occurs: entropy fluctuations couple to the mean pressure gradient to produce vorticity via baroclinic effects, whereas vorticity is damped due to the conservation of angular momentum as the fluid expands. Whether vorticity grows or decays depends upon the ratio of entropic to vortical fluctuations at the location of the front; growth occurs if this ratio is of order unity or larger. In the limit of purely entropic fluctuations in the ambient fluid, a strong rarefaction generates vorticity with a turbulent Mach number on the order of the rms of the ambient entropy fluctuations. The analytical results are shown to compare well with results from two- and three-dimensional numerical simulations. Analytical solutions are also derived in the linear regime of Reynolds-averaged turbulence models. This highlights an inconsistency in standard turbulence models that prevents them from accurately capturing the physics of rarefaction-turbulence interaction. In addition to providing physical insight, the solutions derived here can be used to verify algorithms of both the Reynolds-averaged and direct numerical simulation variety. Finally, dimensional analysis of the equations indicates that rapid distortion of turbulence can give rise to two distinct regimes in the turbulent spectrum: a distortion range at large scales where linear distortion effects dominate, and an inertial range at small scales where nonlinear effects dominate.« less

Calculation of open and closed system elastic coefficients for multicomponent solids

NASA Astrophysics Data System (ADS)

Mishin, Y.

2015-06-01

Thermodynamic equilibrium in multicomponent solids subject to mechanical stresses is a complex nonlinear problem whose exact solution requires extensive computations. A few decades ago, Larché and Cahn proposed a linearized solution of the mechanochemical equilibrium problem by introducing the concept of open system elastic coefficients [Acta Metall. 21, 1051 (1973), 10.1016/0001-6160(73)90021-7]. Using the Ni-Al solid solution as a model system, we demonstrate that open system elastic coefficients can be readily computed by semigrand canonical Monte Carlo simulations in conjunction with the shape fluctuation approach. Such coefficients can be derived from a single simulation run, together with other thermodynamic properties needed for prediction of compositional fields in solid solutions containing defects. The proposed calculation approach enables streamlined solutions of mechanochemical equilibrium problems in complex alloys. Second order corrections to the linear theory are extended to multicomponent systems.

Electromagnetic fluctuations in magnetized plasmas. I. The rigorous relativistic kinetic theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schlickeiser, R., E-mail: rsch@tp4.rub.de, E-mail: yoonp@umd.edu; Yoon, P. H., E-mail: rsch@tp4.rub.de, E-mail: yoonp@umd.edu; School of Space Research, Kyung Hee University, Yongin-Si, Gyeonggi-Do 446-701

2015-07-15

Using the system of the Klimontovich and Maxwell equations, the general linear fluctuation theory for magnetized plasmas is developed. General expressions for the electromagnetic fluctuation spectra (electric and magnetic fields) from uncorrelated plasma particles in plasmas with a uniform magnetic field are derived, which are covariantly correct within the theory of special relativity. The general fluctuation spectra hold for plasmas of arbitrary composition, arbitrary momentum dependences of the plasma particle distribution functions, and arbitrary orientations of the wave vector with respect to the uniform magnetic field. Moreover, no restrictions on the values of the real and the imaginary parts ofmore » the frequency are made. The derived fluctuation spectra apply to both non-collective fluctuations and collective plasma eigenmodes in magnetized plasmas. In the latter case, kinetic equations for the components of fluctuating electric and magnetic fields in magnetized plasmas are derived that include the effect of spontaneous emission and absorption. In the limiting case of an unmagnetized plasmas, the general fluctuation spectra correctly reduce to the unmagnetized fluctuation spectra derived before.« less

Impact of economic fluctuations on suicide mortality in Canada (1926-2008): Testing the Durkheim, Ginsberg, and Henry and Short theories.

PubMed

Thibodeau, Lise; Lachaud, James

2016-01-01

Three theories have been proposed to explain the relationship between suicide and economic fluctuations, including the Durkheim (nonlinear), Ginsberg (procyclical), and Henry and Short (countercyclical) theories. This study tested the effect of economic fluctuations, measured by unemployment rate, on suicide rates in Canada from 1926 to 2008. Autoregressive integrated moving average time-series models were used. The results showed a significant relationship between suicide and economic fluctuation; this association was positive during the contraction period (1926-1950) and negative in the period of economic expansion (1951-1973). Males and females showed differential effects in the period of moderate unemployment (1974-2008). In addition, the suicide rate of mid-adults (45-64) was most impacted by economic fluctuations. Our study tends to support Durkheim's theory and suggests the need for public health responses in times of economic contraction and expansion.

Computing molecular fluctuations in biochemical reaction systems based on a mechanistic, statistical theory of irreversible processes.

PubMed

Kulasiri, Don

2011-01-01

We discuss the quantification of molecular fluctuations in the biochemical reaction systems within the context of intracellular processes associated with gene expression. We take the molecular reactions pertaining to circadian rhythms to develop models of molecular fluctuations in this chapter. There are a significant number of studies on stochastic fluctuations in intracellular genetic regulatory networks based on single cell-level experiments. In order to understand the fluctuations associated with the gene expression in circadian rhythm networks, it is important to model the interactions of transcriptional factors with the E-boxes in the promoter regions of some of the genes. The pertinent aspects of a near-equilibrium theory that would integrate the thermodynamical and particle dynamic characteristics of intracellular molecular fluctuations would be discussed, and the theory is extended by using the theory of stochastic differential equations. We then model the fluctuations associated with the promoter regions using general mathematical settings. We implemented ubiquitous Gillespie's algorithms, which are used to simulate stochasticity in biochemical networks, for each of the motifs. Both the theory and the Gillespie's algorithms gave the same results in terms of the time evolution of means and variances of molecular numbers. As biochemical reactions occur far away from equilibrium-hence the use of the Gillespie algorithm-these results suggest that the near-equilibrium theory should be a good approximation for some of the biochemical reactions. © 2011 Elsevier Inc. All rights reserved.

Statistical Mechanics and Applications in Condensed Matter

NASA Astrophysics Data System (ADS)

Di Castro, Carlo; Raimondi, Roberto

2015-08-01

Preface; 1. Thermodynamics: a brief overview; 2. Kinetics; 3. From Boltzmann to Gibbs; 4. More ensembles; 5. The thermodynamic limit and its thermodynamic stability; 6. Density matrix and quantum statistical mechanics; 7. The quantum gases; 8. Mean-field theories and critical phenomena; 9. Second quantization and Hartree-Fock approximation; 10. Linear response and fluctuation-dissipation theorem in quantum systems: equilibrium and small deviations; 11. Brownian motion and transport in disordered systems; 12. Fermi liquids; 13. The Landau theory of the second order phase transitions; 14. The Landau-Wilson model for critical phenomena; 15. Superfluidity and superconductivity; 16. The scaling theory; 17. The renormalization group approach; 18. Thermal Green functions; 19. The microscopic foundations of Fermi liquids; 20. The Luttinger liquid; 21. Quantum interference effects in disordered electron systems; Appendix A. The central limit theorem; Appendix B. Some useful properties of the Euler Gamma function; Appendix C. Proof of the second theorem of Yang and Lee; Appendix D. The most probable distribution for the quantum gases; Appendix E. Fermi-Dirac and Bose-Einstein integrals; Appendix F. The Fermi gas in a uniform magnetic field: Landau diamagnetism; Appendix G. Ising and gas-lattice models; Appendix H. Sum over discrete Matsubara frequencies; Appendix I. Hydrodynamics of the two-fluid model of superfluidity; Appendix J. The Cooper problem in the theory of superconductivity; Appendix K. Superconductive fluctuations phenomena; Appendix L. Diagrammatic aspects of the exact solution of the Tomonaga Luttinger model; Appendix M. Details on the theory of the disordered Fermi liquid; References; Author index; Index.

When is quasi-linear theory exact. [particle acceleration

NASA Technical Reports Server (NTRS)

Jones, F. C.; Birmingham, T. J.

1975-01-01

We use the cumulant expansion technique of Kubo (1962, 1963) to derive an integrodifferential equation for the average one-particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the equation for this function degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory only for this limited class of fluctuations.

Divergence of perturbation theory in large scale structures

NASA Astrophysics Data System (ADS)

Pajer, Enrico; van der Woude, Drian

2018-05-01

We make progress towards an analytical understanding of the regime of validity of perturbation theory for large scale structures and the nature of some non-perturbative corrections. We restrict ourselves to 1D gravitational collapse, for which exact solutions before shell crossing are known. We review the convergence of perturbation theory for the power spectrum, recently proven by McQuinn and White [1], and extend it to non-Gaussian initial conditions and the bispectrum. In contrast, we prove that perturbation theory diverges for the real space two-point correlation function and for the probability density function (PDF) of the density averaged in cells and all the cumulants derived from it. We attribute these divergences to the statistical averaging intrinsic to cosmological observables, which, even on very large and "perturbative" scales, gives non-vanishing weight to all extreme fluctuations. Finally, we discuss some general properties of non-perturbative effects in real space and Fourier space.

Interactions between similar and dissimilar charged interfaces in the presence of multivalent anions.

PubMed

Moazzami-Gudarzi, Mohsen; Adam, Pavel; Smith, Alexander M; Trefalt, Gregor; Szilágyi, István; Maroni, Plinio; Borkovec, Michal

2018-04-04

Direct force measurements involving amidine latex (AL) and sulfate latex (SL) particles in aqueous solutions containing multivalent ferrocyanide anions are presented. These measurements feature three different pairs of particles, namely SL-SL, AL-SL, and AL-AL. The force profiles are quantitatively interpreted in terms of the theory by Derjaguin, Landau, Verwey, and Overbeek (DLVO) that is combined with a short-ranged exponential attraction. In monovalent salt solutions, the AL particles are positively charged, while the SL particles are negatively charged. In solutions containing ferrocyanide, the charge of the AL particles is reversed as the concentration is increased. The longer-ranged component of all force profiles is fully compatible with DLVO theory, provided effects of charge regulation are included. At shorter distances, an additional exponential attraction must be introduced, whereby the respective decay length is about 2 nm for the AL-AL pair, and below 1 nm for the SL-SL pair. This non-DLVO force is intermediate for the asymmetric AL-SL pair. These additional forces are probably related to charge fluctuations, patch-charged interactions, or hydrophobic forces.

Power Spectrum of Long Eigenlevel Sequences in Quantum Chaotic Systems.

PubMed

Riser, Roman; Osipov, Vladimir Al; Kanzieper, Eugene

2017-05-19

We present a nonperturbative analysis of the power spectrum of energy level fluctuations in fully chaotic quantum structures. Focusing on systems with broken time-reversal symmetry, we employ a finite-N random matrix theory to derive an exact multidimensional integral representation of the power spectrum. The N→∞ limit of the exact solution furnishes the main result of this study-a universal, parameter-free prediction for the power spectrum expressed in terms of a fifth Painlevé transcendent. Extensive numerics lends further support to our theory which, as discussed at length, invalidates a traditional assumption that the power spectrum is merely determined by the spectral form factor of a quantum system.

Excursion set mass functions for hierarchical Gaussian fluctuations

NASA Technical Reports Server (NTRS)

Bond, J. R.; Kaiser, N.; Cole, S.; Efstathiou, G.

1991-01-01

It is pointed out that most schemes for determining the mass function of virialized objects from the statistics of the initial density perturbation field suffer from the cloud-in-cloud problem of miscounting the number of low-mass clumps, many of which would have been subsumed into larger objects. The paper proposes a solution based on the theory of the excursion sets of F(r, R sub f), the four-dimensional initial density perturbation field smoothed with a continuous hierarchy of filters of radii R sub f.

A closed form slug test theory for high permeability aquifers.

PubMed

Ostendorf, David W; DeGroot, Don J; Dunaj, Philip J; Jakubowski, Joseph

2005-01-01

We incorporate a linear estimate of casing friction into the analytical slug test theory of Springer and Gelhar (1991) for high permeability aquifers. The modified theory elucidates the influence of inertia and casing friction on consistent, closed form equations for the free surface, pressure, and velocity fluctuations for overdamped and underdamped conditions. A consistent, but small, correction for kinetic energy is included as well. A characteristic velocity linearizes the turbulent casing shear stress so that an analytical solution for attenuated, phase shifted pressure fluctuations fits a single parameter (damping frequency) to transducer data from any depth in the casing. Underdamped slug tests of 0.3, 0.6, and 1 m amplitudes at five transducer depths in a 5.1 cm diameter PVC well 21 m deep in the Plymouth-Carver Aquifer yield a consistent hydraulic conductivity of 1.5 x 10(-3) m/s. The Springer and Gelhar (1991) model underestimates the hydraulic conductivity for these tests by as much as 25% by improperly ascribing smooth turbulent casing friction to the aquifer. The match point normalization of Butler (1998) agrees with our fitted hydraulic conductivity, however, when friction is included in the damping frequency. Zurbuchen et al. (2002) use a numerical model to establish a similar sensitivity of hydraulic conductivity to nonlinear casing friction.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Düchs, Dominik; Delaney, Kris T., E-mail: kdelaney@mrl.ucsb.edu; Fredrickson, Glenn H., E-mail: ghf@mrl.ucsb.edu

Field-theoretic models have been used extensively to study the phase behavior of inhomogeneous polymer melts and solutions, both in self-consistent mean-field calculations and in numerical simulations of the full theory capturing composition fluctuations. The models commonly used can be grouped into two categories, namely, species models and exchange models. Species models involve integrations of functionals that explicitly depend on fields originating both from species density operators and their conjugate chemical potential fields. In contrast, exchange models retain only linear combinations of the chemical potential fields. In the two-component case, development of exchange models has been instrumental in enabling stable complexmore » Langevin (CL) simulations of the full complex-valued theory. No comparable stable CL approach has yet been established for field theories of the species type. Here, we introduce an extension of the exchange model to an arbitrary number of components, namely, the multi-species exchange (MSE) model, which greatly expands the classes of soft material systems that can be accessed by the complex Langevin simulation technique. We demonstrate the stability and accuracy of the MSE-CL sampling approach using numerical simulations of triblock and tetrablock terpolymer melts, and tetrablock quaterpolymer melts. This method should enable studies of a wide range of fluctuation phenomena in multiblock/multi-species polymer blends and composites.« less

A General Solution for Groundwater Flow in Estuarine Leaky Aquifer System with Considering Aquifer Anisotropy

NASA Astrophysics Data System (ADS)

Chen, Po-Chia; Chuang, Mo-Hsiung; Tan, Yih-Chi

2014-05-01

In recent years the urban and industrial developments near the coastal area are rapid and therefore the associated population grows dramatically. More and more water demand for human activities, agriculture irrigation, and aquaculture relies on heavy pumping in coastal area. The decline of groundwater table may result in the problems of seawater intrusion and/or land subsidence. Since the 1950s, numerous studies focused on the effect of tidal fluctuation on the groundwater flow in the coastal area. Many studies concentrated on the developments of one-dimensional (1D) and two-dimensional (2D) analytical solutions describing the tide-induced head fluctuations. For example, Jacob (1950) derived an analytical solution of 1D groundwater flow in a confined aquifer with a boundary condition subject to sinusoidal oscillation. Jiao and Tang (1999) derived a 1D analytical solution of a leaky confined aquifer by considered a constant groundwater head in the overlying unconfined aquifer. Jeng et al. (2002) studied the tidal propagation in a coupled unconfined and confined costal aquifer system. Sun (1997) presented a 2D solution for groundwater response to tidal loading in an estuary. Tang and Jiao (2001) derived a 2D analytical solution in a leaky confined aquifer system near open tidal water. This study aims at developing a general analytical solution describing the head fluctuations in a 2D estuarine aquifer system consisted of an unconfined aquifer, a confined aquifer, and an aquitard between them. Both the confined and unconfined aquifers are considered to be anisotropic. The predicted head fluctuations from this solution will compare with the simulation results from the MODFLOW program. In addition, the solutions mentioned above will be shown to be special cases of the present solution. Some hypothetical cases regarding the head fluctuation in costal aquifers will be made to investigate the dynamic effects of water table fluctuation, hydrogeological conditions, and characteristics of soil on the groundwater level fluctuations in the 2D estuarine leaky aquifer system.

On the Origin of Time and the Universe

NASA Astrophysics Data System (ADS)

Jejjala, Vishnu; Kavic, Michael; Minic, Djordje; Tze, Chia-Hsiung

We present a novel solution to the low entropy and arrow of time puzzles of the initial state of the universe. Our approach derives from the physics of a specific generalization of Matrix theory put forth in earlier work as the basis for a quantum theory of gravity. The particular dynamical state space of this theory, the infinite-dimensional analogue of the Fubini-Study metric over a complex nonlinear Grassmannian, has recently been studied by Michor and Mumford. The geodesic distance between any two points on this space is zero. Here we show that this mathematical result translates to a description of a hot, zero entropy state and an arrow of time after the Big Bang. This is modeled as a far from equilibrium, large fluctuation driven, "freezing by heating" metastable ordered phase transition of a nonlinear dissipative dynamical system.

Non-perturbative background field calculations

NASA Astrophysics Data System (ADS)

Stephens, C. R.

1988-01-01

New methods are developed for calculating one loop functional determinants in quantum field theory. Instead of relying on a calculation of all the eigenvalues of the small fluctuation equation, these techniques exploit the ability of the proper time formalism to reformulate an infinite dimensional field theoretic problem into a finite dimensional covariant quantum mechanical analog, thereby allowing powerful tools such as the method of Jacobi fields to be used advantageously in a field theory setting. More generally the methods developed herein should be extremely valuable when calculating quantum processes in non-constant background fields, offering a utilitarian alternative to the two standard methods of calculation—perturbation theory in the background field or taking the background field into account exactly. The formalism developed also allows for the approximate calculation of covariances of partial differential equations from a knowledge of the solutions of a homogeneous ordinary differential equation.

Effect of pressure fluctuations on Richtmyer-Meshkov coherent structures

NASA Astrophysics Data System (ADS)

Bhowmick, Aklant K.; Abarzhi, Snezhana

2016-11-01

We investigate the formation and evolution of Richtmyer Meshkov bubbles after the passage of a shock wave across a two fluid interface in the presence of pressure fluctuations. The fluids are ideal and incompressible and the pressure fluctuations are scale invariant in space and time, and are modeled by a power law time dependent acceleration field with exponent -2. Solutions indicate sensitivity to pressure fluctuations. In the linear regime, the growth of curvature and bubble velocity is linear. The growth rate is dominated by the initial velocity for weak pressure fluctuations, and by the acceleration term for strong pressure fluctuations. In the non-linear regime, the bubble curvature is constant and the solutions form a one parameter family (parametrized by the bubble curvature). The solutions are shown to be convergent and asymptotically stable. The physical solution (stable fastest growing) is a flat bubble for small pressure fluctuations and a curved bubble for large pressure fluctuations. The velocity field (in the frame of references accounting for the background motion) involves intense motion of the fluids in a vicinity of the interface, effectively no motion of the fluids away from the interfaces, and formation of vortical structures at the interface. The work is supported by the US National Science Foundation.

Effect of pressure fluctuations on Richtmyer-Meshkov coherent structures

NASA Astrophysics Data System (ADS)

Bhowmick, Aklant K.; Abarzhi, Snezhana

2016-10-01

We investigate the formation and evolution of Richtmyer Meshkov bubbles after the passage of a shock wave across a two fluid interface in the presence of pressure fluctuations. The fluids are ideal and incompressible and the pressure fluctuations are scale invariant in space and time, and are modeled by a power law time dependent acceleration field with exponent -2. Solutions indicate sensitivity to pressure fluctuations. In the linear regime, the growth of curvature and bubble velocity is linear. The growth rate is dominated by the initial velocity for weak pressure fluctuations, and by the acceleration term for strong pressure fluctuations. In the non-linear regime, the bubble curvature is constant and the solutions form a one parameter family (parametrized by the bubble curvature). The solutions are shown to be convergent and asymptotically stable. The physical solution (stable fastest growing) is a flat bubble for small pressure fluctuations and a curved bubble for large pressure fluctuations. The velocity field (in the frame of references accounting for the background motion) involves intense motion of the fluids in a vicinity of the interface, effectively no motion of the fluids away from the interfaces, and formation of vortical structures at the interface. The work is supported by the US National Science Foundation.

Quasi-linear theory of electron density and temperature fluctuations with application to MHD generators and MPD arc thrusters

NASA Technical Reports Server (NTRS)

Smith, M.

1972-01-01

Fluctuations in electron density and temperature coupled through Ohm's law are studied for an ionizable medium. The nonlinear effects are considered in the limit of a third order quasi-linear treatment. Equations are derived for the amplitude of the fluctuation. Conditions under which a steady state can exist in the presence of the fluctuation are examined and effective transport properties are determined. A comparison is made to previously considered second order theory. The effect of third order terms indicates the possibility of fluctuations existing in regions predicted stable by previous analysis.

Finite-g Strings

NASA Astrophysics Data System (ADS)

Vicedo, Benoit

2008-10-01

In view of one day proving the AdS/CFT correspondence, a deeper understanding of string theory on certain curved backgrounds such as AdS_5xS^5 is required. In this dissertation we make a step in this direction by focusing on RxS^3. It was discovered in recent years that string theory on AdS_5xS^5 admits a Lax formulation. However, the complete statement of integrability requires not only the existence of a Lax formulation, but also that the resulting integrals of motion are in pairwise involution. This idea is central to the first part of this thesis. Exploiting this integrability we apply algebro-geometric methods to string theory on RxS^3 and obtain the general finite-gap solution. The construction is based on an invariant algebraic curve previously found in the AdS_5xS^5 case. However, encoding the dynamics of the solution requires specification of additional marked points. By restricting the symplectic structure of the string to this algebro-geometric data we derive the action-angle variables of the system. We then perform a first-principle semiclassical quantisation of string theory on RxS^3 as a toy model for strings on AdS_5xS^5. The result is exactly what one expects from the dual gauge theory perspective, namely the underlying algebraic curve discretises in a natural way. We also derive a general formula for the fluctuation energies around the generic finite-gap solution. The ideas used can be generalised to AdS_5xS^5.

Real Spin Glasses Relax Slowly in the Shade of Hierarchical Trees

NASA Astrophysics Data System (ADS)

Vincent, E.; Hammann, J.; Ocio, M.

2009-06-01

The Parisi solution of the mean-field spin glass has been widely accepted and celebrated. Its marginal stability in 3d and its complexity however raised the question of its relevance to real spin glasses. This paper gives a short overview of the important experimental results which could be understood within the mean-field solution. The existence of a true phase transition and the particular behaviour of the susceptibility below the freezing temperature, predicted by the theory, are clearly confirmed by the experimental results. The behaviour of the complex order parameter and of the Fluctuation Dissipation ratio are in good agreement with results of spontaneous noise measurements. The very particular ultrametric symmetry, the key feature of the theory, provided us with a simple description of the rejuvenation and memory effects observed in experiment. Finally, going a step beyond mean-field, the paper shortly discusses new analyses in terms of correlated domains characterized by their length scales, as well as new experiments on superspin glasses which compare well with recent theoretical simulations.

Quantum propagation in single mode fiber

NASA Technical Reports Server (NTRS)

Joneckis, Lance G.; Shapiro, Jeffrey H.

1994-01-01

This paper presents a theory for quantum light propagation in a single-mode fiber which includes the effects of the Kerr nonlinearity, group-velocity dispersion, and linear loss. The theory reproduces the results of classical self-phase modulation, quantum four-wave mixing, and classical solution physics, within their respective regions of validity. It demonstrates the crucial role played by the Kerr-effect material time constant, in limiting the quantum phase shifts caused by the broadband zero-point fluctuations that accompany any quantized input field. Operator moment equations - approximated, numerically, via a terminated cumulant expansion - are used to obtain results for homodyne-measurement noise spectra when dispersion is negligible. More complicated forms of these equations can be used to incorporate dispersion into the noise calculations.

Linear spin-2 fields in most general backgrounds

NASA Astrophysics Data System (ADS)

Bernard, Laura; Deffayet, Cédric; Schmidt-May, Angnis; von Strauss, Mikael

2016-04-01

We derive the full perturbative equations of motion for the most general background solutions in ghost-free bimetric theory in its metric formulation. Clever field redefinitions at the level of fluctuations enable us to circumvent the problem of varying a square-root matrix appearing in the theory. This greatly simplifies the expressions for the linear variation of the bimetric interaction terms. We show that these field redefinitions exist and are uniquely invertible if and only if the variation of the square-root matrix itself has a unique solution, which is a requirement for the linearized theory to be well defined. As an application of our results we examine the constraint structure of ghost-free bimetric theory at the level of linear equations of motion for the first time. We identify a scalar combination of equations which is responsible for the absence of the Boulware-Deser ghost mode in the theory. The bimetric scalar constraint is in general not manifestly covariant in its nature. However, in the massive gravity limit the constraint assumes a covariant form when one of the interaction parameters is set to zero. For that case our analysis provides an alternative and almost trivial proof of the absence of the Boulware-Deser ghost. Our findings generalize previous results in the metric formulation of massive gravity and also agree with studies of its vielbein version.

Supersaturated Electrolyte Solutions: Theory and Experiment

NASA Technical Reports Server (NTRS)

Izmailov, Alexander F.; Myerson, Allan S.; Na, Han-Soo

1995-01-01

Highly supersaturated electrolyte solutions can be prepared and studied employing an electrodynamic levitator trap (ELT) technique. The ELT technique involves containerless suspension of a microdroplet thus eliminating dust, dirt, and container walls which normally cause heterogeneous nucleation. This allows very high supersaturations to be achieved. A theoretical study of the experimental results obtained for the water activity in microdroplets of various electrolyte solutions is based on the development of the Cahn-Hilliard formalism for electrolyte solutions. In the approach suggested the metastable state for electrolyte solutions is described in terms of the conserved order parameter omega(r,t) associated with fluctuations of the mean solute concentration n(sub 0). Parameters of the corresponding Ginzburg-Landau free energy functional which defines the dynamics of metastable state relaxation are determined and expressed through the experimentally measured quantities. A correspondence of 96-99 % between theory and experiment for all solutions studied was achieved and allowed the determination of an analytical expression for the spinodal concentration n(sub spin), and its calculation for various electrolyte solutions at 298 K. The assumption that subcritical solute clusters consist of the electrically neutral Bjerrum pairs has allowed both analytical and numerical investigation of the number-size N(sub c) of nucleation monomers (aggregates of the Bjerrum pairs) which are elementary units of the solute critical clusters. This has also allowed estimations for the surface tension Alpha, and equilibrium bulk energy Beta per solute molecule in the nucleation monomers. The dependence of these properties on the temperature T and on the solute concentration n(sub 0) through the entire metastable zone (from saturation concentration n(sub sat) to spinodal n(sub spin) is examined. It has been demonstrated that there are the following asymptotics: N(sub c), = I at spinodal concentration and N(sub c) = infinity at saturation.

Theory of slightly fluctuating ratchets

NASA Astrophysics Data System (ADS)

Rozenbaum, V. M.; Shapochkina, I. V.; Lin, S. H.; Trakhtenberg, L. I.

2017-04-01

We consider a Brownian particle moving in a slightly fluctuating potential. Using the perturbation theory on small potential fluctuations, we derive a general analytical expression for the average particle velocity valid for both flashing and rocking ratchets with arbitrary, stochastic or deterministic, time dependence of potential energy fluctuations. The result is determined by the Green's function for diffusion in the time-independent part of the potential and by the features of correlations in the fluctuating part of the potential. The generality of the result allows describing complex ratchet systems with competing characteristic times; these systems are exemplified by the model of a Brownian photomotor with relaxation processes of finite duration.

Superconductivity from a non-Fermi-liquid metal: Kondo fluctuation mechanism in slave-fermion theory

NASA Astrophysics Data System (ADS)

Kim, Ki-Seok

2010-03-01

We propose Kondo fluctuation mechanism of superconductivity, differentiated from the spin-fluctuation theory as the standard model for unconventional superconductivity in the weak-coupling approach. Based on the U(1) slave-fermion representation of an effective Anderson lattice model, where localized spins are described by the Schwinger boson theory and hybridization or Kondo fluctuations weaken antiferromagnetic correlations of localized spins, we found an antiferromagnetic quantum critical point from an antiferromagnetic metal to a heavy-fermion metal in our recent study. The Kondo-induced antiferromagnetic quantum critical point was shown to be described by both conduction electrons and fermionic holons interacting with critical spin fluctuations given by deconfined bosonic spinons with a spin quantum number 1/2. Surprisingly, such critical modes turned out to be described by the dynamical exponent z=3 , giving rise to the well-known non-Fermi-liquid physics such as the divergent Grüneisen ratio with an exponent 2/3 and temperature-linear resistivity in three dimensions. We find that the z=3 antiferromagnetic quantum critical point becomes unstable against superconductivity, where critical spinon excitations give rise to pairing correlations between conduction electrons and between fermionic holons, respectively, via hybridization fluctuations. Such two kinds of pairing correlations result in multigap unconventional superconductivity around the antiferromagnetic quantum critical point of the slave-fermion theory, where s -wave pairing is not favored generically due to strong correlations. We show that the ratio between each superconducting gap for conduction electrons Δc and holons Δf and the transition temperature Tc is 2Δc/Tc˜9 and 2Δf/Tc˜O(10-1) , remarkably consistent with CeCoIn5 . A fingerprint of the Kondo mechanism is emergence of two kinds of resonance modes in not only spin but also charge fluctuations, where the charge resonance mode at an antiferromagnetic wave vector originates from d -wave pairing of spinless holons. We discuss how the Kondo fluctuation theory differs from the spin-fluctuation approach.

Non-Gaussian limit fluctuations in active swimmer suspensions

NASA Astrophysics Data System (ADS)

Kurihara, Takashi; Aridome, Msato; Ayade, Heev; Zaid, Irwin; Mizuno, Daisuke

2017-03-01

We investigate the hydrodynamic fluctuations in suspensions of swimming microorganisms (Chlamydomonas) by observing the probe particles dispersed in the media. Short-term fluctuations of probe particles were superdiffusive and displayed heavily tailed non-Gaussian distributions. The analytical theory that explains the observed distribution was derived by summing the power-law-decaying hydrodynamic interactions from spatially distributed field sources (here, swimming microorganisms). The summing procedure, which we refer to as the physical limit operation, is applicable to a variety of physical fluctuations to which the classical central limiting theory does not apply. Extending the analytical formula to compare to experiments in active swimmer suspensions, we show that the non-Gaussian shape of the observed distribution obeys the analytic theory concomitantly with independently determined parameters such as the strength of force generations and the concentration of Chlamydomonas. Time evolution of the distributions collapsed to a single master curve, except for their extreme tails, for which our theory presents a qualitative explanation. Investigations thereof and the complete agreement with theoretical predictions revealed broad applicability of the formula to dispersions of active sources of fluctuations.

Incoherent scatter radar observations of the ionosphere

NASA Technical Reports Server (NTRS)

Hagfors, Tor

1989-01-01

Incoherent scatter radar (ISR) has become the most powerful means of studying the ionosphere from the ground. Many of the ideas and methods underlying the troposphere and stratosphere (ST) radars have been taken over from ISR. Whereas the theory of refractive index fluctuations in the lower atmosphere, depending as it does on turbulence, is poorly understood, the theory of the refractivity fluctuations in the ionosphere, which depend on thermal fluctuations, is known in great detail. The underlying theory is one of the most successful theories in plasma physics, and allows for many detailed investigations of a number of parameters such as electron density, electron temperature, ion temperature, electron mean velocity, and ion mean velocity as well as parameters pertaining to composition, neutral density and others. Here, the author reviews the fundamental processes involved in the scattering from a plasma undergoing thermal or near thermal fluctuations in density. The fundamental scattering properties of the plasma to the physical parameters characterizing them from first principles. He does not discuss the observation process itself, as the observational principles are quite similar whether they are applied to a neutral gas or a fluctuating plasma.

Remote sensing of Earth terrain

NASA Technical Reports Server (NTRS)

Kong, Jin AU

1987-01-01

Earth terrain covers were modeled as random media characterized by different dielectric constants and correlation functions. In order to model sea ice with brine inclusions and vegetation with row structures, the random medium is assumed to be anisotropic. A three layer model is used to simulate a vegetation field or a snow covered ice field with the top layer being snow or leaves, the middle layer being ice or trunks, and the bottom layer being sea water or ground. The strong fluctuation theory with the distorted Born approximation is applied to the solution of the radar backscattering coefficients.

Collective nuclear stabilization in single quantum dots by noncollinear hyperfine interaction

NASA Astrophysics Data System (ADS)

Yang, Wen; Sham, L. J.

2012-06-01

We present a theory of efficient suppression of the collective nuclear spin fluctuation, which prolongs the electron spin coherence time through the noncollinear hyperfine interaction between the nuclear spins and the hole spin. This provides a general paradigm to combat decoherence by direct control of environmental noise, and a possible solution to the puzzling observation of symmetric broadening of the absorption spectra in two recent experiments [Xu , Nature (London)NATUAS0028-083610.1038/nature08120 459, 1105 (2009) and Latta , Nature Phys.1745-247310.1038/nphys1363 5, 758 (2009)].

Large D-2 theory of superconducting fluctuations in a magnetic field and its application to iron pnictides.

PubMed

Murray, James M; Tesanović, Zlatko

2010-07-16

A Ginzburg-Landau approach to fluctuations of a layered superconductor in a magnetic field is used to show that the interlayer coupling can be incorporated within an interacting self-consistent theory of a single layer, in the limit of a large number of neighboring layers. The theory exhibits two phase transitions-a vortex liquid-to-solid transition is followed by a Bose-Einstein condensation into the Abrikosov lattice-illustrating the essential role of interlayer coupling. By using this theory, explicit expressions for magnetization, specific heat, and fluctuation conductivity are derived. We compare our results with recent experimental data on the iron-pnictide superconductors.

Coherent states formulation of polymer field theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Man, Xingkun; Villet, Michael C.; Materials Research Laboratory, University of California, Santa Barbara, California 93106

2014-01-14

We introduce a stable and efficient complex Langevin (CL) scheme to enable the first direct numerical simulations of the coherent-states (CS) formulation of polymer field theory. In contrast with Edwards’ well-known auxiliary-field (AF) framework, the CS formulation does not contain an embedded nonlinear, non-local, implicit functional of the auxiliary fields, and the action of the field theory has a fully explicit, semi-local, and finite-order polynomial character. In the context of a polymer solution model, we demonstrate that the new CS-CL dynamical scheme for sampling fluctuations in the space of coherent states yields results in good agreement with now-standard AF-CL simulations.more » The formalism is potentially applicable to a broad range of polymer architectures and may facilitate systematic generation of trial actions for use in coarse-graining and numerical renormalization-group studies.« less

Reexamining protein–protein and protein–solvent interactions from Kirkwood-Buff analysis of light scattering in multi-component solutions

PubMed Central

Blanco, Marco A.; Sahin, Erinc; Li, Yi; Roberts, Christopher J.

2011-01-01

The classic analysis of Rayleigh light scattering (LS) is re-examined for multi-component protein solutions, within the context of Kirkwood-Buff (KB) theory as well as a more generalized canonical treatment. Significant differences arise when traditional treatments that approximate constant pressure and neglect concentration fluctuations in one or more (co)solvent∕co-solute species are compared with more rigorous treatments at constant volume and with all species free to fluctuate. For dilute solutions, it is shown that LS can be used to rigorously and unambiguously obtain values for the osmotic second virial coefficient (B22), in contrast with recent arguments regarding protein interactions deduced from LS experiments. For more concentrated solutions, it is shown that conventional analysis over(under)-estimates the magnitude of B22 for significantly repulsive(attractive) conditions, and that protein-protein KB integrals (G22) are the more relevant quantity obtainable from LS. Published data for α–chymotrypsinogen A and a series of monoclonal antibodies at different pH and salt concentrations are re-analyzed using traditional and new treatments. The results illustrate that while traditional analysis may be sufficient if one is interested in only the sign of B22 or G22, the quantitative values can be significantly in error. A simple approach is illustrated for determining whether protein concentration (c2) is sufficiently dilute for B22 to apply, and for correcting B22 values from traditional LS regression at higher c2 values. The apparent molecular weight M2, app obtained from LS is shown to generally not be equal to the true molecular weight, with the differences arising from a combination of protein-solute and protein-cosolute interactions that may, in principle, also be determined from LS. PMID:21682538

Casimir force-induced instability in freestanding nanotweezers and nanoactuators made of cylindrical nanowires

NASA Astrophysics Data System (ADS)

Farrokhabadi, Amin; Abadian, Naeimeh; Kanjouri, Faramarz; Abadyan, Mohamadreza

2014-05-01

The quantum vacuum fluctuation i.e., Casimir attraction can induce mechanical instability in ultra-small devices. Previous researchers have focused on investigating the instability in structures with planar or rectangular cross-section. However, to the best knowledge of the authors, no attention has been paid for modeling this phenomenon in the structures made of nanowires with cylindrical geometry. In this regard, present work is dedicated to simulate the Casimir force-induced instability of freestanding nanoactuator and nanotweezers made of conductive nanowires with circular cross-section. To compute the quantum vacuum fluctuations, two approaches i.e., the proximity force approximation (for small separations) and scattering theory approximation (for large separations), are considered. The Euler-beam model is employed, in conjunction with the size-dependent modified couple stress continuum theory, to derive governing equations of the nanostructures. The governing nonlinear equations are solved via three different approaches, i.e., using lumped parameter model, modified variation iteration method (MVIM) and numerical solution. The deflection of the nanowire from zero to the final stable position is simulated as the Casimir force is increased from zero to its critical value. The detachment length and minimum gap, which prevent the instability, are computed for both nanosystems.

Position-sensitive scanning fluorescence correlation spectroscopy.

PubMed

Skinner, Joseph P; Chen, Yan; Müller, Joachim D

2005-08-01

Fluorescence correlation spectroscopy (FCS) uses a stationary laser beam to illuminate a small sample volume and analyze the temporal behavior of the fluorescence fluctuations within the stationary observation volume. In contrast, scanning FCS (SFCS) collects the fluorescence signal from a moving observation volume by scanning the laser beam. The fluctuations now contain both temporal and spatial information about the sample. To access the spatial information we synchronize scanning and data acquisition. Synchronization allows us to evaluate correlations for every position along the scanned trajectory. We use a circular scan trajectory in this study. Because the scan radius is constant, the phase angle is sufficient to characterize the position of the beam. We introduce position-sensitive SFCS (PSFCS), where correlations are calculated as a function of lag time and phase. We present the theory of PSFCS and derive expressions for diffusion, diffusion in the presence of flow, and for immobilization. To test PSFCS we compare experimental data with theory. We determine the direction and speed of a flowing dye solution and the position of an immobilized particle. To demonstrate the feasibility of the technique for applications in living cells we present data of enhanced green fluorescent protein measured in the nucleus of COS cells.

General Linearized Theory of Quantum Fluctuations around Arbitrary Limit Cycles

NASA Astrophysics Data System (ADS)

Navarrete-Benlloch, Carlos; Weiss, Talitha; Walter, Stefan; de Valcárcel, Germán J.

2017-09-01

The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its accuracy far from critical points or situations where the nonlinearity reaches the strong coupling regime, has turned it into a widespread technique, being the first method of choice in most works on the subject. However, such a technique finds strong practical and conceptual complications when one tries to apply it to situations in which the classical long-time solution is time dependent, a most prominent example being spontaneous limit-cycle formation. Here, we introduce a linearization scheme adapted to such situations, using the driven Van der Pol oscillator as a test bed for the method, which allows us to compare it with full numerical simulations. On a conceptual level, the scheme relies on the connection between the emergence of limit cycles and the spontaneous breaking of the symmetry under temporal translations. On the practical side, the method keeps the simplicity and linear scaling with the size of the problem (number of modes) characteristic of standard linearization, making it applicable to large (many-body) systems.

Residual fluctuations in the matter and radiation distribution after the decoupling epoch. [of early universe

NASA Technical Reports Server (NTRS)

Silk, J.; Wilson, M. L.

1980-01-01

The residual spectra of matter and radiation fluctuations in the early universe are investigated, and the evolution of primordial adiabatic and isothermal fluctuations through the decoupling epoch is studied. Amplification of adiabatic density fluctuations during decoupling, or velocity 'overshoot', is largely suppressed by Compton drag. Consequently, the amplitude of density fluctuations entering the horizon prior to decoupling is larger than hitherto assumed in the adiabatic theory. Damping of primordial adiabatic density fluctuations by an order of magnitude occurs on mass-scales of 3 x 10 to the 13th solar masses (Omega = 1) or 10 to the 14th solar masses (Omega = 0.2). Comparison of the residual radiation fluctuations with observational limits indicates that the adiabatic theory is only acceptable if re-ionization of the intergalactic medium results in additional scattering of the radiation after decoupling. Primordial isothermal fluctuations are found to yield radiation fluctuations which are insensitive to the assumed spectrum and lie a factor of about 5 below current limits

Fluctuation theorem for channel-facilitated membrane transport of interacting and noninteracting solutes.

PubMed

Berezhkovskii, Alexander M; Bezrukov, Sergey M

2008-05-15

In this paper, we discuss the fluctuation theorem for channel-facilitated transport of solutes through a membrane separating two reservoirs. The transport is characterized by the probability, P(n)(t), that n solute particles have been transported from one reservoir to the other in time t. The fluctuation theorem establishes a relation between P(n)(t) and P-(n)(t): The ratio P(n)(t)/P-(n)(t) is independent of time and equal to exp(nbetaA), where betaA is the affinity measured in the thermal energy units. We show that the same fluctuation theorem is true for both single- and multichannel transport of noninteracting particles and particles which strongly repel each other.

Multiple pathways of crystal nucleation in an extremely supersaturated aqueous potassium dihydrogen phosphate (KDP) solution droplet

PubMed Central

Lee, Sooheyong; Wi, Haeng Sub; Jo, Wonhyuk; Cho, Yong Chan; Lee, Hyun Hwi; Jeong, Se-Young; Kim, Yong-Il; Lee, Geun Woo

2016-01-01

Solution studies have proposed that crystal nucleation can take more complex pathways than previously expected in classical nucleation theory, such as formation of prenucleation clusters or densified amorphous/liquid phases. These findings show that it is possible to separate fluctuations in the different order parameters governing crystal nucleation, that is, density and structure. However, a direct observation of the multipathways from aqueous solutions remains a great challenge because heterogeneous nucleation sites, such as container walls, can prevent these paths. Here, we demonstrate the existence of multiple pathways of nucleation in highly supersaturated aqueous KH2PO4 (KDP) solution using the combination of a containerless device (electrostatic levitation), and in situ micro-Raman and synchrotron X-ray scattering. Specifically, we find that, at an unprecedentedly deep level of supersaturation, a high-concentration KDP solution first transforms into a metastable crystal before reaching stability at room temperature. However, a low-concentration solution, with different local structures, directly transforms into the stable crystal phase. These apparent multiple pathways of crystallization depend on the degree of supersaturation. PMID:27791068

Multiple pathways of crystal nucleation in an extremely supersaturated aqueous potassium dihydrogen phosphate (KDP) solution droplet.

PubMed

Lee, Sooheyong; Wi, Haeng Sub; Jo, Wonhyuk; Cho, Yong Chan; Lee, Hyun Hwi; Jeong, Se-Young; Kim, Yong-Il; Lee, Geun Woo

2016-11-29

Solution studies have proposed that crystal nucleation can take more complex pathways than previously expected in classical nucleation theory, such as formation of prenucleation clusters or densified amorphous/liquid phases. These findings show that it is possible to separate fluctuations in the different order parameters governing crystal nucleation, that is, density and structure. However, a direct observation of the multipathways from aqueous solutions remains a great challenge because heterogeneous nucleation sites, such as container walls, can prevent these paths. Here, we demonstrate the existence of multiple pathways of nucleation in highly supersaturated aqueous KH 2 PO 4 (KDP) solution using the combination of a containerless device (electrostatic levitation), and in situ micro-Raman and synchrotron X-ray scattering. Specifically, we find that, at an unprecedentedly deep level of supersaturation, a high-concentration KDP solution first transforms into a metastable crystal before reaching stability at room temperature. However, a low-concentration solution, with different local structures, directly transforms into the stable crystal phase. These apparent multiple pathways of crystallization depend on the degree of supersaturation.

The effects of gusts on the fluctuating airloads of airfoils in transonic flow

NASA Technical Reports Server (NTRS)

Mccroskey, W. J.

1984-01-01

Unsteady interactions of distributed and sharp-edged gusts with a stationary airfoil have been analyzed in two-dimensional transonic flow.A simple method of introducing such disturbances has been numerically implemented within the framework of unsteady, transonic small-disturbance theory. Representative solutions for various airfoils subjected to chordwise and transverse gusts show that the strength and unsteady motion of the shock wave on the airfoil significantly affect the flowfield development and, consequently, the dynamic airloads. Also a study was made of the reductions in the unsteady airloads that can be achieved by the proper active control motion of a trailing-edge flap, and a simple gust-alleviation strategy was developed. However, the chordwise pressure distributions associated with gusts are very different from those produced by trailing-edge flap oscillations. Consequently, the fluctuating lift and the unsteady pitching moments cannot both be eliminated simultaneously.

A theoretical model for investigating the effect of vacuum fluctuations on the electromechanical stability of nanotweezers

NASA Astrophysics Data System (ADS)

Farrokhabadi, A.; Mokhtari, J.; Koochi, A.; Abadyan, M.

2015-06-01

In this paper, the impact of the Casimir attraction on the electromechanical stability of nanowire-fabricated nanotweezers is investigated using a theoretical continuum mechanics model. The Dirichlet mode is considered and an asymptotic solution, based on path integral approach, is applied to consider the effect of vacuum fluctuations in the model. The Euler-Bernoulli beam theory is employed to derive the nonlinear governing equation of the nanotweezers. The governing equations are solved by three different approaches, i.e. the modified variation iteration method, generalized differential quadrature method and using a lumped parameter model. Various perspectives of the problem, including the comparison with the van der Waals force regime, the variation of instability parameters and effects of geometry are addressed in present paper. The proposed approach is beneficial for the precise determination of the electrostatic response of the nanotweezers in the presence of Casimir force.

Experimental Investigation of Triplet Correlation Approximations for Fluid Water.

PubMed

Pallewela, Gayani N; Ploetz, Elizabeth A; Smith, Paul E

2018-08-25

Triplet correlations play a central role in our understanding of fluids and their properties. Of particular interest is the relationship between the pair and triplet correlations. Here we use a combination of Fluctuation Solution Theory and experimental pair radial distribution functions to investigate the accuracy of the Kirkwood Superposition Approximation (KSA), as given by integrals over the relevant pair and triplet correlation functions, at a series of state points for pure water using only experimental quantities. The KSA performs poorly, in agreement with a variety of other studies. Several additional approximate relationships between the pair and triplet correlations in fluids are also investigated and generally provide good agreement for the fluid thermodynamics for regions of the phase diagram where the compressibility is small. A simple power law relationship between the pair and triplet fluctuations is particularly successful for state points displaying low to moderately high compressibilities.

Tree-level correlations in the strong field regime

NASA Astrophysics Data System (ADS)

Gelis, François

2017-09-01

We consider the correlation function of an arbitrary number of local observables in quantum field theory, in situations where the field amplitude is large. Using a quasi-classical approximation (valid for a highly occupied initial mixed state, or for a coherent initial state if the classical dynamics has instabilities), we show that at tree level these correlations are dominated by fluctuations at the initial time. We obtain a general expression of the correlation functions in terms of the classical solution of the field equation of motion and its derivatives with respect to its initial conditions, that can be arranged graphically as the sum of labeled trees where the nodes are the individual observables, and the links are pairs of derivatives acting on them. For 3-point (and higher) correlation functions, there are additional tree-level terms beyond the quasi-classical approximation, generated by fluctuations in the bulk.

Vibrational spectra from atomic fluctuations in dynamics simulations. II. Solvent-induced frequency fluctuations at femtosecond time resolution

NASA Astrophysics Data System (ADS)

Schmitz, Matthias; Tavan, Paul

2004-12-01

The midinfrared (MIR) spectra of molecules in polar solvents exhibit inhomogeneously broadened bands whose spectral positions are shifted as compared to the gas phase. The shifts are caused by interactions with structured solvation shells and the broadenings by fluctuations of these interactions. The MIR spectra can be calculated from hybrid molecular dynamics (MD) simulations, which treat the solute molecule by density functional theory and the solvent by molecular mechanics by the so-called instantaneous normal mode analysis (INMA) or by Fourier transforming the time correlation function (FTTCF) of the molecular dipole moment. In Paper I of this work [M. Schmitz and P. Tavan, J. Chem. Phys. 121, 12233 (2004)] we explored an alternative method based on generalized virial (GV) frequencies noting, however, that GV systematically underestimates frequencies. As shown by us these artifacts are caused by solvent-induced fluctuations of the (i) equilibrium geometry, (ii) force constants, and (iii) normal mode directions as well as by (iv) diagonal and (v) off-diagonal anharmonicities. Here we now show, by analyzing the time scales of fluctuations and sample MD trajectories of formaldehyde in the gas phase and in water, that all these sources of computational artifacts can be made visible by a Fourier analysis of the normal coordinates. Correspondingly, the error sources (i) and (iii)-(v) can be removed by bandpass filtering, as long as the spectral signatures of the respective effects are well separated from the fundamental band. Furthermore, the artifacts arising from effect (ii) can be strongly diminished by a time-resolved version of the GV approach (TF-GV). The TF-GV method then yields for each mode j a trajectory of the vibrational frequency ωj(t|τ) at a time resolution τ>τj, which is only limited by the corresponding oscillation time τj=2π/ωj and, thus, is in the femtosecond range. A correlation analysis of these trajectories clearly separates the librational motions from the conformational dynamics of the solvation shells and yields the inhomogeneously broadened MIR spectra, if the theory of motional narrowing is properly included. The MIR spectrum of formaldehyde in solution obtained by TF-GV agrees very well with the FTTCF result, if one applies the so-called "harmonic approximation" quantum correction factor and a temperature scaling to the FTTCF intensities. Also for INMA an excellent agreement is achieved if one disregards a slight INMA overestimate of linewidths.

Density fluctuations in aqueous solution of ionic liquid with lower critical solution temperature: Mixture of tetrabutylphosphonium trifluoroacetate and water

NASA Astrophysics Data System (ADS)

Nitta, Ayako; Morita, Takeshi; Saita, Shohei; Kohno, Yuki; Ohno, Hiroyuki; Nishikawa, Keiko

2015-05-01

Aqueous solutions of tetrabutylphosphonium trifluoroacetate ([P4444]CF3COO) exhibit a LCST-type phase transition with the critical point near 0.025 in mole fraction of [P4444]CF3COO at T = 302 K. The phase behavior of [P4444]CF3COO-water mixtures was investigated by evaluating their density fluctuations, which provide quantitative descriptions of the mixing states of the solutions. The concentration dependence of the density fluctuations was investigated at 293 and 301 K for the mixtures without distinguishing the components and for the individual components ([P4444]CF3COO and water). A drastic change in the mixing state was observed for the solution when the critical point was approached.

Galileon as a local modification of gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nicolis, Alberto; Rattazzi, Riccardo; Trincherini, Enrico

2009-03-15

In the Dvali-Gabadadze-Porrati (DGP) model, the 'self-accelerating' solution is plagued by a ghost instability, which makes the solution untenable. This fact, as well as all interesting departures from general relativity (GR), are fully captured by a four-dimensional effective Lagrangian, valid at distances smaller than the present Hubble scale. The 4D effective theory involves a relativistic scalar {pi}, universally coupled to matter and with peculiar derivative self-interactions. In this paper, we study the connection between self-acceleration and the presence of ghosts for a quite generic class of theories that modify gravity in the infrared. These theories are defined as those thatmore » at distances shorter than cosmological, reduce to a certain generalization of the DGP 4D effective theory. We argue that for infrared modifications of GR locally due to a universally coupled scalar, our generalization is the only one that allows for a robust implementation of the Vainshtein effect--the decoupling of the scalar from matter in gravitationally bound systems--necessary to recover agreement with solar-system tests. Our generalization involves an internal Galilean invariance, under which {pi}'s gradient shifts by a constant. This symmetry constrains the structure of the {pi} Lagrangian so much so that in 4D there exist only five terms that can yield sizable nonlinearities without introducing ghosts. We show that for such theories in fact there are ''self-accelerating'' de Sitter solutions with no ghostlike instabilities. In the presence of compact sources, these solutions can support spherically symmetric, Vainshtein-like nonlinear perturbations that are also stable against small fluctuations. We investigate a possible infrared completion of these theories at scales of order of the Hubble horizon, and larger. There are however some features of our theories that may constitute a problem at the theoretical or phenomenological level: the presence of superluminal excitations; the extreme subluminality of other excitations, which makes the quasistatic approximation for certain solar-system observables unreliable due to Cherenkov emission; the very low strong-interaction scale for {pi}{pi} scatterings.« less

Computation of the free energy due to electron density fluctuation of a solute in solution: A QM/MM method with perturbation approach combined with a theory of solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Suzuoka, Daiki; Takahashi, Hideaki, E-mail: hideaki@m.tohoku.ac.jp; Morita, Akihiro

2014-04-07

We developed a perturbation approach to compute solvation free energy Δμ within the framework of QM (quantum mechanical)/MM (molecular mechanical) method combined with a theory of energy representation (QM/MM-ER). The energy shift η of the whole system due to the electronic polarization of the solute is evaluated using the second-order perturbation theory (PT2), where the electric field formed by surrounding solvent molecules is treated as the perturbation to the electronic Hamiltonian of the isolated solute. The point of our approach is that the energy shift η, thus obtained, is to be adopted for a novel energy coordinate of the distributionmore » functions which serve as fundamental variables in the free energy functional developed in our previous work. The most time-consuming part in the QM/MM-ER simulation can be, thus, avoided without serious loss of accuracy. For our benchmark set of molecules, it is demonstrated that the PT2 approach coupled with QM/MM-ER gives hydration free energies in excellent agreements with those given by the conventional method utilizing the Kohn-Sham SCF procedure except for a few molecules in the benchmark set. A variant of the approach is also proposed to deal with such difficulties associated with the problematic systems. The present approach is also advantageous to parallel implementations. We examined the parallel efficiency of our PT2 code on multi-core processors and found that the speedup increases almost linearly with respect to the number of cores. Thus, it was demonstrated that QM/MM-ER coupled with PT2 deserves practical applications to systems of interest.« less

Economic Fluctuations and Statistical Physics: Quantifying Extremely Rare and Much Less Rare Events

NASA Astrophysics Data System (ADS)

Stanley, H. Eugene

2008-03-01

Recent analysis of truly huge quantities of empirical data suggests that classic economic theories not only fail for a few outliers, but that there occur similar outliers of every possible size. In fact, if one analyzes only a small data set (say 10^4 data points), then outliers appear to occur as ``rare events.'' However, when we analyze orders of magnitude more data (10^8 data points!), we find orders of magnitude more outliers---so ignoring them is not a responsible option, and studying their properties becomes a realistic goal. We find that the statistical properties of these ``outliers'' are identical to the statistical properties of everyday fluctuations. For example, a histogram giving the number of fluctuations of a given magnitude x for fluctuations ranging in magnitude from everyday fluctuations to extremely rare fluctuations that occur with a probability of only 10-8 is a perfect straight line in a double-log plot. Quantitative analogies between financial fluctuations and earthquakes will be discussed. Two unifying principles that underlie much of the finance analysis we will present are scale invariance and universality [R. N. Mantegna and H. E. Stanley, Introduction to Econophysics: Correlations & Complexity in Finance/ (Cambridge U. Press, 2000)]. Scale invariance is a property not about algebraic equations but rather about functional equations, which have as their solutions not numbers but rather functional forms. The key idea of universality is that the identical set of laws hold across diverse markets, and over diverse time periods. This work was carried out in collaboration with a number of students and colleagues, chief among whom are X. Gabaix (MIT and Princeton) and V. Plerou (Boston University).

Elasticity and Fluctuations of Frustrated Nanoribbons

NASA Astrophysics Data System (ADS)

Grossman, Doron; Sharon, Eran; Diamant, Haim

2016-06-01

We derive a reduced quasi-one-dimensional theory of geometrically frustrated elastic ribbons. Expressed in terms of geometric properties alone, it applies to ribbons over a wide range of scales, allowing the study of their elastic equilibrium, as well as thermal fluctuations. We use the theory to account for the twisted-to-helical transition of ribbons with spontaneous negative curvature and the effect of fluctuations on the corresponding critical exponents. The persistence length of such ribbons changes nonmonotonically with the ribbon's width, dropping to zero at the transition. This and other statistical properties qualitatively differ from those of nonfrustrated fluctuating filaments.

Free-Energy-Based Design Policy for Robust Network Control against Environmental Fluctuation.

PubMed

Iwai, Takuya; Kominami, Daichi; Murata, Masayuki; Yomo, Tetsuya

2015-01-01

Bioinspired network control is a promising approach for realizing robust network controls. It relies on a probabilistic mechanism composed of positive and negative feedback that allows the system to eventually stabilize on the best solution. When the best solution fails due to environmental fluctuation, the system cannot keep its function until the system finds another solution again. To prevent the temporal loss of the function, the system should prepare some solution candidates and stochastically select available one from them. However, most bioinspired network controls are not designed with this issue in mind. In this paper, we propose a thermodynamics-based design policy that allows systems to retain an appropriate degree of randomness depending on the degree of environmental fluctuation, which prepares the system for the occurrence of environmental fluctuation. Furthermore, we verify the design policy by using an attractor selection model-based multipath routing to run simulation experiments.

Composite operators in cubic field theories and link-overlap fluctuations in spin-glass models

NASA Astrophysics Data System (ADS)

Altieri, Ada; Parisi, Giorgio; Rizzo, Tommaso

2016-01-01

We present a complete characterization of the fluctuations and correlations of the squared overlap in the Edwards-Anderson spin-glass model in zero field. The analysis reveals that the energy-energy correlation (and thus the specific heat) has a different critical behavior than the fluctuations of the link overlap in spite of the fact that the average energy and average link overlap have the same critical properties. More precisely the link-overlap fluctuations are larger than the specific heat according to a computation at first order in the 6 -ɛ expansion. An unexpected outcome is that the link-overlap fluctuations have a subdominant power-law contribution characterized by an anomalous logarithmic prefactor which is absent in the specific heat. In order to compute the ɛ expansion we consider the problem of the renormalization of quadratic composite operators in a generic multicomponent cubic field theory: the results obtained have a range of applicability beyond spin-glass theory.

Plasmon mass scale and quantum fluctuations of classical fields on a real time lattice

NASA Astrophysics Data System (ADS)

Kurkela, Aleksi; Lappi, Tuomas; Peuron, Jarkko

2018-03-01

Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Above the Debye scale the classical Yang-Mills (CYM) theory can be matched smoothly to kinetic theory. First we study the limits of the quasiparticle picture of the CYM fields by determining the plasmon mass of the system using 3 different methods. Then we argue that one needs a numerical calculation of a system of classical gauge fields and small linearized fluctuations, which correspond to quantum fluctuations, in a way that keeps the separation between the two manifest. We demonstrate and test an implementation of an algorithm with the linearized fluctuation showing that the linearization indeed works and that the Gauss's law is conserved.

Kinetic Roughening and Energetics of Tetragonal Lysozyme Crystal Growth: A Preliminary Atomic Force Microscopy Investigation

NASA Technical Reports Server (NTRS)

Gorti, Sridhar; Forsythe, Elizabeth L.; Pusey, Marc L.

2004-01-01

We examined particulars of crystal growth from measurements obtained at both microscopic and molecular levels. The crystal growth measurements performed at the microscopic level are well characterized by a model that balances the flux of macromolecules towards the crystal surface with the flux of the crystal surface. Numerical evaluation of model with measurements of crystal growth, in time, provided accurate estimates for the average growth velocities. Growth velocities thus obtained were also interpreted using well-established phenomenological theories. Moreover, we find that microscopic measurements of growth velocity measurements obtained as a function of temperature best characterizes changes in crystal growth modes, when present. We also examined the possibility of detecting a change in crystal growth modes at the molecular level using atomic force microscopy, AFM. From preliminary AFM measurements performed at various supersaturations, we find that magnitude of surface height fluctuations, h(x), increases with supersaturation. Further examination of surface height fluctuations using methods established for fluctuation spectroscopy also enabled the discovery of the existence of a characteristic length, c, which may possibly determine the mode of crystal growth. Although the results are preliminary, we establish the non- critical divergence of 5 and the root-mean-square (rms) magnitude of height-height fluctuations as the kinetic roughening transition temperatures are approached. Moreover, we also examine approximate models for interpreting the non-critical behavior of both 6 and rms magnitude of height-height fluctuations, as the solution supersaturation is increased towards the kinetic roughening supersaturation.

Nernst effect from fluctuating pairs in the pseudogap phase of the cuprates.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Levchenko, A.; Norman, M. R.; Varlamov, A. A.

2011-01-31

The observation of a large Nernst signal in cuprates above the superconducting transition temperature has attracted much attention. A potential explanation is that it originates from superconducting fluctuations. Although the Nernst signal is indeed consistent with Gaussian fluctuations for overdoped cuprates, Gaussian theory fails to describe the temperature dependence seen for underdoped cuprates. Here, we consider the vertex correction to Gaussian theory resulting from the pseudogap. This yields a Nernst signal in good agreement with the data.

Electronic Noise and Fluctuations in Solids

NASA Astrophysics Data System (ADS)

Kogan, Sh.

2008-07-01

Preface; Part I. Introduction. Some Basic Concepts of the Theory of Random Processes: 1. Probability density functions. Moments. Stationary processes; 2. Correlation function; 3. Spectral density of noise; 4. Ergodicity and nonergodicity of random processes; 5. Random pulses and shot noise; 6. Markov processes. General theory; 7. Discrete Markov processes. Random telegraph noise; 8. Quasicontinuous (Diffusion-like) Markov processes; 9. Brownian motion; 10. Langevin approach to the kinetics of fluctuations; Part II. Fluctuation-Dissipation Relations in Equilibrium Systems: 11. Derivation of fluctuation-dissipation relations; 12. Equilibrium noise in quasistationary circuits. Nyquist theorem; 13. Fluctuations of electromagnetic fields in continuous media; Part III. Fluctuations in Nonequilibrium Gases: 14. Some basic concepts of hot-electrons' physics; 15. Simple model of current fluctuations in a semiconductor with hot electrons; 16. General kinetic theory of quasiclassical fluctuations in a gas of particles. The Boltzmann-Langevin equation; 17. Current fluctuations and noise temperature; 18. Current fluctuations and diffusion in a gas of hot electrons; 19. One-time correlation in nonequilibrium gases; 20. Intervalley noise in multivalley semiconductors; 21. Noise of hot electrons emitting optical phonons in the streaming regime; 22. Noise in a semiconductor with a postbreakdown stable current filament; Part IV. Generation-recombination noise: 23. G-R noise in uniform unipolar semiconductors; 24. Noise produced by recombination and diffusion; Part V. Noise in quantum ballistic systems: 25. Introduction; 26. Equilibrium noise and shot noise in quantum conductors; 27. Modulation noise in quantum point contacts; 28. Transition from a ballistic conductor to a macroscopic one; 29. Noise in tunnel junctions; Part VI. Resistance noise in metals: 30. Incoherent scattering of electrons by mobile defects; 31. Effect of mobile scattering centers on the electron interference pattern; 32. Fluctuations of the number of diffusing scattering centers; 33. Temperature fluctuations and the corresponding noise; Part VII. Noise in strongly disordered conductors: 34. Basic ideas of the percolation theory; 35. Resistance fluctuations in percolation systems. 36. Experiments; Part VIII. Low-frequency noise with an 1/f-type spectrum and random telegraph noise: 37. Introduction; 38. Some general properties of 1/f noise; 39. Basic models of 1/f noise; 40./f noise in metals; 41. Low-frequency noise in semiconductors; 42. Magnetic noise in spin glasses and some other magnetic systems; 43. Temperature fluctuations as a possible source of 1/f noise; 44. Random telegraph noise; 45. Fluctuations with 1/f spectrum in other systems; 46. General conclusions on 1/f noise; Part IX. Noise in Superconductors and Superconducting Structures: 47. Noise in Josephson junctions; 48. Noise in type II superconductors; References; Subject index.

Spatial irregularities in Jupiter's upper ionosphere observed by Voyager radio occultations

NASA Technical Reports Server (NTRS)

Hinson, D. P.; Tyler, G. L.

1982-01-01

Radio scintillations (at 3.6 and 13 cm) produced by scattering from ionospheric irregularities during the Voyager occultations are interpreted using a weak-scattering theory. Least squares solutions for ionospheric parameters derived from the observed fluctuation spectra yield estimates of (1) the axial ratio, (2) angular orientation of the anisotropic irregularities, (3) the power law exponent of the spatial spectrum of irregularities, and (4) the magnitude of the spatial variations in electron density. It is shown that the measured angular orientation of the anisotropic irregularities indicates magnetic field direction and may provide a basis for refining Jovian magnetic field models.

Microcanonical fluctuations of the condensate in weakly interacting Bose gases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Idziaszek, Zbigniew

2005-05-15

We study fluctuations of the number of Bose condensed atoms in a weakly interacting homogeneous and trapped gases. For a homogeneous system we apply the particle-number-conserving formulation of the Bogoliubov theory and calculate the condensate fluctuations within the canonical and the microcanonical ensembles. We demonstrate that, at least in the low-temperature regime, predictions of the particle-number-conserving and traditional, nonconserving theory are identical, and lead to the anomalous scaling of fluctuations. Furthermore, the microcanonical fluctuations differ from the canonical ones by a quantity which scales normally in the number of particles, thus predictions of both ensembles are equivalent in the thermodynamicmore » limit. We observe a similar behavior for a weakly interacting gas in a harmonic trap. This is in contrast to the trapped, ideal gas, where microcanonical and canonical fluctuations are different in the thermodynamic limit.« less

Steady-state EB cap size fluctuations are determined by stochastic microtubule growth and maturation

PubMed Central

Rickman, Jamie; Duellberg, Christian; Cade, Nicholas I.; Griffin, Lewis D.; Surrey, Thomas

2017-01-01

Growing microtubules are protected from depolymerization by the presence of a GTP or GDP/Pi cap. End-binding proteins of the EB1 family bind to the stabilizing cap, allowing monitoring of its size in real time. The cap size has been shown to correlate with instantaneous microtubule stability. Here we have quantitatively characterized the properties of cap size fluctuations during steady-state growth and have developed a theory predicting their timescale and amplitude from the kinetics of microtubule growth and cap maturation. In contrast to growth speed fluctuations, cap size fluctuations show a characteristic timescale, which is defined by the lifetime of the cap sites. Growth fluctuations affect the amplitude of cap size fluctuations; however, cap size does not affect growth speed, indicating that microtubules are far from instability during most of their time of growth. Our theory provides the basis for a quantitative understanding of microtubule stability fluctuations during steady-state growth. PMID:28280102

Gradient Driven Fluctuations

NASA Technical Reports Server (NTRS)

Cannell, David

2005-01-01

We have worked with our collaborators at the University of Milan (Professor Marzio Giglio and his group-supported by ASI) to define the science required to measure gradient driven fluctuations in the microgravity environment. Such a study would provide an accurate test of the extent to which the theory of fluctuating hydrodynamics can be used to predict the properties of fluids maintained in a stressed, non-equilibrium state. As mentioned above, the results should also provide direct visual insight into the behavior of a variety of fluid systems containing gradients or interfaces, when placed in the microgravity environment. With support from the current grant, we have identified three key systems for detailed investigation. These three systems are: 1) A single-component fluid to be studied in the presence of a temperature gradient; 2) A mixture of two organic liquids to be studied both in the presence of a temperature gradient, which induces a steady-state concentration gradient, and with the temperature gradient removed, but while the concentration gradient is dying by means of diffusion; 3) Various pairs of liquids undergoing free diffusion, including a proteidbuffer solution and pairs of mixtures having different concentrations, to allow us to vary the differences in fluid properties in a controlled manner.

Energy flow in non-equilibrium conformal field theory

NASA Astrophysics Data System (ADS)

Bernard, Denis; Doyon, Benjamin

2012-09-01

We study the energy current and its fluctuations in quantum gapless 1d systems far from equilibrium modeled by conformal field theory, where two separated halves are prepared at distinct temperatures and glued together at a point contact. We prove that these systems converge towards steady states, and give a general description of such non-equilibrium steady states in terms of quantum field theory data. We compute the large deviation function, also called the full counting statistics, of energy transfer through the contact. These are universal and satisfy fluctuation relations. We provide a simple representation of these quantum fluctuations in terms of classical Poisson processes whose intensities are proportional to Boltzmann weights.

Attenuation of sound in sand sediments due to porosity fluctuations.

PubMed

Hefner, Brian T; Jackson, Darrell R

2014-08-01

At high frequencies, the attenuation measured in sand sediments is larger than that predicted by Biot theory. To account for this discrepancy, perturbation theory is used to incorporate losses due to scattering by porosity variations into both Biot's poroelastic equations and the effective density fluid model. While previous results showed that fluctuations in the bulk frame modulus were insufficient to produce significant attenuation in a sand sediment, modest levels of fluctuations in the porosity produce significant scattering loss. By using the sediment parameters and the heterogeneity power spectrum measured during the Sediment Acoustics Experiment in 2004, the perturbation theory result shows good agreement with the sound speed and attenuation data without any free parameters.

Synaptic shot noise and conductance fluctuations affect the membrane voltage with equal significance.

PubMed

Richardson, Magnus J E; Gerstner, Wulfram

2005-04-01

The subthreshold membrane voltage of a neuron in active cortical tissue is a fluctuating quantity with a distribution that reflects the firing statistics of the presynaptic population. It was recently found that conductance-based synaptic drive can lead to distributions with a significant skew. Here it is demonstrated that the underlying shot noise caused by Poissonian spike arrival also skews the membrane distribution, but in the opposite sense. Using a perturbative method, we analyze the effects of shot noise on the distribution of synaptic conductances and calculate the consequent voltage distribution. To first order in the perturbation theory, the voltage distribution is a gaussian modulated by a prefactor that captures the skew. The gaussian component is identical to distributions derived using current-based models with an effective membrane time constant. The well-known effective-time-constant approximation can therefore be identified as the leading-order solution to the full conductance-based model. The higher-order modulatory prefactor containing the skew comprises terms due to both shot noise and conductance fluctuations. The diffusion approximation misses these shot-noise effects implying that analytical approaches such as the Fokker-Planck equation or simulation with filtered white noise cannot be used to improve on the gaussian approximation. It is further demonstrated that quantities used for fitting theory to experiment, such as the voltage mean and variance, are robust against these non-Gaussian effects. The effective-time-constant approximation is therefore relevant to experiment and provides a simple analytic base on which other pertinent biological details may be added.

Large deviation theory for the kinetics and energetics of turnover of enzyme catalysis in a chemiostatic flow.

PubMed

Das, Biswajit; Gangopadhyay, Gautam

2018-05-07

In the framework of large deviation theory, we have characterized nonequilibrium turnover statistics of enzyme catalysis in a chemiostatic flow with externally controllable parameters, like substrate injection rate and mechanical force. In the kinetics of the process, we have shown the fluctuation theorems in terms of the symmetry of the scaled cumulant generating function (SCGF) in the transient and steady state regime and a similar symmetry rule is reflected in a large deviation rate function (LDRF) as a property of the dissipation rate through boundaries. Large deviation theory also gives the thermodynamic force of a nonequilibrium steady state, as is usually recorded experimentally by a single molecule technique, which plays a key role responsible for the dynamical symmetry of the SCGF and LDRF. Using some special properties of the Legendre transformation, here, we have provided a relation between the fluctuations of fluxes and dissipation rates, and among them, the fluctuation of the turnover rate is routinely estimated but the fluctuation in the dissipation rate is yet to be characterized for small systems. Such an enzymatic reaction flow system can be a very good testing ground to systematically understand the rare events from the large deviation theory which is beyond fluctuation theorem and central limit theorem.

Large deviation theory for the kinetics and energetics of turnover of enzyme catalysis in a chemiostatic flow

NASA Astrophysics Data System (ADS)

Das, Biswajit; Gangopadhyay, Gautam

2018-05-01

In the framework of large deviation theory, we have characterized nonequilibrium turnover statistics of enzyme catalysis in a chemiostatic flow with externally controllable parameters, like substrate injection rate and mechanical force. In the kinetics of the process, we have shown the fluctuation theorems in terms of the symmetry of the scaled cumulant generating function (SCGF) in the transient and steady state regime and a similar symmetry rule is reflected in a large deviation rate function (LDRF) as a property of the dissipation rate through boundaries. Large deviation theory also gives the thermodynamic force of a nonequilibrium steady state, as is usually recorded experimentally by a single molecule technique, which plays a key role responsible for the dynamical symmetry of the SCGF and LDRF. Using some special properties of the Legendre transformation, here, we have provided a relation between the fluctuations of fluxes and dissipation rates, and among them, the fluctuation of the turnover rate is routinely estimated but the fluctuation in the dissipation rate is yet to be characterized for small systems. Such an enzymatic reaction flow system can be a very good testing ground to systematically understand the rare events from the large deviation theory which is beyond fluctuation theorem and central limit theorem.

Molecules with an induced dipole moment in a stochastic electric field.

PubMed

Band, Y B; Ben-Shimol, Y

2013-10-01

The mean-field dynamics of a molecule with an induced dipole moment (e.g., a homonuclear diatomic molecule) in a deterministic and a stochastic (fluctuating) electric field is solved to obtain the decoherence properties of the system. The average (over fluctuations) electric dipole moment and average angular momentum as a function of time for a Gaussian white noise electric field are determined via perturbative and nonperturbative solutions in the fluctuating field. In the perturbative solution, the components of the average electric dipole moment and the average angular momentum along the deterministic electric field direction do not decay to zero, despite fluctuations in all three components of the electric field. This is in contrast to the decay of the average over fluctuations of a magnetic moment in a Gaussian white noise magnetic field. In the nonperturbative solution, the component of the average electric dipole moment and the average angular momentum in the deterministic electric field direction also decay to zero.

Critical phenomena at the complex tensor ordering phase transition

NASA Astrophysics Data System (ADS)

Boettcher, Igor; Herbut, Igor F.

2018-02-01

We investigate the critical properties of the phase transition towards complex tensor order that has been proposed to occur in spin-orbit-coupled superconductors. For this purpose, we formulate the bosonic field theory for fluctuations of the complex irreducible second-rank tensor order parameter close to the transition. We then determine the scale dependence of the couplings of the theory by means of the perturbative renormalization group (RG). For the isotropic system, we generically detect a fluctuation-induced first-order phase transition. The initial values for the running couplings are determined by the underlying microscopic model for the tensorial order. As an example, we study three-dimensional Luttinger semimetals with electrons at a quadratic band-touching point. Whereas the strong-coupling transition of the model receives substantial fluctuation corrections, the weak-coupling transition at low temperatures is rendered only weakly first order due to the presence of a fixed point in the vicinity of the RG trajectory. If the number of fluctuating complex components of the order parameter is reduced by cubic anisotropy, the theory maps onto the field theory for frustrated magnetism.

Dynamic density functional theory with hydrodynamic interactions and fluctuations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Donev, Aleksandar, E-mail: donev@courant.nyu.edu; Vanden-Eijnden, Eric, E-mail: eve2@courant.nyu.edu

2014-06-21

We derive a closed equation for the empirical concentration of colloidal particles in the presence of both hydrodynamic and direct interactions. The ensemble average of our functional Langevin equation reproduces known deterministic Dynamic Density Functional Theory (DDFT) [M. Rex and H. Löwen, “Dynamical density functional theory with hydrodynamic interactions and colloids in unstable traps,” Phys. Rev. Lett. 101(14), 148302 (2008)], and, at the same time, it also describes the microscopic fluctuations around the mean behavior. We suggest separating the ideal (non-interacting) contribution from additional corrections due to pairwise interactions. We find that, for an incompressible fluid and in the absencemore » of direct interactions, the mean concentration follows Fick's law just as for uncorrelated walkers. At the same time, the nature of the stochastic terms in fluctuating DDFT is shown to be distinctly different for hydrodynamically-correlated and uncorrelated walkers. This leads to striking differences in the behavior of the fluctuations around Fick's law, even in the absence of pairwise interactions. We connect our own prior work [A. Donev, T. G. Fai, and E. Vanden-Eijnden, “A reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick's law,” J. Stat. Mech.: Theory Exp. (2014) P04004] on fluctuating hydrodynamics of diffusion in liquids to the DDFT literature, and demonstrate that the fluid cannot easily be eliminated from consideration if one wants to describe the collective diffusion in colloidal suspensions.« less

Predictive Sampling of Rare Conformational Events in Aqueous Solution: Designing a Generalized Orthogonal Space Tempering Method.

PubMed

Lu, Chao; Li, Xubin; Wu, Dongsheng; Zheng, Lianqing; Yang, Wei

2016-01-12

In aqueous solution, solute conformational transitions are governed by intimate interplays of the fluctuations of solute-solute, solute-water, and water-water interactions. To promote molecular fluctuations to enhance sampling of essential conformational changes, a common strategy is to construct an expanded Hamiltonian through a series of Hamiltonian perturbations and thereby broaden the distribution of certain interactions of focus. Due to a lack of active sampling of configuration response to Hamiltonian transitions, it is challenging for common expanded Hamiltonian methods to robustly explore solvent mediated rare conformational events. The orthogonal space sampling (OSS) scheme, as exemplified by the orthogonal space random walk and orthogonal space tempering methods, provides a general framework for synchronous acceleration of slow configuration responses. To more effectively sample conformational transitions in aqueous solution, in this work, we devised a generalized orthogonal space tempering (gOST) algorithm. Specifically, in the Hamiltonian perturbation part, a solvent-accessible-surface-area-dependent term is introduced to implicitly perturb near-solute water-water fluctuations; more importantly in the orthogonal space response part, the generalized force order parameter is generalized as a two-dimension order parameter set, in which essential solute-solvent and solute-solute components are separately treated. The gOST algorithm is evaluated through a molecular dynamics simulation study on the explicitly solvated deca-alanine (Ala10) peptide. On the basis of a fully automated sampling protocol, the gOST simulation enabled repetitive folding and unfolding of the solvated peptide within a single continuous trajectory and allowed for detailed constructions of Ala10 folding/unfolding free energy surfaces. The gOST result reveals that solvent cooperative fluctuations play a pivotal role in Ala10 folding/unfolding transitions. In addition, our assessment analysis suggests that because essential conformational events are mainly driven by the compensating fluctuations of essential solute-solvent and solute-solute interactions, commonly employed "predictive" sampling methods are unlikely to be effective on this seemingly "simple" system. The gOST development presented in this paper illustrates how to employ the OSS scheme for physics-based sampling method designs.

Testing approximate theories of first-order phase transitions on the two-dimensional Potts model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dasgupta, C.; Pandit, R.

The two-dimensional, q-state (q > 4) Potts model is used as a testing ground for approximate theories of first-order phase transitions. In particular, the predictions of a theory analogous to the Ramakrishnan-Yussouff theory of freezing are compared with those of ordinary mean-field (Curie-Wiess) theory. It is found that the Curie-Weiss theory is a better approximation than the Ramakrishnan-Yussouff theory, even though the former neglects all fluctuations. It is shown that the Ramakrishnan-Yussouff theory overestimates the effects of fluctuations in this system. The reasons behind the failure of the Ramakrishnan-Yussouff approximation and the suitability of using the two-dimensional Potts model asmore » a testing ground for these theories are discussed.« less

Ion aggregation in high salt solutions. III. Computational vibrational spectroscopy of HDO in aqueous salt solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Choi, Jun-Ho; Lim, Sohee; Chon, Bonghwan

The vibrational frequency, frequency fluctuation dynamics, and transition dipole moment of the O—D stretch mode of HDO molecule in aqueous solutions are strongly dependent on its local electrostatic environment and hydrogen-bond network structure. Therefore, the time-resolved vibrational spectroscopy the O—D stretch mode has been particularly used to investigate specific ion effects on water structure. Despite prolonged efforts to understand the interplay of O—D vibrational dynamics with local water hydrogen-bond network and ion aggregate structures in high salt solutions, still there exists a gap between theory and experiment due to a lack of quantitative model for accurately describing O—D stretch frequencymore » in high salt solutions. To fill this gap, we have performed numerical simulations of Raman scattering and IR absorption spectra of the O—D stretch mode of HDO in highly concentrated NaCl and KSCN solutions and compared them with experimental results. Carrying out extensive quantum chemistry calculations on not only water clusters but also ion-water clusters, we first developed a distributed vibrational solvatochromic charge model for the O—D stretch mode in aqueous salt solutions. Furthermore, the non-Condon effect on the vibrational transition dipole moment of the O—D stretch mode was fully taken into consideration with the charge response kernel that is non-local polarizability density. From the fluctuating O—D stretch mode frequencies and transition dipole vectors obtained from the molecular dynamics simulations, the O—D stretch Raman scattering and IR absorption spectra of HDO in salt solutions could be calculated. The polarization effect on the transition dipole vector of the O—D stretch mode is shown to be important and the asymmetric line shapes of the O—D stretch Raman scattering and IR absorption spectra of HDO especially in highly concentrated NaCl and KSCN solutions are in quantitative agreement with experimental results. We anticipate that this computational approach will be of critical use in interpreting linear and nonlinear vibrational spectroscopies of HDO molecule that is considered as an excellent local probe for monitoring local electrostatic and hydrogen-bonding environment in not just salt but also other confined and crowded solutions.« less

Safe medication management in specialized home healthcare - an observational study.

PubMed

Lindblad, Marléne; Flink, Maria; Ekstedt, Mirjam

2017-08-24

Medication management is a complex, error-prone process. The aim of this study was to explore what constitutes the complexity of the medication management process (MMP) in specialized home healthcare and how healthcare professionals handle this complexity. The study is theoretically based in resilience engineering. Data were collected during the MMP at three specialized home healthcare units in Sweden using two strategies: observation of workplaces and shadowing RNs in everyday work, including interviews. Transcribed material was analysed using grounded theory. The MMP in home healthcare was dynamic and complex with unclear boundaries of responsibilities, inadequate information systems and fluctuating work conditions. Healthcare professionals adapted their everyday clinical work by sharing responsibility and simultaneously being authoritative and preserving patients' active participation, autonomy and integrity. To promote a safe MMP, healthcare professionals constantly re-prioritized goals, handled gaps in communication and information transmission at a distance by creating new bridging solutions. Trade-offs and workarounds were necessary elements, but also posed a threat to patient safety, as these interim solutions were not systematically evaluated or devised learning strategies. To manage a safe medication process in home healthcare, healthcare professionals need to adapt to fluctuating conditions and create bridging strategies through multiple parallel activities distributed over time, space and actors. The healthcare professionals' strategies could be integrated in continuous learning, while preserving boundaries of safety, instead of being more or less interim solutions. Patients' and family caregivers' as active partners in the MMP may be an underestimated resource for a resilient home healthcare.

Amplitude Scintillation due to Atmospheric Turbulence for the Deep Space Network Ka-Band Downlink

NASA Technical Reports Server (NTRS)

Ho, C.; Wheelon, A.

2004-01-01

Fast amplitude variations due to atmospheric scintillation are the main concerns for the Deep Space Network (DSN) Ka-band downlink under clear weather conditions. A theoretical study of the amplitude scintillation variances for a finite aperture antenna is presented. Amplitude variances for weak scattering scenarios are examined using turbulence theory to describe atmospheric irregularities. We first apply the Kolmogorov turbulent spectrum to a point receiver for three different turbulent profile models, especially for an exponential model varying with altitude. These analytic solutions then are extended to a receiver with a finite aperture antenna for the three profile models. Smoothing effects of antenna aperture are expressed by gain factors. A group of scaling factor relations is derived to show the dependences of amplitude variances on signal wavelength, antenna size, and elevation angle. Finally, we use these analytic solutions to estimate the scintillation intensity for a DSN Goldstone 34-m receiving station. We find that the (rms) amplitude fluctuation is 0.13 dB at 20-deg elevation angle for an exponential model, while the fluctuation is 0.05 dB at 90 deg. These results will aid us in telecommunication system design and signal-fading prediction. They also provide a theoretical basis for further comparison with other measurements at Ka-band.

Investigation of detection limits for solutes in water measured by laser raman spectrometry

USGS Publications Warehouse

Goldberg, M.C.

1977-01-01

The influence of experimental parameters on detection sensitivity was determined for laser Raman analysis of dissolved solutes in water. Individual solutions of nitrate, sulfate, carbonate, bicarbonate, monohydrogen phosphate, dihydrogen phosphate, acetate ion, and acetic acid were measured. An equation is derived which expresses the signal-to-noise ratio in terms of solute concentration, measurement time, spectral slit width, laser power fluctuations, and solvent background intensity. Laser beam intensity fluctuations at the sample and solvent background intensity are the most important limiting factors.

The diversity and unit of reactor noise theory

NASA Astrophysics Data System (ADS)

Kuang, Zhifeng

The study of reactor noise theory concerns questions about cause and effect relationships, and utilisation of random noise in nuclear reactor systems. The diversity of reactor noise theory arises from the variety of noise sources, the various mathematical treatments applied and various practical purposes. The neutron noise in zero- energy systems arises from the fluctuations in the number of neutrons per fission, the time between nuclear events, and the type of reactions. It can be used to evaluate system parameters. The mathematical treatment is based on the master equation of stochastic branching processes. The noise in power reactor systems is given rise by random processes of technological origin such as vibration of mechanical parts, boiling of the coolant, fluctuations of temperature and pressure. It can be used to monitor reactor behaviour with the possibility of detecting malfunctions at an early stage. The mathematical treatment is based on the Langevin equation. The unity of reactor noise theory arises from the fact that useful information from noise is embedded in the second moments of random variables, which lends the possibility of building up a unified mathematical description and analysis of the various reactor noise sources. Exploring such possibilities is the main subject among the three major topics reported in this thesis. The first subject is within the zero power noise in steady media, and we reported on the extension of the existing theory to more general cases. In Paper I, by use of the master equation approach, we have derived the most general Feynman- and Rossi-alpha formulae so far by taking the full joint statistics of the prompt and all the six groups of delayed neutron precursors, and a multiple emission source into account. The involved problems are solved with a combination of effective analytical techniques and symbolic algebra codes (Mathematica). Paper II gives a numerical evaluation of these formulae. An assessment of the contribution of the terms that are novel as compared to the traditional formulae has been made. The second subject treats a problem in power reactor noise with the Langevin formalism. With a very few exceptions, in all previous work the diffusion approximation was used. In order to extend the treatment to transport theory, in Paper III, we introduced a novel method, i.e. Padé approximation via Lanczos algorithm to calculate the transfer function of a finite slab reactor described by one-group transport equation. It was found that the local-global decomposition of the neutron noise, formerly only reproduced in at least 2- group theory, can be reconstructed. We have also showed the existence of a boundary layer of the neutron noise close to the boundary. Finally, we have explored the possibility of building up a unified theory to account for the coexistence of zero power and power reactor noise in a system. In Paper IV, a unified description of the neutron noise is given by the use of backward master equations in a model where the cross section fluctuations are given as a simple binary pseudorandom process. The general solution contains both the zero power and power reactor noise concurrently, and they can be extracted individually as limiting cases of the general solution. It justified the separate treatments of zero power and power reactor noise. The result was extended to the case including one group of delayed neutron precursors in Paper V.

Magnetic Field in a Screw Flow with Fluctuations

NASA Astrophysics Data System (ADS)

Titov, V. V.; Stepanov, R. A.; Sokoloff, D. D.

2018-04-01

We consider the influence of fluctuations in a screw flow of a conducting liquid on the effect of magnetic field self-excitation; the solution of this problem is important for experimental realization of a turbulent dynamo. We propose a theoretical approach based on the solution of averaged equations obtained in the limit of a short correlation time. The applicability of this approach is confirmed by direct numerical simulation of the initial equations. We demonstrate the influence of the correlation of fluctuations on the dynamo effect threshold. It is shown that the solution of the mean-field equations differs from the solution based on direct numerical simulation for a finite correlation time. The advantages and disadvantages of the two approaches are estimates, as well as the importance of the discovered difference in the context of problems of magnetic field self-excitation. The influence of helicity and intermittency on the type of the solution is considered.

Fluctuation-dissipation relations for motions of center of mass in driven granular fluids under gravity.

PubMed

Wakou, Jun'ichi; Isobe, Masaharu

2012-06-01

We investigated the validity of fluctuation-dissipation relations in the nonequilibrium stationary state of fluidized granular media under gravity by two independent approaches, based on theory and numerical simulations. A phenomenological Langevin-type theory describing the fluctuation of center of mass height, which was originally constructed for a one-dimensional granular gas on a vibrating bottom plate, was generalized to any dimensionality, even for the case in which the vibrating bottom plate is replaced by a thermal wall. The theory predicts a fluctuation-dissipation relation known to be satisfied at equilibrium, with a modification that replaces the equilibrium temperature by an effective temperature defined by the center of mass kinetic energy. To test the validity of the fluctuation-dissipation relation, we performed extensive and accurate event-driven molecular dynamics simulations for the model system with a thermal wall at the bottom. The power spectrum and response function of the center of mass height were measured and closely compared with theoretical predictions. It is shown that the fluctuation-dissipation relation for the granular system is satisfied, especially in the high-frequency (short time) region, for a wide range of system parameters. Finally, we describe the relationship between systematic deviations in the low-frequency (long time) region and the time scales of the driven granular system.

Raman correlation spectroscopy: A feasibility study of a new optical correlation technique and development of multi-component nanoparticles using the reprecipitation method

NASA Astrophysics Data System (ADS)

Nishida, Maki

The feasibility of Raman correlation spectroscopy (RCS) is investigated as a new temporal optical fluctuation spectroscopy in this dissertation. RCS analyzes the correlations of the intensity fluctuations of Raman scattering from particles in a suspension that undergo Brownian motion. Because each Raman emission line arises from a specific molecular bond, the RCS method could yield diffusion behavior of specific chemical species within a dispersion. Due to the nature of Raman scattering as a coherent process, RCS could provide similar information as acquired in dynamic light scattering (DLS) and be practical for various applications that requires the chemical specificity in dynamical information. The theoretical development is discussed, and four experimental implementations of this technique are explained. The autocorrelation of the intensity fluctuations from a beta-carotene solution is obtained using the some configurations; however, the difficulty in precise alignment and weak nature of Raman scattering prevented the achievement of high sensitivity and resolution. Possible fluctuations of the phase of Raman scattering could also be affecting the results. A possible explanation of the observed autocorrelation in terms of number fluctuations of particles is also examined to test the feasibility of RCS as a new optical characterization method. In order to investigate the complex systems for which RCS would be useful, strategies for the creation of a multicomponent nanoparticle system are also explored. Using regular solution theory along with the concept of Hansen solubility parameters, an analytical model is developed to predict whether two or more components will form single nanoparticles, and what effect various processing conditions would have. The reprecipitation method was used to demonstrate the formation of the multi-component system of the charge transfer complex perylene:TCNQ (tetracyanoquinodimethane) and the active pharmaceutical ingredient cocrystal of CBZ:NCT (carbamazepine:nicotinamide). The experimental results with various characterization methods including DLS, absorption spectroscopy, powder x-ray diffraction, and SEM imaging, verify formation of the multicomponent cocrystals. The observation of the self-assembly of TCNQ crystals is also discussed.

Permeability modes in fluctuating lipid membranes with DNA-translocating pores.

PubMed

Moleiro, L H; Mell, M; Bocanegra, R; López-Montero, I; Fouquet, P; Hellweg, Th; Carrascosa, J L; Monroy, F

2017-09-01

Membrane pores can significantly alter not only the permeation dynamics of biological membranes but also their elasticity. Large membrane pores able to transport macromolecular contents represent an interesting model to test theoretical predictions that assign active-like (non-equilibrium) behavior to the permeability contributions to the enhanced membrane fluctuations existing in permeable membranes [Maneville et al. Phys. Rev. Lett. 82, 4356 (1999)]. Such high-amplitude active contributions arise from the forced transport of solvent and solutes through the open pores, which becomes even dominant at large permeability. In this paper, we present a detailed experimental analysis of the active shape fluctuations that appear in highly permeable lipid vesicles with large macromolecular pores inserted in the lipid membrane, which are a consequence of transport permeability events occurred in an osmotic gradient. The experimental results are found in quantitative agreement with theory, showing a remarkable dependence with the density of membrane pores and giving account of mechanical compliances and permeability rates that are compatible with the large size of the membrane pore considered. The presence of individual permeation events has been detected in the fluctuation time-series, from which a stochastic distribution of the permeation events compatible with a shot-noise has been deduced. The non-equilibrium character of the membrane fluctuations in a permeation field, even if the membrane pores are mere passive transporters, is clearly demonstrated. Finally, a bio-nano-technology outlook of the proposed synthetic concept is given on the context of prospective uses as active membrane DNA-pores exploitable in gen-delivery applications based on lipid vesicles. Copyright © 2017 Elsevier B.V. All rights reserved.

COSMOS-e'-soft Higgsotic attractors

NASA Astrophysics Data System (ADS)

Choudhury, Sayantan

2017-07-01

In this work, we have developed an elegant algorithm to study the cosmological consequences from a huge class of quantum field theories (i.e. superstring theory, supergravity, extra dimensional theory, modified gravity, etc.), which are equivalently described by soft attractors in the effective field theory framework. In this description we have restricted our analysis for two scalar fields - dilaton and Higgsotic fields minimally coupled with Einstein gravity, which can be generalized for any arbitrary number of scalar field contents with generalized non-canonical and non-minimal interactions. We have explicitly used R^2 gravity, from which we have studied the attractor and non-attractor phases by exactly computing two point, three point and four point correlation functions from scalar fluctuations using the In-In (Schwinger-Keldysh) and the δ N formalisms. We have also presented theoretical bounds on the amplitude, tilt and running of the primordial power spectrum, various shapes (equilateral, squeezed, folded kite or counter-collinear) of the amplitude as obtained from three and four point scalar functions, which are consistent with observed data. Also the results from two point tensor fluctuations and the field excursion formula are explicitly presented for the attractor and non-attractor phase. Further, reheating constraints, scale dependent behavior of the couplings and the dynamical solution for the dilaton and Higgsotic fields are also presented. New sets of consistency relations between two, three and four point observables are also presented, which shows significant deviation from canonical slow-roll models. Additionally, three possible theoretical proposals have presented to overcome the tachyonic instability at the time of late time acceleration. Finally, we have also provided the bulk interpretation from the three and four point scalar correlation functions for completeness.

On the dimensionally correct kinetic theory of turbulence for parallel propagation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gaelzer, R., E-mail: rudi.gaelzer@ufrgs.br, E-mail: yoonp@umd.edu, E-mail: 007gasun@khu.ac.kr, E-mail: luiz.ziebell@ufrgs.br; Ziebell, L. F., E-mail: rudi.gaelzer@ufrgs.br, E-mail: yoonp@umd.edu, E-mail: 007gasun@khu.ac.kr, E-mail: luiz.ziebell@ufrgs.br; Yoon, P. H., E-mail: rudi.gaelzer@ufrgs.br, E-mail: yoonp@umd.edu, E-mail: 007gasun@khu.ac.kr, E-mail: luiz.ziebell@ufrgs.br

2015-03-15

Yoon and Fang [Phys. Plasmas 15, 122312 (2008)] formulated a second-order nonlinear kinetic theory that describes the turbulence propagating in directions parallel/anti-parallel to the ambient magnetic field. Their theory also includes discrete-particle effects, or the effects due to spontaneously emitted thermal fluctuations. However, terms associated with the spontaneous fluctuations in particle and wave kinetic equations in their theory contain proper dimensionality only for an artificial one-dimensional situation. The present paper extends the analysis and re-derives the dimensionally correct kinetic equations for three-dimensional case. The new formalism properly describes the effects of spontaneous fluctuations emitted in three-dimensional space, while the collectivelymore » emitted turbulence propagates predominantly in directions parallel/anti-parallel to the ambient magnetic field. As a first step, the present investigation focuses on linear wave-particle interaction terms only. A subsequent paper will include the dimensionally correct nonlinear wave-particle interaction terms.« less

Mass hierarchy, mass gap and corrections to Newton's law on thick branes with Poincaré symmetry

NASA Astrophysics Data System (ADS)

Barbosa-Cendejas, Nandinii; Herrera-Aguilar, Alfredo; Kanakoglou, Konstantinos; Nucamendi, Ulises; Quiros, Israel

2014-01-01

We consider a scalar thick brane configuration arising in a 5D theory of gravity coupled to a self-interacting scalar field in a Riemannian manifold. We start from known classical solutions of the corresponding field equations and elaborate on the physics of the transverse traceless modes of linear fluctuations of the classical background, which obey a Schrödinger-like equation. We further consider two special cases in which this equation can be solved analytically for any massive mode with , in contrast with numerical approaches, allowing us to study in closed form the massive spectrum of Kaluza-Klein (KK) excitations and to analytically compute the corrections to Newton's law in the thin brane limit. In the first case we consider a novel solution with a mass gap in the spectrum of KK fluctuations with two bound states—the massless 4D graviton free of tachyonic instabilities and a massive KK excitation—as well as a tower of continuous massive KK modes which obey a Legendre equation. The mass gap is defined by the inverse of the brane thickness, allowing us to get rid of the potentially dangerous multiplicity of arbitrarily light KK modes. It is shown that due to this lucky circumstance, the solution of the mass hierarchy problem is much simpler and transparent than in the thin Randall-Sundrum (RS) two-brane configuration. In the second case we present a smooth version of the RS model with a single massless bound state, which accounts for the 4D graviton, and a sector of continuous fluctuation modes with no mass gap, which obey a confluent Heun equation in the Ince limit. (The latter seems to have physical applications for the first time within braneworld models). For this solution the mass hierarchy problem is solved with positive branes as in the Lykken-Randall (LR) model and the model is completely free of naked singularities. We also show that the scalar-tensor system is stable under scalar perturbations with no scalar modes localized on the braneworld configuration.

Gravitational waves during inflation from a 5D large-scale repulsive gravity model

NASA Astrophysics Data System (ADS)

Reyes, Luz M.; Moreno, Claudia; Madriz Aguilar, José Edgar; Bellini, Mauricio

2012-10-01

We investigate, in the transverse traceless (TT) gauge, the generation of the relic background of gravitational waves, generated during the early inflationary stage, on the framework of a large-scale repulsive gravity model. We calculate the spectrum of the tensor metric fluctuations of an effective 4D Schwarzschild-de Sitter metric on cosmological scales. This metric is obtained after implementing a planar coordinate transformation on a 5D Ricci-flat metric solution, in the context of a non-compact Kaluza-Klein theory of gravity. We found that the spectrum is nearly scale invariant under certain conditions. One interesting aspect of this model is that it is possible to derive the dynamical field equations for the tensor metric fluctuations, valid not just at cosmological scales, but also at astrophysical scales, from the same theoretical model. The astrophysical and cosmological scales are determined by the gravity-antigravity radius, which is a natural length scale of the model, that indicates when gravity becomes repulsive in nature.

Quantum critical singularities in two-dimensional metallic XY ferromagnets

NASA Astrophysics Data System (ADS)

Varma, Chandra M.; Gannon, W. J.; Aronson, M. C.; Rodriguez-Rivera, J. A.; Qiu, Y.

2018-02-01

An important problem in contemporary physics concerns quantum-critical fluctuations in metals. A scaling function for the momentum, frequency, temperature, and magnetic field dependence of the correlation function near a 2D-ferromagnetic quantum-critical point (QCP) is constructed, and its singularities are determined by comparing to the recent calculations of the correlation functions of the dissipative quantum XY model (DQXY). The calculations are motivated by the measured properties of the metallic compound YFe2Al10 , which is a realization of the DQXY model in 2D. The frequency, temperature, and magnetic field dependence of the scaling function as well as the singularities measured in the experiments are given by the theory without adjustable exponents. The same model is applicable to the superconductor-insulator transitions, classes of metallic AFM-QCPs, and as fluctuations of the loop-current ordered state in hole-doped cuprates. The results presented here lend credence to the solution found for the 2D-DQXY model and its applications in understanding quantum-critical properties of diverse systems.

Application of an Extended Parabolic Equation to the Calculation of the Mean Field and the Transverse and Longitudinal Mutual Coherence Functions Within Atmospheric Turbulence

NASA Technical Reports Server (NTRS)

Manning, Robert M.

2005-01-01

Solutions are derived for the generalized mutual coherence function (MCF), i.e., the second order moment, of a random wave field propagating through a random medium within the context of the extended parabolic equation. Here, "generalized" connotes the consideration of both the transverse as well as the longitudinal second order moments (with respect to the direction of propagation). Such solutions will afford a comparison between the results of the parabolic equation within the pararaxial approximation and those of the wide-angle extended theory. To this end, a statistical operator method is developed which gives a general equation for an arbitrary spatial statistical moment of the wave field. The generality of the operator method allows one to obtain an expression for the second order field moment in the direction longitudinal to the direction of propagation. Analytical solutions to these equations are derived for the Kolmogorov and Tatarskii spectra of atmospheric permittivity fluctuations within the Markov approximation.

Communication: Appearance of undershoots in start-up shear: Experimental findings captured by tumbling-snake dynamics

NASA Astrophysics Data System (ADS)

Stephanou, Pavlos S.; Schweizer, Thomas; Kröger, Martin

2017-04-01

Our experimental data unambiguously show (i) a damping behavior (the appearance of an undershoot following the overshoot) in the transient shear viscosity of a concentrated polymeric solution, and (ii) the absence of a corresponding behavior in the transient normal stress coefficients. Both trends are shown to be quantitatively captured by the bead-link chain kinetic theory for concentrated polymer solutions and entangled polymer melts proposed by Curtiss and Bird, supplemented by a non-constant link tension coefficient that we relate to the nematic order parameter. The observed phenomena are attributed to the tumbling behavior of the links, triggered by rotational fluctuations, on top of reptation. Using model parameters deduced from stationary data, we calculate the transient behavior of the stress tensor for this "tumbling-snake" model after startup of shear flow efficiently via simple Brownian dynamics. The unaltered method is capable of handling arbitrary homogeneous flows and has the promising capacity to improve our understanding of the transient behavior of concentrated polymer solutions.

Origin of density fluctuations in extended inflation

NASA Technical Reports Server (NTRS)

Kolb, Edward W.; Salopek, David S.; Turner, Michael S.

1990-01-01

The density fluctuations (both curvature and isocurvature) that arise due to quantum fluctuations in a simple model of extended inflation based upon the Jordan-Brans-Dicke theory are calculated. Curvature fluctuations arise due to quantum fluctuations in the Brans-Dicke field, in general have a nonscale-invariant spectrum, and can have an amplitude that is cosmologically acceptable and interesting without having to tune any coupling constant to a very small value. The density perturbations that arise due to the inflation field are subdominant. If there are other massless fields in the theory, e.g., an axion or an ilion, then isocurvature fluctuations arise in these fields too. Production of gravitational waves and the massless particles associated with excitations of the Brans-Dicke field are also discussed. Several attempts at more realistic models of extended inflation are also analyzed. The importance of the Einstein conformal frame in calculating curvature fluctuations is emphasized. When viewed in this frame, extended inflation closely resembles slow-rollover inflation with an exponential potential and the usual formula for the amplitude of curvature perturbations applies.

How does non-linear dynamics affect the baryon acoustic oscillation?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sugiyama, Naonori S.; Spergel, David N., E-mail: nao.s.sugiyama@gmail.com, E-mail: dns@astro.princeton.edu

2014-02-01

We study the non-linear behavior of the baryon acoustic oscillation in the power spectrum and the correlation function by decomposing the dark matter perturbations into the short- and long-wavelength modes. The evolution of the dark matter fluctuations can be described as a global coordinate transformation caused by the long-wavelength displacement vector acting on short-wavelength matter perturbation undergoing non-linear growth. Using this feature, we investigate the well known cancellation of the high-k solutions in the standard perturbation theory. While the standard perturbation theory naturally satisfies the cancellation of the high-k solutions, some of the recently proposed improved perturbation theories do notmore » guarantee the cancellation. We show that this cancellation clarifies the success of the standard perturbation theory at the 2-loop order in describing the amplitude of the non-linear power spectrum even at high-k regions. We propose an extension of the standard 2-loop level perturbation theory model of the non-linear power spectrum that more accurately models the non-linear evolution of the baryon acoustic oscillation than the standard perturbation theory. The model consists of simple and intuitive parts: the non-linear evolution of the smoothed power spectrum without the baryon acoustic oscillations and the non-linear evolution of the baryon acoustic oscillations due to the large-scale velocity of dark matter and due to the gravitational attraction between dark matter particles. Our extended model predicts the smoothing parameter of the baryon acoustic oscillation peak at z = 0.35 as ∼ 7.7Mpc/h and describes the small non-linear shift in the peak position due to the galaxy random motions.« less

De Sitter Space Without Dynamical Quantum Fluctuations

NASA Astrophysics Data System (ADS)

Boddy, Kimberly K.; Carroll, Sean M.; Pollack, Jason

2016-06-01

We argue that, under certain plausible assumptions, de Sitter space settles into a quiescent vacuum in which there are no dynamical quantum fluctuations. Such fluctuations require either an evolving microstate, or time-dependent histories of out-of-equilibrium recording devices, which we argue are absent in stationary states. For a massive scalar field in a fixed de Sitter background, the cosmic no-hair theorem implies that the state of the patch approaches the vacuum, where there are no fluctuations. We argue that an analogous conclusion holds whenever a patch of de Sitter is embedded in a larger theory with an infinite-dimensional Hilbert space, including semiclassical quantum gravity with false vacua or complementarity in theories with at least one Minkowski vacuum. This reasoning provides an escape from the Boltzmann brain problem in such theories. It also implies that vacuum states do not uptunnel to higher-energy vacua and that perturbations do not decohere while slow-roll inflation occurs, suggesting that eternal inflation is much less common than often supposed. On the other hand, if a de Sitter patch is a closed system with a finite-dimensional Hilbert space, there will be Poincaré recurrences and dynamical Boltzmann fluctuations into lower-entropy states. Our analysis does not alter the conventional understanding of the origin of density fluctuations from primordial inflation, since reheating naturally generates a high-entropy environment and leads to decoherence, nor does it affect the existence of non-dynamical vacuum fluctuations such as those that give rise to the Casimir effect.

Fluctuation-dissipation theory of input-output interindustrial relations

NASA Astrophysics Data System (ADS)

Iyetomi, Hiroshi; Nakayama, Yasuhiro; Aoyama, Hideaki; Fujiwara, Yoshi; Ikeda, Yuichi; Souma, Wataru

2011-01-01

In this study, the fluctuation-dissipation theory is invoked to shed light on input-output interindustrial relations at a macroscopic level by its application to indices of industrial production (IIP) data for Japan. Statistical noise arising from finiteness of the time series data is carefully removed by making use of the random matrix theory in an eigenvalue analysis of the correlation matrix; as a result, two dominant eigenmodes are detected. Our previous study successfully used these two modes to demonstrate the existence of intrinsic business cycles. Here a correlation matrix constructed from the two modes describes genuine interindustrial correlations in a statistically meaningful way. Furthermore, it enables us to quantitatively discuss the relationship between shipments of final demand goods and production of intermediate goods in a linear response framework. We also investigate distinctive external stimuli for the Japanese economy exerted by the current global economic crisis. These stimuli are derived from residuals of moving-average fluctuations of the IIP remaining after subtracting the long-period components arising from inherent business cycles. The observation reveals that the fluctuation-dissipation theory is applicable to an economic system that is supposed to be far from physical equilibrium.

Work and heat fluctuations in two-state systems: a trajectory thermodynamics formalism

NASA Astrophysics Data System (ADS)

Ritort, F.

2004-10-01

Two-state models provide phenomenological descriptions of many different systems, ranging from physics to chemistry and biology. We investigate work fluctuations in an ensemble of two-state systems driven out of equilibrium under the action of an external perturbation. We calculate the probability density PN(W) that work equal to W is exerted upon the system (of size N) along a given non-equilibrium trajectory and introduce a trajectory thermodynamics formalism to quantify work fluctuations in the large-N limit. We then define a trajectory entropy SN(W) that counts the number of non-equilibrium trajectories PN(W) = exp(SN(W)/kBT) with work equal to W and characterizes fluctuations of work trajectories around the most probable value Wmp. A trajectory free energy {\\cal F}_N(W) can also be defined, which has a minimum at W = W†, this being the value of the work that has to be efficiently sampled to quantitatively test the Jarzynski equality. Within this formalism a Lagrange multiplier is also introduced, the inverse of which plays the role of a trajectory temperature. Our general solution for PN(W) exactly satisfies the fluctuation theorem by Crooks and allows us to investigate heat fluctuations for a protocol that is invariant under time reversal. The heat distribution is then characterized by a Gaussian component (describing small and frequent heat exchange events) and exponential tails (describing the statistics of large deviations and rare events). For the latter, the width of the exponential tails is related to the aforementioned trajectory temperature. Finite-size effects to the large-N theory and the recovery of work distributions for finite N are also discussed. Finally, we pay particular attention to the case of magnetic nanoparticle systems under the action of a magnetic field H where work and heat fluctuations are predicted to be observable in ramping experiments in micro-SQUIDs.

Evolution of statistical averages: An interdisciplinary proposal using the Chapman-Enskog method

NASA Astrophysics Data System (ADS)

Mariscal-Sanchez, A.; Sandoval-Villalbazo, A.

2017-08-01

This work examines the idea of applying the Chapman-Enskog (CE) method for approximating the solution of the Boltzmann equation beyond the realm of physics, using an information theory approach. Equations describing the evolution of averages and their fluctuations in a generalized phase space are established up to first-order in the Knudsen parameter which is defined as the ratio of the time between interactions (mean free time) and a characteristic macroscopic time. Although the general equations here obtained may be applied in a wide range of disciplines, in this paper, only a particular case related to the evolution of averages in speculative markets is examined.

DIFFUSED SOLUTE-SOLVENT INTERFACE WITH POISSON-BOLTZMANN ELECTROSTATICS: FREE-ENERGY VARIATION AND SHARP-INTERFACE LIMIT.

PubMed

Li, B O; Liu, Yuan

A phase-field free-energy functional for the solvation of charged molecules (e.g., proteins) in aqueous solvent (i.e., water or salted water) is constructed. The functional consists of the solute volumetric and solute-solvent interfacial energies, the solute-solvent van der Waals interaction energy, and the continuum electrostatic free energy described by the Poisson-Boltzmann theory. All these are expressed in terms of phase fields that, for low free-energy conformations, are close to one value in the solute phase and another in the solvent phase. A key property of the model is that the phase-field interpolation of dielectric coefficient has the vanishing derivative at both solute and solvent phases. The first variation of such an effective free-energy functional is derived. Matched asymptotic analysis is carried out for the resulting relaxation dynamics of the diffused solute-solvent interface. It is shown that the sharp-interface limit is exactly the variational implicit-solvent model that has successfully captured capillary evaporation in hydrophobic confinement and corresponding multiple equilibrium states of underlying biomolecular systems as found in experiment and molecular dynamics simulations. Our phase-field approach and analysis can be used to possibly couple the description of interfacial fluctuations for efficient numerical computations of biomolecular interactions.

Grand minima and equatorial symmetry breaking in axisymmetric dynamo models

NASA Astrophysics Data System (ADS)

Brooke, John M.; Pelt, Jaan; Tavakol, Reza; Tworkowski, Andrew

1998-04-01

We consider the manner in which time-periodic solutions of an axisymmetric dynamo model can undergo breaking of equatorial symmetry, i.e. loss of pure dipolar or quadrupolar symmetry. By considering the symmetry group underlying the solutions, we show that the fluctuations responsible for the symmetry-breaking can be constrained such that they are in resonance with the former solution. They can then be amplified until they are comparable in magnitude to the former solution. If the bifurcation is supercritical, the amplitude of the fluctuation is stabilised and a stable mixed parity limit cycle is formed. If it is subcritical it gives rise to a recently identified form of intermittency, called icicle intermittency. This produces episodes in which the original solution and the fluctuation are almost exactly synchronised and the fluctuation grows exponentially in amplitude, interrupted by brief episodes where synchronicity is lost and the amplitude of the fluctuation declines rapidly by several orders of magnitude. During these latter episodes there is a significant dip in the amplitude of the total magnetic field. This model-independent analysis can produce quantitative predictions for the behaviour of this bifurcation and we provide evidence for this behaviour by analysing timeseries from four different mean-field dynamo models, where intermittency is observed without the need for stochastic, or chaotically driven, forcing terms in the dynamo equations. We compare these results with recent work on intermittency in dynamo models and consider their relevance to the intermittency present in solar and stellar cycles.

Ginzburg-Landau theory, strong coupling corrections and exchange enhancements: Can spin fluctuations give high T c's?

NASA Astrophysics Data System (ADS)

Quader, Khandker F.; Salamon, M. B.

1988-06-01

Ginzburg-Landau theory is used to explore the thermodynamic and electrodynamic properties of YBa 2Cu 3O 7-δ, and to determine γ, m ∗/m and the exchange enhancement. This material is found to be in a moderately strong coupling regime, intermediate between dirty and clean limits; strong coupling corrections are estimated. It is shown that, irrespective of the choice of the carrier density, spin fluctuations are unable to give a sufficiently large T c. An upper bound is given for the T c due spin-fluctuation-mediated pairing.

A non-linear theory of the parallel firehose and gyrothermal instabilities in a weakly collisional plasma

NASA Astrophysics Data System (ADS)

Rosin, M. S.; Schekochihin, A. A.; Rincon, F.; Cowley, S. C.

2011-05-01

Weakly collisional magnetized cosmic plasmas have a dynamical tendency to develop pressure anisotropies with respect to the local direction of the magnetic field. These anisotropies trigger plasma instabilities at scales just above the ion Larmor radius ρi and much below the mean free path λmfp. They have growth rates of a fraction of the ion cyclotron frequency, which is much faster than either the global dynamics or even local turbulence. Despite their microscopic nature, these instabilities dramatically modify the transport properties and, therefore, the macroscopic dynamics of the plasma. The non-linear evolution of these instabilities is expected to drive pressure anisotropies towards marginal stability values, controlled by the plasma beta βi. Here this non-linear evolution is worked out in an ab initio kinetic calculation for the simplest analytically tractable example - the parallel (k⊥= 0) firehose instability in a high-beta plasma. An asymptotic theory is constructed, based on a particular physical ordering and leading to a closed non-linear equation for the firehose turbulence. In the non-linear regime, both the analytical theory and the numerical solution predict secular (∝t) growth of magnetic fluctuations. The fluctuations develop a k-3∥ spectrum, extending from scales somewhat larger than ρi to the maximum scale that grows secularly with time (∝t1/2); the relative pressure anisotropy (p⊥-p∥)/p∥ tends to the marginal value -2/βi. The marginal state is achieved via changes in the magnetic field, not particle scattering. When a parallel ion heat flux is present, the parallel firehose mutates into the new gyrothermal instability (GTI), which continues to exist up to firehose-stable values of pressure anisotropy, which can be positive and are limited by the magnitude of the ion heat flux. The non-linear evolution of the GTI also features secular growth of magnetic fluctuations, but the fluctuation spectrum is eventually dominated by modes around a maximal scale ˜ρilT/λmfp, where lT is the scale of the parallel temperature variation. Implications for momentum and heat transport are speculated about. This study is motivated by our interest in the dynamics of galaxy cluster plasmas (which are used as the main astrophysical example), but its relevance to solar wind and accretion flow plasmas is also briefly discussed.

Binary collision approximations for the memory function for density fluctuations in equilibrium atomic liquids

NASA Astrophysics Data System (ADS)

Noah, Joyce E.

Time correlation functions of density fluctuations of liquids at equilibrium can be used to relate the microscopic dynamics of a liquid to its macroscopic transport properties. Time correlation functions are especially useful since they can be generated in a variety of ways, from scattering experiments to computer simulation to analytic theory. The kinetic theory of fluctuations in equilibrium liquids is an analytic theory for calculating correlation functions using memory functions. In this work, we use a diagrammatic formulation of the kinetic theory to develop a series of binary collision approximations for the collisional part of the memory function. We define binary collisions as collisions between two distinct density fluctuations whose identities are fixed during the duration of a collsion. R approximations are for the short time part of the memory function, and build upon the work of Ranganathan and Andersen. These approximations have purely repulsive interactions between the fluctuations. The second type of approximation, RA approximations, is for the longer time part of the memory function, where the density fluctuations now interact via repulsive and attractive forces. Although RA approximations are a natural extension of R approximations, they permit two density fluctuations to become trapped in the wells of the interaction potential, leading to long-lived oscillatory behavior, which is unphysical. Therefore we consider S approximations which describe binary particles which experience the random effect of the surroundings while interacting via repulsive or repulsive and attractive interactions. For each of these approximations for the memory function we numerically solve the kinetic equation to generate correlation functions. These results are compared to molecular dynamics results for the correlation functions. Comparing the successes and failures of the different approximations, we conclude that R approximations give more accurate intermediate and long time results while RA and S approximations do particularly well at predicting the short time behavior. Lastly, we also develop a series of non-graphically derived approximations and use an optimization procedure to determine the underlying memory function from the simulation data. These approaches provide valuable information about the memory function that will be used in the development of future kinetic theories.

Reexamination of relaxation of spins due to a magnetic field gradient: Identity of the Redfield and Torrey theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Golub, R.; Rohm, Ryan M.; Swank, C. M.

2011-02-15

There is an extensive literature on magnetic-gradient-induced spin relaxation. Cates, Schaefer, and Happer, in a seminal publication, have solved the problem in the regime where diffusion theory (the Torrey equation) is applicable using an expansion of the density matrix in diffusion equation eigenfunctions and angular momentum tensors. McGregor has solved the problem in the same regime using a slightly more general formulation using the Redfield theory formulated in terms of the autocorrelation function of the fluctuating field seen by the spins and calculating the correlation functions using the diffusion-theory Green's function. The results of both calculations were shown to agreemore » for a special case. In the present work, we show that the eigenfunction expansion of the Torrey equation yields the expansion of the Green's function for the diffusion equation, thus showing the identity of this approach with that of the Redfield theory. The general solution can also be obtained directly from the Torrey equation for the density matrix. Thus, the physical content of the Redfield and Torrey approaches are identical. We then introduce a more general expression for the position autocorrelation function of particles moving in a closed cell, extending the range of applicability of the theory.« less

Barometric fluctuations in wells tapping deep unconfined aquifers

USGS Publications Warehouse

Weeks, Edwin P.

1979-01-01

Water levels in wells screened only below the water table in unconfined aquifers fluctuate in response to atmospheric pressure changes. These fluctuations occur because the materials composing the unsaturated zone resist air movement and have capacity to store air with a change in pressure. Consequently, the translation of any pressure change at land surface is slowed as it moves through the unsaturated zone to the water table, but it reaches the water surface in the well instantaneously. Thus a pressure imbalance is created that results in a water level fluctuation. Barometric effects on water levels in unconfined aquifers can be computed by solution of the differential equation governing the flow of gas in the unsaturated zone subject to the appropriate boundary conditions. Solutions to this equation for two sets of boundary conditions were applied to compute water level response in a well tapping the Ogallala Formation near Lubbock, Texas from simultaneous microbarograph records. One set of computations, based on the step function unit response solution and convolution, resulted in a very good match between computed and measured water levels. A second set of computations, based on analysis of the amplitude ratios of simultaneous cyclic microbarograph and water level fluctuations, gave inconsistent results in terms of the unsaturated zone pneumatic properties but provided useful insights on the nature of unconfined-aquifer water level fluctuations.

Elasticity of short DNA molecules: theory and experiment for contour lengths of 0.6-7 microm.

PubMed

Seol, Yeonee; Li, Jinyu; Nelson, Philip C; Perkins, Thomas T; Betterton, M D

2007-12-15

The wormlike chain (WLC) model currently provides the best description of double-stranded DNA elasticity for micron-sized molecules. This theory requires two intrinsic material parameters-the contour length L and the persistence length p. We measured and then analyzed the elasticity of double-stranded DNA as a function of L (632 nm-7.03 microm) using the classic solution to the WLC model. When the elasticity data were analyzed using this solution, the resulting fitted value for the persistence length p(wlc) depended on L; even for moderately long DNA molecules (L = 1300 nm), this apparent persistence length was 10% smaller than its limiting value for long DNA. Because p is a material parameter, and cannot depend on length, we sought a new solution to the WLC model, which we call the "finite wormlike chain (FWLC)," to account for effects not considered in the classic solution. Specifically we accounted for the finite chain length, the chain-end boundary conditions, and the bead rotational fluctuations inherent in optical trapping assays where beads are used to apply the force. After incorporating these corrections, we used our FWLC solution to generate force-extension curves, and then fit those curves with the classic WLC solution, as done in the standard experimental analysis. These results qualitatively reproduced the apparent dependence of p(wlc) on L seen in experimental data when analyzed with the classic WLC solution. Directly fitting experimental data to the FWLC solution reduces the apparent dependence of p(fwlc) on L by a factor of 3. Thus, the FWLC solution provides a significantly improved theoretical framework in which to analyze single-molecule experiments over a broad range of experimentally accessible DNA lengths, including both short (a few hundred nanometers in contour length) and very long (microns in contour length) molecules.

Exact solution for the energy spectrum of Kelvin-wave turbulence in superfluids

NASA Astrophysics Data System (ADS)

Boué, Laurent; Dasgupta, Ratul; Laurie, Jason; L'Vov, Victor; Nazarenko, Sergey; Procaccia, Itamar

2011-08-01

We study the statistical and dynamical behavior of turbulent Kelvin waves propagating on quantized vortices in superfluids and address the controversy concerning the energy spectrum that is associated with these excitations. Finding the correct energy spectrum is important because Kelvin waves play a major role in the dissipation of energy in superfluid turbulence at near-zero temperatures. In this paper, we show analytically that the solution proposed by [L’vov and Nazarenko, JETP Lett.JTPLA20021-364010.1134/S002136401008014X 91, 428 (2010)] enjoys existence, uniqueness, and regularity of the prefactor. Furthermore, we present numerical results of the dynamical equation that describes to leading order the nonlocal regime of the Kelvin-wave dynamics. We compare our findings with the analytical results from the proposed local and nonlocal theories for Kelvin-wave dynamics and show an agreement with the nonlocal predictions. Accordingly, the spectrum proposed by L’vov and Nazarenko should be used in future theories of quantum turbulence. Finally, for weaker wave forcing we observe an intermittent behavior of the wave spectrum with a fluctuating dissipative scale, which we interpreted as a finite-size effect characteristic of mesoscopic wave turbulence.

The intrinsic periodic fluctuation of forest: a theoretical model based on diffusion equation

NASA Astrophysics Data System (ADS)

Zhou, J.; Lin, G., Sr.

2015-12-01

Most forest dynamic models predict the stable state of size structure as well as the total basal area and biomass in mature forest, the variation of forest stands are mainly driven by environmental factors after the equilibrium has been reached. However, although the predicted power-law size-frequency distribution does exist in analysis of many forest inventory data sets, the estimated distribution exponents are always shifting between -2 and -4, and has a positive correlation with the mean value of DBH. This regular pattern can not be explained by the effects of stochastic disturbances on forest stands. Here, we adopted the partial differential equation (PDE) approach to deduce the systematic behavior of an ideal forest, by solving the diffusion equation under the restricted condition of invariable resource occupation, a periodic solution was gotten to meet the variable performance of forest size structure while the former models with stable performance were just a special case of the periodic solution when the fluctuation frequency equals zero. In our results, the number of individuals in each size class was the function of individual growth rate(G), mortality(M), size(D) and time(T), by borrowing the conclusion of allometric theory on these parameters, the results perfectly reflected the observed "exponent-mean DBH" relationship and also gave a logically complete description to the time varying form of forest size-frequency distribution. Our model implies that the total biomass of a forest can never reach a stable equilibrium state even in the absence of disturbances and climate regime shift, we propose the idea of intrinsic fluctuation property of forest and hope to provide a new perspective on forest dynamics and carbon cycle research.

Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pribram-Jones, Aurora; Grabowski, Paul E.; Burke, Kieron

We present that the van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. Finally, this produces a natural method for generating new thermal exchange-correlation approximations.

Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem

DOE PAGES

Pribram-Jones, Aurora; Grabowski, Paul E.; Burke, Kieron

2016-06-08

We present that the van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. Finally, this produces a natural method for generating new thermal exchange-correlation approximations.

Neutrino flavour evolution through fluctuating matter

NASA Astrophysics Data System (ADS)

Yang, Y.; Kneller, J. P.

2018-04-01

A neutrino propagating through fluctuating matter can experience large amplitude transitions between its states. Such transitions occur in supernovae and compact object mergers due to turbulent matter profiles and neutrino self-interactions. In this paper we study, both numerically and analytically, three-flavour neutrino transformation through fluctuating matter built from two and three Fourier modes (FMs). We find flavour transformation effects which cannot occur with just two flavours. For the case of two FMs we observe the equivalent of ‘induced transparency’ from quantum optics whereby transitions between a given pair of states are suppressed due to the presence of a resonant mode between another pair. When we add a third FM we find a new effect whereby the third mode can manipulate the transition probabilities of the two mode case so as to force complete transparency or, alternatively, restore ‘opacity’ meaning the perturbative Hamiltonian regains its ability to induce neutrino flavour transitions. In both applications we find analytic solutions are able to match the amplitude and wavenumber of the numerical results to within a few percent. We then consider a case of turbulence and show how the theory can be used to understand the very different response of a neutrino to what appears to be two, almost identical, instances of turbulence.

A two-dimensional analytical model for groundwater flow in a leaky aquifer extending finite distance under the estuary

NASA Astrophysics Data System (ADS)

Chuang, Mo-Hsiung; Hung, Chi-Tung; -Yen Lin, Wen; Ma, Kuo-chen

2017-04-01

In recent years, cities and industries in the vicinity of the estuarine region have developed rapidly, resulting in a sharp increase in the population concerned. The increasing demand for human activities, agriculture irrigation, and aquaculture relies on massive pumping of water in estuarine area. Since the 1950s, numerous studies have focused on the effects of tidal fluctuations on groundwater flow in the estuarine area. Tide-induced head fluctuation in a two-dimensional estuarine aquifer system is complicated and rather important in dealing with many groundwater management or remediation problems. The conceptual model of the aquifer system considered is multi-layered with estuarine bank and the leaky aquifer extend finite distance under the estuary. The solution of the model describing the groundwater head distribution in such an estuarine aquifer system and subject to the tidal fluctuation effects from estuarine river is developed based on the method of separation of variables along with river boundary. The solutions by Sun (Sun H. A two-dimensional analytical solution of groundwater response to tidal loading in an estuary, Water Resour. Res. 1997; 33:1429-35) as well as Tang and Jiao (Tang Z. and J. J. Jiao, A two-dimensional analytical solution for groundwater flow in a leaky confined aquifer system near open tidal water, Hydrological Processes, 2001; 15: 573-585) can be shown to be special cases of the present solution. On the basis of the analytical solution, the groundwater head distribution in response to estuarine boundary is examined and the influences of leakage, hydraulic parameters, and loading effect on the groundwater head fluctuation due to tide are investigated and discussed. KEYWORDS: analytical model, estuarine river, groundwater fluctuation, leaky aquifer.

q-deformed Einstein's model to describe specific heat of solid

NASA Astrophysics Data System (ADS)

Guha, Atanu; Das, Prasanta Kumar

2018-04-01

Realistic phenomena can be described more appropriately using generalized canonical ensemble, with proper parameter sets involved. We have generalized the Einstein's theory for specific heat of solid in Tsallis statistics, where the temperature fluctuation is introduced into the theory via the fluctuation parameter q. At low temperature the Einstein's curve of the specific heat in the nonextensive Tsallis scenario exactly lies on the experimental data points. Consequently this q-modified Einstein's curve is found to be overlapping with the one predicted by Debye. Considering only the temperature fluctuation effect(even without considering more than one mode of vibration is being triggered) we found that the CV vs T curve is as good as obtained by considering the different modes of vibration as suggested by Debye. Generalizing the Einstein's theory in Tsallis statistics we found that a unique value of the Einstein temperature θE along with a temperature dependent deformation parameter q(T) , can well describe the phenomena of specific heat of solid i.e. the theory is equivalent to Debye's theory with a temperature dependent θD.

On the stability of non-supersymmetric supergravity solutions

NASA Astrophysics Data System (ADS)

Imaanpur, Ali; Zameni, Razieh

2017-09-01

We examine the stability of some non-supersymmetric supergravity solutions that have been found recently. The first solution is AdS5 ×M6, for M6 an stretched CP3. We consider breathing and squashing mode deformations of the metric, and find that the solution is stable against small fluctuations of this kind. Next we consider type IIB solution of AdS2 ×M8, where the compact space is a U (1) bundle over N (1 , 1). We study its stability under the deformation of M8 and the 5-form flux. In this case we also find that the solution is stable under small fluctuation modes of the corresponding deformations.

Generalized global symmetries and dissipative magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Grozdanov, Sašo; Hofman, Diego M.; Iqbal, Nabil

2017-05-01

The conserved magnetic flux of U (1 ) electrodynamics coupled to matter in four dimensions is associated with a generalized global symmetry. We study the realization of such a symmetry at finite temperature and develop the hydrodynamic theory describing fluctuations of a conserved 2-form current around thermal equilibrium. This can be thought of as a systematic derivation of relativistic magnetohydrodynamics, constrained only by symmetries and effective field theory. We construct the entropy current and show that at first order in derivatives, there are seven dissipative transport coefficients. We present a universal definition of resistivity in a theory of dynamical electromagnetism and derive a direct Kubo formula for the resistivity in terms of correlation functions of the electric field operator. We also study fluctuations and collective modes, deriving novel expressions for the dissipative widths of magnetosonic and Alfvén modes. Finally, we demonstrate that a nontrivial truncation of the theory can be performed at low temperatures compared to the magnetic field: this theory has an emergent Lorentz invariance along magnetic field lines, and hydrodynamic fluctuations are now parametrized by a fluid tensor rather than a fluid velocity. Throughout, no assumption is made of weak electromagnetic coupling. Thus, our theory may have phenomenological relevance for dense electromagnetic plasmas.

Simplified combustion noise theory yielding a prediction of fluctuating pressure level

NASA Technical Reports Server (NTRS)

Huff, R. G.

1984-01-01

The first order equations for the conservation of mass and momentum in differential form are combined for an ideal gas to yield a single second order partial differential equation in one dimension and time. Small perturbation analysis is applied. A Fourier transformation is performed that results in a second order, constant coefficient, nonhomogeneous equation. The driving function is taken to be the source of combustion noise. A simplified model describing the energy addition via the combustion process gives the required source information for substitution in the driving function. This enables the particular integral solution of the nonhomogeneous equation to be found. This solution multiplied by the acoustic pressure efficiency predicts the acoustic pressure spectrum measured in turbine engine combustors. The prediction was compared with the overall sound pressure levels measured in a CF6-50 turbofan engine combustor and found to be in excellent agreement.

Method of model reduction and multifidelity models for solute transport in random layered porous media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, Zhijie; Tartakovsky, Alexandre M.

This work presents a hierarchical model for solute transport in bounded layered porous media with random permeability. The model generalizes the Taylor-Aris dispersion theory to stochastic transport in random layered porous media with a known velocity covariance function. In the hierarchical model, we represent (random) concentration in terms of its cross-sectional average and a variation function. We derive a one-dimensional stochastic advection-dispersion-type equation for the average concentration and a stochastic Poisson equation for the variation function, as well as expressions for the effective velocity and dispersion coefficient. We observe that velocity fluctuations enhance dispersion in a non-monotonic fashion: the dispersionmore » initially increases with correlation length λ, reaches a maximum, and decreases to zero at infinity. Maximum enhancement can be obtained at the correlation length about 0.25 the size of the porous media perpendicular to flow.« less

Fluctuations of wormlike micelle fluids in capillary flow

NASA Astrophysics Data System (ADS)

Salipante, Paul; Meek, Stephen; Hudson, Steven; Polymers; Complex Fluids Group Team

2017-11-01

We investigate the effect of entrance geometry on the flow stability of wormlike micelles solutions in capillary flow. These solutions exhibit strong shear thinning behavior resulting from micelle breakage and have been observed to undergo large flow rate fluctuations. We investigate these fluctuations using simultaneous measurements of flow rate and pressure drop across a capillary, and we adjust entrance geometry. With a tapered constriction, we observe large persistent fluctuations above a critical flow rate, characterized by rapid decreases in the pressure drop with corresponding increase in flow rate followed by a period of recovery where pressure increases and flow rate decreases. Flow field observations in the tapered entrance show large flow circulations. An abrupt contraction produces smaller transient fluidized jets forming upstream of the constriction and the magnitude of the fluctuations are significantly diminished. The effect of fluid properties is studied by comparing the magnitude and timescales of the fluctuations for surfactant systems with different relaxation times. The onset of fluctuations is compared to a criterion for the onset of elastic instabilities and the magnitude is compared to estimates for changes in channel resistance. NIST on a Chip.

Current Fluctuations in Stochastic Lattice Gases

NASA Astrophysics Data System (ADS)

Bertini, L.; de Sole, A.; Gabrielli, D.; Jona-Lasinio, G.; Landim, C.

2005-01-01

We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a large deviation theory for the space-time fluctuations of the empirical current which include the previous results. We then estimate the probability of a fluctuation of the average current over a large time interval. It turns out that recent results by Bodineau and Derrida [Phys. Rev. Lett.922004180601] in certain cases underestimate this probability due to the occurrence of dynamical phase transitions.

Giant enhancement of fluctuation in small biological systems under external fields

NASA Astrophysics Data System (ADS)

Hayashi, Kumiko; Hasegawa, Shin; Tsunoda, Satoshi P.

2016-05-01

The giant enhancement (GE) of fluctuation under an external field is a universal phenomenon predicted by the theoretical analysis given in (Reimann et al 2001 Phys. Rev. Lett.). Here, we propose the application of the theory of the GE of fluctuation to estimate the energy barrier of a biomolecule that exhibits its function subject to thermal noise. The rotary motor protein F1 was used as a model, which is a component of FoF1 adenosine triphosphate (ATP)-synthase. In the single-molecule experiment on F1, the diffusion coefficients of a rotary probe attached to F1, which characterised the fluctuation of the system, were measured under the influence of an electro-rotary field. These diffusion coefficients were then used to estimate a high-energy barrier of the rotary potential of F1 based on the theory of the GE of fluctuation. Furthermore, the ion channel protein channelrhodopsin (ChR) was used as another research model. The current fluctuations of ions moving through ChR were numerically investigated using a simulation model of the protein in the presence of an external voltage. The energy barrier for ion conduction is discussed based on the current fluctuations.

Statistics of velocity fluctuations of Geldart A particles in a circulating fluidized bed riser

DOE PAGES

Vaidheeswaran, Avinash; Shaffer, Franklin; Gopalan, Balaji

2017-11-21

Here, the statistics of fluctuating velocity components are studied in the riser of a closed-loop circulating fluidized bed with fluid catalytic cracking catalyst particles. Our analysis shows distinct similarities as well as deviations compared to existing theories and bench-scale experiments. The study confirms anisotropic and non-Maxwellian distribution of fluctuating velocity components. The velocity distribution functions (VDFs) corresponding to transverse fluctuations exhibit symmetry, and follow a stretched-exponential behavior up to three standard deviations. The form of the transverse VDF is largely determined by interparticle interactions. The tails become more overpopulated with an increase in particle loading. The observed deviations from themore » Gaussian distribution are represented using the leading order term in the Sonine expansion, which is commonly used to approximate the VDFs in kinetic theory for granular flows. The vertical fluctuating VDFs are asymmetric and the skewness shifts as the wall is approached. In comparison to transverse fluctuations, the vertical VDF is determined by the local hydrodynamics. This is an observation of particle velocity fluctuations in a large-scale system and their quantitative comparison with the Maxwell-Boltzmann statistics.« less

Time-dependent behavior in a transport-barrier model for the quasi-single helcity state

NASA Astrophysics Data System (ADS)

Terry, P. W.; Whelan, G. G.

2014-09-01

Time-dependent behavior that follows from a recent theory of the quasi-single-helicity (QSH) state of the reversed field pinch is considered. The theory (Kim and Terry 2012 Phys. Plasmas 19 122304) treats QSH as a core fluctuation structure tied to a tearing mode of the same helicity, and shows that strong magnetic and velocity shears in the structure suppress the nonlinear interaction with other fluctuations. By summing the multiple helicity fluctuation energies over wavenumber, we reduce the theory to a predator-prey model. The suppression of the nonlinear interaction is governed by the single helicity energy, which, for fixed radial structure, controls the magnetic and velocity shearing rates. It is also controlled by plasma current which, in the theory, sets the shearing threshold for suppression. The model shows a limit cycle oscillation in which the system toggles between QSH and multiple helicity states, with the single helicity phase becoming increasingly long-lived relative to the multiple helicity phase as plasma current increases.

Fluctuating chemohydrodynamics and the stochastic motion of self-diffusiophoretic particles

NASA Astrophysics Data System (ADS)

Gaspard, Pierre; Kapral, Raymond

2018-04-01

The propulsion of active particles by self-diffusiophoresis is driven by asymmetric catalytic reactions on the particle surface that generate a mechanochemical coupling between the fluid velocity and the concentration fields of fuel and product in the surrounding solution. Because of thermal and molecular fluctuations in the solution, the motion of micrometric or submicrometric active particles is stochastic. Coupled Langevin equations describing the translation, rotation, and reaction of such active particles are deduced from fluctuating chemohydrodynamics and fluctuating boundary conditions at the interface between the fluid and the particle. These equations are consistent with microreversibility and the Onsager-Casimir reciprocal relations between affinities and currents and provide a thermodynamically consistent basis for the investigation of the dynamics of active particles propelled by diffusiophoretic mechanisms.

Concentration Fluctuations and Capacitive Response in Dense Ionic Solutions.

PubMed

Uralcan, Betul; Aksay, Ilhan A; Debenedetti, Pablo G; Limmer, David T

2016-07-07

We use molecular dynamics simulations in a constant potential ensemble to study the effects of solution composition on the electrochemical response of a double layer capacitor. We find that the capacitance first increases with ion concentration following its expected ideal solution behavior but decreases upon approaching a pure ionic liquid in agreement with recent experimental observations. The nonmonotonic behavior of the capacitance as a function of ion concentration results from the competition between the independent motion of solvated ions in the dilute regime and solvation fluctuations in the concentrated regime. Mirroring the capacitance, we find that the characteristic decay length of charge density correlations away from the electrode is also nonmonotonic. The correlation length first decreases with ion concentration as a result of better electrostatic screening but increases with ion concentration as a result of enhanced steric interactions. When charge fluctuations induced by correlated ion-solvent fluctuations are large relative to those induced by the pure ionic liquid, such capacitive behavior is expected to be generic.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vaidheeswaran, Avinash; Shaffer, Franklin; Gopalan, Balaji

Here, the statistics of fluctuating velocity components are studied in the riser of a closed-loop circulating fluidized bed with fluid catalytic cracking catalyst particles. Our analysis shows distinct similarities as well as deviations compared to existing theories and bench-scale experiments. The study confirms anisotropic and non-Maxwellian distribution of fluctuating velocity components. The velocity distribution functions (VDFs) corresponding to transverse fluctuations exhibit symmetry, and follow a stretched-exponential behavior up to three standard deviations. The form of the transverse VDF is largely determined by interparticle interactions. The tails become more overpopulated with an increase in particle loading. The observed deviations from themore » Gaussian distribution are represented using the leading order term in the Sonine expansion, which is commonly used to approximate the VDFs in kinetic theory for granular flows. The vertical fluctuating VDFs are asymmetric and the skewness shifts as the wall is approached. In comparison to transverse fluctuations, the vertical VDF is determined by the local hydrodynamics. This is an observation of particle velocity fluctuations in a large-scale system and their quantitative comparison with the Maxwell-Boltzmann statistics.« less

An analytical solution of groundwater level fluctuation in a U-shaped leaky coastal aquifer

NASA Astrophysics Data System (ADS)

Huang, Fu-Kuo; Chuang, Mo-Hsiung; Wang, Shu-chuan

2017-04-01

Tide-induced groundwater level fluctuations in coastal aquifers have attracted much attention in past years, especially for the issues associated with the impact of the coastline shape, multi-layered leaky aquifer system, and anisotropy of aquifers. In this study, a homogeneous but anisotropic multi-layered leaky aquifer system with U-shaped coastline is considered, where the subsurface system consisting of an unconfined aquifer, a leaky confined aquifer, and a semi-permeable layer between them. The analytical solution of the model obtained herein may be considered as an extended work of two solutions; one was developed by Huang et al. (Huang et al. Tide-induced groundwater level fluctuation in a U-shaped coastal aquifer, J. Hydrol. 2015; 530: 291-305) for two-dimensional interacting tidal waves bounded by three water-land boundaries while the other was by Li and Jiao (Li and Jiao. Tidal groundwater level fluctuations in L-shaped leaky coastal aquifer system, J. Hydrol. 2002; 268: 234-243) for two-dimensional interacting tidal waves of leaky coastal aquifer system adjacent to a cross-shore estuary. In this research, the effects of leakage and storativity of the semi-permeable layer on the amplitude and phase shift of the tidal head fluctuation, and the influence of anisotropy of the aquifer are all examined for the U-shaped leaky coastal aquifer. Some existing solutions in literatures can be regarded as the special cases of the present solution if the aquifer system is isotropic and non-leaky. The results obtained will be beneficial to coastal development and management for water resources.

Theory of the magnetic susceptibility including zero-point spin fluctuations of itinerant nearly ferromagnetic compounds

NASA Astrophysics Data System (ADS)

Konno, Rikio; Hatayama, Nobukuni; Takahashi, Yoshinori

2018-05-01

We have investigated the temperature dependence of the magnetic susceptibility of itinerant nearly ferromagnetic compounds based on the spin fluctuation theory. It is based on the conservation of the local spin amplitude that consists of both the thermal and the zero-point components. The linear dependence of the zero-point spin fluctuation amplitude on the inverse of magnetic susceptibility is usually assumed. The purpose of our present study is to include its higher order terms and to see their effects on the magnetic susceptibility. For the thermal amplitude, it shows T2-linear temperature dependence at low temperatures.

Cosmological consequences of grand unified theories on density fluctuations

NASA Astrophysics Data System (ADS)

Lindley, D.

1981-05-01

Recent investigations into the cosmological consequences of grand unified theories (GUTs) of elementary particles have shown that the observed matter-antimatter asymmetry of the Universe can be explained without recourse to the hypothesis of specific initial conditions. It is shown here that the origin of inhomogeneities in the matter distribution, which are thought to be responsible for the later formation of galaxies, cannot be explained by a simple addition of density fluctuations to the standard model. The appearance of these fluctuations, after the epoch when baryon number is fixed, is almost purely adiabatic, any departure from adiabaticity falling off in inverse proportion to the mass of the perturbation.

Exact solution of the Lifshitz equations governing the growth of fluctuations in cosmology

NASA Technical Reports Server (NTRS)

Adams, P. J.; Canuto, V.

1975-01-01

The exact solution of the Lifshitz equations governing the cosmological evolution of an initial fluctuation is presented. Lifshitz results valid for squares of the sound velocity equal to zero and 1/3 are extended in closed form to any equation of state where the pressure equals the total energy density times the square of the sound velocity. The solutions embody all the results found previously for special cases of the square of the sound velocity. It is found that the growth of any initial fluctuation is only an exponential function of time with an exponent of not more than 4/3 and is insufficient to produce galaxies unless the initial fluctuation is very large. A possible way to produce very large initial fluctuations by modifying the equation of state by including gravitational interactions is also examined. It is found that a phase transition can occur at baryonic density of 1 nucleon per cubic Planck length or equivalently, at a time of about 10 to the -43rd power sec. At those early times, the masses allowed by causality requirements are too small to be of interest in galaxy formation.

Electromagnetic fluctuations for anisotropic media and the generalized Kirchhoff's law

NASA Technical Reports Server (NTRS)

Yueh, Simon H.; Kwok, R.

1993-01-01

In this paper the polarimetric emission parameters for anisotropic media are derived using the generalized Kirchhoff's law for media with a uniform temperature and the fluctuation-dissipation theory for media with a temperature profile. Both finite-size objects and half-space media are considered. When the object has a uniform temperature across its body, the Kirchhoff's law, based on the condition of energy conservation in thermal equilibrium is generalized to obtain the emission parameters of an anisotropic medium, which can be interpreted as the absorptivity or the absorption cross section of the complementary object with a permittivity that is the transpose of the original object. When the medium has a nonuniform temperature distribution, the fluctuation-dissipation theory is applied for deriving the covariances between vector components of the thermal currents and, consequently, the covariances of the polarizations of electric fields radiated by the thermal currents. To verify the formulas derived from the fluctuation-dissipation theory, we let the temperature of the object be a constant and show that the results reduce to those obtained from the generalized Kirchhoff's law.

Motion of Euglena gracilis: Active fluctuations and velocity distribution

NASA Astrophysics Data System (ADS)

Romanczuk, P.; Romensky, M.; Scholz, D.; Lobaskin, V.; Schimansky-Geier, L.

2015-07-01

We study the velocity distribution of unicellular swimming algae Euglena gracilis using optical microscopy and active Brownian particle theory. To characterize a peculiar feature of the experimentally observed distribution at small velocities we use the concept of active fluctuations, which was recently proposed for the description of stochastically self-propelled particles [Romanczuk, P. and Schimansky-Geier, L., Phys. Rev. Lett. 106, 230601 (2011)]. In this concept, the fluctuating forces arise due to internal random performance of the propulsive motor. The fluctuating forces are directed in parallel to the heading direction, in which the propulsion acts. In the theory, we introduce the active motion via the depot model [Schweitzer, et al., Phys. Rev. Lett. 80(23), 5044 (1998)]. We demonstrate that the theoretical predictions based on the depot model with active fluctuations are consistent with the experimentally observed velocity distributions. In addition to the model with additive active noise, we obtain theoretical results for a constant propulsion with multiplicative noise.

Magnetic disorder in superconductors: Enhancement by mesoscopic fluctuations

NASA Astrophysics Data System (ADS)

Burmistrov, I. S.; Skvortsov, M. A.

2018-01-01

We study the density of states (DOS) and the transition temperature Tc in a dirty superconducting film with rare classical magnetic impurities of an arbitrary strength described by the Poissonian statistics. We take into account that the potential disorder is a source of mesoscopic fluctuations of the local DOS, and, consequently, of the effective strength of magnetic impurities. We find that these mesoscopic fluctuations result in a nonzero DOS for all energies in the region of the phase diagram where without this effect the DOS is zero within the standard mean-field theory. This mechanism can be more efficient in filling the mean-field superconducting gap than rare fluctuations of the potential disorder (instantons). Depending on the magnetic impurity strength, the suppression of Tc by spin-flip scattering can be faster or slower than in the standard mean-field theory.

Protein Signaling Networks from Single Cell Fluctuations and Information Theory Profiling

PubMed Central

Shin, Young Shik; Remacle, F.; Fan, Rong; Hwang, Kiwook; Wei, Wei; Ahmad, Habib; Levine, R.D.; Heath, James R.

2011-01-01

Protein signaling networks among cells play critical roles in a host of pathophysiological processes, from inflammation to tumorigenesis. We report on an approach that integrates microfluidic cell handling, in situ protein secretion profiling, and information theory to determine an extracellular protein-signaling network and the role of perturbations. We assayed 12 proteins secreted from human macrophages that were subjected to lipopolysaccharide challenge, which emulates the macrophage-based innate immune responses against Gram-negative bacteria. We characterize the fluctuations in protein secretion of single cells, and of small cell colonies (n = 2, 3,···), as a function of colony size. Measuring the fluctuations permits a validation of the conditions required for the application of a quantitative version of the Le Chatelier's principle, as derived using information theory. This principle provides a quantitative prediction of the role of perturbations and allows a characterization of a protein-protein interaction network. PMID:21575571

Charge conservation in electronegativity equalization and its implications for the electrostatic properties of fluctuating-charge models.

PubMed

Chen, Jiahao; Martínez, Todd J

2009-07-28

An analytical solution of fluctuating-charge models using Gaussian elimination allows us to isolate the contribution of charge conservation effects in determining the charge distribution. We use this analytical solution to calculate dipole moments and polarizabilities and show that charge conservation plays a critical role in maintaining the correct translational invariance of the electrostatic properties predicted by these models.

Plasma fluctuations as Markovian noise.

PubMed

Li, B; Hazeltine, R D; Gentle, K W

2007-12-01

Noise theory is used to study the correlations of stationary Markovian fluctuations that are homogeneous and isotropic in space. The relaxation of the fluctuations is modeled by the diffusion equation. The spatial correlations of random fluctuations are modeled by the exponential decay. Based on these models, the temporal correlations of random fluctuations, such as the correlation function and the power spectrum, are calculated. We find that the diffusion process can give rise to the decay of the correlation function and a broad frequency spectrum of random fluctuations. We also find that the transport coefficients may be estimated by the correlation length and the correlation time. The theoretical results are compared with the observed plasma density fluctuations from the tokamak and helimak experiments.

Mathematical analysis of the multiband BCS gap equations in superconductivity

NASA Astrophysics Data System (ADS)

Yang, Yisong

2005-01-01

In this paper, we present a mathematical analysis for the phonon-dominated multiband isotropic and anisotropic BCS gap equations at any finite temperature T. We establish the existence of a critical temperature T so that, when TT, the only nonnegative gap solution is the zero solution, representing the normal phase. Furthermore, when T=T, we prove that the only gap solution is the zero solution and that the positive gap solution depend on the temperature T

Application of the quantum spin glass theory to image restoration.

PubMed

Inoue, J I

2001-04-01

Quantum fluctuation is introduced into the Markov random-field model for image restoration in the context of a Bayesian approach. We investigate the dependence of the quantum fluctuation on the quality of a black and white image restoration by making use of statistical mechanics. We find that the maximum posterior marginal (MPM) estimate based on the quantum fluctuation gives a fine restoration in comparison with the maximum a posteriori estimate or the thermal fluctuation based MPM estimate.

Random Dopant Induced Threshold Voltage Lowering and Fluctuations in Sub-0.1 (micron)meter MOSFET's: A 3-D 'Atomistic' Simulation Study

NASA Technical Reports Server (NTRS)

Asenov, Asen

1998-01-01

A three-dimensional (3-D) "atomistic" simulation study of random dopant induced threshold voltage lowering and fluctuations in sub-0.1 microns MOSFET's is presented. For the first time a systematic analysis of random dopant effects down to an individual dopant level was carried out in 3-D on a scale sufficient to provide quantitative statistical predictions. Efficient algorithms based on a single multigrid solution of the Poisson equation followed by the solution of a simplified current continuity equation are used in the simulations. The effects of various MOSFET design parameters, including the channel length and width, oxide thickness and channel doping, on the threshold voltage lowering and fluctuations are studied using typical samples of 200 atomistically different MOSFET's. The atomistic results for the threshold voltage fluctuations were compared with two analytical models based on dopant number fluctuations. Although the analytical models predict the general trends in the threshold voltage fluctuations, they fail to describe quantitatively the magnitude of the fluctuations. The distribution of the atomistically calculated threshold voltage and its correlation with the number of dopants in the channel of the MOSFET's was analyzed based on a sample of 2500 microscopically different devices. The detailed analysis shows that the threshold voltage fluctuations are determined not only by the fluctuation in the dopant number, but also in the dopant position.

Gross domestic product growth rates as confined Lévy flights: Towards a unifying theory of economic growth rate fluctuations

NASA Astrophysics Data System (ADS)

Lera, Sandro Claudio; Sornette, Didier

2018-01-01

A model that combines economic growth rate fluctuations at the microscopic and macroscopic levels is presented. At the microscopic level, firms are growing at different rates while also being exposed to idiosyncratic shocks at the firm and sector levels. We describe such fluctuations as independent Lévy-stable fluctuations, varying over multiple orders of magnitude. These fluctuations are aggregated and measured at the macroscopic level in averaged economic output quantities such as GDP. A fundamental question is thereby to what extent individual firm size fluctuations can have a noticeable impact on the overall economy. We argue that this question can be answered by considering the Lévy fluctuations as embedded in a steep confining potential well, ensuring nonlinear mean-reversal behavior, without having to rely on microscopic details of the system. The steepness of the potential well directly controls the extent to which idiosyncratic shocks to firms and sectors are damped at the level of the economy. Additionally, the theory naturally accounts for business cycles, represented in terms of a bimodal economic output distribution and thus connects two so far unrelated fields in economics. By analyzing 200 years of U.S. gross domestic product growth rates, we find that the model is in good agreement with the data.

Gross domestic product growth rates as confined Lévy flights: Towards a unifying theory of economic growth rate fluctuations.

PubMed

Lera, Sandro Claudio; Sornette, Didier

2018-01-01

A model that combines economic growth rate fluctuations at the microscopic and macroscopic levels is presented. At the microscopic level, firms are growing at different rates while also being exposed to idiosyncratic shocks at the firm and sector levels. We describe such fluctuations as independent Lévy-stable fluctuations, varying over multiple orders of magnitude. These fluctuations are aggregated and measured at the macroscopic level in averaged economic output quantities such as GDP. A fundamental question is thereby to what extent individual firm size fluctuations can have a noticeable impact on the overall economy. We argue that this question can be answered by considering the Lévy fluctuations as embedded in a steep confining potential well, ensuring nonlinear mean-reversal behavior, without having to rely on microscopic details of the system. The steepness of the potential well directly controls the extent to which idiosyncratic shocks to firms and sectors are damped at the level of the economy. Additionally, the theory naturally accounts for business cycles, represented in terms of a bimodal economic output distribution and thus connects two so far unrelated fields in economics. By analyzing 200 years of U.S. gross domestic product growth rates, we find that the model is in good agreement with the data.

The Atmospheric Mutual Coherence Function From the First and Second Rytov Approximations and Its Comparison to That of Strong Fluctuation Theory

NASA Technical Reports Server (NTRS)

Manning, Robert M.

2011-01-01

An expression for the mutual coherence function (MCF) of an electromagnetic beam wave propagating through atmospheric turbulence is derived within the confines of the Rytov approximation. It is shown that both the first and second Rytov approximations are required. The Rytov MCF is then compared to that which issues from the parabolic equation method of strong fluctuation theory. The agreement is found to be quite good in the weak fluctuation case. However, an instability is observed for the special case of beam wave intensities. The source of the instabilities is identified to be the characteristic way beam wave amplitudes are treated within the Rytov method.

Mathematical modeling of alignment dynamics in active motor-filament systems

NASA Astrophysics Data System (ADS)

Swaminathan, Sumanth

The formation of the cytoskeleton, via motor-mediated microtubule self-organization, is an important subject of study in the biological sciences as well as in nonequilibrium, soft matter physics. Accurate modeling of the dynamics is a formidable task as it involves intrinsic nonlinearities, structural anisotropies, nonequilibrium processes, and a broad window of time scales, length scales, and densities. In this thesis, we study the ordering dynamics and pattern formations arising from motor-mediated microtubule self-organization in dilute and semi-dilute filament solutions. In the dilute case, we use a probabilistic model in which microtubules interact through motor induced, inelastic binary collisions. This model shows that initially disordered filament solutions exhibit an ordering transition resulting in the emergence of well aligned rod bundles. We study the existence and dynamic interaction of microtubule bundles analytically and numerically. Our results show a long term attraction and coalescing of bundles indicating a clear coarsening in the system; microtubule bundles concentrate into fewer orientations on a slow logarithmic time scale. In the semi-dilute case, multiple motors can bind a filament to several others and, for a critical motor density, induce a transition to an ordered state with a nonzero mean orientation. We develop a spatially homogeneous, mean-field theory that explicitly accounts for motor forcing and thermal fluctuations which enter into the model as multiplicative and additive noises respectively. Our model further incorporates a force-dependent detachment rate of motors, which in turn affects the mean and the fluctuations of the net force acting on a filament. We demonstrate that the transition to the oriented state changes from second order to first order when the force-dependent detachment becomes important. In our final analysis, we add complex spatial inhomogeneities to our mean field theory. The revised model consists of a system of stochastic differential equations governing the time evolution of the orientation and center of mass of each filament; microtubules translate and rotate under the influence of motor forces and intrinsic thermal fluctuations. We show through a molecular dynamics type stochastic simulation that initially disordered systems of microtubules exhibit an ordering transition resulting in the formation of bundles and vortices. This finding is compared with previous binary interaction and hydrodynamic models and shown to be consistent with in vitro experiments on motor-mediated self-organization of microtubules and actin filaments.

Dynamic Light Scattering Study of Pig Vitreous Body

NASA Astrophysics Data System (ADS)

Matsuura, Toyoaki; Idota, Naokazu; Hara, Yoshiaki; Annaka, Masahiko

The phase behaviors and dynamical properties of pig vitreous body were studied by macroscopic observation of swelling behavior and dynamic light scattering under various conditions. From the observations of the dynamics of light scattered by the pig vitreous body under physiological condition, intensity autocorrelation functions that revealed two diffusion coefficients, D fast and D slow were obtained. We developed the theory for describing the density fluctuation of the entities in the vitreous gel system with sodium hyaluronate filled in the meshes of collagen fiber network. The dynamics of collagen and sodium hyaluronate explains two relaxation modes of the fluctuation. The diffusion coefficient of collagen obtained from D fast and D slow is very close to that in aqueous solution, which suggests the vitreous body is in the swollen state. Divergent behavior in the measured total scattered light intensities and diffusion coefficients upon varying the concentration of salt (NaCl and CaCl2) was observed. Namely, a slowing down of the dynamic modes accompanied by increased “static” scattered intensities was observed. This is indicative of the occurrence of a phase transition upon salt concentration.

Density Fluctuation in Aqueous Solutions and Molecular Origin of Salting-Out Effect for CO 2

DOE PAGES

Ho, Tuan Anh; Ilgen, Anastasia

2017-10-26

Using molecular dynamics simulation, we studied the density fluctuations and cavity formation probabilities in aqueous solutions and their effect on the hydration of CO 2. With increasing salt concentration, we report an increased probability of observing a larger than the average number of species in the probe volume. Our energetic analyses indicate that the van der Waals and electrostatic interactions between CO 2 and aqueous solutions become more favorable with increasing salt concentration, favoring the solubility of CO 2 (salting in). However, due to the decreasing number of cavities forming when salt concentration is increased, the solubility of CO 2more » decreases. The formation of cavities was found to be the primary control on the dissolution of gas, and is responsible for the observed CO 2 salting-out effect. Finally, our results provide the fundamental understanding of the density fluctuation in aqueous solutions and the molecular origin of the salting-out effect for real gas.« less

Density Fluctuation in Aqueous Solutions and Molecular Origin of Salting-Out Effect for CO 2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ho, Tuan Anh; Ilgen, Anastasia

Using molecular dynamics simulation, we studied the density fluctuations and cavity formation probabilities in aqueous solutions and their effect on the hydration of CO 2. With increasing salt concentration, we report an increased probability of observing a larger than the average number of species in the probe volume. Our energetic analyses indicate that the van der Waals and electrostatic interactions between CO 2 and aqueous solutions become more favorable with increasing salt concentration, favoring the solubility of CO 2 (salting in). However, due to the decreasing number of cavities forming when salt concentration is increased, the solubility of CO 2more » decreases. The formation of cavities was found to be the primary control on the dissolution of gas, and is responsible for the observed CO 2 salting-out effect. Finally, our results provide the fundamental understanding of the density fluctuation in aqueous solutions and the molecular origin of the salting-out effect for real gas.« less

Learning in neural networks based on a generalized fluctuation theorem

NASA Astrophysics Data System (ADS)

Hayakawa, Takashi; Aoyagi, Toshio

2015-11-01

Information maximization has been investigated as a possible mechanism of learning governing the self-organization that occurs within the neural systems of animals. Within the general context of models of neural systems bidirectionally interacting with environments, however, the role of information maximization remains to be elucidated. For bidirectionally interacting physical systems, universal laws describing the fluctuation they exhibit and the information they possess have recently been discovered. These laws are termed fluctuation theorems. In the present study, we formulate a theory of learning in neural networks bidirectionally interacting with environments based on the principle of information maximization. Our formulation begins with the introduction of a generalized fluctuation theorem, employing an interpretation appropriate for the present application, which differs from the original thermodynamic interpretation. We analytically and numerically demonstrate that the learning mechanism presented in our theory allows neural networks to efficiently explore their environments and optimally encode information about them.

Microscopic Phase-Space Exploration Modeling of ^{258}Fm Spontaneous Fission.

PubMed

Tanimura, Yusuke; Lacroix, Denis; Ayik, Sakir

2017-04-14

We show that the total kinetic energy (TKE) of nuclei after the spontaneous fission of ^{258}Fm can be well reproduced using simple assumptions on the quantum collective phase space explored by the nucleus after passing the fission barrier. Assuming energy conservation and phase-space exploration according to the stochastic mean-field approach, a set of initial densities is generated. Each density is then evolved in time using the nuclear time-dependent density-functional theory with pairing. This approach goes beyond the mean-field theory by allowing spontaneous symmetry breaking as well as a wider dynamical phase-space exploration leading to larger fluctuations in collective space. The total kinetic energy and mass distributions are calculated. New information on the fission process: fluctuations in scission time, strong correlation between TKE and collective deformation, as well as prescission particle emission, are obtained. We conclude that fluctuations of the TKE and mass are triggered by quantum fluctuations.

Charging a capacitor from an external fluctuating potential using a single conical nanopore.

PubMed

Gomez, Vicente; Ramirez, Patricio; Cervera, Javier; Nasir, Saima; Ali, Mubarak; Ensinger, Wolfgang; Mafe, Salvador

2015-04-01

We explore the electrical rectification of large amplitude fluctuating signals by an asymmetric nanostructure operating in aqueous solution. We show experimentally and theoretically that a load capacitor can be charged to voltages close to 1 V within a few minutes by converting zero time-average potentials of amplitudes in the range 0.5-3 V into average net currents using a single conical nanopore. This process suggests that significant energy conversion and storage from an electrically fluctuating environment is feasible with a nanoscale pore immersed in a liquid electrolyte solution, a system characteristic of bioelectronics interfaces, electrochemical cells, and nanoporous membranes.

Charging a Capacitor from an External Fluctuating Potential using a Single Conical Nanopore

PubMed Central

Gomez, Vicente; Ramirez, Patricio; Cervera, Javier; Nasir, Saima; Ali, Mubarak; Ensinger, Wolfgang; Mafe, Salvador

2015-01-01

We explore the electrical rectification of large amplitude fluctuating signals by an asymmetric nanostructure operating in aqueous solution. We show experimentally and theoretically that a load capacitor can be charged to voltages close to 1 V within a few minutes by converting zero time-average potentials of amplitudes in the range 0.5–3 V into average net currents using a single conical nanopore. This process suggests that significant energy conversion and storage from an electrically fluctuating environment is feasible with a nanoscale pore immersed in a liquid electrolyte solution, a system characteristic of bioelectronics interfaces, electrochemical cells, and nanoporous membranes. PMID:25830563

Flow and thermal characteristics of high Reynolds number (2800-17,000) dye cell: simulation and experiment.

PubMed

Mishra, G K; Kumar, Abhay; Prakash, O; Biswal, R; Dixit, S K; Nakhe, S V

2015-04-10

This paper presents computational and experimental studies on wavelength/frequency fluctuation characteristics of a high pulse repetition rate (18 kHz) dye laser pumped by a frequency-doubled Nd:YAG laser (532 nm). The temperature gradient in the dye solution is found to be responsible for wavelength fluctuations of the dye laser at low flow rates (2800

Test-particle simulations in increasingly strong turbulence

NASA Technical Reports Server (NTRS)

Pontius, D. H., Jr.; Gray, P. C.; Matthaeus, W. H.

1995-01-01

Quasi-linear theory supposes that the energy in resonant fluctuations is small compared to that in the mean magnetic field. This is evident in the fact that the zeroth-order particle trajectories are helices about a mean field B(sub o) that is spatially uniform over many correlation lengths. However, in the solar wind it is often the case that the fluctuating part of the field is comparable in magnitude to the mean part. It is generally expected that quasi-linear theory remains viable for particles that are in resonance with a region of the fluctuation spectrum having only small energy density, but even so, care must be taken when comparing simulations to theoretical predictions. We have performed a series of test-particle simulations to explore the evolution of ion distributions in turbulent situations with varying levels of magnetic fluctuations. As delta-B/B(sub o) is increased the distinctions among absolute pitch angle (defined relative to B(sub o)), local pitch angle (defined relative to B(x)), and magnetic moment become important, some of them exhibiting periodic sloshing unrelated to the nonadiabatic processes of interest. Comparing and contrasting the various runs illustrates the phenomena that must be considered when the premise underlying quasi-linear theory are relaxed.

Stabilization of hydrodynamic flows by small viscosity variations.

PubMed

Govindarajan, Rama; L'vov, Victor S; Procaccia, Itamar; Sameen, A

2003-02-01

Motivated by the large effect of turbulent drag reduction by minute concentrations of polymers, we study the effects of a weakly space-dependent viscosity on the stability of hydrodynamic flows. In a recent paper [Phys. Rev. Lett. 87, 174501, (2001)], we exposed the crucial role played by a localized region where the energy of fluctuations is produced by interactions with the mean flow (the "critical layer"). We showed that a layer of a weakly space-dependent viscosity placed near the critical layer can have a very large stabilizing effect on hydrodynamic fluctuations, retarding significantly the onset of turbulence. In this paper we extend these observations in two directions: first we show that the strong stabilization of the primary instability is also obtained when the viscosity profile is realistic (inferred from simulations of turbulent flows with a small concentration of polymers). Second, we analyze the secondary instability (around the time-dependent primary instability) and find similar strong stabilization. Since the secondary instability develops around a time-dependent solution and is three dimensional, this brings us closer to the turbulent case. We reiterate that the large effect is not due to a modified dissipation (as is assumed in some theories of drag reduction), but due to reduced energy intake from the mean flow to the fluctuations. We propose that similar physics act in turbulent drag reduction.

Double diffusivity model under stochastic forcing

NASA Astrophysics Data System (ADS)

Chattopadhyay, Amit K.; Aifantis, Elias C.

2017-05-01

The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into account all boundary layer fluctuations. Our stochastic-ILG diffusion calculation confirms rapprochement between theory and experiment, thereby benchmarking a new generation of gradient-based continuum models that conform closer to real-life fluctuating environments.

Porous media fracturing dynamics: stepwise crack advancement and fluid pressure oscillations

NASA Astrophysics Data System (ADS)

Cao, Toan D.; Hussain, Fazle; Schrefler, Bernhard A.

2018-02-01

We present new results explaining why fracturing in saturated porous media is not smooth and continuous but is a distinct stepwise process concomitant with fluid pressure oscillations. All exact solutions and almost all numerical models yield smooth fracture advancement and fluid pressure evolution, while recent experimental results, mainly from the oil industry, observation from geophysics and a very few numerical results for the quasi-static case indeed reveal the stepwise phenomenon. We summarize first these new experiments and these few numerical solutions for the quasi-static case. Both mechanical loading and pressure driven fractures are considered because their behaviours differ in the direction of the pressure jumps. Then we explore stepwise crack tip advancement and pressure fluctuations in dynamic fracturing with a hydro-mechanical model of porous media based on the Hybrid Mixture Theory. Full dynamic analyses of examples dealing with both hydraulic fracturing and mechanical loading are presented. The stepwise fracture advancement is confirmed in the dynamic setting as well as in the pressure fluctuations, but there are substantial differences in the frequency contents of the pressure waves in the two loading cases. Comparison between the quasi-static and fully dynamic solutions reveals that the dynamic response gives much more information such as the type of pressure oscillations and related frequencies and should be applied whenever there is a doubt about inertia forces playing a role - the case in most fracturing events. In the absence of direct relevant dynamic tests on saturated media some experimental results on dynamic fracture in dry materials, a fast hydraulic fracturing test and observations from geophysics confirm qualitatively the obtained results such as the type of pressure oscillations and the substantial difference in the behaviour under the two loading cases.

Modeling the influence of the Casimir force on the pull-in instability of nanowire-fabricated nanotweezers

NASA Astrophysics Data System (ADS)

Farrokhabadi, Amin; Mokhtari, Javad; Rach, Randolph; Abadyan, Mohamadreza

2015-09-01

The Casimir force can strongly interfere with the pull-in performance of ultra-small structures. The strength of the Casimir force is significantly affected by the geometries of interacting bodies. Previous investigators have exclusively studied the effect of the Casimir force on the electromechanical instability of nanostructures with planar geometries. However no work has yet considered this effect on the pull-in instability of systems with cylindrical geometries such as nanotweezers fabricated from nanotube/nanowires. In our present work, the influence of the Casimir attraction on the electrostatic response and pull-in instability of nanotweezers fabricated from cylindrical conductive nanowires/nanotubes is theoretically investigated. An asymptotic solution, based on scattering theory, is applied to consider the effect of vacuum fluctuations in the theoretical model. The Euler-Bernoulli beam model is employed, in conjunction with the size-dependent modified couple stress continuum theory, to derive the governing equation of the nanotweezers. The governing nonlinear equations are solved by two different approaches, i.e., the modified Adomian-Padé method (MAD-Padé) and a numerical solution. Various aspects of the problem, i.e., the variation of pull-in parameters, effect of geometry, coupling between the Casimir force and size dependency effects and comparison with the van der Waals force regime are discussed.

Fluctuation spectroscopy: From Rayleigh-Jeans waves to Abrikosov vortex clusters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Varlamov, A. A.; Galda, A.; Glatz, A.

Superconducting (SC) fluctuations, discovered in the late 1960s, have constituted an important research area in superconductivity as they are manifest in a variety of phenomena. Indeed, the underlying physics of SC fluctuations makes it possible to elucidate the fundamental properties of the superconducting state. The interest in SC fluctuation phenomena was further enhanced with the discovery of cuprate high-temperature superconductors (HTSs). In these materials, superconducting fluctuations appear over a wide range of temperatures due to the superconductors extremely short coherence lengths and low effective dimensionality of the electron systems. These strong fluctuations lead to anomalous properties of the normal statemore » in some HTS materials. Within the framework of the phenomenological Ginzburg-Landau theory, and more extensively in the diagrammatic microscopic approach based on BCS theory, SC fluctuations as well as other quantum contributions (weak localization, etc.) enabled a new way to investigate and characterize disordered electron systems, granular metals, Josephson structures, artificial superlattices, and others. The characteristic feature of SC fluctuations is its strong dependence on temperature and magnetic field in the vicinity of the superconducting phase transition. This dependence allows the separation of fluctuation effects from other contributions and provides information about the microscopic parameters of a material, in particular, the critical temperature and the zero-temperature critical magnetic field. As such, SC fluctuations are very sensitive to the relaxation processes that break phase coherence and can be used as a versatile characterization instrument for SCs: Fluctuation spectroscopy has emerged as a powerful tool for studying the properties of superconducting systems on a quantitative level. Here the physics of SC fluctuations is reviewed, commencing from a qualitative description of thermodynamic fluctuations close to the critical temperature and quantum fluctuations at zero temperature in the vicinity of the second critical field. The analysis of the latter allows us to present fluctuation formation as a fragmentation of the Abrikosov lattice. Finally, this review highlights a series of experimental findings followed by microscopic description and numerical analysis of the effects of fluctuations on numerous properties of superconductors in the entire phase diagram and beyond the superconducting phase.« less

Fluctuation spectroscopy: From Rayleigh-Jeans waves to Abrikosov vortex clusters

DOE PAGES

Varlamov, A. A.; Galda, A.; Glatz, A.

2018-03-27

Superconducting (SC) fluctuations, discovered in the late 1960s, have constituted an important research area in superconductivity as they are manifest in a variety of phenomena. Indeed, the underlying physics of SC fluctuations makes it possible to elucidate the fundamental properties of the superconducting state. The interest in SC fluctuation phenomena was further enhanced with the discovery of cuprate high-temperature superconductors (HTSs). In these materials, superconducting fluctuations appear over a wide range of temperatures due to the superconductors extremely short coherence lengths and low effective dimensionality of the electron systems. These strong fluctuations lead to anomalous properties of the normal statemore » in some HTS materials. Within the framework of the phenomenological Ginzburg-Landau theory, and more extensively in the diagrammatic microscopic approach based on BCS theory, SC fluctuations as well as other quantum contributions (weak localization, etc.) enabled a new way to investigate and characterize disordered electron systems, granular metals, Josephson structures, artificial superlattices, and others. The characteristic feature of SC fluctuations is its strong dependence on temperature and magnetic field in the vicinity of the superconducting phase transition. This dependence allows the separation of fluctuation effects from other contributions and provides information about the microscopic parameters of a material, in particular, the critical temperature and the zero-temperature critical magnetic field. As such, SC fluctuations are very sensitive to the relaxation processes that break phase coherence and can be used as a versatile characterization instrument for SCs: Fluctuation spectroscopy has emerged as a powerful tool for studying the properties of superconducting systems on a quantitative level. Here the physics of SC fluctuations is reviewed, commencing from a qualitative description of thermodynamic fluctuations close to the critical temperature and quantum fluctuations at zero temperature in the vicinity of the second critical field. The analysis of the latter allows us to present fluctuation formation as a fragmentation of the Abrikosov lattice. Finally, this review highlights a series of experimental findings followed by microscopic description and numerical analysis of the effects of fluctuations on numerous properties of superconductors in the entire phase diagram and beyond the superconducting phase.« less

Fluctuation spectroscopy: From Rayleigh-Jeans waves to Abrikosov vortex clusters

NASA Astrophysics Data System (ADS)

Varlamov, A. A.; Galda, A.; Glatz, A.

2018-01-01

Superconducting (SC) fluctuations, discovered in the late 1960s, have constituted an important research area in superconductivity as they are manifest in a variety of phenomena. Indeed, the underlying physics of SC fluctuations makes it possible to elucidate the fundamental properties of the superconducting state. The interest in SC fluctuation phenomena was further enhanced with the discovery of cuprate high-temperature superconductors (HTSs). In these materials, superconducting fluctuations appear over a wide range of temperatures due to the superconductors extremely short coherence lengths and low effective dimensionality of the electron systems. These strong fluctuations lead to anomalous properties of the normal state in some HTS materials. Within the framework of the phenomenological Ginzburg-Landau theory, and more extensively in the diagrammatic microscopic approach based on BCS theory, SC fluctuations as well as other quantum contributions (weak localization, etc.) enabled a new way to investigate and characterize disordered electron systems, granular metals, Josephson structures, artificial superlattices, and others. The characteristic feature of SC fluctuations is its strong dependence on temperature and magnetic field in the vicinity of the superconducting phase transition. This dependence allows the separation of fluctuation effects from other contributions and provides information about the microscopic parameters of a material, in particular, the critical temperature and the zero-temperature critical magnetic field. As such, SC fluctuations are very sensitive to the relaxation processes that break phase coherence and can be used as a versatile characterization instrument for SCs: Fluctuation spectroscopy has emerged as a powerful tool for studying the properties of superconducting systems on a quantitative level. Here the physics of SC fluctuations is reviewed, commencing from a qualitative description of thermodynamic fluctuations close to the critical temperature and quantum fluctuations at zero temperature in the vicinity of the second critical field. The analysis of the latter allows us to present fluctuation formation as a fragmentation of the Abrikosov lattice. This review highlights a series of experimental findings followed by microscopic description and numerical analysis of the effects of fluctuations on numerous properties of superconductors in the entire phase diagram and beyond the superconducting phase.

Measurable characteristics of lysozyme crystal growth

NASA Technical Reports Server (NTRS)

Gorti, Sridhar; Forsythe, Elizabeth L.; Pusey, Marc L.

2005-01-01

The behavior of protein crystal growth is estimated from measurements performed at both the microscopic and molecular levels. In the absence of solutal flow, it was determined that a model that balances the macromolecular flux toward the crystal surface with the flux of the crystal surface well characterizes crystal growth observed using microscopic methods. Namely, it was determined that the model provides accurate estimates for the crystal-growth velocities upon evaluation of crystal-growth measurements obtained in time. Growth velocities thus determined as a function of solution supersaturation were further interpreted using established deterministic models. From analyses of crystal-growth velocities, it was found that the mode of crystal growth varies with respect to increasing solution supersaturation, possibly owing to kinetic roughening. To verify further the hypothesis of kinetic roughening, crystal growth at the molecular level was examined using atomic force microscopy (AFM). From the AFM measurements, it was found that the magnitude of surface-height fluctuations, h(x), increases with increasing solution supersaturation. In contrast, the estimated characteristic length, xi, decreases rapidly upon increasing solution supersaturation. It was conjectured that the magnitude of both h(x) and xi could possibly determine the mode of crystal growth. Although the data precede any exact theory, the non-critical divergence of h(x) and xi with respect to increasing solution supersaturation was nevertheless preliminarily established. Moreover, approximate models to account for behavior of both h(x) and xi are also presented.

Evaluation of experimental parameters for growth of homogeneous solid solutions

NASA Astrophysics Data System (ADS)

Scheel, Hans J.; Swendsen, Robert H.

2001-12-01

In this paper, we discuss the experimental conditions required to grow large two-component crystals from homogeneous solid solutions. Building on the work of Burton, Prim, and Slichter and that of Van Erk, we are able to establish that the concentration fluctuations for diffusion-limited growth are rather insensitive to hydrodynamic fluctuations. This enables a crystal grower to take advantage of forced convection to optimize growth rates without aggravating the striation problem.

In Situ Visualization of the Growth and Fluctuations of Nanoparticle Superlattice in Liquids

NASA Astrophysics Data System (ADS)

Ou, Zihao; Shen, Bonan; Chen, Qian

We use liquid phase transmission electron microscopy to image and understand the crystal growth front and interfacial fluctuation of a nanoparticle superlattice. With single particle resolution and hundreds of nanoscale building blocks in view, we are able to identify the interface between ordered lattice and disordered structure and visualize the kinetics of single building block attachment at the lattice growth front. The spatial interfacial fluctuation profiles support the capillary wave theory, from which we derive a surface stiffness value consistent with scaling analysis. Our experiments demonstrate the potential of extending model study on collective systems to nanoscale with single particle resolution and testing fundamental theories of condensed matter at a length scale linking atoms and micron-sized colloids.

Altruistic behavior pays, or the importance of fluctuations in evolutionary game theory

NASA Astrophysics Data System (ADS)

Sánchez, Angel; Cuesta, José A.; Roca, Carlos P.

2005-07-01

Human behavior is one of the main problems for evolution, as it is often the case that human actions are disadvantageous for the self and advantageous for other people. Behind this puzzle are our beliefs about rational behavior, based on game theory. Here we show that by going beyond the standard game-theoretical conventions, apparently altruistic behavior can be understood as self-interested. We discuss in detail an example related to the so called Ultimatum game and illustrate the appearance of altruistic behavior induced by fluctuations. In addition, we claim that in general settings, fluctuations play a very relevant role, and we support this claim by considering a completely different example, namely the Stag-Hunt game.

Chiral vacuum fluctuations in quantum gravity.

PubMed

Magueijo, João; Benincasa, Dionigi M T

2011-03-25

We examine tensor perturbations around a de Sitter background within the framework of Ashtekar's variables and its cousins parameterized by the Immirzi parameter γ. At the classical level we recover standard cosmological perturbation theory, with illuminating insights. Quantization leads to real novelties. In the low energy limit we find a second quantized theory of gravitons which displays different vacuum fluctuations for right and left gravitons. Nonetheless right and left gravitons have the same (positive) energies, resolving a number of paradoxes suggested in the literature. The right-left asymmetry of the vacuum fluctuations depends on γ and the ordering of the Hamiltonian constraint, and it would leave a distinctive imprint in the polarization of the cosmic microwave background, thus opening quantum gravity to observational test.

Turbulent solutions of equations of fluid motion

NASA Technical Reports Server (NTRS)

Deissler, R. G.

1985-01-01

Some turbulent solutions of the unaveraged Navier-Stokes equations (equations of fluid motion) are reviewed. Those equations are solved numerically in order to study the nonlinear physics of incompressible turbulent flow. The three components of the mean-square velocity fluctuations are initially equal for the conditions chosen. The resulting solutions show characteristics of turbulence, such as the linear and nonlinear excitation of small-scale fluctuations. For the stronger fluctuations the initially nonrandom flow develops into an apparently random turbulence. The cases considered include turbulence that is statistically homogeneous or inhomogeneous and isotropic or anisotropic. A statistically steady-state turbulence is obtained by using a spatially periodic body force. Various turbulence processes, including the transfer of energy between eddy sizes and between directional components and the production, dissipation, and spatial diffusion of turbulence, are considered. It is concluded that the physical processes occurring in turbulence can be profitably studied numerically.

Cosmic ray diffusion: Report of the Workshop in Cosmic Ray Diffusion Theory

NASA Technical Reports Server (NTRS)

Birmingham, T. J.; Jones, F. C.

1975-01-01

A workshop in cosmic ray diffusion theory was held at Goddard Space Flight Center on May 16-17, 1974. Topics discussed and summarized are: (1) cosmic ray measurements as related to diffusion theory; (2) quasi-linear theory, nonlinear theory, and computer simulation of cosmic ray pitch-angle diffusion; and (3) magnetic field fluctuation measurements as related to diffusion theory.

The culmination of an inverse cascade: Mean flow and fluctuations

NASA Astrophysics Data System (ADS)

Frishman, Anna

2017-12-01

Two dimensional turbulence has a remarkable tendency to self-organize into large, coherent structures, forming a mean flow. The purpose of this paper is to elucidate how these structures are sustained and what determines them and the fluctuations around them. A recent theory for the mean flow will be reviewed. The theory assumes that turbulence is excited by a forcing supported on small scales and uses a linear shear model to relate the turbulent momentum flux to the mean shear rate. Extending the theory, it will be shown here that the relation between the momentum flux and mean shear is valid, and the momentum flux is non-zero, for both an isotropic forcing and an anisotropic forcing, independent of the dissipation mechanism at small scales. This conclusion requires taking into account that the linear shear model is an approximation to the real system. The proportionality between the momentum flux and the inverse of the shear can then be inferred most simply on dimensional grounds. Moreover, for a homogeneous pumping, the proportionality constant can be determined by symmetry considerations, recovering the result of the original theory. The regime of applicability of the theory, its compatibility with observations from simulations, a formula for the momentum flux for an inhomogeneous pumping, and results for the statistics of fluctuations will also be discussed.

Reducing background contributions in fluorescence fluctuation time-traces for single-molecule measurements in solution.

PubMed

Földes-Papp, Zeno; Liao, Shih-Chu Jeff; You, Tiefeng; Barbieri, Beniamino

2009-08-01

We first report on the development of new microscope means that reduce background contributions in fluorescence fluctuation methods: i) excitation shutter, ii) electronic switches, and iii) early and late time-gating. The elements allow for measuring molecules at low analyte concentrations. We first found conditions of early and late time-gating with time-correlated single-photon counting that made the fluorescence signal as bright as possible compared with the fluctuations in the background count rate in a diffraction-limited optical set-up. We measured about a 140-fold increase in the amplitude of autocorrelated fluorescence fluctuations at the lowest analyte concentration of about 15 pM, which gave a signal-to-background advantage of more than two-orders of magnitude. The results of this original article pave the way for single-molecule detection in solution and in live cells without immobilization or hydrodynamic/electrokinetic focusing at longer observation times than are currently available.

Modeling the free energy surfaces of electron transfer in condensed phases

NASA Astrophysics Data System (ADS)

Matyushov, Dmitry V.; Voth, Gregory A.

2000-10-01

We develop a three-parameter model of electron transfer (ET) in condensed phases based on the Hamiltonian of a two-state solute linearly coupled to a harmonic, classical solvent mode with different force constants in the initial and final states (a classical limit of the quantum Kubo-Toyozawa model). The exact analytical solution for the ET free energy surfaces demonstrates the following features: (i) the range of ET reaction coordinates is limited by a one-sided fluctuation band, (ii) the ET free energies are infinite outside the band, and (iii) the free energy surfaces are parabolic close to their minima and linear far from the minima positions. The model provides an analytical framework to map physical phenomena conflicting with the Marcus-Hush two-parameter model of ET. Nonlinear solvation, ET in polarizable charge-transfer complexes, and configurational flexibility of donor-acceptor complexes are successfully mapped onto the model. The present theory leads to a significant modification of the energy gap law for ET reactions.

Coupled Kardar-Parisi-Zhang Equations in One Dimension

NASA Astrophysics Data System (ADS)

Ferrari, Patrik L.; Sasamoto, Tomohiro; Spohn, Herbert

2013-11-01

Over the past years our understanding of the scaling properties of the solutions to the one-dimensional KPZ equation has advanced considerably, both theoretically and experimentally. In our contribution we export these insights to the case of coupled KPZ equations in one dimension. We establish equivalence with nonlinear fluctuating hydrodynamics for multi-component driven stochastic lattice gases. To check the predictions of the theory, we perform Monte Carlo simulations of the two-component AHR model. Its steady state is computed using the matrix product ansatz. Thereby all coefficients appearing in the coupled KPZ equations are deduced from the microscopic model. Time correlations in the steady state are simulated and we confirm not only the scaling exponent, but also the scaling function and the non-universal coefficients.

Numerical approach on dynamic self-assembly of colloidal particles

NASA Astrophysics Data System (ADS)

Ibrahimi, Muhamet; Ilday, Serim; Makey, Ghaith; Pavlov, Ihor; Yavuz, Özgàn; Gulseren, Oguz; Ilday, Fatih Omer

Far from equilibrium systems of artificial ensembles are crucial for understanding many intelligent features in self-organized natural systems. However, the lack of established theory underlies a need for numerical implementations. Inspired by a novel work, we simulate a solution-suspended colloidal system that dynamically self assembles due to convective forces generated in the solvent when heated by a laser. In order to incorporate with random fluctuations of particles and continuously changing flow, we exploit a random-walk based Brownian motion model and a fluid dynamics solver prepared for games, respectively. Simulation results manage to fit to experiments and show many quantitative features of a non equilibrium dynamic self assembly, including phase space compression and an ensemble-energy input feedback loop.

Application of the bridged crack model for evaluation of materials repairing and self-healing

NASA Astrophysics Data System (ADS)

Perelmuter, M.

2017-12-01

The bridged crack model is used for analysis of repairing and self-healing of cracked structures. Material repairing is treated as insertions of external ligaments into cracks or placement of the reinforcing patches over cracks. Bonds destruction and regeneration at the crack bridged zone is evaluated by the thermo-fluctuation kinetic theory. The healing time is dependent on the chemical reaction rate of the healing agent, the crack size and the external loads. The decreasing of the stress intensity factors is used as the measure of the repairing and healing effects. The mathematical background of the problem solution is based on the methods of the singular integral-differential equations. The model can be used for the evaluation of composite materials durability.

Radiation effects studies for the high-resolution spectrograph

NASA Technical Reports Server (NTRS)

Smith, L. C.; Becher, J.

1982-01-01

The generation and collection of charge carriers created during the passage of energetic protons through a silicon photodiode array are modeled. Pulse height distributions of noise charge collected during exposure of a digicon type diode array to 21 and 75 MeV protons were obtained. The magnitude of charge collected by a diode from each proton event is determined not only by diffusion, but by statistical considerations involving the ionization process itself. Utilizing analytical solutions to the diffusion equation for transport of minority carriers, together with the Vavilov theory of energy loss fluctuations in thin absorbers, simulations of the pulse height spectra which follow the experimental distributions fairly well are presented and an estimate for the minority carrier diffusion length L sub d is provided.

Flux and Hall states in ABJM with dynamical flavors

NASA Astrophysics Data System (ADS)

Bea, Yago; Jokela, Niko; Lippert, Matthew; Ramallo, Alfonso V.; Zoakos, Dimitrios

2015-03-01

We study the physics of probe D6-branes with quantized internal worldvolume flux in the ABJM background with unquenched massless flavors. This flux breaks parity in the (2+1)-dimensional gauge theory and allows quantum Hall states. Parity breaking is also explicitly demonstrated via the helicity dependence of the meson spectrum. We obtain general expressions for the conductivities, both in the gapped Minkowski embeddings and in the compressible black hole ones. These conductivities depend on the flux and contain a contribution from the dynamical flavors which can be regarded as an effect of intrinsic disorder due to quantum fluctuations of the fundamentals. We present an explicit, analytic family of supersymmetric solutions with nonzero charge density, electric, and magnetic fields.

Nonisothermal fluctuating hydrodynamics and Brownian motion

NASA Astrophysics Data System (ADS)

Falasco, G.; Kroy, K.

2016-03-01

The classical theory of Brownian dynamics follows from coarse graining the underlying linearized fluctuating hydrodynamics of the solvent. We extend this procedure to globally nonisothermal conditions, requiring only a local thermal equilibration of the solvent. Starting from the conservation laws, we establish the stochastic equations of motion for the fluid momentum fluctuations in the presence of a suspended Brownian particle. These are then contracted to the nonisothermal generalized Langevin description of the suspended particle alone, for which the coupling to stochastic temperature fluctuations is found to be negligible under typical experimental conditions.

Exact solutions for kinetic models of macromolecular dynamics.

PubMed

Chemla, Yann R; Moffitt, Jeffrey R; Bustamante, Carlos

2008-05-15

Dynamic biological processes such as enzyme catalysis, molecular motor translocation, and protein and nucleic acid conformational dynamics are inherently stochastic processes. However, when such processes are studied on a nonsynchronized ensemble, the inherent fluctuations are lost, and only the average rate of the process can be measured. With the recent development of methods of single-molecule manipulation and detection, it is now possible to follow the progress of an individual molecule, measuring not just the average rate but the fluctuations in this rate as well. These fluctuations can provide a great deal of detail about the underlying kinetic cycle that governs the dynamical behavior of the system. However, extracting this information from experiments requires the ability to calculate the general properties of arbitrarily complex theoretical kinetic schemes. We present here a general technique that determines the exact analytical solution for the mean velocity and for measures of the fluctuations. We adopt a formalism based on the master equation and show how the probability density for the position of a molecular motor at a given time can be solved exactly in Fourier-Laplace space. With this analytic solution, we can then calculate the mean velocity and fluctuation-related parameters, such as the randomness parameter (a dimensionless ratio of the diffusion constant and the velocity) and the dwell time distributions, which fully characterize the fluctuations of the system, both commonly used kinetic parameters in single-molecule measurements. Furthermore, we show that this formalism allows calculation of these parameters for a much wider class of general kinetic models than demonstrated with previous methods.

Local oscillator induced degradation of medium-term stability in passive atomic frequency standards

NASA Technical Reports Server (NTRS)

Dick, G. John; Prestage, John D.; Greenhall, Charles A.; Maleki, Lute

1990-01-01

As the performance of passive atomic frequency standards improves, a new limitation is encountered due to frequency fluctuations in an ancillary local oscillator (L.O.). The effect is due to time variation in the gain of the feedback which compensates L.O. frequency fluctuations. The high performance promised by new microwave and optical trapped ion standards may be severely compromised by this effect. Researchers present an analysis of this performance limitation for the case of sequentially interrogated standards. The time dependence of the sensitivity of the interrogation process to L.O. frequency fluctuations is evaluated for single-pulse and double-pulse Ramsey RF interrogation and for amplitude modulated pulses. The effect of these various time dependencies on performance of the standard is calculated for an L.O. with frequency fluctuations showing a typical 1/f spectral density. A limiting 1/sq. root gamma dependent deviation of frequency fluctuations is calculated as a function of pulse lengths, dead time, and pulse overlap. Researchers also present conceptual and hardware-oriented solutions to this problem which achieve a much more nearly constant sensitivity to L.O. fluctuations. Solutions involve use of double-pulse interrogation; alternate interrogation of multiple traps so that the dead time of one trap can be covered by operation of the other; and the use of double-pulse interrogation for two traps, so that during the time of the RF pulses, the increasing sensitivity of one trap tends to compensate for the decreasing sensitivity of the other. A solution making use of amplified-modulated pulses is also presented which shows nominally zero time variation.

Turbulent solutions of the equations of fluid motion

NASA Technical Reports Server (NTRS)

Deissler, R. G.

1984-01-01

Some turbulent solutions of the unaveraged Navier-Stokes equations (equations of fluid motion) are reviewed. Those equations are solved numerically in order to study the nonlinear physics of incompressible turbulent flow. Initial three-dimensional cosine velocity fluctuations and periodic boundary conditions are used in most of the work considered. The three components of the mean-square velocity fluctuations are initially equal for the conditions chosen. The resulting solutions show characteristics of turbulence such as the linear and nonlinear excitation of small-scale fluctuations. For the stronger fluctuations, the initially nonrandom flow develops into an apparently random turbulence. Thus randomness or turbulence can arise as a consequence of the structure of the Navier-Stokes equations. The cases considered include turbulence which is statistically homogeneous or inhomogeneous and isotropic or anisotropic. A mean shear is present in some cases. A statistically steady-state turbulence is obtained by using a spatially periodic body force. Various turbulence processes, including the transfer of energy between eddy sizes and between directional components, and the production, dissipation, and spatial diffusion of turbulence, are considered. It is concluded that the physical processes occurring in turbulence can be profitably studied numerically.

General framework for fluctuating dynamic density functional theory

NASA Astrophysics Data System (ADS)

Durán-Olivencia, Miguel A.; Yatsyshin, Peter; Goddard, Benjamin D.; Kalliadasis, Serafim

2017-12-01

We introduce a versatile bottom-up derivation of a formal theoretical framework to describe (passive) soft-matter systems out of equilibrium subject to fluctuations. We provide a unique connection between the constituent-particle dynamics of real systems and the time evolution equation of their measurable (coarse-grained) quantities, such as local density and velocity. The starting point is the full Hamiltonian description of a system of colloidal particles immersed in a fluid of identical bath particles. Then, we average out the bath via Zwanzig’s projection-operator techniques and obtain the stochastic Langevin equations governing the colloidal-particle dynamics. Introducing the appropriate definition of the local number and momentum density fields yields a generalisation of the Dean-Kawasaki (DK) model, which resembles the stochastic Navier-Stokes description of a fluid. Nevertheless, the DK equation still contains all the microscopic information and, for that reason, does not represent the dynamical law of observable quantities. We address this controversial feature of the DK description by carrying out a nonequilibrium ensemble average. Adopting a natural decomposition into local-equilibrium and nonequilibrium contribution, where the former is related to a generalised version of the canonical distribution, we finally obtain the fluctuating-hydrodynamic equation governing the time-evolution of the mesoscopic density and momentum fields. Along the way, we outline the connection between the ad hoc energy functional introduced in previous DK derivations and the free-energy functional from classical density-functional theory. The resultant equation has the structure of a dynamical density-functional theory (DDFT) with an additional fluctuating force coming from the random interactions with the bath. We show that our fluctuating DDFT formalism corresponds to a particular version of the fluctuating Navier-Stokes equations, originally derived by Landau and Lifshitz. Our framework thus provides the formal apparatus for ab initio derivations of fluctuating DDFT equations capable of describing the dynamics of soft-matter systems in and out of equilibrium.

Critical point in the phase diagram of primordial quark-gluon matter from black hole physics

NASA Astrophysics Data System (ADS)

Critelli, Renato; Noronha, Jorge; Noronha-Hostler, Jacquelyn; Portillo, Israel; Ratti, Claudia; Rougemont, Romulo

2017-11-01

Strongly interacting matter undergoes a crossover phase transition at high temperatures T ˜1012 K and zero net-baryon density. A fundamental question in the theory of strong interactions, QCD, is whether a hot and dense system of quarks and gluons displays critical phenomena when doped with more quarks than antiquarks, where net-baryon number fluctuations diverge. Recent lattice QCD work indicates that such a critical point can only occur in the baryon dense regime of the theory, which defies a description from first principles calculations. Here we use the holographic gauge/gravity correspondence to map the fluctuations of baryon charge in the dense quark-gluon liquid onto a numerically tractable gravitational problem involving the charge fluctuations of holographic black holes. This approach quantitatively reproduces ab initio results for the lowest order moments of the baryon fluctuations and makes predictions for the higher-order baryon susceptibilities and also for the location of the critical point, which is found to be within the reach of heavy-ion collision experiments.

Quasi-Lagrangian measurements of density surface fluctuations and power spectra in the stratosphere

NASA Technical Reports Server (NTRS)

Quinn, Elizabeth P.; Holzworth, Robert H.

1987-01-01

Pressure and temperature data from eight superpressure balloon flights at 26 km in the southern hemisphere stratosphere are analyzed. The balloons, which float on a constant density surface, travel steadily westward during summer and eastward during winter, as expected from local climatology. Two types of fluctuations are observed: neutral buoyancy oscillations (NBO) of around 4 min, and 0.1- to 1-hour oscillations that are characterized as small-amplitude density surface fluctuations. Lapse rates and densities are calculated and found to agree well with the expected values. Examples of wave damping and simultaneous fluctuation at two nearby balloons are presented. Spectral analysis is performed clearly showing the NBO and that the majority of the power is in the mesoscale range. Spectral slopes of power versus frequency are measured to be on the average -2.18 + or - 0.24 for pressure and -1.72 + or - 0.24 for temperature. These slopes are compared to the predictions of turbulence theories and the theory of a universal gravity wave spectrum.

Generalization of the Förster resonance energy transfer theory for quantum mechanical modulation of the donor-acceptor coupling

NASA Astrophysics Data System (ADS)

Jang, Seogjoo

2007-11-01

The Förster resonance energy transfer theory is generalized for inelastic situations with quantum mechanical modulation of the donor-acceptor coupling. Under the assumption that the modulations are independent of the electronic excitation of the donor and the acceptor, a general rate expression is derived, which involves two dimensional frequency-domain convolution of the donor emission line shape, the acceptor absorption line shape, and the spectral density of the modulation of the donor-acceptor coupling. For two models of modulation, detailed rate expressions are derived. The first model is the fluctuation of the donor-acceptor distance, approximated as a quantum harmonic oscillator coupled to a bath of other quantum harmonic oscillators. The distance fluctuation results in additional terms in the rate, which in the small fluctuation limit depend on the inverse eighth power of the donor-acceptor distance. The second model is the fluctuation of the torsional angle between the two transition dipoles, which is modeled as a quantum harmonic oscillator coupled to a bath of quantum harmonic oscillators and causes sinusoidal modulation of the donor-acceptor coupling. The rate expression has new elastic and inelastic terms, depending sensitively on the value of the minimum energy torsional angle. Experimental implications of the present theory and some of the open theoretical issues are discussed.

Unsteady Crystal Growth Due to Step-Bunch Cascading

NASA Technical Reports Server (NTRS)

Vekilov, Peter G.; Lin, Hong; Rosenberger, Franz

1997-01-01

Based on our experimental findings of growth rate fluctuations during the crystallization of the protein lysozym, we have developed a numerical model that combines diffusion in the bulk of a solution with diffusive transport to microscopic growth steps that propagate on a finite crystal facet. Nonlinearities in layer growth kinetics arising from step interaction by bulk and surface diffusion, and from step generation by surface nucleation, are taken into account. On evaluation of the model with properties characteristic for the solute transport, and the generation and propagation of steps in the lysozyme system, growth rate fluctuations of the same magnitude and characteristic time, as in the experiments, are obtained. The fluctuation time scale is large compared to that of step generation. Variations of the governing parameters of the model reveal that both the nonlinearity in step kinetics and mixed transport-kinetics control of the crystallization process are necessary conditions for the fluctuations. On a microscopic scale, the fluctuations are associated with a morphological instability of the vicinal face, in which a step bunch triggers a cascade of new step bunches through the microscopic interfacial supersaturation distribution.

Pressure fluctuations on the surface of a cylinder in uniform flow

NASA Technical Reports Server (NTRS)

Ayoub, A.; Karamcheti, K.

1976-01-01

The problem of determining the pressure fluctuations induced on the surface of a cylinder by the fluctuating wake behind it is formulated. A formal solution relating the unsteady surface pressure field to the velocity field in the wake is derived and used to obtain general results independent of cylinder shape and Reynolds number. The case of the circular cylinder is then examined in detail.

BOOK REVIEW: Cosmology

NASA Astrophysics Data System (ADS)

Silk, Joseph

2008-11-01

The field of cosmology has been transformed since the glorious decades of the 1920's and 1930's when theory and observation converged to develop the current model of the expanding universe. It was a triumph of the theory of general relativity and astronomy. The first revolution came when the nuclear physicists entered the fray. This marked the debut of the hot big bang, in which the light elements were synthesized in the first three minutes. It was soon realised that elements like carbon and iron were synthesized in exploding stars. However helium, as well as deuterium and lithium, remain as George Gamow envisaged, the detritus of the big bang. The climax arrived with one of the most remarkable discoveries of the twentieth century, the cosmic microwave background radiation, in 1964. The fossil glow turned out to have the spectrum of an ideal black body. One could not imagine a stronger confirmation of the hot and dense origin of the universe. This discovery set the scene for the next major advance. It was now the turn of the particle physicists, who realized that the energies attained near the beginning of the universe, and unachievable in any conceivable terrestrial accelerator, provided a unique testing ground for theories of grand unification of the fundamental forces. This led Alan Guth and Andrei Linde in 1980 to propose the theory of inflation, which solved outstanding puzzles of the big bang. One could now understand why the universe is so large and homogeneous, and the origin of the seed fluctuations that gave rise to large-scale structure. A key prediction was that the universe should have Euclidean geometry, now verified to a precision of a few percent. Modern cosmology is firmly embedded in particle physics. It merits a text written by a particle physicist who can however appreciate the contributions of astronomy that provide the foundation and infrastructure for the theory of the expanding universe. There are now several such texts available. The most recent, and comprehensive, is Cosmology, in which the University of Texas physicist and Nobel Laureate, Steven Weinberg provides a concise introduction to modern cosmology. The book is aimed at the level of a final year physics undergraduate, or a first year graduate student. The discussion is self-contained, with numerous derivations. It begins with an overview of the standard cosmological model, and presents a detailed treatment of fluctuation growth. There are sections on gravitational lensing and inflationary cosmology, on microwave background fluctuations and structure growth. There are aspects however where a supplementary book is essential for the physicist being introduced to cosmology. The text is lacking in physical cosmology. The baryon physics of galaxy formation is barely mentioned, apart from a discussion of the Jeans mass. And it ignores one of the greatest contributions to the field by Russian cosmologist Yaakov Zel'dovich, who discovered the only nonspherical solution to the nonlinear evolution of density fluctuations, one that has since dominated our understanding of the large-scale structure of the universe via the cosmic web. But these are minor quibbles about what provides an outstanding introduction to modern cosmology, and one that takes us from the physics fundamentals up to the cosmic frontier. I recommend Cosmology for anyone wishing to enter the field and with a good physics background. It is ideal for the astronomer who may only have a sketchy knowledge of general relativity or particle physics. She will learn about vielbeins and scalar fields, gauge-invariant fluctuation theory and inflation. Steven Weinberg is a leading physicist who has also made important contributions to cosmology. The text provides a rigorous treatment of the standard model of cosmology, and of structure formation. Numerous exercises are provided. It provides an excellent core for a course on cosmology.

Modeling and Optimization of Coordinative Operation of Hydro-wind-photovoltaic Considering Power Generation and Output Fluctuation

NASA Astrophysics Data System (ADS)

Wang, Xianxun; Mei, Yadong

2017-04-01

Coordinative operation of hydro-wind-photovoltaic is the solution of mitigating the conflict of power generation and output fluctuation of new energy and conquering the bottleneck of new energy development. Due to the deficiencies of characterizing output fluctuation, depicting grid construction and disposal of power abandon, the research of coordinative mechanism is influenced. In this paper, the multi-object and multi-hierarchy model of coordinative operation of hydro-wind-photovoltaic is built with the aim of maximizing power generation and minimizing output fluctuation and the constraints of topotaxy of power grid and balanced disposal of power abandon. In the case study, the comparison of uncoordinative and coordinative operation is carried out with the perspectives of power generation, power abandon and output fluctuation. By comparison from power generation, power abandon and output fluctuation between separate operation and coordinative operation of multi-power, the coordinative mechanism is studied. Compared with running solely, coordinative operation of hydro-wind-photovoltaic can gain the compensation benefits. Peak-alternation operation reduces the power abandon significantly and maximizes resource utilization effectively by compensating regulation of hydropower. The Pareto frontier of power generation and output fluctuation is obtained through multiple-objective optimization. It clarifies the relationship of mutual influence between these two objects. When coordinative operation is taken, output fluctuation can be markedly reduced at the cost of a slight decline of power generation. The power abandon also drops sharply compared with operating separately. Applying multi-objective optimization method to optimize the coordinate operation, Pareto optimal solution set of power generation and output fluctuation is achieved.

Principle of minimal work fluctuations.

PubMed

Xiao, Gaoyang; Gong, Jiangbin

2015-08-01

Understanding and manipulating work fluctuations in microscale and nanoscale systems are of both fundamental and practical interest. For example, in considering the Jarzynski equality 〈e-βW〉=e-βΔF, a change in the fluctuations of e-βW may impact how rapidly the statistical average of e-βW converges towards the theoretical value e-βΔF, where W is the work, β is the inverse temperature, and ΔF is the free energy difference between two equilibrium states. Motivated by our previous study aiming at the suppression of work fluctuations, here we obtain a principle of minimal work fluctuations. In brief, adiabatic processes as treated in quantum and classical adiabatic theorems yield the minimal fluctuations in e-βW. In the quantum domain, if a system initially prepared at thermal equilibrium is subjected to a work protocol but isolated from a bath during the time evolution, then a quantum adiabatic process without energy level crossing (or an assisted adiabatic process reaching the same final states as in a conventional adiabatic process) yields the minimal fluctuations in e-βW, where W is the quantum work defined by two energy measurements at the beginning and at the end of the process. In the classical domain where the classical work protocol is realizable by an adiabatic process, then the classical adiabatic process also yields the minimal fluctuations in e-βW. Numerical experiments based on a Landau-Zener process confirm our theory in the quantum domain, and our theory in the classical domain explains our previous numerical findings regarding the suppression of classical work fluctuations [G. Y. Xiao and J. B. Gong, Phys. Rev. E 90, 052132 (2014)].

Influence of spin and charge fluctuations on spectra of the two-dimensional Hubbard model

NASA Astrophysics Data System (ADS)

Sherman, A.

2018-05-01

The influence of spin and charge fluctuations on spectra of the two-dimensional fermionic Hubbard model is considered using the strong coupling diagram technique. Infinite sequences of diagrams containing ladder inserts, which describe the interaction of electrons with these fluctuations, are summed, and obtained equations are self-consistently solved for the ranges of Hubbard repulsions , temperatures and electron concentrations with t the intersite hopping constant. For all considered U the system exhibits a transition to the long-range antiferromagnetic order at . At the same time no indication of charge ordering is observed. Obtained solutions agree satisfactorily with results of other approaches and obey moments sum rules. In the considered region of the U-T plane, the curve separating metallic solutions passes from at the highest temperatures to U  =  2t at for half-filling. If only short-range fluctuations are allowed for the remaining part of this region is occupied by insulating solutions. Taking into account long-range fluctuations leads to strengthening of maxima tails, which transform a part of insulating solutions into bad-metal states. For low T, obtained results allow us to trace the gradual transition from the regime of strong correlations with the pronounced four-band structure and well-defined Mott gap for to the Slater regime of weak correlations with the spectral intensity having a dip along the boundary of the magnetic Brillouin zone due to an antiferromagnetic ordering for . For and doping leads to the occurrence of a pseudogap near the Fermi level, which is a consequence of the splitting out of a narrow band from a Hubbard subband. Obtained spectra feature waterfalls and Fermi arcs, which are similar to those observed in hole-doped cuprates.

The cosmic microwave background

NASA Technical Reports Server (NTRS)

Silk, Joseph

1991-01-01

Recent limits on spectral distortions and angular anisotropies in the cosmic microwave background are reviewed. The various backgrounds are described, and the theoretical implications are assessed. Constraints on inflationary cosmology dominated by cold dark matter (CDM) and on open cosmological models dominated by baryonic dark matter (BDM), with, respectively, primordial random phase scale-invariant curvature fluctuations or non-gaussian isocurvature fluctuations are described. More exotic theories are addressed, and I conclude with the 'bottom line': what theorists expect experimentalists to be measuring within the next two to three years without having to abandon their most cherished theories.

Statistical field theory description of inhomogeneous polarizable soft matter

NASA Astrophysics Data System (ADS)

Martin, Jonathan M.; Li, Wei; Delaney, Kris T.; Fredrickson, Glenn H.

2016-10-01

We present a new molecularly informed statistical field theory model of inhomogeneous polarizable soft matter. The model is based on fluid elements, referred to as beads, that can carry a net monopole of charge at their center of mass and a fixed or induced dipole through a Drude-type distributed charge approach. The beads are thus polarizable and naturally manifest attractive van der Waals interactions. Beyond electrostatic interactions, beads can be given soft repulsions to sustain fluid phases at arbitrary densities. Beads of different types can be mixed or linked into polymers with arbitrary chain models and sequences of charged and uncharged beads. By such an approach, it is possible to construct models suitable for describing a vast range of soft-matter systems including electrolyte and polyelectrolyte solutions, ionic liquids, polymerized ionic liquids, polymer blends, ionomers, and block copolymers, among others. These bead models can be constructed in virtually any ensemble and converted to complex-valued statistical field theories by Hubbard-Stratonovich transforms. One of the fields entering the resulting theories is a fluctuating electrostatic potential; other fields are necessary to decouple non-electrostatic interactions. We elucidate the structure of these field theories, their consistency with macroscopic electrostatic theory in the absence and presence of external electric fields, and the way in which they embed van der Waals interactions and non-uniform dielectric properties. Their suitability as a framework for computational studies of heterogeneous soft matter systems using field-theoretic simulation techniques is discussed.

Statistical field theory description of inhomogeneous polarizable soft matter.

PubMed

Martin, Jonathan M; Li, Wei; Delaney, Kris T; Fredrickson, Glenn H

2016-10-21

We present a new molecularly informed statistical field theory model of inhomogeneous polarizable soft matter. The model is based on fluid elements, referred to as beads, that can carry a net monopole of charge at their center of mass and a fixed or induced dipole through a Drude-type distributed charge approach. The beads are thus polarizable and naturally manifest attractive van der Waals interactions. Beyond electrostatic interactions, beads can be given soft repulsions to sustain fluid phases at arbitrary densities. Beads of different types can be mixed or linked into polymers with arbitrary chain models and sequences of charged and uncharged beads. By such an approach, it is possible to construct models suitable for describing a vast range of soft-matter systems including electrolyte and polyelectrolyte solutions, ionic liquids, polymerized ionic liquids, polymer blends, ionomers, and block copolymers, among others. These bead models can be constructed in virtually any ensemble and converted to complex-valued statistical field theories by Hubbard-Stratonovich transforms. One of the fields entering the resulting theories is a fluctuating electrostatic potential; other fields are necessary to decouple non-electrostatic interactions. We elucidate the structure of these field theories, their consistency with macroscopic electrostatic theory in the absence and presence of external electric fields, and the way in which they embed van der Waals interactions and non-uniform dielectric properties. Their suitability as a framework for computational studies of heterogeneous soft matter systems using field-theoretic simulation techniques is discussed.

Propagation peculiarities of mean field massive gravity

DOE PAGES

Deser, S.; Waldron, A.; Zahariade, G.

2015-07-28

Massive gravity (mGR) describes a dynamical “metric” on a fiducial, background one. We investigate fluctuations of the dynamics about mGR solutions, that is about its “mean field theory”. Analyzing mean field massive gravity (m¯GR) propagation characteristics is not only equivalent to studying those of the full non-linear theory, but also in direct correspondence with earlier analyses of charged higher spin systems, the oldest example being the charged, massive spin 3/2 Rarita–Schwinger (RS) theory. The fiducial and mGR mean field background metrics in the m¯GR model correspond to the RS Minkowski metric and external EM field. The common implications in bothmore » systems are that hyperbolicity holds only in a weak background-mean-field limit, immediately ruling both theories out as fundamental theories; a situation in stark contrast with general relativity (GR) which is at least a consistent classical theory. Moreover, even though both m¯GR and RS theories can still in principle be considered as predictive effective models in the weak regime, their lower helicities then exhibit superluminal behavior: lower helicity gravitons are superluminal as compared to photons propagating on either the fiducial or background metric. Thus our approach has uncovered a novel, dispersive, “crystal-like” phenomenon of differing helicities having differing propagation speeds. As a result, this applies both to m¯GR and mGR, and is a peculiar feature that is also problematic for consistent coupling to matter.« less

Hydrodynamic fluctuations, nonequilibrium equations of state, and the shift of the spinodal line in polymer solutions under flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Criado-Sancho, M.; Casas-Vazquez, J.; Jou, D.

1997-08-01

In the literature, the shift of the spinodal line of polymer solutions under flow is attributed either to an actual shift of the spinodal due to a nonequilibrium modification of the equation of state for the chemical potential, or to an apparent shift due to an increase of hydrodynamic fluctuations owing to the flow. Here we see that both approaches are compatible and that both effects add up. {copyright} {ital 1997} {ital The American Physical Society}

Density fluctuations from strings and galaxy formation

NASA Technical Reports Server (NTRS)

Vilenkin, A.; Shafi, Q.

1983-01-01

The spectra of density fluctuations caused by strings in a universe dominated either by baryons, neutrinos, or axions are presented. Realistic scenarios for galaxy formation seem possible in all three cases. Examples of grand unified theories which lead to strings with the desired mass scales are given.

Deconstructing zero: resurgence, supersymmetry and complex saddles

DOE PAGES

Dunne, Gerald V.; Ünsal, Mithat

2016-12-01

We explain how a vanishing, or truncated, perturbative expansion, such as often arises in semi-classically tractable supersymmetric theories, can nevertheless be related to fluctuations about non-perturbative sectors via resurgence. We also demonstrate that, in the same class of theories, the vanishing of the ground state energy (unbroken supersymmetry) can be attributed to the cancellation between a real saddle and a complex saddle (with hidden topological angle π), and positivity of the ground state energy (broken supersymmetry) can be interpreted as the dominance of complex saddles. In either case, despite the fact that the ground state energy is zero to allmore » orders in perturbation theory, all orders of fluctuations around non-perturbative saddles are encoded in the perturbative E (N, g). Finally, we illustrate these ideas with examples from supersymmetric quantum mechanics and quantum field theory.« less

Statistical theory of dynamo

NASA Astrophysics Data System (ADS)

Kim, E.; Newton, A. P.

2012-04-01

One major problem in dynamo theory is the multi-scale nature of the MHD turbulence, which requires statistical theory in terms of probability distribution functions. In this contribution, we present the statistical theory of magnetic fields in a simplified mean field α-Ω dynamo model by varying the statistical property of alpha, including marginal stability and intermittency, and then utilize observational data of solar activity to fine-tune the mean field dynamo model. Specifically, we first present a comprehensive investigation into the effect of the stochastic parameters in a simplified α-Ω dynamo model. Through considering the manifold of marginal stability (the region of parameter space where the mean growth rate is zero), we show that stochastic fluctuations are conductive to dynamo. Furthermore, by considering the cases of fluctuating alpha that are periodic and Gaussian coloured random noise with identical characteristic time-scales and fluctuating amplitudes, we show that the transition to dynamo is significantly facilitated for stochastic alpha with random noise. Furthermore, we show that probability density functions (PDFs) of the growth-rate, magnetic field and magnetic energy can provide a wealth of useful information regarding the dynamo behaviour/intermittency. Finally, the precise statistical property of the dynamo such as temporal correlation and fluctuating amplitude is found to be dependent on the distribution the fluctuations of stochastic parameters. We then use observations of solar activity to constrain parameters relating to the effect in stochastic α-Ω nonlinear dynamo models. This is achieved through performing a comprehensive statistical comparison by computing PDFs of solar activity from observations and from our simulation of mean field dynamo model. The observational data that are used are the time history of solar activity inferred for C14 data in the past 11000 years on a long time scale and direct observations of the sun spot numbers obtained in recent years 1795-1995 on a short time scale. Monte Carlo simulations are performed on these data to obtain PDFs of the solar activity on both long and short time scales. These PDFs are then compared with predicted PDFs from numerical simulation of our α-Ω dynamo model, where α is assumed to have both mean α0 and fluctuating α' parts. By varying the correlation time of fluctuating α', the ratio of the amplitude of the fluctuating to mean alpha <α'2>/α02 (where angular brackets <> denote ensemble average), and the ratio of poloidal to toroidal magnetic fields, we show that the results from our stochastic dynamo model can match the PDFs of solar activity on both long and short time scales. In particular, a good agreement is obtained when the fluctuation in alpha is roughly equal to the mean part with a correlation time shorter than the solar period.

Angle-of-Arrival Fluctuations of Light Propagating through the Intermittent Nocturnal Atmospheric Surface Layer

NASA Astrophysics Data System (ADS)

Muschinski, A.; Hu, K.; Root, L. M.; Tichkule, S.; Wijesundara, S. N.

2010-12-01

Mean values and fluctuations of angles-of-arrival (AOAs) of light emitted from astronomical or terrestrial sources and observed through a telescope equipped with a CCD camera carry quantitative information about certain statistics of the wind and temperature field, integrated along the propagation path. While scintillometry (i.e., the retrieval of atmospheric quantities from light intensity fluctuations) has been a popular technique among micrometeorologists for many years, there have been relatively few attempts to utilize AOA observations to probe the atmospheric surface layer (ASL). Here we report results from a field experiment that we conducted at the Boulder Atmospheric Observatory (BAO) site near Erie, CO, in June 2010. During the night of 15/16 June, the ASL was characterized by intermittent turbulence and intermittent gravity-wave events. We measured temperature and wind with 12 sonics (R.M. Young, Model 81000, sampling rate 31 Hz) mounted on two portable towers at altitudes between 1.45 m and 4.84 m AGL; air pressure with two quartz-crystal barometers (Paroscientific, 10 Hz); and AOAs by means of a CCD camera (Lumenera, Model 075M, thirty 640x480 frames per second) attached to a 14-inch, Schmidt-Cassegrain telescope (Meade, Model LX200GPS) pointing at a rectangular array of four test lights (LEDs, vertical spacing 8 cm, horizontal spacing 10 cm) located at a distance of 182 m. The optical path was horizontal and 1.7 m above flat ground. The two towers were located 2 m away from the optical path. In our presentation, we focus on AOA retrievals of the following quantities: temporal fluctuations of the path-averaged, vertical temperature gradient; mean values and fluctuations of the path-averaged, lateral wind velocity; and mean values and fluctuations of the path-averaged temperature turbulence structure parameter. We compare the AOA retrievals with the collocated and simultaneous point measurements obtained with the sonics, and we analyze our observations in the framework of the Monin-Obukhov theory. The AOA techniques enable us to detect temporal fluctuations of the path-averaged vertical temperature gradient (estimated over a height increment defined by the telescope's aperture diameter) down to a few millikelvins per meter, which probably cannot be achieved with sonics. Extremely small wind velocities can also be resolved. Therefore, AOA techniques are well suited for observations of the nocturnal surface layer under quiet conditions. AOA retrieval techniques have major advantages over scintillometric techniques because AOAs can be understood within the framework of the weak-scattering theory or even geometrical optics (the eikonal-fluctuation theory), while the well-known "saturation effect" makes the weak-scattering theory invalid for intensity fluctuations in the majority of cases of practical relevance.

Analytical theory of mesoscopic Bose-Einstein condensation in an ideal gas

NASA Astrophysics Data System (ADS)

Kocharovsky, Vitaly V.; Kocharovsky, Vladimir V.

2010-03-01

We find the universal structure and scaling of the Bose-Einstein condensation (BEC) statistics and thermodynamics (Gibbs free energy, average energy, heat capacity) for a mesoscopic canonical-ensemble ideal gas in a trap with an arbitrary number of atoms, any volume, and any temperature, including the whole critical region. We identify a universal constraint-cutoff mechanism that makes BEC fluctuations strongly non-Gaussian and is responsible for all unusual critical phenomena of the BEC phase transition in the ideal gas. The main result is an analytical solution to the problem of critical phenomena. It is derived by, first, calculating analytically the universal probability distribution of the noncondensate occupation, or a Landau function, and then using it for the analytical calculation of the universal functions for the particular physical quantities via the exact formulas which express the constraint-cutoff mechanism. We find asymptotics of that analytical solution as well as its simple analytical approximations which describe the universal structure of the critical region in terms of the parabolic cylinder or confluent hypergeometric functions. The obtained results for the order parameter, all higher-order moments of BEC fluctuations, and thermodynamic quantities perfectly match the known asymptotics outside the critical region for both low and high temperature limits. We suggest two- and three-level trap models of BEC and find their exact solutions in terms of the cutoff negative binomial distribution (which tends to the cutoff gamma distribution in the continuous limit) and the confluent hypergeometric distribution, respectively. Also, we present an exactly solvable cutoff Gaussian model of BEC in a degenerate interacting gas. All these exact solutions confirm the universality and constraint-cutoff origin of the strongly non-Gaussian BEC statistics. We introduce a regular refinement scheme for the condensate statistics approximations on the basis of the infrared universality of higher-order cumulants and the method of superposition and show how to model BEC statistics in the actual traps. In particular, we find that the three-level trap model with matching the first four or five cumulants is enough to yield remarkably accurate results for all interesting quantities in the whole critical region. We derive an exact multinomial expansion for the noncondensate occupation probability distribution and find its high-temperature asymptotics (Poisson distribution) and corrections to it. Finally, we demonstrate that the critical exponents and a few known terms of the Taylor expansion of the universal functions, which were calculated previously from fitting the finite-size simulations within the phenomenological renormalization-group theory, can be easily obtained from the presented full analytical solutions for the mesoscopic BEC as certain approximations in the close vicinity of the critical point.

Nonequilibrium free diffusion in seed leachate

NASA Astrophysics Data System (ADS)

Ortiz G., Luis; Riquelme P., Pablo; Guzmán, R.

2013-11-01

In this work, we use a Schlieren-like Near Field Scattering (SNFS) setup to study nonequilibrium free diffusion behavior of a colloidal solution obtained from seeds leachate. The main objective is to compare the temporal behavior of the diffusion coefficient of seed leachate with an electric conductivity based vigor test. SNFS sizing measurements, based on Mie theory, were carried out to ensure its reliability and sensitivity. Then, we performed a typical nonequilibrium free diffusion experiment of a glycerol-water mixture. In this way, we confirmed that SNFS setup is sensitive to giant concentration fluctuations of nanocolloidal solutions. The results obtained in this stage reproduce properly the data reported elsewhere in literature. Moreover, seed leachate diffuse, in water, in a similar way that glycerol does. In both cases we used the same method (dynamic structure factor) to determine thermo-physical properties. We show that time evolution of diffusion coefficient of Lupinus Albus leachate exhibits three defined regimes as electric conductivity measurements. The results also exhibit a correspondence between the behavior of the diffusion coefficient and electric conductivity values of the two regions in the temporal range studied. Finally, we discuss biological processes involved in germination that could modulate this dependence, and the role played by the electrolytic nature of solutes.

Hydrogen: A Promising Fuel and Energy Storage Solution - Continuum

Science.gov Websites

Magazine | NREL Hydrogen: A Promising Fuel and Energy Storage Solution Fuel cell electric Ainscough, NREL Hydrogen: A Promising Fuel and Energy Storage Solution Electrolysis-generated hydrogen may provide a solution to fluctuations in renewable-sourced energy. As electricity from renewable resources

Active and Passive Remote Sensing of Ice.

DTIC Science & Technology

1985-01-01

This is a report on the progress that has been made in the study of active and passive remote sensing of ice during the period of August 1, 1984...active and passive microwave remote sensing , (2) used the strong fluctuation theory and the fluctuation-dissipation theorem to calculate the brightness

The correlation function for density perturbations in an expanding universe. I - Linear theory

NASA Technical Reports Server (NTRS)

Mcclelland, J.; Silk, J.

1977-01-01

The evolution of the two-point correlation function for adiabatic density perturbations in the early universe is studied. Analytical solutions are obtained for the evolution of linearized spherically symmetric adiabatic density perturbations and the two-point correlation function for these perturbations in the radiation-dominated portion of the early universe. The results are then extended to the regime after decoupling. It is found that: (1) adiabatic spherically symmetric perturbations comparable in scale with the maximum Jeans length would survive the radiation-dominated regime; (2) irregular fluctuations are smoothed out up to the scale of the maximum Jeans length in the radiation era, but regular fluctuations might survive on smaller scales; (3) in general, the only surviving structures for irregularly shaped adiabatic density perturbations of arbitrary but finite scale in the radiation regime are the size of or larger than the maximum Jeans length in that regime; (4) infinite plane waves with a wavelength smaller than the maximum Jeans length but larger than the critical dissipative damping scale could survive the radiation regime; and (5) black holes would also survive the radiation regime and might accrete sufficient mass after decoupling to nucleate the formation of galaxies.

Modeling the color of natural dyes

NASA Astrophysics Data System (ADS)

Ge, Xiaochuan; Calzolari, Arrigo; Binnie, Simon; Baroni, Stefano

2013-03-01

We report on a theoretical study, based on time-dependent density-functional theory, of various factors affecting the optical properties of a few representative anthocyanins, a class of molecules responsible for the color of many fruits, flowers, and leaves, which have also aroused some interest for photovoltaic applications. We first address the influence of substituting different side groups in the phenyl ring of flavylium dyes. We find that these dyes can be classified into three broad classes, according to the number of peaks (1, 2, or 3) featured in the visible range, and give a rationale to this finding. We then examine the effects of solvent-induced thermal fluctuations and dielectric screening, by calculating the spectrum of a representative molecule in solution, for each one these classes. This is achieved by first running an ab initio molecular dynamics simulation of an explicit model for the water-solvated molecule, and then accumulating time averages of the optical spectra calculated on the fly. The effects of thermal fluctuations are shown to overshadow those of dielectric screening, and more dramatic the larger the number of peaks in the gas phase. The effects of different functionals (GGA vs. hybrids) on the calculated spectra are also addressed.

Preferential binding effects on protein structure and dynamics revealed by coarse-grained Monte Carlo simulation

NASA Astrophysics Data System (ADS)

Pandey, R. B.; Jacobs, D. J.; Farmer, B. L.

2017-05-01

The effect of preferential binding of solute molecules within an aqueous solution on the structure and dynamics of the histone H3.1 protein is examined by a coarse-grained Monte Carlo simulation. The knowledge-based residue-residue and hydropathy-index-based residue-solvent interactions are used as input to analyze a number of local and global physical quantities as a function of the residue-solvent interaction strength (f). Results from simulations that treat the aqueous solution as a homogeneous effective solvent medium are compared to when positional fluctuations of the solute molecules are explicitly considered. While the radius of gyration (Rg) of the protein exhibits a non-monotonic dependence on solvent interaction over a wide range of f within an effective medium, an abrupt collapse in Rg occurs in a narrow range of f when solute molecules rapidly bind to a preferential set of sites on the protein. The structure factor S(q) of the protein with wave vector (q) becomes oscillatory in the collapsed state, which reflects segmental correlations caused by spatial fluctuations in solute-protein binding. Spatial fluctuations in solute binding also modify the effective dimension (D) of the protein in fibrous (D ˜ 1.3), random-coil (D ˜ 1.75), and globular (D ˜ 3) conformational ensembles as the interaction strength increases, which differ from an effective medium with respect to the magnitude of D and the length scale.

Protein denaturants at aqueous-hydrophobic interfaces: self-consistent correlation between induced interfacial fluctuations and denaturant stability at the interface.

PubMed

Cui, Di; Ou, Shu-Ching; Patel, Sandeep

2015-01-08

The notion of direct interaction between denaturing cosolvent and protein residues has been proposed in dialogue relevant to molecular mechanisms of protein denaturation. Here we consider the correlation between free energetic stability and induced fluctuations of an aqueous-hydrophobic interface between a model hydrophobically associating protein, HFBII, and two common protein denaturants, guanidinium cation (Gdm(+)) and urea. We compute potentials of mean force along an order parameter that brings the solute molecule close to the known hydrophobic region of the protein. We assess potentials of mean force for different relative orientations between the protein and denaturant molecule. We find that in both cases of guanidinium cation and urea relative orientations of the denaturant molecule that are parallel to the local protein-water interface exhibit greater stability compared to edge-on or perpendicular orientations. This behavior has been observed for guanidinium/methylguanidinium cations at the liquid-vapor interface of water, and thus the present results further corroborate earlier findings. Further analysis of the induced fluctuations of the aqueous-hydrophobic interface upon approach of the denaturant molecule indicates that the parallel orientation, displaying a greater stability at the interface, also induces larger fluctuations of the interface compared to the perpendicular orientations. The correlation of interfacial stability and induced interface fluctuation is a recurring theme for interface-stable solutes at hydrophobic interfaces. Moreover, observed correlations between interface stability and induced fluctuations recapitulate connections to local hydration structure and patterns around solutes as evidenced by experiment (Cooper et al., J. Phys. Chem. A 2014, 118, 5657.) and high-level ab initio/DFT calculations (Baer et al., Faraday Discuss 2013, 160, 89).

Protein Denaturants at Aqueous–Hydrophobic Interfaces: Self-Consistent Correlation between Induced Interfacial Fluctuations and Denaturant Stability at the Interface

PubMed Central

2015-01-01

The notion of direct interaction between denaturing cosolvent and protein residues has been proposed in dialogue relevant to molecular mechanisms of protein denaturation. Here we consider the correlation between free energetic stability and induced fluctuations of an aqueous–hydrophobic interface between a model hydrophobically associating protein, HFBII, and two common protein denaturants, guanidinium cation (Gdm+) and urea. We compute potentials of mean force along an order parameter that brings the solute molecule close to the known hydrophobic region of the protein. We assess potentials of mean force for different relative orientations between the protein and denaturant molecule. We find that in both cases of guanidinium cation and urea relative orientations of the denaturant molecule that are parallel to the local protein–water interface exhibit greater stability compared to edge-on or perpendicular orientations. This behavior has been observed for guanidinium/methylguanidinium cations at the liquid–vapor interface of water, and thus the present results further corroborate earlier findings. Further analysis of the induced fluctuations of the aqueous–hydrophobic interface upon approach of the denaturant molecule indicates that the parallel orientation, displaying a greater stability at the interface, also induces larger fluctuations of the interface compared to the perpendicular orientations. The correlation of interfacial stability and induced interface fluctuation is a recurring theme for interface-stable solutes at hydrophobic interfaces. Moreover, observed correlations between interface stability and induced fluctuations recapitulate connections to local hydration structure and patterns around solutes as evidenced by experiment (Cooper et al., J. Phys. Chem. A2014, 118, 5657.) and high-level ab initio/DFT calculations (Baer et al., Faraday Discuss2013, 160, 89). PMID:25536388

Fluctuations of radiative heat exchange between two bodies

NASA Astrophysics Data System (ADS)

Biehs, S.-A.; Ben-Abdallah, P.

2018-05-01

We present a theory to describe the fluctuations of nonequilibrium radiative heat transfer between two bodies both in the far- and near-field regimes. As predicted by the blackbody theory, in the far field, we show that the variance of radiative heat flux is of the same order of magnitude as its mean value. However, in the near-field regime, we demonstrate that the presence of surface polaritons makes this variance more than one order of magnitude larger than the mean flux. We further show that the correlation time of heat flux in this regime is comparable to the relaxation time of heat carriers in each medium. This theory could open the way to an experimental investigation of heat exchanges far from the thermal equilibrium condition.

Thermal noise in a boost-invariant matter expansion in relativistic heavy-ion collisions

NASA Astrophysics Data System (ADS)

Chattopadhyay, Chandrodoy; Bhalerao, Rajeev S.; Pal, Subrata

2018-05-01

We formulate a general theory of thermal fluctuations within causal second-order viscous hydrodynamic evolution of matter formed in relativistic heavy-ion collisions. The fluctuation is treated perturbatively on top of a boost-invariant longitudinal expansion. Numerical simulation of thermal noise is performed for a lattice quantum chromodynamics equation of state and for various second-order dissipative evolution equations. Phenomenological effects of thermal fluctuations on the two-particle rapidity correlations are studied.

Inflaton and metric fluctuations in the early universe from a 5D vacuum state

NASA Astrophysics Data System (ADS)

Membiela, Agustin; Bellini, Mauricio

2006-04-01

In this Letter we complete a previously introduced formalism to study the gauge-invariant metric fluctuations from a noncompact Kaluza Klein theory of gravity, to study the evolution of the early universe. The evolution of both, metric and inflaton field fluctuations are reciprocally related. We obtain that <δρ>/ρ depends on the coupling of Φ with δφ and the spectral index of its spectrum is 0.9483

Advanced first-principles theory of superconductivity including both lattice vibrations and spin fluctuations: The case of FeB4

NASA Astrophysics Data System (ADS)

Bekaert, J.; Aperis, A.; Partoens, B.; Oppeneer, P. M.; Milošević, M. V.

2018-01-01

We present an advanced method to study spin fluctuations in superconductors quantitatively and entirely from first principles. This method can be generally applied to materials where electron-phonon coupling and spin fluctuations coexist. We employ it here to examine the recently synthesized superconductor iron tetraboride (FeB4) with experimental Tc˜2.4 K [H. Gou et al., Phys. Rev. Lett. 111, 157002 (2013), 10.1103/PhysRevLett.111.157002]. We prove that FeB4 is particularly prone to ferromagnetic spin fluctuations due to the presence of iron, resulting in a large Stoner interaction strength, I =1.5 eV, as calculated from first principles. The other important factor is its Fermi surface that consists of three separate sheets, among which two are nested ellipsoids. The resulting susceptibility has a ferromagnetic peak around q =0 , from which we calculated the repulsive interaction between Cooper pair electrons using the random phase approximation. Subsequently, we combined the electron-phonon interaction calculated from first principles with the spin fluctuation interaction in fully anisotropic Eliashberg theory calculations. We show that the resulting superconducting gap spectrum is conventional, yet very strongly depleted due to coupling to the spin fluctuations. The critical temperature decreases from Tc=41 K, if they are not taken into account, to Tc=1.7 K, in good agreement with the experimental value.

Unsteady sedimentation of a sphere in wormlike micellar fluids

NASA Astrophysics Data System (ADS)

Zhang, Yiran; Muller, Susan J.

2018-04-01

The unsteady sedimentation of a sphere in wormlike micellar fluids is studied experimentally through shear and extensional rheometry, sphere trajectory tracking, and particle image velocimetry. Unsteady sphere sedimentation characterized by fluctuations in the sphere settling velocity was observed for a range of sphere size and density in two non-shear-banding wormlike micellar solutions, a cetylpyridinium chloride (CpCl)-sodium salicylate (NaSal) solution and a cetyltrimethylammonium p-toluenesulfonate (CTAT)-NaCl solution. The onset of the transition from steady to unsteady sphere motion is characterized by an extensional Deborah number, D eext , defined locally in the negative wake of the falling sphere. This instability criterion is in agreement with previous findings by Mohammadigoushki and Muller [J. Rheol. 60, 587 (2016), 10.1122/1.4948800] in the wormlike micelle system of cetyltrimethylammonium bromide (CTAB) and NaSal, and appears to be universally valid independent of micelle chemistry or solution rheology (e.g., shear banding or not). Moreover, the frequency at which the sphere velocity fluctuates is found to be linearly correlated with an average shear Deborah number D es , which is a measure of the overall flow strength. This suggests that a constant critical strain is accumulated before the flow instability takes place in each velocity oscillation. The velocity fluctuations are found to become increasingly disordered with increasing elastic Mach number, M ae , indicating that the interactions between the flow instability and elastic wave propagation result in more chaotic velocity fluctuations.

Quantum Feynman Ratchet

NASA Astrophysics Data System (ADS)

Goyal, Ketan; Kawai, Ryoichi

As nanotechnology advances, understanding of the thermodynamic properties of small systems becomes increasingly important. Such systems are found throughout physics, biology, and chemistry manifesting striking properties that are a direct result of their small dimensions where fluctuations become predominant. The standard theory of thermodynamics for macroscopic systems is powerless for such ever fluctuating systems. Furthermore, as small systems are inherently quantum mechanical, influence of quantum effects such as discreteness and quantum entanglement on their thermodynamic properties is of great interest. In particular, the quantum fluctuations due to quantum uncertainty principles may play a significant role. In this talk, we investigate thermodynamic properties of an autonomous quantum heat engine, resembling a quantum version of the Feynman Ratchet, in non-equilibrium condition based on the theory of open quantum systems. The heat engine consists of multiple subsystems individually contacted to different thermal environments.

Nonequilibrium fluctuations during diffusion in liquid layers

NASA Astrophysics Data System (ADS)

Brogioli, Doriano; Vailati, Alberto

2017-07-01

Theoretical analysis and experiments have provided compelling evidence of the presence of long-range nonequilibrium concentration fluctuations during diffusion processes in fluids. In this paper, we investigate the dependence of the features of the fluctuations from the dimensionality of the system. In three-dimensional fluids the amplitude of nonequilibrium fluctuations can become several orders of magnitude larger than that of equilibrium fluctuations. Notwithstanding that, the amplitude of nonequilibrium fluctuations remains small with respect to the concentration difference driving the diffusion process. By extending the theory to two-dimensional systems, such as liquid monolayers and bilayers, we show that the amplitude of the fluctuations becomes much stronger than in three-dimensional systems. We investigate the properties of the fronts of diffusion and show that they have a self-affine structure characterized by a Hurst exponent H =1 . We discuss the implications of these results for diffusion in liquid crystals and in cellular membranes of living organisms.

Nonequilibrium fluctuations during diffusion in liquid layers.

PubMed

Brogioli, Doriano; Vailati, Alberto

2017-07-01

Theoretical analysis and experiments have provided compelling evidence of the presence of long-range nonequilibrium concentration fluctuations during diffusion processes in fluids. In this paper, we investigate the dependence of the features of the fluctuations from the dimensionality of the system. In three-dimensional fluids the amplitude of nonequilibrium fluctuations can become several orders of magnitude larger than that of equilibrium fluctuations. Notwithstanding that, the amplitude of nonequilibrium fluctuations remains small with respect to the concentration difference driving the diffusion process. By extending the theory to two-dimensional systems, such as liquid monolayers and bilayers, we show that the amplitude of the fluctuations becomes much stronger than in three-dimensional systems. We investigate the properties of the fronts of diffusion and show that they have a self-affine structure characterized by a Hurst exponent H=1. We discuss the implications of these results for diffusion in liquid crystals and in cellular membranes of living organisms.

Non-perturbative theory of dispersion interactions

NASA Astrophysics Data System (ADS)

Boström, M.; Thiyam, P.; Persson, C.; Parsons, D. F.; Buhmann, S. Y.; Brevik, I.; Sernelius, Bo E.

2015-03-01

Some open questions exist with fluctuation-induced forces between extended dipoles. Conventional intuition derives from large-separation perturbative approximations to dispersion force theory. Here, we present a full non-perturbative theory. In addition, we discuss how one can take into account finite dipole size corrections. It is of fundamental value to investigate the limits of validity of the perturbative dispersion force theory.

Event-by-Event Hydrodynamics+Jet Energy Loss: A Solution to the R_{AA}⊗v_{2} Puzzle.

PubMed

Noronha-Hostler, Jacquelyn; Betz, Barbara; Noronha, Jorge; Gyulassy, Miklos

2016-06-24

High p_{T}>10  GeV elliptic flow, which is experimentally measured via the correlation between soft and hard hadrons, receives competing contributions from event-by-event fluctuations of the low-p_{T} elliptic flow and event-plane angle fluctuations in the soft sector. In this Letter, a proper account of these event-by-event fluctuations in the soft sector, modeled via viscous hydrodynamics, is combined with a jet-energy-loss model to reveal that the positive contribution from low-p_{T} v_{2} fluctuations overwhelms the negative contributions from event-plane fluctuations. This leads to an enhancement of high-p_{T}>10  GeV elliptic flow in comparison to previous calculations and provides a natural solution to the decade-long high-p_{T} R_{AA}⊗v_{2} puzzle. We also present the first theoretical calculation of high-p_{T} v_{3}, which is shown to be compatible with current LHC data. Furthermore, we discuss how short-wavelength jet-medium physics can be deconvoluted from the physics of soft, bulk event-by-event flow observables using event-shape engineering techniques.

Low Mach number fluctuating hydrodynamics for electrolytes

NASA Astrophysics Data System (ADS)

Péraud, Jean-Philippe; Nonaka, Andy; Chaudhri, Anuj; Bell, John B.; Donev, Aleksandar; Garcia, Alejandro L.

2016-11-01

We formulate and study computationally the low Mach number fluctuating hydrodynamic equations for electrolyte solutions. We are interested in studying transport in mixtures of charged species at the mesoscale, down to scales below the Debye length, where thermal fluctuations have a significant impact on the dynamics. Continuing our previous work on fluctuating hydrodynamics of multicomponent mixtures of incompressible isothermal miscible liquids [A. Donev et al., Phys. Fluids 27, 037103 (2015), 10.1063/1.4913571], we now include the effect of charged species using a quasielectrostatic approximation. Localized charges create an electric field, which in turn provides additional forcing in the mass and momentum equations. Our low Mach number formulation eliminates sound waves from the fully compressible formulation and leads to a more computationally efficient quasi-incompressible formulation. We demonstrate our ability to model saltwater (NaCl) solutions in both equilibrium and nonequilibrium settings. We show that our algorithm is second order in the deterministic setting and for length scales much greater than the Debye length gives results consistent with an electroneutral approximation. In the stochastic setting, our model captures the predicted dynamics of equilibrium and nonequilibrium fluctuations. We also identify and model an instability that appears when diffusive mixing occurs in the presence of an applied electric field.

Statistical mechanical theory for steady state systems. II. Reciprocal relations and the second entropy.

PubMed

Attard, Phil

2005-04-15

The concept of second entropy is introduced for the dynamic transitions between macrostates. It is used to develop a theory for fluctuations in velocity, and is exemplified by deriving Onsager reciprocal relations for Brownian motion. The cases of free, driven, and pinned Brownian particles are treated in turn, and Stokes' law is derived. The second entropy analysis is applied to the general case of thermodynamic fluctuations, and the Onsager reciprocal relations for these are derived using the method. The Green-Kubo formulas for the transport coefficients emerge from the analysis, as do Langevin dynamics.

A comprehensive model to determine the effects of temperature and species fluctuations on reaction rates in turbulent reacting flows

NASA Technical Reports Server (NTRS)

Chinitz, W.; Foy, E.; Rowan, G.; Goldstein, D.

1982-01-01

The use of probability theory to determine the effects of turbulent fluctuations on reaction rates in turbulent combustion systems is briefly reviewed. Results are presented for the effect of species fluctuations in particular. It is found that turbulent fluctuations of species act to reduce the reaction rates, in contrast with the temperature fluctuations previously determined to increase Arrhenius reaction rate constants. For the temperature fluctuations, a criterion is set forth for determining if, in a given region of a turbulent flow field, the temperature can be expected to exhibit ramp like fluctuations. Using the above results, along with results previously obtained, a model is described for testing the effects of turbulent fluctuations of temperature and species on reaction rates in computer programs dealing with turbulent reacting flows. An alternative model which employs three variable probability density functions (temperature and two species) and is currently being formulated is discussed as well.

Ericson fluctuations in an open deterministic quantum system: theory meets experiment.

PubMed

Madroñero, Javier; Buchleitner, Andreas

2005-12-31

We provide numerically exact photoexcitation cross sections of rubidium Rydberg states in crossed, static electric, and magnetic fields, in quantitative agreement with recent experimental results. Their spectral backbone underpins a clear transition towards the Ericson regime, associated with a universal, fluctuating behavior of the cross section of strongly coupled, fragmenting quantum systems.

Nonlocal and collective relaxation in stellar systems

NASA Technical Reports Server (NTRS)

Weinberg, Martin D.

1993-01-01

The modal response of stellar systems to fluctuations at large scales is presently investigated by means of analytic theory and n-body simulation; the stochastic excitation of these modes is shown to increase the relaxation rate even for a system which is moderately far from instability. The n-body simulations, when designed to suppress relaxation at small scales, clearly show the effects of large-scale fluctuations. It is predicted that large-scale fluctuations will be largest for such marginally bound systems as forming star clusters and associations.

Energy Current Cumulants in One-Dimensional Systems in Equilibrium

NASA Astrophysics Data System (ADS)

Dhar, Abhishek; Saito, Keiji; Roy, Anjan

2018-06-01

A recent theory based on fluctuating hydrodynamics predicts that one-dimensional interacting systems with particle, momentum, and energy conservation exhibit anomalous transport that falls into two main universality classes. The classification is based on behavior of equilibrium dynamical correlations of the conserved quantities. One class is characterized by sound modes with Kardar-Parisi-Zhang scaling, while the second class has diffusive sound modes. The heat mode follows Lévy statistics, with different exponents for the two classes. Here we consider heat current fluctuations in two specific systems, which are expected to be in the above two universality classes, namely, a hard particle gas with Hamiltonian dynamics and a harmonic chain with momentum conserving stochastic dynamics. Numerical simulations show completely different system-size dependence of current cumulants in these two systems. We explain this numerical observation using a phenomenological model of Lévy walkers with inputs from fluctuating hydrodynamics. This consistently explains the system-size dependence of heat current fluctuations. For the latter system, we derive the cumulant-generating function from a more microscopic theory, which also gives the same system-size dependence of cumulants.

Thermal and active fluctuations of a compressible bilayer vesicle

NASA Astrophysics Data System (ADS)

Sachin Krishnan, T. V.; Yasuda, Kento; Okamoto, Ryuichi; Komura, Shigeyuki

2018-05-01

We discuss thermal and active fluctuations of a compressible bilayer vesicle by using the results of hydrodynamic theory for vesicles. Coupled Langevin equations for the membrane deformation and the density fields are employed to calculate the power spectral density matrix of membrane fluctuations. Thermal contribution is obtained by means of the fluctuation dissipation theorem, whereas active contribution is calculated from exponentially decaying time correlation functions of active random forces. We obtain the total power spectral density as a sum of thermal and active contributions. An apparent response function is further calculated in order to compare with the recent microrheology experiment on red blood cells. An enhanced response is predicted in the low-frequency regime for non-thermal active fluctuations.

Adaptation to Temporally Fluctuating Environments by the Evolution of Maternal Effects.

PubMed

Dey, Snigdhadip; Proulx, Stephen R; Teotónio, Henrique

2016-02-01

All organisms live in temporally fluctuating environments. Theory predicts that the evolution of deterministic maternal effects (i.e., anticipatory maternal effects or transgenerational phenotypic plasticity) underlies adaptation to environments that fluctuate in a predictably alternating fashion over maternal-offspring generations. In contrast, randomizing maternal effects (i.e., diversifying and conservative bet-hedging), are expected to evolve in response to unpredictably fluctuating environments. Although maternal effects are common, evidence for their adaptive significance is equivocal since they can easily evolve as a correlated response to maternal selection and may or may not increase the future fitness of offspring. Using the hermaphroditic nematode Caenorhabditis elegans, we here show that the experimental evolution of maternal glycogen provisioning underlies adaptation to a fluctuating normoxia-anoxia hatching environment by increasing embryo survival under anoxia. In strictly alternating environments, we found that hermaphrodites evolved the ability to increase embryo glycogen provisioning when they experienced normoxia and to decrease embryo glycogen provisioning when they experienced anoxia. At odds with existing theory, however, populations facing irregularly fluctuating normoxia-anoxia hatching environments failed to evolve randomizing maternal effects. Instead, adaptation in these populations may have occurred through the evolution of fitness effects that percolate over multiple generations, as they maintained considerably high expected growth rates during experimental evolution despite evolving reduced fecundity and reduced embryo survival under one or two generations of anoxia. We develop theoretical models that explain why adaptation to a wide range of patterns of environmental fluctuations hinges on the existence of deterministic maternal effects, and that such deterministic maternal effects are more likely to contribute to adaptation than randomizing maternal effects.

Adaptation to Temporally Fluctuating Environments by the Evolution of Maternal Effects

PubMed Central

Dey, Snigdhadip; Proulx, Stephen R.; Teotónio, Henrique

2016-01-01

All organisms live in temporally fluctuating environments. Theory predicts that the evolution of deterministic maternal effects (i.e., anticipatory maternal effects or transgenerational phenotypic plasticity) underlies adaptation to environments that fluctuate in a predictably alternating fashion over maternal-offspring generations. In contrast, randomizing maternal effects (i.e., diversifying and conservative bet-hedging), are expected to evolve in response to unpredictably fluctuating environments. Although maternal effects are common, evidence for their adaptive significance is equivocal since they can easily evolve as a correlated response to maternal selection and may or may not increase the future fitness of offspring. Using the hermaphroditic nematode Caenorhabditis elegans, we here show that the experimental evolution of maternal glycogen provisioning underlies adaptation to a fluctuating normoxia–anoxia hatching environment by increasing embryo survival under anoxia. In strictly alternating environments, we found that hermaphrodites evolved the ability to increase embryo glycogen provisioning when they experienced normoxia and to decrease embryo glycogen provisioning when they experienced anoxia. At odds with existing theory, however, populations facing irregularly fluctuating normoxia–anoxia hatching environments failed to evolve randomizing maternal effects. Instead, adaptation in these populations may have occurred through the evolution of fitness effects that percolate over multiple generations, as they maintained considerably high expected growth rates during experimental evolution despite evolving reduced fecundity and reduced embryo survival under one or two generations of anoxia. We develop theoretical models that explain why adaptation to a wide range of patterns of environmental fluctuations hinges on the existence of deterministic maternal effects, and that such deterministic maternal effects are more likely to contribute to adaptation than randomizing maternal effects. PMID:26910440

Constraints on galaxy formation theories

NASA Technical Reports Server (NTRS)

Szalay, A. S.

1986-01-01

The present theories of galaxy formation are reviewed. The relation between peculiar velocities, temperature fluctuations of the microwave background and the correlation function of galaxies point to the possibility that galaxies do not form uniformly everywhere. The velocity data provide strong constraints on the theories even in the case when light does not follow mass of the universe.

Formulation and closure of compressible turbulence equations in the light of kinetic theory

NASA Technical Reports Server (NTRS)

Tsuge, S.; Sagara, K.

1976-01-01

Fluid-dynamic moment equations, based on a kinetic hierarchy system, are derived governing the interaction between turbulent and thermal fluctuations. The kinetic theory is shown to reduce the inherent complexity of the conventional formalism of compressible turbulence theory and to minimize arbitrariness in formulating the closure condition.

Diagrammar in classical scalar field theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cattaruzza, E., E-mail: Enrico.Cattaruzza@gmail.com; Gozzi, E., E-mail: gozzi@ts.infn.it; INFN, Sezione di Trieste

2011-09-15

In this paper we analyze perturbatively a g{phi}{sup 4}classical field theory with and without temperature. In order to do that, we make use of a path-integral approach developed some time ago for classical theories. It turns out that the diagrams appearing at the classical level are many more than at the quantum level due to the presence of extra auxiliary fields in the classical formalism. We shall show that a universal supersymmetry present in the classical path-integral mentioned above is responsible for the cancelation of various diagrams. The same supersymmetry allows the introduction of super-fields and super-diagrams which considerably simplifymore » the calculations and make the classical perturbative calculations almost 'identical' formally to the quantum ones. Using the super-diagrams technique, we develop the classical perturbation theory up to third order. We conclude the paper with a perturbative check of the fluctuation-dissipation theorem. - Highlights: > We provide the Feynman diagrams of perturbation theory for a classical field theory. > We give a super-formalism which links the quantum diagrams to the classical ones. > We check perturbatively the fluctuation-dissipation theorem.« less

An analysis of macroeconomic fluctuations for a small open oil-based economy: The case of Saudi Arabia

NASA Astrophysics Data System (ADS)

Al-Abdulkarim, Bander B.

The increasing fluctuations in the oil prices through the last decades have been transferred to the oil exporting countries. Thus, many oil exporting countries experienced significant changes in the economic activity due to changes in the oil markets. In light of this, oil exporting countries have attempted to implement a policy that would stabilize the fluctuations in the oil markets recognizing the adverse effects of such behavior on oil exporting countries, as well as oil importing countries. Saudi Arabia, as the largest oil-exporting country and a member of OPEC, takes the role of oil-markets stabilizer by behaving as the swing producer. This role has caused the global economic fluctuations to transfer into the domestic economy. In addition, Saudi Arabian government has adopted a fixed exchange rate currency regime. Although it has contributed to domestic price stabilizations, this policy has also exposed the country to global economic disturbances. The purpose of the study is to empirically investigate these aspects for Saudi Arabia. First, the effects of shocks originated in the international markets on the Saudi Arabian economy. Second, how the fixed exchange rate regimes influences the domestic macroeconomic variables. Third, to what extent the oil sector contributes to the non-oil domestic fluctuations. Finally, how the findings from the study can be explained by economic theory. In pursuing this, there are four economic theories that are considered to explain the causes of business cycles. These theories are Classical Theory, Keynesian Theory, Monetarist Theory, and the Real Business Cycles. In addition, a theoretical model is derived that is suitable for an oil-based economy. The model follows the set up of McCallum and Nelson (1999). Then, the empirical models of Structural Vector Autoregression (SVAR) and Error Correction Model (ECM) are implemented with three different specifications: Choleski Decomposition, Block Exogeneity and long-run Cointegration Model. The empirical models then are applied to sets of data from 1980 to 2002 for Saudi Arabia, Kuwait, Venezuela and Norway. The rationale of including other oil-exporting countries is to distinguish whether the shocks are country-specific, regional-specific, or global. Two sets of shocks are considered: international shocks and domestic shocks. Three types of international shocks are chosen: commodity-price (oil price) shock, international financial (interest rate) shock, and international real (output) shock. In addition, five domestic shocks which are non-oil output shock, oil production shock, price level shock, monetary shock, and exchange rate shock. The findings reached in the study demonstrate that the international shocks are responsible for a high proportion of fluctuations in the economic activity in Saudi Arabia. Most importantly, the international financial shocks represented by the US interest rate and oil price shocks are the major sources of fluctuations in the Saudi Arabian economy. Domestically, the economy is mostly affected by the oil production and the non-oil output shocks for Saudi Arabia. These results emphasize that the Saudi Arabia's role in the international oil market and its fixed exchange rate regime have significant implications on the domestic economy. Thus, special considerations should be placed on designing the appropriate policies to lessen the dependency on the oil sector and strengthen the role of private sector to diversify the economic base, and provide an independent sound monetary policy to steer the economy from the fluctuations in the global economy. (Abstract shortened by UMI.)

Studies on the formulation of thermodynamics and stochastic theory for systems far from equilibrium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ross, J.

We have been working for some time on the formulation of thermodynamics and the theory of fluctuations in systems far from equilibrium and progress in several aspects of that development are reported here.

Extreme fluctuations of active Brownian motion

NASA Astrophysics Data System (ADS)

Pietzonka, Patrick; Kleinbeck, Kevin; Seifert, Udo

2016-05-01

In active Brownian motion, an internal propulsion mechanism interacts with translational and rotational thermal noise and other internal fluctuations to produce directed motion. We derive the distribution of its extreme fluctuations and identify its universal properties using large deviation theory. The limits of slow and fast internal dynamics give rise to a kink-like and parabolic behavior of the corresponding rate functions, respectively. For dipolar Janus particles in two- and three-dimensions interacting with a field, we predict a novel symmetry akin to, but different from, the one related to entropy production. Measurements of these extreme fluctuations could thus be used to infer properties of the underlying, often hidden, network of states.

Modern Thermodynamics: From Heat Engines to Dissipative Structures (by Dilip Kodepudi and Ilya Prigogine)

NASA Astrophysics Data System (ADS)

Kovac, Reviewed By Jeffrey

1999-11-01

In the preface to his excellent textbook, Thermodynamics: Principles and Applications (Wiley-Interscience, 1971), Frank C. Andrews remarks, "It is almost an act of intellectual arrogance to write another thermodynamics text these days, so many and varied are the texts already available." Since I first read it, Andrews's comment has been my standard for judging new thermodynamics textbooks: what does a new book offer that is significantly different, and better, than one of the many fine books already on my shelf? Modern Thermodynamics by Dilip Kondepudi, Professor of Chemistry at Wake Forest University, and 1977 Nobel Laureate Ilya Prigogine does provide something quite different: a historically conscious, integrated approach to both equilibrium and nonequilibrium thermodynamics. The essential role of fluctuations in determining the properties of equilibrium and nonequilibrium systems was first elucidated by Einstein at the turn of the century. Subsequently, Lars Onsager used fluctuation theory to demonstrate the famous reciprocal relations that provide the basis for the theory of linear nonequilibrium thermodynamics. Unfortunately, thermodynamics is often taught to chemists as if it only applies to uniform equilibrium systems. Fluctuations are rarely mentioned. One of the unusual features of this book is that it begins by explicitly discussing both nonuniform and nonequilibrium systems. While most of the traditional topics of a course in chemical thermodynamics are included in this book, these applications are treated in the context of a more general formalism that can be used to discuss both linear and nonlinear nonequilibrium systems. Another interesting and important feature of this book is the integration of historical material into the presentation. While the presentation follows the usual sequencepreliminary concepts, first law, second law, etc.the ideas are placed in a historical context as they are developed. As expected, there is considerable emphasis on the contributions of Theophile De Donder, founder of the Brussels school of thermodynamics. The text is generously illustrated with portraits of many of the important figures in the development of thermodynamics. The stories and pictures help to make the subject come alive. The first 11 chapters of the book provide material for a one-semester course in equilibrium thermodynamics. The overall coverage in this section is fairly standard, including real gases, solutions, electrochemical systems, and phase transitions. As noted above, the important difference in this presentation is that the traditional topics are presented in terms of a general formalism that leads naturally to the discussion of both nonuniform and nonequilibrium systems. Chapters 12-19 explicitly consider fluctuations and stability theory, linear nonequilibrium thermodynamics, and, finally, nonlinear systems and dissipative structures. Each chapter is followed by a number of problems and students are encouraged to use Mathematica or Maple to do the more tedious calculations. A brief appendix to Chapter 1 includes some sample Mathematica codes. The book has relatively few worked examples, however, so students who need to see a lot of examples will have to look elsewhere. Unfortunately, there are no worked examples in Chapters 12-19. Since I first learned nonequilibrium thermodynamics from Prigogine's earlier book, Introduction to the Thermodynamics of Irreversible Processes (Interscience, 1961), I found the treatment in the second part of the book to be clear and logical. I think that most readers will agree. There is a nice treatment of Gaussian fluctuation theory and a proof of the Onsager reciprocal relations. Chapters 18 and 19 provide an introduction to the most important ideas in nonlinear nonequilibrium thermodynamics, including stability analysis. The book concludes with a chapter on the frontiers of research in thermodynamics. As the title promises, this book is a modern treatment of the full scope of thermodynamics emphasizing the importance of fluctuations. I hope that the appearance of this accessible treatment will stimulate faculty to rethink their teaching of thermodynamics and present it as a general and powerful way to understand both equilibrium and nonequilibrium systems.

On the mode-coupling treatment of collective density fluctuations for quantum liquids: para-hydrogen and normal liquid helium.

PubMed

Kletenik-Edelman, Orly; Reichman, David R; Rabani, Eran

2011-01-28

A novel quantum mode coupling theory combined with a kinetic approach is developed for the description of collective density fluctuations in quantum liquids characterized by Boltzmann statistics. Three mode-coupling approximations are presented and applied to study the dynamic response of para-hydrogen near the triple point and normal liquid helium above the λ-transition. The theory is compared with experimental results and to the exact imaginary time data generated by path integral Monte Carlo simulations. While for liquid para-hydrogen the combination of kinetic and quantum mode-coupling theory provides semi-quantitative results for both short and long time dynamics, it fails for normal liquid helium. A discussion of this failure based on the ideal gas limit is presented.

Motor contributions to the temporal precision of auditory attention

PubMed Central

Morillon, Benjamin; Schroeder, Charles E.; Wyart, Valentin

2014-01-01

In temporal—or dynamic—attending theory, it is proposed that motor activity helps to synchronize temporal fluctuations of attention with the timing of events in a task-relevant stream, thus facilitating sensory selection. Here we develop a mechanistic behavioural account for this theory by asking human participants to track a slow reference beat, by noiseless finger pressing, while extracting auditory target tones delivered on-beat and interleaved with distractors. We find that overt rhythmic motor activity improves the segmentation of auditory information by enhancing sensitivity to target tones while actively suppressing distractor tones. This effect is triggered by cyclic fluctuations in sensory gain locked to individual motor acts, scales parametrically with the temporal predictability of sensory events and depends on the temporal alignment between motor and attention fluctuations. Together, these findings reveal how top-down influences associated with a rhythmic motor routine sharpen sensory representations, enacting auditory ‘active sensing’. PMID:25314898

Logarithmic Superdiffusion in Two Dimensional Driven Lattice Gases

NASA Astrophysics Data System (ADS)

Krug, J.; Neiss, R. A.; Schadschneider, A.; Schmidt, J.

2018-03-01

The spreading of density fluctuations in two-dimensional driven diffusive systems is marginally anomalous. Mode coupling theory predicts that the diffusivity in the direction of the drive diverges with time as (ln t)^{2/3} with a prefactor depending on the macroscopic current-density relation and the diffusion tensor of the fluctuating hydrodynamic field equation. Here we present the first numerical verification of this behavior for a particular version of the two-dimensional asymmetric exclusion process. Particles jump strictly asymmetrically along one of the lattice directions and symmetrically along the other, and an anisotropy parameter p governs the ratio between the two rates. Using a novel massively parallel coupling algorithm that strongly reduces the fluctuations in the numerical estimate of the two-point correlation function, we are able to accurately determine the exponent of the logarithmic correction. In addition, the variation of the prefactor with p provides a stringent test of mode coupling theory.

Supersonic jet noise generated by large scale instabilities

NASA Technical Reports Server (NTRS)

Seiner, J. M.; Mclaughlin, D. K.; Liu, C. H.

1982-01-01

The role of large scale wavelike structures as the major mechanism for supersonic jet noise emission is examined. With the use of aerodynamic and acoustic data for low Reynolds number, supersonic jets at and below 70 thousand comparisons are made with flow fluctuation and acoustic measurements in high Reynolds number, supersonic jets. These comparisons show that a similar physical mechanism governs the generation of sound emitted in he principal noise direction. These experimental data are further compared with a linear instability theory whose prediction for the axial location of peak wave amplitude agrees satisfactorily with measured phased averaged flow fluctuation data in the low Reynolds number jets. The agreement between theory and experiment in the high Reynolds number flow differs as to the axial location for peak flow fluctuations and predicts an apparent origin for sound emission far upstream of the measured acoustic data.

Evolutionary dynamics with fluctuating population sizes and strong mutualism.

PubMed

Chotibut, Thiparat; Nelson, David R

2015-08-01

Game theory ideas provide a useful framework for studying evolutionary dynamics in a well-mixed environment. This approach, however, typically enforces a strictly fixed overall population size, deemphasizing natural growth processes. We study a competitive Lotka-Volterra model, with number fluctuations, that accounts for natural population growth and encompasses interaction scenarios typical of evolutionary games. We show that, in an appropriate limit, the model describes standard evolutionary games with both genetic drift and overall population size fluctuations. However, there are also regimes where a varying population size can strongly influence the evolutionary dynamics. We focus on the strong mutualism scenario and demonstrate that standard evolutionary game theory fails to describe our simulation results. We then analytically and numerically determine fixation probabilities as well as mean fixation times using matched asymptotic expansions, taking into account the population size degree of freedom. These results elucidate the interplay between population dynamics and evolutionary dynamics in well-mixed systems.

Evolutionary dynamics with fluctuating population sizes and strong mutualism

NASA Astrophysics Data System (ADS)

Chotibut, Thiparat; Nelson, David R.

2015-08-01

Game theory ideas provide a useful framework for studying evolutionary dynamics in a well-mixed environment. This approach, however, typically enforces a strictly fixed overall population size, deemphasizing natural growth processes. We study a competitive Lotka-Volterra model, with number fluctuations, that accounts for natural population growth and encompasses interaction scenarios typical of evolutionary games. We show that, in an appropriate limit, the model describes standard evolutionary games with both genetic drift and overall population size fluctuations. However, there are also regimes where a varying population size can strongly influence the evolutionary dynamics. We focus on the strong mutualism scenario and demonstrate that standard evolutionary game theory fails to describe our simulation results. We then analytically and numerically determine fixation probabilities as well as mean fixation times using matched asymptotic expansions, taking into account the population size degree of freedom. These results elucidate the interplay between population dynamics and evolutionary dynamics in well-mixed systems.

Large Fluctuations for Spatial Diffusion of Cold Atoms

NASA Astrophysics Data System (ADS)

Aghion, Erez; Kessler, David A.; Barkai, Eli

2017-06-01

We use a new approach to study the large fluctuations of a heavy-tailed system, where the standard large-deviations principle does not apply. Large-deviations theory deals with tails of probability distributions and the rare events of random processes, for example, spreading packets of particles. Mathematically, it concerns the exponential falloff of the density of thin-tailed systems. Here we investigate the spatial density Pt(x ) of laser-cooled atoms, where at intermediate length scales the shape is fat tailed. We focus on the rare events beyond this range, which dominate important statistical properties of the system. Through a novel friction mechanism induced by the laser fields, the density is explored with the recently proposed non-normalized infinite-covariant density approach. The small and large fluctuations give rise to a bifractal nature of the spreading packet. We derive general relations which extend our theory to a class of systems with multifractal moments.

Motor contributions to the temporal precision of auditory attention.

PubMed

Morillon, Benjamin; Schroeder, Charles E; Wyart, Valentin

2014-10-15

In temporal-or dynamic-attending theory, it is proposed that motor activity helps to synchronize temporal fluctuations of attention with the timing of events in a task-relevant stream, thus facilitating sensory selection. Here we develop a mechanistic behavioural account for this theory by asking human participants to track a slow reference beat, by noiseless finger pressing, while extracting auditory target tones delivered on-beat and interleaved with distractors. We find that overt rhythmic motor activity improves the segmentation of auditory information by enhancing sensitivity to target tones while actively suppressing distractor tones. This effect is triggered by cyclic fluctuations in sensory gain locked to individual motor acts, scales parametrically with the temporal predictability of sensory events and depends on the temporal alignment between motor and attention fluctuations. Together, these findings reveal how top-down influences associated with a rhythmic motor routine sharpen sensory representations, enacting auditory 'active sensing'.

Angular fluctuations of a multi-component order describe the pseudogap regime of the cuprate superconductors

NASA Astrophysics Data System (ADS)

Sachdev, Subir

2014-03-01

The hole-doped cuprate high temperature superconductors enter the pseudogap regime as their superconducting critical temperature, Tc, falls with decreasing hole density. Experiments have probed this regime for over two decades, but we argue that decisive new information has emerged from recent X-ray scattering experiments. The experiments observe incommensurate charge density wave fluctuations whose strength rises gradually over a wide temperature range above Tc, but then decreases as the temperature is lowered below Tc. We propose a theory in which the superconducting and charge-density wave orders exhibit angular fluctuations in a 6-dimensional space. The theory provides a natural quantitative fit to the X-ray data, and is consistent with other observed characteristics of the pseudogap. Results will also be presented on the microscopic origins of these order parameters. Work in collaboration with Lauren Hayward, Roger Melko, David Hawthorn, and Jay Sau.

Capillary wave theory of adsorbed liquid films and the structure of the liquid-vapor interface

NASA Astrophysics Data System (ADS)

MacDowell, Luis G.

2017-08-01

In this paper we try to work out in detail the implications of a microscopic theory for capillary waves under the assumption that the density is given along lines normal to the interface. Within this approximation, which may be justified in terms of symmetry arguments, the Fisk-Widom scaling of the density profile holds for frozen realizations of the interface profile. Upon thermal averaging of capillary wave fluctuations, the resulting density profile yields results consistent with renormalization group calculations in the one-loop approximation. The thermal average over capillary waves may be expressed in terms of a modified convolution approximation where normals to the interface are Gaussian distributed. In the absence of an external field we show that the phenomenological density profile applied to the square-gradient free energy functional recovers the capillary wave Hamiltonian exactly. We extend the theory to the case of liquid films adsorbed on a substrate. For systems with short-range forces, we recover an effective interface Hamiltonian with a film height dependent surface tension that stems from the distortion of the liquid-vapor interface by the substrate, in agreement with the Fisher-Jin theory of short-range wetting. In the presence of long-range interactions, the surface tension picks up an explicit dependence on the external field and recovers the wave vector dependent logarithmic contribution observed by Napiorkowski and Dietrich. Using an error function for the intrinsic density profile, we obtain closed expressions for the surface tension and the interface width. We show the external field contribution to the surface tension may be given in terms of the film's disjoining pressure. From literature values of the Hamaker constant, it is found that the fluid-substrate forces may be able to double the surface tension for films in the nanometer range. The film height dependence of the surface tension described here is in full agreement with results of the capillary wave spectrum obtained recently in computer simulations, and the predicted translation mode of surface fluctuations reproduces to linear order in field strength an exact solution of the density correlation function for the Landau-Ginzburg-Wilson Hamiltonian in an external field.

Sound Transmission through Cylindrical Shell Structures Excited by Boundary Layer Pressure Fluctuations

NASA Technical Reports Server (NTRS)

Tang, Yvette Y.; Silcox, Richard J.; Robinson, Jay H.

1996-01-01

This paper examines sound transmission into two concentric cylindrical sandwich shells subject to turbulent flow on the exterior surface of the outer shell. The interior of the shells is filled with fluid medium and there is an airgap between the shells in the annular space. The description of the pressure field is based on the cross-spectral density formulation of Corcos, Maestrello, and Efimtsov models of the turbulent boundary layer. The classical thin shell theory and the first-order shear deformation theory are applied for the inner and outer shells, respectively. Modal expansion and the Galerkin approach are used to obtain closed-form solutions for the shell displacements and the radiation and transmission pressures in the cavities including both the annular space and the interior. The average spectral density of the structural responses and the transmitted interior pressures are expressed explicitly in terms of the summation of the cross-spectral density of generalized force induced by the boundary layer turbulence. The effects of acoustic and hydrodynamic coincidences on the spectral density are observed. Numerical examples are presented to illustrate the method for both subsonic and supersonic flows.

"Fluctuoscopy" of Superconductors

NASA Astrophysics Data System (ADS)

Varlamov, A. A.

Study of fluctuation phenomena in superconductors (SCs) is the subject of great fundamental and practical importance. Understanding of their physics allowed to clear up the fundamental properties of SC state. Being predicted in 1968, one of the fluctuation effects, namely paraconductivity, was experimentally observed almost simultaneously. Since this time, fluctuations became a noticeable part of research in the field of superconductivity, and a variety of fluctuation effects have been discovered. The new wave of interest to fluctuations (FL) in superconductors was generated by the discovery of cuprate oxide superconductors (high-temperature superconductors, HTS), where, due to extremely short coherence length and low effective dimensionality of the electron system, superconductive fluctuations manifest themselves in a wide range of temperatures. Moreover, anomalous properties of the normal state of HTS were attributed by many theorists to strong FL in these systems. Being studied in the framework of the phenomenological Ginzburg-Landau theory and, more extensively, in diagrammatic microscopic approach, SC FLs side by side with other quantum corrections (weak localization, etc.) became a new tool for investigation and characterization of such new systems as HTS, disordered electron systems, granular metals, Josephson structures, artificial super-lattices, etc. The characteristic feature of SC FL is their strong dependence on temperature and magnetic fields in the vicinity of phase transition. This allows one to definitely separate the fluctuation effects from other contributions and to use them as the source of information about the microscopic parameters of a material. By their origin, SC FLs are very sensitive to relaxation processes, which break phase coherence. This allows using them for versatile characterization of SC. Today, one can speak about the " fluctuoscopy" of superconductive systems. In review, we present the qualitative picture both of thermodynamic fluctuations close to critical temperature T c0and quantum fluctuations at zero temperature and in vicinity of the second critical field H c2(0). Then in the frameworks of the Ginzburg-Landau theory, we discuss the characteristic crossovers in fluctuation properties of superconductive nanoparticles and layered superconductors. We present the general expression for fluctuation magneto-conductivity valid through all phase diagram of superconductor and apply it to study of the quantum phase transition close to H c2(0). Fluctuation analysis of this transition allows us to present the scenario of fluctuation defragmentation of the Abrikosov lattice.

Smoothed particle hydrodynamics model for Landau-Lifshitz-Navier-Stokes and advection-diffusion equations.

PubMed

Kordilla, Jannes; Pan, Wenxiao; Tartakovsky, Alexandre

2014-12-14

We propose a novel smoothed particle hydrodynamics (SPH) discretization of the fully coupled Landau-Lifshitz-Navier-Stokes (LLNS) and stochastic advection-diffusion equations. The accuracy of the SPH solution of the LLNS equations is demonstrated by comparing the scaling of velocity variance and the self-diffusion coefficient with kinetic temperature and particle mass obtained from the SPH simulations and analytical solutions. The spatial covariance of pressure and velocity fluctuations is found to be in a good agreement with theoretical models. To validate the accuracy of the SPH method for coupled LLNS and advection-diffusion equations, we simulate the interface between two miscible fluids. We study formation of the so-called "giant fluctuations" of the front between light and heavy fluids with and without gravity, where the light fluid lies on the top of the heavy fluid. We find that the power spectra of the simulated concentration field are in good agreement with the experiments and analytical solutions. In the absence of gravity, the power spectra decay as the power -4 of the wavenumber-except for small wavenumbers that diverge from this power law behavior due to the effect of finite domain size. Gravity suppresses the fluctuations, resulting in much weaker dependence of the power spectra on the wavenumber. Finally, the model is used to study the effect of thermal fluctuation on the Rayleigh-Taylor instability, an unstable dynamics of the front between a heavy fluid overlaying a light fluid. The front dynamics is shown to agree well with the analytical solutions.

Vibrational spectroscopic determination of local solvent electric field, solute-solvent electrostatic interaction energy, and their fluctuation amplitudes.

PubMed

Lee, Hochan; Lee, Gayeon; Jeon, Jonggu; Cho, Minhaeng

2012-01-12

IR probes have been extensively used to monitor local electrostatic and solvation dynamics. Particularly, their vibrational frequencies are highly sensitive to local solvent electric field around an IR probe. Here, we show that the experimentally measured vibrational frequency shifts can be inversely used to determine local electric potential distribution and solute-solvent electrostatic interaction energy. In addition, the upper limits of their fluctuation amplitudes are estimated by using the vibrational bandwidths. Applying this method to fully deuterated N-methylacetamide (NMA) in D(2)O and examining the solvatochromic effects on the amide I' and II' mode frequencies, we found that the solvent electric potential difference between O(═C) and D(-N) atoms of the peptide bond is about 5.4 V, and thus, the approximate solvent electric field produced by surrounding water molecules on the NMA is 172 MV/cm on average if the molecular geometry is taken into account. The solute-solvent electrostatic interaction energy is estimated to be -137 kJ/mol, by considering electric dipole-electric field interaction. Furthermore, their root-mean-square fluctuation amplitudes are as large as 1.6 V, 52 MV/cm, and 41 kJ/mol, respectively. We found that the water electric potential on a peptide bond is spatially nonhomogeneous and that the fluctuation in the electrostatic peptide-water interaction energy is about 10 times larger than the thermal energy at room temperature. This indicates that the peptide-solvent interactions are indeed important for the activation of chemical reactions in aqueous solution.

Smoothed particle hydrodynamics model for Landau-Lifshitz Navier-Stokes and advection-diffusion equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kordilla, Jannes; Pan, Wenxiao; Tartakovsky, Alexandre M.

2014-12-14

We propose a novel Smoothed Particle Hydrodynamics (SPH) discretization of the fully-coupled Landau-Lifshitz-Navier-Stokes (LLNS) and advection-diffusion equations. The accuracy of the SPH solution of the LLNS equations is demonstrated by comparing the scaling of velocity variance and self-diffusion coefficient with kinetic temperature and particle mass obtained from the SPH simulations and analytical solutions. The spatial covariance of pressure and velocity fluctuations are found to be in a good agreement with theoretical models. To validate the accuracy of the SPH method for the coupled LLNS and advection-diffusion equations, we simulate the interface between two miscible fluids. We study the formation ofmore » the so-called giant fluctuations of the front between light and heavy fluids with and without gravity, where the light fluid lays on the top of the heavy fluid. We find that the power spectra of the simulated concentration field is in good agreement with the experiments and analytical solutions. In the absence of gravity the the power spectra decays as the power -4 of the wave number except for small wave numbers which diverge from this power law behavior due to the effect of finite domain size. Gravity suppresses the fluctuations resulting in the much weaker dependence of the power spectra on the wave number. Finally the model is used to study the effect of thermal fluctuation on the Rayleigh-Taylor instability, an unstable dynamics of the front between a heavy fluid overlying a light fluid. The front dynamics is shown to agree well with the analytical solutions.« less

A Functional Central Limit Theorem for the Becker-Döring Model

NASA Astrophysics Data System (ADS)

Sun, Wen

2018-04-01

We investigate the fluctuations of the stochastic Becker-Döring model of polymerization when the initial size of the system converges to infinity. A functional central limit problem is proved for the vector of the number of polymers of a given size. It is shown that the stochastic process associated to fluctuations is converging to the strong solution of an infinite dimensional stochastic differential equation (SDE) in a Hilbert space. We also prove that, at equilibrium, the solution of this SDE is a Gaussian process. The proofs are based on a specific representation of the evolution equations, the introduction of a convenient Hilbert space and several technical estimates to control the fluctuations, especially of the first coordinate which interacts with all components of the infinite dimensional vector representing the state of the process.

Influence of spin and charge fluctuations on spectra of the two-dimensional Hubbard model.

PubMed

Sherman, A

2018-05-16

The influence of spin and charge fluctuations on spectra of the two-dimensional fermionic Hubbard model is considered using the strong coupling diagram technique. Infinite sequences of diagrams containing ladder inserts, which describe the interaction of electrons with these fluctuations, are summed, and obtained equations are self-consistently solved for the ranges of Hubbard repulsions [Formula: see text], temperatures [Formula: see text] and electron concentrations [Formula: see text] with t the intersite hopping constant. For all considered U the system exhibits a transition to the long-range antiferromagnetic order at [Formula: see text]. At the same time no indication of charge ordering is observed. Obtained solutions agree satisfactorily with results of other approaches and obey moments sum rules. In the considered region of the U-T plane, the curve separating metallic solutions passes from [Formula: see text] at the highest temperatures to U  =  2t at [Formula: see text] for half-filling. If only short-range fluctuations are allowed for the remaining part of this region is occupied by insulating solutions. Taking into account long-range fluctuations leads to strengthening of maxima tails, which transform a part of insulating solutions into bad-metal states. For low T, obtained results allow us to trace the gradual transition from the regime of strong correlations with the pronounced four-band structure and well-defined Mott gap for [Formula: see text] to the Slater regime of weak correlations with the spectral intensity having a dip along the boundary of the magnetic Brillouin zone due to an antiferromagnetic ordering for [Formula: see text]. For [Formula: see text] and [Formula: see text] doping leads to the occurrence of a pseudogap near the Fermi level, which is a consequence of the splitting out of a narrow band from a Hubbard subband. Obtained spectra feature waterfalls and Fermi arcs, which are similar to those observed in hole-doped cuprates.

Renormalization-group flow of the effective action of cosmological large-scale structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Floerchinger, Stefan; Garny, Mathias; Tetradis, Nikolaos

Following an approach of Matarrese and Pietroni, we derive the functional renormalization group (RG) flow of the effective action of cosmological large-scale structures. Perturbative solutions of this RG flow equation are shown to be consistent with standard cosmological perturbation theory. Non-perturbative approximate solutions can be obtained by truncating the a priori infinite set of possible effective actions to a finite subspace. Using for the truncated effective action a form dictated by dissipative fluid dynamics, we derive RG flow equations for the scale dependence of the effective viscosity and sound velocity of non-interacting dark matter, and we solve them numerically. Physically,more » the effective viscosity and sound velocity account for the interactions of long-wavelength fluctuations with the spectrum of smaller-scale perturbations. We find that the RG flow exhibits an attractor behaviour in the IR that significantly reduces the dependence of the effective viscosity and sound velocity on the input values at the UV scale. This allows for a self-contained computation of matter and velocity power spectra for which the sensitivity to UV modes is under control.« less

Bottom-up view of water network-mediated CO2 reduction using cryogenic cluster ion spectroscopy and direct dynamics simulations.

PubMed

Breen, Kristin J; DeBlase, Andrew F; Guasco, Timothy L; Voora, Vamsee K; Jordan, Kenneth D; Nagata, Takashi; Johnson, Mark A

2012-01-26

The transition states of a chemical reaction in solution are generally accessed through exchange of thermal energy between the solvent and the reactants. As such, an ensemble of reacting systems approaches the transition state configuration of reactant and surrounding solvent in an incoherent manner that does not lend itself to direct experimental observation. Here we describe how gas-phase cluster chemistry can provide a detailed picture of the microscopic mechanics at play when a network of six water molecules mediates the trapping of a highly reactive "hydrated electron" onto a neutral CO(2) molecule to form a radical anion. The exothermic reaction is triggered from a metastable intermediate by selective excitation of either the reactant CO(2) or the water network, which is evidenced by the evaporative decomposition of the product cluster. Ab initio molecular dynamics simulations of energized CO(2)·(H(2)O)(6)(-) clusters are used to elucidate the nature of the network deformations that mediate intracluster electron capture, thus revealing the detailed solvent fluctuations implicit in the Marcus theory for electron-transfer kinetics in solution.

Open string fluctuations in AdS space with and without torsion

NASA Astrophysics Data System (ADS)

Larsen, A. L.; Lomholt, M. A.

2003-09-01

The equations of motion and boundary conditions for the fluctuations around a classical open string, in a curved space-time with torsion, are considered in compact and world-sheet covariant form. The rigidly rotating open strings in anti de Sitter space with and without torsion are investigated in detail. By carefully analyzing the tangential fluctuations at the boundary, we show explicitly that the physical fluctuations (which at the boundary are combinations of normal and tangential fluctuations) are finite, even though the world-sheet is singular there. The divergent 2-curvature thus seems less dangerous than expected in these cases. The general formalism can be straightforwardly used also to study the (bosonic part of the) fluctuations around the closed strings, recently considered in connection with the AdS/conformal field theory duality, on AdS5×S5 and AdS3×S3×T4.

Kinetic theory of Jeans instability of a dusty plasma.

PubMed

Pandey, B P; Lakhina, G S; Krishan, V

1999-12-01

A kinetic theory of the Jeans instability of a dusty plasma has been developed in the present work. The effect of grain charge fluctuations due to the attachment of electrons and ions to the grain surface has been considered in the framework of Krook's collisional model. We demonstrate that the grain charge fluctuations alter the growth rate of the gravitational collapse of the dusty plasma. The Jeans length has been derived under limiting cases, and its dependence on the attachment frequency is shown. In the absence of gravity, we see that the damping rate of the dust acoustic mode is proportional to the electron-dust collision frequency.

Super-Hubble de Sitter fluctuations and the dynamical RG

NASA Astrophysics Data System (ADS)

Burgess, C. P.; Leblond, L.; Holman, R.; Shandera, S.

2010-03-01

Perturbative corrections to correlation functions for interacting theories in de Sitter spacetime often grow secularly with time, due to the properties of fluctuations on super-Hubble scales. This growth can lead to a breakdown of perturbation theory at late times. We argue that Dynamical Renormalization Group (DRG) techniques provide a convenient framework for interpreting and resumming these secularly growing terms. In the case of a massless scalar field in de Sitter with quartic self-interaction, the resummed result is also less singular in the infrared, in precisely the manner expected if a dynamical mass is generated. We compare this improved infrared behavior with large-N expansions when applicable.

Heat transfer in the coolant channel of a heat-exchanger system based on fluctuation theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Diaz-Guilera, A.; Rodriguez, M.A.; Rubi, J.M.

1988-11-01

We present a model to study the heat transfer in the coolant channel of a heat-exchanger system. Such a model introduces thermal fluctuations as well as external noises due to different mechanisms of heat interchange. A unified treatment of both kinds of noise is carried out. The stationary mean value of the channel temperature is studied, obtaining effective transport coefficients which affect the stability of the system. The effects of the different noises are visualized in a correlation length obtained from the temperature correlation function. The model has practical implications in the field of nuclear-reactor noise theory.

Hetero-phase fluctuations in the pre-melting region in ionic crystals

NASA Astrophysics Data System (ADS)

Matsunaga, S.; Tamaki, S.

2008-06-01

The theory of the pre-melting phenomena in ionic crystals on the basis of the concept of the hetero phase fluctuation has been applied to KCl and AgCl crystal. The large scale molecular dynamics simulations (MD) in KCl and AgCl crystals are also performed to examine the ionic configuration in premelting region in the vicinity of their melting points. The size of the liquid like clusters are estimated by the theory and MD. The structural features of liquid like clusters are discussed by MD results using the Lindemann instability condition. The ionic conductivities in the pre-melting region are also discussed on the same theoretical basis.

Intrinsic measurement errors for the speed of light in vacuum

NASA Astrophysics Data System (ADS)

Braun, Daniel; Schneiter, Fabienne; Fischer, Uwe R.

2017-09-01

The speed of light in vacuum, one of the most important and precisely measured natural constants, is fixed by convention to c=299 792 458 m s-1 . Advanced theories predict possible deviations from this universal value, or even quantum fluctuations of c. Combining arguments from quantum parameter estimation theory and classical general relativity, we here establish rigorously the existence of lower bounds on the uncertainty to which the speed of light in vacuum can be determined in a given region of space-time, subject to several reasonable restrictions. They provide a novel perspective on the experimental falsifiability of predictions for the quantum fluctuations of space-time.

Kinetic theory of coupled oscillators.

PubMed

Hildebrand, Eric J; Buice, Michael A; Chow, Carson C

2007-02-02

We present an approach for the description of fluctuations that are due to finite system size induced correlations in the Kuramoto model of coupled oscillators. We construct a hierarchy for the moments of the density of oscillators that is analogous to the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy in the kinetic theory of plasmas and gases. To calculate the lowest order system size effect, we truncate this hierarchy at second order and solve the resulting closed equations for the two-oscillator correlation function around the incoherent state. We use this correlation function to compute the fluctuations of the order parameter, including the effect of transients, and compare this computation with numerical simulations.

Theory of Aging, Rejuvenation, and the Nonequilibrium Steady State in Deformed Polymer Glasses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Kang

The nonlinear Langevin equation theory of segmental relaxation, elasticity, and mechanical response of polymer glasses is extended to describe the coupled effects of physical aging, mechanical rejuvenation, and thermal history. The key structural variable is the amplitude of density fluctuations, and segmental dynamics proceeds via stress-modified activated barrier hopping on a dynamic free-energy profile. Mechanically generated disorder rejuvenation is quantified by a dissipative work argument and increases the amplitude of density fluctuations, thereby speeding up relaxation beyond that induced by the landscape tilting mechanism. The theory makes testable predictions for the time evolution and nonequilibrium steady state of the alphamore » relaxation time, density fluctuation amplitude, elastic modulus, and other properties. Model calculations reveal a rich dependence of these quantities on preaging time, applied stress, and temperature that reflects the highly nonlinear competition between physical aging and mechanical disordering. Thermal history is erased in the long-time limit, although the nonequilibrium steady state is not the literal fully rejuvenated freshly quenched glass. The present work provides the conceptual foundation for a quantitative treatment of the nonlinear mechanical response of polymer glasses under a variety of deformation protocols.« less

Non-gaussianity versus nonlinearity of cosmological perturbations.

PubMed

Verde, L

2001-06-01

Following the discovery of the cosmic microwave background, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us toward a physical theory for the origin of structures. The statistical distribution of cosmological perturbations, as we observe them, can deviate from the gaussian distribution in several different ways. Even if perturbations start off gaussian, nonlinear gravitational evolution can introduce non-gaussian features. Additionally, our knowledge of the Universe comes principally from the study of luminous material such as galaxies, but galaxies might not be faithful tracers of the underlying mass distribution. The relationship between fluctuations in the mass and in the galaxies distribution (bias), is often assumed to be local, but could well be nonlinear. Moreover, galaxy catalogues use the redshift as third spatial coordinate: the resulting redshift-space map of the galaxy distribution is nonlinearly distorted by peculiar velocities. Nonlinear gravitational evolution, biasing, and redshift-space distortion introduce non-gaussianity, even in an initially gaussian fluctuation field. I investigate the statistical tools that allow us, in principle, to disentangle the above different effects, and the observational datasets we require to do so in practice.

New boundary conditions for fluid interaction with hydrophobic surface

NASA Astrophysics Data System (ADS)

Pochylý, František; Fialová, Simona; Havlásek, Michal

2018-06-01

Solution of both laminar and turbulent flow with consideration of hydrophobic surface is based on the original Navier assumption that the shear stress on the hydrophobic surface is directly proportional to the slipping velocity. In the previous work a laminar flow analysis with different boundary conditions was performed. The shear stress value on the tube walls directly depends on the pressure gradient. In the solution of the turbulent flow by the k-ɛ model, the occurrence of the fluctuation components of velocity on the hydrophobic surface is considered. The fluctuation components of the velocity affect the size of the adhesive forces. We assume that the boundary condition for ɛ depending on the velocity gradients will not need to be changed. When the liquid slips over the surface, non-zero fluctuation velocity components occur in the turbulent flow. These determine the non-zero value of the turbulent kinetic energy K. In addition, the fluctuation velocity components also influence the value of the adhesive forces, so it is necessary to include these in the formulation of new boundary conditions for turbulent flow on the hydrophobic surface.

Molecular dynamics approach to dissipative relativistic hydrodynamics: Propagation of fluctuations

NASA Astrophysics Data System (ADS)

Shahsavar, Leila; Ghodrat, Malihe; Montakhab, Afshin

2016-12-01

Relativistic generalization of hydrodynamic theory has attracted much attention from a theoretical point of view. However, it has many important practical applications in high energy as well as astrophysical contexts. Despite various attempts to formulate relativistic hydrodynamics, no definitive consensus has been achieved. In this work, we propose to test the predictions of four types of first-order hydrodynamic theories for nonperfect fluids in the light of numerically exact molecular dynamics simulations of a fully relativistic particle system in the low density regime. In this regard, we study the propagation of density, velocity, and heat fluctuations in a wide range of temperatures using extensive simulations and compare them to the corresponding analytic expressions we obtain for each of the proposed theories. As expected, in the low temperature classical regime all theories give the same results, consistent with the numerics. In the high temperature extremely relativistic regime, not all considered theories are distinguishable from one another. However, in the intermediate regime, a meaningful distinction exists in the predictions of various theories considered here. We find that the predictions of the recent formulation due to Tsumura, Kunihiro, and Ohnishi are more consistent with our numerical results than the traditional theories: the Meixner, modified Eckart, and modified Marle-Stewart theories.

Leptokurtic portfolio theory

NASA Astrophysics Data System (ADS)

Kitt, R.; Kalda, J.

2006-03-01

The question of optimal portfolio is addressed. The conventional Markowitz portfolio optimisation is discussed and the shortcomings due to non-Gaussian security returns are outlined. A method is proposed to minimise the likelihood of extreme non-Gaussian drawdowns of the portfolio value. The theory is called Leptokurtic, because it minimises the effects from “fat tails” of returns. The leptokurtic portfolio theory provides an optimal portfolio for investors, who define their risk-aversion as unwillingness to experience sharp drawdowns in asset prices. Two types of risks in asset returns are defined: a fluctuation risk, that has Gaussian distribution, and a drawdown risk, that deals with distribution tails. These risks are quantitatively measured by defining the “noise kernel” — an ellipsoidal cloud of points in the space of asset returns. The size of the ellipse is controlled with the threshold parameter: the larger the threshold parameter, the larger return are accepted for investors as normal fluctuations. The return vectors falling into the kernel are used for calculation of fluctuation risk. Analogously, the data points falling outside the kernel are used for the calculation of drawdown risks. As a result the portfolio optimisation problem becomes three-dimensional: in addition to the return, there are two types of risks involved. Optimal portfolio for drawdown-averse investors is the portfolio minimising variance outside the noise kernel. The theory has been tested with MSCI North America, Europe and Pacific total return stock indices.

Pressure effects on collective density fluctuations in water and protein solutions

PubMed Central

Russo, Daniela; Laloni, Alessio; Filabozzi, Alessandra; Heyden, Matthias

2017-01-01

Neutron Brillouin scattering and molecular dynamics simulations have been used to investigate protein hydration water density fluctuations as a function of pressure. Our results show significant differences between the pressure and density dependence of collective dynamics in bulk water and in concentrated protein solutions. Pressure-induced changes in the tetrahedral order of the water HB network have direct consequences for the high-frequency sound velocity and damping coefficients, which we find to be a sensitive probe for changes in the HB network structure as well as the wetting of biomolecular surfaces. PMID:29073065

Derivation of the spin-glass order parameter from stochastic thermodynamics

NASA Astrophysics Data System (ADS)

Crisanti, A.; Picco, M.; Ritort, F.

2018-05-01

A fluctuation relation is derived to extract the order parameter function q (x ) in weakly ergodic systems. The relation is based on measuring and classifying entropy production fluctuations according to the value of the overlap q between configurations. For a fixed value of q , entropy production fluctuations are Gaussian distributed allowing us to derive the quasi-FDT so characteristic of aging systems. The theory is validated by extracting the q (x ) in various types of glassy models. It might be generally applicable to other nonequilibrium systems and experimental small systems.

Electromagnetic fluctuation spectra of collective oscillations in magnetized Maxwellian plasmas for parallel wave vectors

NASA Astrophysics Data System (ADS)

Vafin, S.; Schlickeiser, R.; Yoon, P. H.

2016-05-01

The general electromagnetic fluctuation theory for magnetized plasmas is used to calculate the steady-state wave number spectra and total electromagnetic field strength of low-frequency collective weakly damped eigenmodes with parallel wavevectors in a Maxwellian electron-proton plasma. These result from the equilibrium of spontaneous emission and collisionless damping, and they represent the minimum electromagnetic fluctuations guaranteed in quiet thermal space plasmas, including the interstellar and interplanetary medium. Depending on the plasma beta, the ratio of |δB |/B0 can be as high as 10-12 .

Will nonlinear peculiar velocity and inhomogeneous reionization spoil 21 cm cosmology from the epoch of reionization?

PubMed

Shapiro, Paul R; Mao, Yi; Iliev, Ilian T; Mellema, Garrelt; Datta, Kanan K; Ahn, Kyungjin; Koda, Jun

2013-04-12

The 21 cm background from the epoch of reionization is a promising cosmological probe: line-of-sight velocity fluctuations distort redshift, so brightness fluctuations in Fourier space depend upon angle, which linear theory shows can separate cosmological from astrophysical information. Nonlinear fluctuations in ionization, density, and velocity change this, however. The validity and accuracy of the separation scheme are tested here for the first time, by detailed reionization simulations. The scheme works reasonably well early in reionization (≲40% ionized), but not late (≳80% ionized).

Entropic Repulsion Between Fluctuating Surfaces

NASA Astrophysics Data System (ADS)

Janke, W.

The statistical mechanics of fluctuating surfaces plays an important role in a variety of physical systems, ranging from biological membranes to world sheets of strings in theories of fundamental interactions. In many applications it is a good approximation to assume that the surfaces possess no tension. Their statistical properties are then governed by curvature energies only, which allow for gigantic out-of-plane undulations. These fluctuations are the “entropic” origin of long-range repulsive forces in layered surface systems. Theoretical estimates of these forces for simple model surfaces are surveyed and compared with recent Monte Carlo simulations.

Thermal fluctuations of dilaton black holes in gravity's rainbow

NASA Astrophysics Data System (ADS)

Dehghani, M.

2018-06-01

In this work, thermodynamics and phase transition of some new dilaton black hole solutions have been explored in the presence of the rainbow functions. By introducing an energy dependent space time, the dilaton potential has been obtained as the linear combination of two Liouville-type potentials and three new classes of black hole solutions have been constructed. The conserved and thermodynamic quantities of the new dilaton black holes have been calculated in the energy dependent space times. It has been shown that, even if some of the thermodynamic quantities are affected by the rainbow functions, the thermodynamical first law still remains valid. Also, the impacts of rainbow functions on the stability or phase transition of the new black hole solutions have been investigated. Finally, the quantum gravitational effects on the thermodynamics and phase transition of the solutions have been studied through consideration of the thermal fluctuations.

Nonlinear Dynamics and Nucleation Kinetics in Near-Critical Liquids

NASA Technical Reports Server (NTRS)

Patashinski, Alexander Z.; Ratner, Mark A.; Pines, Vladimir

1996-01-01

The objective of our study is to model the nonlinear behavior of a near-critical liquid following a rapid change of the temperature and/or other thermodynamic parameters (pressure, external electric or gravitational field). The thermodynamic critical point is manifested by large, strongly correlated fluctuations of the order parameter (particle density in liquid-gas systems, concentration in binary solutions) in the critical range of scales. The largest critical length scale is the correlation radius r(sub c). According to the scaling theory, r(sub c) increases as r(sub c) = r(sub 0)epsilon(exp -alpha) when the nondimensional distance epsilon = (T - T(sub c))/T(sub c) to the critical point decreases. The normal gravity alters the nature of correlated long-range fluctuations when one reaches epsilon approximately equal to 10(exp -5), and correspondingly the relaxation time, tau(r(sub c)), is approximately equal to 10(exp -3) seconds; this time is short when compared to the typical experimental time. Close to the critical point, a rapid, relatively small temperature change may perturb the thermodynamic equilibrium on many scales. The critical fluctuations have a hierarchical structure, and the relaxation involves many length and time scales. Above the critical point, in the one-phase region, we consider the relaxation of the liquid following a sudden temperature change that simultaneously violates the equilibrium on many scales. Below T(sub c), a non-equilibrium state may include a distribution of small scale phase droplets; we consider the relaxation of such a droplet following a temperature change that has made the phase of the matrix stable.

On the microscopic fluctuations driving the NMR relaxation of quadrupolar ions in water

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carof, Antoine; Salanne, Mathieu; Rotenberg, Benjamin, E-mail: benjamin.rotenberg@upmc.fr

Nuclear Magnetic Resonance (NMR) relaxation is sensitive to the local structure and dynamics around the probed nuclei. The Electric Field Gradient (EFG) is the key microscopic quantity to understand the NMR relaxation of quadrupolar ions, such as {sup 7}Li{sup +}, {sup 23}Na{sup +}, {sup 25}Mg{sup 2+}, {sup 35}Cl{sup −}, {sup 39}K{sup +}, or {sup 133}Cs{sup +}. Using molecular dynamics simulations, we investigate the statistical and dynamical properties of the EFG experienced by alkaline, alkaline Earth, and chloride ions at infinite dilution in water. Specifically, we analyze the effect of the ionic charge and size on the distribution of the EFGmore » tensor and on the multi-step decay of its auto-correlation function. The main contribution to the NMR relaxation time arises from the slowest mode, with a characteristic time on the picosecond time scale. The first solvation shell of the ion plays a dominant role in the fluctuations of the EFG, all the more that the ion radius is small and its charge is large. We propose an analysis based on a simplified charge distribution around the ion, which demonstrates that the auto-correlation of the EFG, hence the NMR relaxation time, reflects primarily the collective translational motion of water molecules in the first solvation shell of the cations. Our findings provide a microscopic route to the quantitative interpretation of NMR relaxation measurements and open the way to the design of improved analytical theories for NMR relaxation for small ionic solutes, which should focus on water density fluctuations around the ion.« less

Low Mach number fluctuating hydrodynamics for electrolytes

DOE PAGES

Péraud, Jean-Philippe; Nonaka, Andy; Chaudhri, Anuj; ...

2016-11-18

Here, we formulate and study computationally the low Mach number fluctuating hydrodynamic equations for electrolyte solutions. We are also interested in studying transport in mixtures of charged species at the mesoscale, down to scales below the Debye length, where thermal fluctuations have a significant impact on the dynamics. Continuing our previous work on fluctuating hydrodynamics of multicomponent mixtures of incompressible isothermal miscible liquids (A. Donev, et al., Physics of Fluids, 27, 3, 2015), we now include the effect of charged species using a quasielectrostatic approximation. Localized charges create an electric field, which in turn provides additional forcing in the massmore » and momentum equations. Our low Mach number formulation eliminates sound waves from the fully compressible formulation and leads to a more computationally efficient quasi-incompressible formulation. Furthermore, we demonstrate our ability to model saltwater (NaCl) solutions in both equilibrium and nonequilibrium settings. We show that our algorithm is second-order in the deterministic setting, and for length scales much greater than the Debye length gives results consistent with an electroneutral/ambipolar approximation. In the stochastic setting, our model captures the predicted dynamics of equilibrium and nonequilibrium fluctuations. We also identify and model an instability that appears when diffusive mixing occurs in the presence of an applied electric field.« less

Interaction of the electron density fluctuations with electron cyclotron waves from the equatorial launcher in ITER

NASA Astrophysics Data System (ADS)

Snicker, A.; Poli, E.; Maj, O.; Guidi, L.; Köhn, A.; Weber, H.; Conway, G. D.; Henderson, M.; Saibene, G.

2018-01-01

We present a numerical investigation of electron cyclotron beams interacting with electron density fluctuations in the ITER 15 MA H-mode scenario. In particular, here we study how the beam from the equatorial launcher, which shall be utilized to influence the sawtooth instability, is affected by the fluctuations. Moreover, we present the theory and first estimates of the power that is scattered from the injected O-mode to a secondary X-mode in the presence of the fluctuations. It is shown that for ITER parameters the scattered power stays within acceptable limits and broadening of the equatorial beams is less than those from the upper launcher.

Quantum fluctuations of radiation in a ring Nd : YAG chip laser

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lariontsev, E G; Firsov, V V

2015-07-31

We report theoretical and experimental investigation of intensity fluctuations in a travelling-wave ring Nd : YAG chip laser, caused by the noise of spontaneous emission. In accordance with theory and experiment, quantum intensity fluctuations in the laser under study decrease dramatically with increasing pump over the threshold. As a result of the research performed, the factor β is found, which determines the ratio of the rate of spontaneous emission into the generated mode to the total rate of spontaneous emission into all modes. The effect of the relaxation rate from the lower laser level on quantum fluctuations of the radiationmore » intensity is found. (control of radiation parameters)« less

Theory of waves incoherently scattered

NASA Technical Reports Server (NTRS)

Bauer, P.

1974-01-01

Electromagnetic waves impinging upon a plasma at frequencies larger than the plasma frequency, suffer weak scattering. The scattering arises from the existence of electron density fluctuations. The received signal corresponds to a particular spatial Fourier component of the fluctuations, the wave vector of which is a function of the wavelength of the radiowave. Wavelengths short with respect to the Debye length of the medium relate to fluctuations due to non-interacting Maxwellian electrons, while larger wavelengths relate to fluctuations due to collective Coulomb interactions. In the latter case, the scattered signal exhibits a spectral distribution which is characteristic of the main properties of the electron and ion gases and, therefore, provides a powerful diagnosis of the state of the ionosphere.

Condensate fluctuations of interacting Bose gases within a microcanonical ensemble.

PubMed

Wang, Jianhui; He, Jizhou; Ma, Yongli

2011-05-01

Based on counting statistics and Bogoliubov theory, we present a recurrence relation for the microcanonical partition function for a weakly interacting Bose gas with a finite number of particles in a cubic box. According to this microcanonical partition function, we calculate numerically the distribution function, condensate fraction, and condensate fluctuations for a finite and isolated Bose-Einstein condensate. For ideal and weakly interacting Bose gases, we compare the condensate fluctuations with those in the canonical ensemble. The present approach yields an accurate account of the condensate fluctuations for temperatures close to the critical region. We emphasize that the interactions between excited atoms turn out to be important for moderate temperatures.

TESTING THE PROPAGATING FLUCTUATIONS MODEL WITH A LONG, GLOBAL ACCRETION DISK SIMULATION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hogg, J Drew; Reynolds, Christopher S.

2016-07-20

The broadband variability of many accreting systems displays characteristic structures; log-normal flux distributions, root-mean square (rms)-flux relations, and long inter-band lags. These characteristics are usually interpreted as inward propagating fluctuations of the mass accretion rate in an accretion disk driven by stochasticity of the angular momentum transport mechanism. We present the first analysis of propagating fluctuations in a long-duration, high-resolution, global three-dimensional magnetohydrodynamic (MHD) simulation of a geometrically thin ( h / r ≈ 0.1) accretion disk around a black hole. While the dynamical-timescale turbulent fluctuations in the Maxwell stresses are too rapid to drive radially coherent fluctuations in themore » accretion rate, we find that the low-frequency quasi-periodic dynamo action introduces low-frequency fluctuations in the Maxwell stresses, which then drive the propagating fluctuations. Examining both the mass accretion rate and emission proxies, we recover log-normality, linear rms-flux relations, and radial coherence that would produce inter-band lags. Hence, we successfully relate and connect the phenomenology of propagating fluctuations to modern MHD accretion disk theory.« less

Collisionless Isotropization of the Solar-Wind Protons by Compressive Fluctuations and Plasma Instabilities

NASA Astrophysics Data System (ADS)

Verscharen, D.; Chandran, B. D. G.; Klein, K. G.; Quataert, E.

2016-12-01

Compressive fluctuations are a minor yet significant component of astrophysical plasma turbulence. In the solar wind, long-wavelength compressive slow-mode fluctuations lead to changes in β∥p ≡ 8πnpkBT∥p/B2 and in Rp ≡ T⊥p/T∥p, where T⊥p and T∥p are the perpendicular and parallel temperatures of the protons, B is the magnetic field strength, and np is the proton density. If the amplitude of the compressive fluctuations is large enough, Rp crosses one or more instability thresholds for anisotropy-driven micro-instabilities. The enhanced field fluctuations from these micro-instabilities scatter the protons so as to reduce the anisotropy of the pressure tensor, driving the average value of Rp away from the marginal stability boundary until the fluctuating value of Rp stops crossing the boundary. We model this "fluctuating-anisotropy effect" using linear Vlasov-Maxwell theory to describe the large-scale compressive fluctuations. We show that this effect can explain why, in the nearly collisionless solar wind, the average value of Rp is close to unity.

Le Chatelier Principle for Out-of-Equilibrium and Boundary-Driven Systems: Application to Dynamical Phase Transitions.

PubMed

Shpielberg, O; Akkermans, E

2016-06-17

A stability analysis is presented for boundary-driven and out-of-equilibrium systems in the framework of the hydrodynamic macroscopic fluctuation theory. A Hamiltonian description is proposed which allows us to thermodynamically interpret the additivity principle. A necessary and sufficient condition for the validity of the additivity principle is obtained as an extension of the Le Chatelier principle. These stability conditions result from a diagonal quadratic form obtained using the cumulant generating function. This approach allows us to provide a proof for the stability of the weakly asymmetric exclusion process and to reduce the search for stability to the solution of two coupled linear ordinary differential equations instead of nonlinear partial differential equations. Additional potential applications of these results are discussed in the realm of classical and quantum systems.

Le Chatelier Principle for Out-of-Equilibrium and Boundary-Driven Systems: Application to Dynamical Phase Transitions

NASA Astrophysics Data System (ADS)

Shpielberg, O.; Akkermans, E.

2016-06-01

A stability analysis is presented for boundary-driven and out-of-equilibrium systems in the framework of the hydrodynamic macroscopic fluctuation theory. A Hamiltonian description is proposed which allows us to thermodynamically interpret the additivity principle. A necessary and sufficient condition for the validity of the additivity principle is obtained as an extension of the Le Chatelier principle. These stability conditions result from a diagonal quadratic form obtained using the cumulant generating function. This approach allows us to provide a proof for the stability of the weakly asymmetric exclusion process and to reduce the search for stability to the solution of two coupled linear ordinary differential equations instead of nonlinear partial differential equations. Additional potential applications of these results are discussed in the realm of classical and quantum systems.

Biodiversity of plankton by species oscillations and chaos

NASA Astrophysics Data System (ADS)

Huisman, Jef; Weissing, Franz J.

1999-11-01

Biodiversity has both fascinated and puzzled biologists. In aquatic ecosystems, the biodiversity puzzle is particularly troublesome, and known as the `paradox of the plankton'. Competition theory predicts that, at equilibrium, the number of coexisting species cannot exceed the number of limiting resources. For phytoplankton, only a few resources are potentially limiting: nitrogen, phosphorus, silicon, iron, light, inorganic carbon, and sometimes a few trace metals or vitamins. However, in natural waters dozens of phytoplankton species coexist. Here we offer a solution to the plankton paradox. First, we show that resource competition models can generate oscillations and chaos when species compete for three or more resources. Second, we show that these oscillations and chaotic fluctuations in species abundances allow the coexistence of many species on a handful of resources. This model of planktonic biodiversity may be broadly applicable to the biodiversity of many ecosystems.

Dynamical Vertex Approximation for the Hubbard Model

NASA Astrophysics Data System (ADS)

Toschi, Alessandro

A full understanding of correlated electron systems in the physically relevant situations of three and two dimensions represents a challenge for the contemporary condensed matter theory. However, in the last years considerable progress has been achieved by means of increasingly more powerful quantum many-body algorithms, applied to the basic model for correlated electrons, the Hubbard Hamiltonian. Here, I will review the physics emerging from studies performed with the dynamical vertex approximation, which includes diagrammatic corrections to the local description of the dynamical mean field theory (DMFT). In particular, I will first discuss the phase diagram in three dimensions with a special focus on the commensurate and incommensurate magnetic phases, their (quantum) critical properties, and the impact of fluctuations on electronic lifetimes and spectral functions. In two dimensions, the effects of non-local fluctuations beyond DMFT grow enormously, determining the appearance of a low-temperature insulating behavior for all values of the interaction in the unfrustrated model: Here the prototypical features of the Mott-Hubbard metal-insulator transition, as well as the existence of magnetically ordered phases, are completely overwhelmed by antiferromagnetic fluctuations of exponentially large extension, in accordance with the Mermin-Wagner theorem. Eventually, by a fluctuation diagnostics analysis of cluster DMFT self-energies, the same magnetic fluctuations are identified as responsible for the pseudogap regime in the holed-doped frustrated case, with important implications for the theoretical modeling of the cuprate physics.

l en configuration dite de "Bridgman verticale" avec un tirage vers le haut. Pour des valeurs élevées du nombre de Rayleigh solutal, nous suivons les diverses branches de solutions stationnaires jusqu'aux seuils d'apparition des phénomènes instationnaires. Ces transitions à l'instationnarité sont étudiées en fonction du confinement et, le long de ces nouvelles branches de solution, nous estimons l'ordre de grandeur de la fluctuation temporelle de la composition à l'interface. Cette dernière étant responsable d'une striation qui est incorporée par le solide lors de sa croissance, nous caractérisons ce phénomène en termes d'amplitude de striation (i.e. intensité de la fluctuation de composition) et de période spatiale de striation.

NASA Astrophysics Data System (ADS)

Haldenwang, P.; Guérin, R.; Le Marec, C.

1999-06-01

2-D unsteady flow patterns in upward Bridgman solidification are numerically investigated. The alloy under study is Pb-30%Tl. The purpose of the contribution is to characterise the striations induced by unsteadiness in the growing crystal. Unsteady solution branches are studied from onset threshold of unsteadiness to chaos. We report two examples for which time behaviour of a given solution branch is studied versus Rayleigh number. We then estimate the magnitude of the time fluctuations in solute composition that the crystal incorporates. The period of the striations is also discussed. Nous étudions numériquement les structures hydrodynamiques de la convection solutale dans le bain fondu, lors de la solidification dirigée d'alliages binaires. Plus précisément, cette étude porte

First-principles calculations of shear moduli for Monte Carlo-simulated Coulomb solids

NASA Technical Reports Server (NTRS)

Ogata, Shuji; Ichimaru, Setsuo

1990-01-01

The paper presents a first-principles study of the shear modulus tensor for perfect and imperfect Coulomb solids. Allowance is made for the effects of thermal fluctuations for temperatures up to the melting conditions. The present theory treats the cases of the long-range Coulomb interaction, where volume fluctuations should be avoided in the Ewald sums.

The way from microscopic many-particle theory to macroscopic hydrodynamics.

PubMed

Haussmann, Rudolf

2016-03-23

Starting from the microscopic description of a normal fluid in terms of any kind of local interacting many-particle theory we present a well defined step by step procedure to derive the hydrodynamic equations for the macroscopic phenomena. We specify the densities of the conserved quantities as the relevant hydrodynamic variables and apply the methods of non-equilibrium statistical mechanics with projection operator techniques. As a result we obtain time-evolution equations for the hydrodynamic variables with three kinds of terms on the right-hand sides: reversible, dissipative and fluctuating terms. In their original form these equations are completely exact and contain nonlocal terms in space and time which describe nonlocal memory effects. Applying a few approximations the nonlocal properties and the memory effects are removed. As a result we find the well known hydrodynamic equations of a normal fluid with Gaussian fluctuating forces. In the following we investigate if and how the time-inversion invariance is broken and how the second law of thermodynamics comes about. Furthermore, we show that the hydrodynamic equations with fluctuating forces are equivalent to stochastic Langevin equations and the related Fokker-Planck equation. Finally, we investigate the fluctuation theorem and find a modification by an additional term.

Holographic curvature perturbations in a cosmology with a space-like singularity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ferreira, Elisa G.M.; Brandenberger, Robert; Institute for Theoretical Studies, ETH Zürich,Clausiusstr. 47, Zürich, CH-8092

2016-07-19

We study the evolution of cosmological perturbations in an anti-de-Sitter (AdS) bulk through a cosmological singularity by mapping the dynamics onto the boundary conformal fields theory by means of the AdS/CFT correspondence. We consider a deformed AdS space-time obtained by considering a time-dependent dilaton which induces a curvature singularity in the bulk at a time which we call t=0, and which asymptotically approaches AdS both for large positive and negative times. The boundary field theory becomes free when the bulk curvature goes to infinity. Hence, the evolution of the fluctuations is under better controle on the boundary than in themore » bulk. To avoid unbounded particle production across the bounce it is necessary to smooth out the curvature singularity at very high curvatures. We show how the bulk cosmological perturbations can be mapped onto boundary gauge field fluctuations. We evolve the latter and compare the spectrum of fluctuations on the infrared scales relevant for cosmological observations before and after the bounce point. We find that the index of the power spectrum of fluctuations is the same before and after the bounce.« less

Kinetic theory and turbulent discontinuities. [shock tube flow

NASA Technical Reports Server (NTRS)

Johnson, J. A., III; I, L.; Li, Y.; Ramaian, R.; Santigo, J. P.

1981-01-01

Shock tube discontinuities were used to test and extend a kinetic theory of turbulence. In shock wave and contact surface fluctuations, coherent phenomena were found which provide new support for the microscopic nonempirical approach to turbulent systems, especially those with boundary layer-like instabilities.

Incorporating both physical and kinetic limitations in quantifying dissolved oxygen flux to aquatic sediments

USGS Publications Warehouse

O'Connor, B.L.; Hondzo, Miki; Harvey, J.W.

2009-01-01

Traditionally, dissolved oxygen (DO) fluxes have been calculated using the thin-film theory with DO microstructure data in systems characterized by fine sediments and low velocities. However, recent experimental evidence of fluctuating DO concentrations near the sediment-water interface suggests that turbulence and coherent motions control the mass transfer, and the surface renewal theory gives a more mechanistic model for quantifying fluxes. Both models involve quantifying the mass transfer coefficient (k) and the relevant concentration difference (??C). This study compared several empirical models for quantifying k based on both thin-film and surface renewal theories, as well as presents a new method for quantifying ??C (dynamic approach) that is consistent with the observed DO concentration fluctuations near the interface. Data were used from a series of flume experiments that includes both physical and kinetic uptake limitations of the flux. Results indicated that methods for quantifying k and ??C using the surface renewal theory better estimated the DO flux across a range of fluid-flow conditions. ?? 2009 ASCE.

Higher order mode laser beam intensity fluctuations in strong oceanic turbulence

NASA Astrophysics Data System (ADS)

Baykal, Yahya

2017-05-01

Intensity fluctuations of the higher order mode laser beams are evaluated when these beams propagate in a medium exhibiting strong oceanic turbulence. Our formulation involves the modified Rytov solution that extends the Rytov solution to cover strong turbulence as well, and our recently reported expression that relates the atmospheric turbulence structure constant to the oceanic turbulence parameters and oceanic wireless optical communication link parameters. The variations of the intensity fluctuations are reported against the changes of the ratio of temperature to salinity contributions to the refractive index spectrum, rate of dissipation of kinetic energy per unit mass of fluid, rate of dissipation of mean-squared temperature, viscosity and the source size of the higher order mode laser beam. Our results indicate that under any oceanic turbulence parameters, it is advantageous to employ higher order laser modes in reducing the scintillation noise in wireless optical communication links operating in a strongly turbulent ocean.

Aerofoil broadband and tonal noise modelling using stochastic sound sources and incorporated large scale fluctuations

NASA Astrophysics Data System (ADS)

Proskurov, S.; Darbyshire, O. R.; Karabasov, S. A.

2017-12-01

The present work discusses modifications to the stochastic Fast Random Particle Mesh (FRPM) method featuring both tonal and broadband noise sources. The technique relies on the combination of incorporated vortex-shedding resolved flow available from Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulation with the fine-scale turbulence FRPM solution generated via the stochastic velocity fluctuations in the context of vortex sound theory. In contrast to the existing literature, our method encompasses a unified treatment for broadband and tonal acoustic noise sources at the source level, thus, accounting for linear source interference as well as possible non-linear source interaction effects. When sound sources are determined, for the sound propagation, Acoustic Perturbation Equations (APE-4) are solved in the time-domain. Results of the method's application for two aerofoil benchmark cases, with both sharp and blunt trailing edges are presented. In each case, the importance of individual linear and non-linear noise sources was investigated. Several new key features related to the unsteady implementation of the method were tested and brought into the equation. Encouraging results have been obtained for benchmark test cases using the new technique which is believed to be potentially applicable to other airframe noise problems where both tonal and broadband parts are important.

Thermal noise due to surface-charge effects within the Debye layer of endogenous structures in dendrites.

PubMed

Poznanski, Roman R

2010-02-01

An assumption commonly used in cable theory is revised by taking into account electrical amplification due to intracellular capacitive effects in passive dendritic cables. A generalized cable equation for a cylindrical volume representation of a dendritic segment is derived from Maxwell's equations under assumptions: (i) the electric-field polarization is restricted longitudinally along the cable length; (ii) extracellular isopotentiality; (iii) quasielectrostatic conditions; and (iv) homogeneous medium with constant conductivity and permittivity. The generalized cable equation is identical to Barenblatt's equation arising in the theory of infiltration in fissured strata with a known analytical solution expressed in terms of a definite integral involving a modified Bessel function and the solution to a linear one-dimensional classical cable equation. Its solution is used to determine the impact of thermal noise on voltage attenuation with distance at any particular time. A regular perturbation expansion for the membrane potential about the linear one-dimensional classical cable equation solution is derived in terms of a Green's function in order to describe the dynamics of free charge within the Debye layer of endogenous structures in passive dendritic cables. The asymptotic value of the first perturbative term is explicitly evaluated for small values of time to predict how the slowly fluctuating (in submillisecond range) electric field attributed to intracellular capacitive effects alters the amplitude of the membrane potential. It was found that capacitive effects are almost negligible for cables with electrotonic lengths L>0.5 , contributes up to 10% of the signal for cables with electrotonic lengths in the range between 0.25

Magnetofluid Turbulence in the Solar Wind

NASA Technical Reports Server (NTRS)

Goldstein, Melvyn L.

2008-01-01

The solar wind shows striking characteristics that suggest that it is a turbulent magnetofluid, but the picture is not altogether simple. From the earliest observations, a strong correlation between magnetic fluctuations and plasma velocity fluctuations was noted. The high corrections suggest that the fluctuations are Alfven waves. In addition, the power spectrum of the magnetic fluctuation showed evidence of an inertial range that resembled that seen in fully-developed fluid turbulence. Alfven waves, however, are exact solutions of the equations of incompressible magnetohydrodynamics. Thus, there was a puzzle: how can a magnetofluid consisting of Alfven waves be turbulent? The answer lay in the role of velocity shears in the solar wind that could drive turbulent evolution. Puzzles remain: for example, the power spectrum of the velocity fluctuations is less steep than the slope of the magnetic fluctuations, nor do we understand even now why the solar wind appears to be nearly incompressible with a -5/3 power-spectral index.

Weight Vector Fluctuations in Adaptive Antenna Arrays Tuned Using the Least-Mean-Square Error Algorithm with Quadratic Constraint

NASA Astrophysics Data System (ADS)

Zimina, S. V.

2015-06-01

We present the results of statistical analysis of an adaptive antenna array tuned using the least-mean-square error algorithm with quadratic constraint on the useful-signal amplification with allowance for the weight-coefficient fluctuations. Using the perturbation theory, the expressions for the correlation function and power of the output signal of the adaptive antenna array, as well as the formula for the weight-vector covariance matrix are obtained in the first approximation. The fluctuations are shown to lead to the signal distortions at the antenna-array output. The weight-coefficient fluctuations result in the appearance of additional terms in the statistical characteristics of the antenna array. It is also shown that the weight-vector fluctuations are isotropic, i.e., identical in all directions of the weight-coefficient space.

Mode-coupling theory

NASA Astrophysics Data System (ADS)

Reichman, David R.; Charbonneau, Patrick

2005-05-01

In this set of lecture notes we review the mode-coupling theory of the glass transition from several perspectives. First, we derive mode-coupling equations for the description of density fluctuations from microscopic considerations with the use the Mori Zwanzig projection operator technique. We also derive schematic mode-coupling equations of a similar form from a field-theoretic perspective. We review the successes and failures of mode-coupling theory, and discuss recent advances in the applications of the theory.

Comparison of non-ideal solution theories for multi-solute solutions in cryobiology and tabulation of required coefficients.

PubMed

Zielinski, Michal W; McGann, Locksley E; Nychka, John A; Elliott, Janet A W

2014-10-01

Thermodynamic solution theories allow the prediction of chemical potentials in solutions of known composition. In cryobiology, such models are a critical component of many mathematical models that are used to simulate the biophysical processes occurring in cells and tissues during cryopreservation. A number of solution theories, both thermodynamically ideal and non-ideal, have been proposed for use with cryobiological solutions. In this work, we have evaluated two non-ideal solution theories for predicting water chemical potential (i.e. osmolality) in multi-solute solutions relevant to cryobiology: the Elliott et al. form of the multi-solute osmotic virial equation, and the Kleinhans and Mazur freezing point summation model. These two solution theories require fitting to only single-solute data, although they can make predictions in multi-solute solutions. The predictions of these non-ideal solution theories were compared to predictions made using ideal dilute assumptions and to available literature multi-solute experimental osmometric data. A single, consistent set of literature single-solute solution data was used to fit for the required solute-specific coefficients for each of the non-ideal models. Our results indicate that the two non-ideal solution theories have similar overall performance, and both give more accurate predictions than ideal models. These results can be used to select between the non-ideal models for a specific multi-solute solution, and the updated coefficients provided in this work can be used to make the desired predictions. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

Integrability in AdS/CFT correspondence: quasi-classical analysis

NASA Astrophysics Data System (ADS)

Gromov, Nikolay

2009-06-01

In this review, we consider a quasi-classical method applicable to integrable field theories which is based on a classical integrable structure—the algebraic curve. We apply it to the Green-Schwarz superstring on the AdS5 × S5 space. We show that the proposed method reproduces perfectly the earlier results obtained by expanding the string action for some simple classical solutions. The construction is explicitly covariant and is not based on a particular parameterization of the fields and as a result is free from ambiguities. On the other hand, the finite size corrections in some particularly important scaling limit are studied in this paper for a system of Bethe equations. For the general superalgebra \\su(N|K) , the result for the 1/L corrections is obtained. We find an integral equation which describes these corrections in a closed form. As an application, we consider the conjectured Beisert-Staudacher (BS) equations with the Hernandez-Lopez dressing factor where the finite size corrections should reproduce quasi-classical results around a general classical solution. Indeed, we show that our integral equation can be interpreted as a sum of all physical fluctuations and thus prove the complete one-loop consistency of the BS equations. We demonstrate that any local conserved charge (including the AdS energy) computed from the BS equations is indeed given at one loop by the sum of the charges of fluctuations with an exponential precision for large S5 angular momentum of the string. As an independent result, the BS equations in an \\su(2) sub-sector were derived from Zamolodchikovs's S-matrix. The paper is based on the author's PhD thesis.

The Late Integrated Sachs-Wolfe Effect and its detectability in galaxy-redshift surveys

NASA Astrophysics Data System (ADS)

Valencia-Díaz, D. R.; Muñoz-Cuartas, J. C.

2017-07-01

The late Integrated Sachs-Wolfe (ISW) effect is underwent by the Cosmic Microwave Background (CMB) photons due to the presence of the Large-Scale Structures (LSS) in an expanding Universe and can be measured through the temperature fluctuations of the CMB. In this work we use numerical simulations of structure formation to study the detectability of the ISW effect. Our method comprises the estimation of the density field through a Cloud-In-Cell mass assignment scheme. With the help of Fourier transforms we estimate the time derivative of the gravitational potential field in Fourier and in coordinate's space. Finally, this field is integrated numerically to know the ISW contribution. We study the time derivative of the potential in two approaches. First, an exact solution that makes use of the full velocity field. Second, a linear approximation related with the linear theory for the formation of LSS. We apply the method to three cosmological simulations. First, a box of 400 h-1 Mpc; second, the MultiDark1 simulation; third, the MultiDark-Plank simulation. For all cases we obtain coherent results with the expected in the literature for a ΛCDM cosmology: with the exact solution the temperature fluctuation is near the ± 30 μ K; the linear approximation shows a signal in the expected range of ± 20 μ K. This positive detection on simulations is important in order to know an expectation for the results we should obtain when working with observational data and will have important implications due to the lack of consensus about the detection of the ISW effect in previous works. Acknowledgements: This work was supported by Colciencias and Universidad de Antioquia, Convenio Beca-Pasantía Joven Investigador Convocatoria 645 de 2014.

Applying Chaos Theory to Careers: Attraction and Attractors

ERIC Educational Resources Information Center

Pryor, Robert G. L.; Bright, Jim E. H.

2007-01-01

This article presents the Chaos Theory of Careers with particular reference to the concepts of "attraction" and "attractors". Attractors are defined in terms of characteristic trajectories, feedback mechanisms, end states, ordered boundedness, reality visions and equilibrium and fluctuation. The identified types of attractors (point, pendulum,…

An analytical solution of groundwater response to tidal fluctuation in a leaky confined aquifer

NASA Astrophysics Data System (ADS)

Jiao, Jiu Jimmy; Tang, Zhonghua

1999-03-01

An analytical solution is derived to investigate the influence of leakage on tidal response in a coastal leaky confined aquifer system. The analytical solution developed here is more general than the traditional solution obtained by Ferris [1951], which can be regarded as a special case of the solution presented in this paper. This solution is based on a conceptual model under the assumption that the groundwater level in the confined aquifer fluctuates in response to sea tide while that of the overlying unconfined aquifer remains constant. This conceptual model is supported by numerous field studies by previous researchers which have demonstrated that the tidal response in an unconfined aquifer may be negligible compared to that in a confined aquifer. The leakage has a significant impact on the tidal behavior of the confined aquifer. Hypothetical studies indicate that both tidal amplitude of groundwater head in the aquifer and the distance over which the aquifer can be disturbed by the sea tide will be considerably reduced because of the existence of leakage. This analytical solution is used to investigate the tidal and piezometer data at the Chek Lap Kok airport, Hong Kong Special Administrative Region, People's Republic of China.

Perturbation Theory of Spin-Triplet Superconductivity for Sr 2RuO 4

NASA Astrophysics Data System (ADS)

Nomura, Takuji; Yamada, Kosaku

2000-11-01

We discuss the possibility of spin-triplet superconductivity within the third order perturbation theory with respect to on-site Coulomb repulsion U. Critical temperature T c for spin-triplet pairing state is calculated in a single-band two-dimensional Hubbard modeland relatively high T c is obtained for moderately large U. The present situation considered here is particularly intended for the main branch γ in Sr2RuO4. According to the calculation, third order vertex correction terms, which are not direct contribution from spin fluctuation, are important, while the bare susceptibility χ0(q) need not always have a prominent peak at q=0 for the spin-triplet pairing state. The picture that strong ferromagnetic spin fluctuations mainly induce the spin-triplet superconductivity in Sr2RuO4 may not be appropriate, and such momentum dependence of renormalized effective interaction between quasi-particles as is not sufficiently taken into accountin spin fluctuation mediated interaction is essential for realizing the spin-triplet pairing.

Spatial averaging of a dissipative particle dynamics model for active suspensions

NASA Astrophysics Data System (ADS)

Panchenko, Alexander; Hinz, Denis F.; Fried, Eliot

2018-03-01

Starting from a fine-scale dissipative particle dynamics (DPD) model of self-motile point particles, we derive meso-scale continuum equations by applying a spatial averaging version of the Irving-Kirkwood-Noll procedure. Since the method does not rely on kinetic theory, the derivation is valid for highly concentrated particle systems. Spatial averaging yields stochastic continuum equations similar to those of Toner and Tu. However, our theory also involves a constitutive equation for the average fluctuation force. According to this equation, both the strength and the probability distribution vary with time and position through the effective mass density. The statistics of the fluctuation force also depend on the fine scale dissipative force equation, the physical temperature, and two additional parameters which characterize fluctuation strengths. Although the self-propulsion force entering our DPD model contains no explicit mechanism for aligning the velocities of neighboring particles, our averaged coarse-scale equations include the commonly encountered cubically nonlinear (internal) body force density.

Quantum Gravity, Information Theory and the CMB

NASA Astrophysics Data System (ADS)

Kempf, Achim

2018-04-01

We review connections between the metric of spacetime and the quantum fluctuations of fields. We start with the finding that the spacetime metric can be expressed entirely in terms of the 2-point correlator of the fluctuations of quantum fields. We then discuss the open question whether the knowledge of only the spectra of the quantum fluctuations of fields also suffices to determine the spacetime metric. This question is of interest because spectra are geometric invariants and their quantization would, therefore, have the benefit of not requiring the modding out of diffeomorphisms. Further, we discuss the fact that spacetime at the Planck scale need not necessarily be either discrete or continuous. Instead, results from information theory show that spacetime may be simultaneously discrete and continuous in the same way that information can. Finally, we review the recent finding that a covariant natural ultraviolet cutoff at the Planck scale implies a signature in the cosmic microwave background (CMB) that may become observable.

Elastic constants from microscopic strain fluctuations

PubMed

Sengupta; Nielaba; Rao; Binder

2000-02-01

Fluctuations of the instantaneous local Lagrangian strain epsilon(ij)(r,t), measured with respect to a static "reference" lattice, are used to obtain accurate estimates of the elastic constants of model solids from atomistic computer simulations. The measured strains are systematically coarse-grained by averaging them within subsystems (of size L(b)) of a system (of total size L) in the canonical ensemble. Using a simple finite size scaling theory we predict the behavior of the fluctuations as a function of L(b)/L and extract elastic constants of the system in the thermodynamic limit at nonzero temperature. Our method is simple to implement, efficient, and general enough to be able to handle a wide class of model systems, including those with singular potentials without any essential modification. We illustrate the technique by computing isothermal elastic constants of "hard" and "soft" disk triangular solids in two dimensions from Monte Carlo and molecular dynamics simulations. We compare our results with those from earlier simulations and theory.

Non-linear corrections to the time-covariance function derived from a multi-state chemical master equation.

PubMed

Scott, M

2012-08-01

The time-covariance function captures the dynamics of biochemical fluctuations and contains important information about the underlying kinetic rate parameters. Intrinsic fluctuations in biochemical reaction networks are typically modelled using a master equation formalism. In general, the equation cannot be solved exactly and approximation methods are required. For small fluctuations close to equilibrium, a linearisation of the dynamics provides a very good description of the relaxation of the time-covariance function. As the number of molecules in the system decrease, deviations from the linear theory appear. Carrying out a systematic perturbation expansion of the master equation to capture these effects results in formidable algebra; however, symbolic mathematics packages considerably expedite the computation. The authors demonstrate that non-linear effects can reveal features of the underlying dynamics, such as reaction stoichiometry, not available in linearised theory. Furthermore, in models that exhibit noise-induced oscillations, non-linear corrections result in a shift in the base frequency along with the appearance of a secondary harmonic.

Parametric instability of spinning elastic rings excited by fluctuating space-fixed stiffnesses

NASA Astrophysics Data System (ADS)

Liu, Chunguang; Cooley, Christopher G.; Parker, Robert G.

2017-07-01

This study investigates the vibration of rotating elastic rings that are dynamically excited by an arbitrary number of space-fixed discrete stiffnesses with periodically fluctuating stiffnesses. The rotating, elastic ring is modeled using thin-ring theory with radial and tangential deformations. Primary and combination instability regions are determined in closed-form using the method of multiple scales. The ratio of peak-to-peak fluctuation to average discrete stiffness is used as the perturbation parameter, so the resulting perturbation analysis is not limited to small mean values of discrete stiffnesses. The natural frequencies and vibration modes are determined by discretizing the governing equations using Galerkin's method. Results are demonstrated for compliant gear applications. The perturbation results are validated by direct numerical integration of the equations of motion and Floquet theory. The bandwidths of the instability regions correlate with the fractional strain energy stored in the discrete stiffnesses. For rings with multiple discrete stiffnesses, the phase differences between them can eliminate large amplitude response under certain conditions.

On the valence fluctuation in the early actinide metals

DOE PAGES

Soderlind, P.; Landa, A.; Tobin, J. G.; ...

2015-12-15

In this study, recent X-ray measurements suggest a degree of valence fluctuation in plutonium and uranium intermetallics. We are applying a novel scheme, in conjunction with density functional theory, to predict 5f configuration fractions of states with valence fluctuations for the early actinide metals. For this purpose we perform constrained integer f-occupation calculations for the α phases of uranium, neptunium, and plutonium metals. For plutonium we also investigate the δ phase. The model predicts uranium and neptunium to be dominated by the f 3 and f 4 configurations, respectively, with only minor contributions from other configurations. For plutonium (both αmore » and δ phase) the scenario is dramatically different. Here, the calculations predict a relatively even distribution between three valence configurations. The δ phase has a greater configuration fraction of f 6 compared to that of the α phase. The theory is consistent with the interpretations of modern X-ray experiments and we present resonant X-ray emission spectroscopy results for α-uranium.« less

Cosmological density fluctuations produced by vacuum strings

NASA Astrophysics Data System (ADS)

Vilenkin, A.

1981-04-01

Consideration is given to the possible role of vacuum domain strings produced in the grand unification phase transition in the early universe in the generation of the density fluctuations giving rise to galaxies. The cosmological evolution of the strings formed in the grand unification phase transition is analyzed, with attention given to possible mechanisms for the damping out of oscillations produced by tension in convoluted strings and closed loops. The cosmological density fluctuations introduced by infinite strings and closed loops smaller than the horizon are then shown to be capable of giving rise to mass condensations on a scale of approximately 10 to the 9th solar masses at the time of the decoupling of radiation from matter, around which the galaxies condense. Differences between the present theory and that suggested by Zel'dovich (1980) are pointed out, and it is noted that string formation at the grand unification phase transition is possible only if the manifold of the degenerate vacua of the gauge theory is not simply connected.

Pseudogap Regime of a Two-dimensional Uniform Fermi Gas

NASA Astrophysics Data System (ADS)

Matsumoto, Morio; Hanai, Ryo; Inotani, Daisuke; Ohashi, Yoji

2018-01-01

We investigate pseudogap phenomena in a two-dimensional Fermi gas. Including pairing fluctuations within a self-consistent T-matrix approximation, we determine the pseudogap temperature T* below which a dip appears in the density of states ρ(ω) around the Fermi level. Evaluating T*, we identify the pseudogap region in the phase diagram of this system. We find that, while the observed Berezinskii-Kosterlitz-Thouless (BKT) transition temperature TBKTexp in a 6Li Fermi gas is in the pseudogap regime, the detailed pseudogap structure in ρ(ω) at TBKTexp still differs from a fully-gapped one, indicating the importance of amplitude fluctuations in the Cooper channel there. Since the observed TBKTexp in the weak-coupling regime cannot be explained by the recent BKT theory which only includes phase fluctuations, our results may provide a hint about how to improve this BKT theory. Although ρ(ω) has not been measured in this system, we show that the assessment of our results is still possible by using the observable Tan's contact.

The glassy random laser: replica symmetry breaking in the intensity fluctuations of emission spectra

PubMed Central

Antenucci, Fabrizio; Crisanti, Andrea; Leuzzi, Luca

2015-01-01

The behavior of a newly introduced overlap parameter, measuring the correlation between intensity fluctuations of waves in random media, is analyzed in different physical regimes, with varying amount of disorder and non-linearity. This order parameter allows to identify the laser transition in random media and describes its possible glassy nature in terms of emission spectra data, the only data so far accessible in random laser measurements. The theoretical analysis is performed in terms of the complex spherical spin-glass model, a statistical mechanical model describing the onset and the behavior of random lasers in open cavities. Replica Symmetry Breaking theory allows to discern different kinds of randomness in the high pumping regime, including the most complex and intriguing glassy randomness. The outcome of the theoretical study is, eventually, compared to recent intensity fluctuation overlap measurements demonstrating the validity of the theory and providing a straightforward interpretation of qualitatively different spectral behaviors in different random lasers. PMID:26616194

Detection of polarization in the cosmic microwave background using DASI. Degree Angular Scale Interferometer.

PubMed

Kovac, J M; Leitch, E M; Pryke, C; Carlstrom, J E; Halverson, N W; Holzapfel, W L

The past several years have seen the emergence of a standard cosmological model, in which small temperature differences in the cosmic microwave background (CMB) radiation on angular scales of the order of a degree are understood to arise from acoustic oscillations in the hot plasma of the early Universe, arising from primordial density fluctuations. Within the context of this model, recent measurements of the temperature fluctuations have led to profound conclusions about the origin, evolution and composition of the Universe. Using the measured temperature fluctuations, the theoretical framework predicts the level of polarization of the CMB with essentially no free parameters. Therefore, a measurement of the polarization is a critical test of the theory and thus of the validity of the cosmological parameters derived from the CMB measurements. Here we report the detection of polarization of the CMB with the Degree Angular Scale Interferometer (DASI). The polarization is deteced with high confidence, and its level and spatial distribution are in excellent agreement with the predictions of the standard theory.

Truly work-like work extraction via a single-shot analysis.

PubMed

Aberg, Johan

2013-01-01

The work content of non-equilibrium systems in relation to a heat bath is often analysed in terms of expectation values of an underlying random work variable. However, when optimizing the expectation value of the extracted work, the resulting extraction process is subject to intrinsic fluctuations, uniquely determined by the Hamiltonian and the initial distribution of the system. These fluctuations can be of the same order as the expected work content per se, in which case the extracted energy is unpredictable, thus intuitively more heat-like than work-like. This raises the question of the 'truly' work-like energy that can be extracted. Here we consider an alternative that corresponds to an essentially fluctuation-free extraction. We show that this quantity can be expressed in terms of a one-shot relative entropy measure introduced in information theory. This suggests that the relations between information theory and statistical mechanics, as illustrated by concepts like Maxwell's demon, Szilard engines and Landauer's principle, extends to the single-shot regime.

Nonlinear fluctuations-induced rate equations for linear birth-death processes

NASA Astrophysics Data System (ADS)

Honkonen, J.

2008-05-01

The Fock-space approach to the solution of master equations for one-step Markov processes is reconsidered. It is shown that in birth-death processes with an absorbing state at the bottom of the occupation-number spectrum and occupation-number independent annihilation probability of occupation-number fluctuations give rise to rate equations drastically different from the polynomial form typical of birth-death processes. The fluctuation-induced rate equations with the characteristic exponential terms are derived for Mikhailov’s ecological model and Lanchester’s model of modern warfare.

Small Angle Neutron Scattering Observation of Chain Retraction after a Large Step Deformation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blanchard, A.; Heinrich, M.; Pyckhout-Hintzen, W.

The process of retraction in entangled linear chains after a fast nonlinear stretch was detected from time-resolved but quenched small angle neutron scattering (SANS) experiments on long, well-entangled polyisoprene chains. The statically obtained SANS data cover the relevant time regime for retraction, and they provide a direct, microscopic verification of this nonlinear process as predicted by the tube model. Clear, quantitative agreement is found with recent theories of contour length fluctuations and convective constraint release, using parameters obtained mainly from linear rheology. The theory captures the full range of scattering vectors once the crossover to fluctuations on length scales belowmore » the tube diameter is accounted for.« less

Scattering theory of efficient quantum transport across finite networks

NASA Astrophysics Data System (ADS)

Walschaers, Mattia; Mulet, Roberto; Buchleitner, Andreas

2017-11-01

We present a scattering theory for the efficient transmission of an excitation across a finite network with designed disorder. We show that the presence of randomly positioned network sites allows significant acceleration of the excitation transfer processes as compared to a dimer structure, but only if the disordered Hamiltonians are constrained to be centrosymmetric and exhibit a dominant doublet in their spectrum. We identify the cause of this efficiency enhancement to be the constructive interplay between disorder-induced fluctuations of the dominant doublet’s splitting and the coupling strength between the input and output sites to the scattering channels. We find that the characteristic strength of these fluctuations together with the channel coupling fully control the transfer efficiency.

Water Dynamics in the Hydration Shells of Biomolecules

PubMed Central

2017-01-01

The structure and function of biomolecules are strongly influenced by their hydration shells. Structural fluctuations and molecular excitations of hydrating water molecules cover a broad range in space and time, from individual water molecules to larger pools and from femtosecond to microsecond time scales. Recent progress in theory and molecular dynamics simulations as well as in ultrafast vibrational spectroscopy has led to new and detailed insight into fluctuations of water structure, elementary water motions, electric fields at hydrated biointerfaces, and processes of vibrational relaxation and energy dissipation. Here, we review recent advances in both theory and experiment, focusing on hydrated DNA, proteins, and phospholipids, and compare dynamics in the hydration shells to bulk water. PMID:28248491

Effective field theory of statistical anisotropies for primordial bispectrum and gravitational waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rostami, Tahereh; Karami, Asieh; Firouzjahi, Hassan, E-mail: t.rostami@ipm.ir, E-mail: karami@ipm.ir, E-mail: firouz@ipm.ir

2017-06-01

We present the effective field theory studies of primordial statistical anisotropies in models of anisotropic inflation. The general action in unitary gauge is presented to calculate the leading interactions between the gauge field fluctuations, the curvature perturbations and the tensor perturbations. The anisotropies in scalar power spectrum and bispectrum are calculated and the dependence of these anisotropies to EFT couplings are presented. In addition, we calculate the statistical anisotropy in tensor power spectrum and the scalar-tensor cross correlation. Our EFT approach incorporates anisotropies generated in models with non-trivial speed for the gauge field fluctuations and sound speed for scalar perturbationsmore » such as in DBI inflation.« less

Instantaneous and time-averaged dispersion and measurement models for estimation theory applications with elevated point source plumes

NASA Technical Reports Server (NTRS)

Diamante, J. M.; Englar, T. S., Jr.; Jazwinski, A. H.

1977-01-01

Estimation theory, which originated in guidance and control research, is applied to the analysis of air quality measurements and atmospheric dispersion models to provide reliable area-wide air quality estimates. A method for low dimensional modeling (in terms of the estimation state vector) of the instantaneous and time-average pollutant distributions is discussed. In particular, the fluctuating plume model of Gifford (1959) is extended to provide an expression for the instantaneous concentration due to an elevated point source. Individual models are also developed for all parameters in the instantaneous and the time-average plume equations, including the stochastic properties of the instantaneous fluctuating plume.

Energy transfer between two vacuum-gapped metal plates: Coulomb fluctuations and electron tunneling

NASA Astrophysics Data System (ADS)

Zhang, Zu-Quan; Lü, Jing-Tao; Wang, Jian-Sheng

2018-05-01

Recent experimental measurements for near-field radiative heat transfer between two bodies have been able to approach the gap distance within 2 nm , where the contributions of Coulomb fluctuation and electron tunneling are comparable. Using the nonequilibrium Green's function method in the G0W0 approximation, based on a tight-binding model, we obtain for the energy current a Caroli formula from the Meir-Wingreen formula in the local equilibrium approximation. Also, the Caroli formula is consistent with the evanescent part of the heat transfer from the theory of fluctuational electrodynamics. We go beyond the local equilibrium approximation to study the energy transfer in the crossover region from electron tunneling to Coulomb fluctuation based on a numerical calculation.

Super-resolution study of polymer mobility fluctuations near c*.

PubMed

King, John T; Yu, Changqian; Wilson, William L; Granick, Steve

2014-09-23

Nanoscale dynamic heterogeneities in synthetic polymer solutions are detected using super-resolution optical microscopy. To this end, we map concentration fluctuations in polystyrene-toluene solutions with spatial resolution below the diffraction limit, focusing on critical fluctuations near the polymer overlap concentration, c*. Two-photon super-resolution microscopy was adapted to be applicable in an organic solvent, and a home-built STED-FCS system with stimulated emission depletion (STED) was used to perform fluorescence correlation spectroscopy (FCS). The polystyrene serving as the tracer probe (670 kg mol(-1), radius of gyration RG ≈ 35 nm, end-labeled with a bodipy derivative chromophore) was dissolved in toluene at room temperature (good solvent) and mixed with matrix polystyrene (3,840 kg mol(-1), RG ≈ 97 nm, Mw/Mn = 1.04) whose concentration was varied from dilute to more than 10c*. Whereas for dilute solutions the intensity-intensity correlation function follows a single diffusion process, it splits starting at c* to imply an additional relaxation process provided that the experimental focal area does not greatly exceed the polymer blob size. We identify the slower mode as self-diffusion and the increasingly rapid mode as correlated segment fluctuations that reflect the cooperative diffusion coefficient, Dcoop. These real-space measurements find quantitative agreement between correlation lengths inferred from dynamic measurements and those from determining the limit below which diffusion coefficients are independent of spot size. This study is considered to illustrate the potential of importing into polymer science the techniques of super-resolution imaging.

Canonical Structure and Orthogonality of Forces and Currents in Irreversible Markov Chains

NASA Astrophysics Data System (ADS)

Kaiser, Marcus; Jack, Robert L.; Zimmer, Johannes

2018-03-01

We discuss a canonical structure that provides a unifying description of dynamical large deviations for irreversible finite state Markov chains (continuous time), Onsager theory, and Macroscopic Fluctuation Theory (MFT). For Markov chains, this theory involves a non-linear relation between probability currents and their conjugate forces. Within this framework, we show how the forces can be split into two components, which are orthogonal to each other, in a generalised sense. This splitting allows a decomposition of the pathwise rate function into three terms, which have physical interpretations in terms of dissipation and convergence to equilibrium. Similar decompositions hold for rate functions at level 2 and level 2.5. These results clarify how bounds on entropy production and fluctuation theorems emerge from the underlying dynamical rules. We discuss how these results for Markov chains are related to similar structures within MFT, which describes hydrodynamic limits of such microscopic models.

Pressure dependence of critical temperature of bulk FeSe from spin fluctuation theory

NASA Astrophysics Data System (ADS)

Hirschfeld, Peter; Kreisel, Andreas; Wang, Yan; Tomic, Milan; Jeschke, Harald; Jacko, Anthony; Valenti, Roser; Maier, Thomas; Scalapino, Douglas

2013-03-01

The critical temperature of the 8K superconductor FeSe is extremely sensitive to pressure, rising to a maximum of 40K at about 10GPa. We test the ability of the current generation of fluctuation exchange pairing theories to account for this effect, by downfolding the density functional theory electronic structure for each pressure to a tight binding model. The Fermi surface found in such a procedure is then used with fixed Hubbard parameters to determine the pairing strength using the random phase approximation for the spin singlet pairing vertex. We find that the evolution of the Fermi surface captured by such an approach is alone not sufficient to explain the observed pressure dependence, and discuss alternative approaches. PJH, YW, AK were supported by DOE DE-FG02-05ER46236, the financial support of MT, HJ, and RV from the DFG Schwerpunktprogramm 1458 is kindly acknowledged.

Gravity with free initial conditions: A solution to the cosmological constant problem testable by CMB B -mode polarization

NASA Astrophysics Data System (ADS)

Totani, Tomonori

2017-10-01

In standard general relativity the universe cannot be started with arbitrary initial conditions, because four of the ten components of the Einstein's field equations (EFE) are constraints on initial conditions. In the previous work it was proposed to extend the gravity theory to allow free initial conditions, with a motivation to solve the cosmological constant problem. This was done by setting four constraints on metric variations in the action principle, which is reasonable because the gravity's physical degrees of freedom are at most six. However, there are two problems about this theory; the three constraints in addition to the unimodular condition were introduced without clear physical meanings, and the flat Minkowski spacetime is unstable against perturbations. Here a new set of gravitational field equations is derived by replacing the three constraints with new ones requiring that geodesic paths remain geodesic against metric variations. The instability problem is then naturally solved. Implications for the cosmological constant Λ are unchanged; the theory converges into EFE with nonzero Λ by inflation, but Λ varies on scales much larger than the present Hubble horizon. Then galaxies are formed only in small Λ regions, and the cosmological constant problem is solved by the anthropic argument. Because of the increased degrees of freedom in metric dynamics, the theory predicts new non-oscillatory modes of metric anisotropy generated by quantum fluctuation during inflation, and CMB B -mode polarization would be observed differently from the standard predictions by general relativity.

Kinetic theory of age-structured stochastic birth-death processes

NASA Astrophysics Data System (ADS)

Greenman, Chris D.; Chou, Tom

2016-01-01

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov--Born--Green--Kirkwood--Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution.

Derivation of dynamo current drive in a closed-current volume and stable current sustainment in the HIT-SI experiment

DOE PAGES

Hossack, A. C.; Sutherland, D. A.; Jarboe, T. R.

2017-02-01

A derivation is given showing that the current inside a closed-current volume can be sustained against resistive dissipation by appropriately phased magnetic perturbations. Imposed-dynamo current drive (IDCD) theory is used to predict the toroidal current evolution in the HIT-SI experiment as a function of magnetic fluctuations at the edge. Analysis of magnetic fields from a HIT-SI discharge shows that the injector-imposed fluctuations are sufficient to sustain the measured toroidal current without instabilities whereas the small, plasma-generated magnetic fluctuations are not sufficiently large to sustain the current.

Derivation of dynamo current drive in a closed-current volume and stable current sustainment in the HIT-SI experiment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hossack, A. C.; Sutherland, D. A.; Jarboe, T. R.

A derivation is given showing that the current inside a closed-current volume can be sustained against resistive dissipation by appropriately phased magnetic perturbations. Imposed-dynamo current drive (IDCD) theory is used to predict the toroidal current evolution in the HIT-SI experiment as a function of magnetic fluctuations at the edge. Analysis of magnetic fields from a HIT-SI discharge shows that the injector-imposed fluctuations are sufficient to sustain the measured toroidal current without instabilities whereas the small, plasma-generated magnetic fluctuations are not sufficiently large to sustain the current.

Quantum statistical mechanics of nonrelativistic membranes: crumpling transition at finite temperature

NASA Astrophysics Data System (ADS)

Borelli, M. E. S.; Kleinert, H.; Schakel, Adriaan M. J.

2000-03-01

The effect of quantum fluctuations on a nearly flat, nonrelativistic two-dimensional membrane with extrinsic curvature stiffness and tension is investigated. The renormalization group analysis is carried out in first-order perturbative theory. In contrast to thermal fluctuations, which soften the membrane at large scales and turn it into a crumpled surface, quantum fluctuations are found to stiffen the membrane, so that it exhibits a Hausdorff dimension equal to two. The large-scale behavior of the membrane is further studied at finite temperature, where a nontrivial fixed point is found, signaling a crumpling transition.

An Introduction to the Onsager Reciprocal Relations

ERIC Educational Resources Information Center

Monroe, Charles W.; Newman, John

2007-01-01

The Onsager reciprocal relations are essential to multicomponent transport theory. A discussion of the principles that should be used to derive flux laws for coupled diffusion is presented here. Fluctuation theory is employed to determine the reciprocal relation for transport coefficients that characterize coupled mass and heat transfer in binary…

Spectra of turbulent static pressure fluctuations in jet mixing layers

NASA Technical Reports Server (NTRS)

Jones, B. G.; Adrian, R. J.; Nithianandan, C. K.; Planchon, H. P., Jr.

1977-01-01

Spectral similarity laws are derived for the power spectra of turbulent static pressure fluctuations by application of dimensional analysis in the limit of large turbulent Reynolds number. The theory predicts that pressure spectra are generated by three distinct types of interaction in the velocity fields: a fourth order interaction between fluctuating velocities, an interaction between the first order mean shear and the third order velocity fluctuations, and an interaction between the second order mean shear rate and the second order fluctuating velocity. Measurements of one-dimensional power spectra of the turbulent static pressure fluctuations in the driven mixing layer of a subsonic, circular jet are presented, and the spectra are examined for evidence of spectral similarity. Spectral similarity is found for the low wavenumber range when the large scale flow on the centerline of the mixing layer is self-preserving. The data are also consistent with the existence of universal inertial subranges for the spectra of each interaction mode.

Catalysis-Enhancement via Rotary Fluctuation of F1-ATPase

PubMed Central

Watanabe, Rikiya; Hayashi, Kumiko; Ueno, Hiroshi; Noji, Hiroyuki

2013-01-01

Protein conformational fluctuations modulate the catalytic powers of enzymes. The frequency of conformational fluctuations may modulate the catalytic rate at individual reaction steps. In this study, we modulated the rotary fluctuation frequency of F1-ATPase (F1) by attaching probes with different viscous drag coefficients at the rotary shaft of F1. Individual rotation pauses of F1 between rotary steps correspond to the waiting state of a certain elementary reaction step of ATP hydrolysis. This allows us to investigate the impact of the frequency modulation of the rotary fluctuation on the rate of the individual reaction steps by measuring the duration of rotation pauses. Although phosphate release was significantly decelerated, the ATP-binding and hydrolysis steps were less sensitive or insensitive to the viscous drag coefficient of the probe. Brownian dynamics simulation based on a model similar to the Sumi-Marcus theory reproduced the experimental results, providing a theoretical framework for the role of rotational fluctuation in F1 rate enhancement. PMID:24268150

Smoothed dissipative particle dynamics model for mesoscopic multiphase flows in the presence of thermal fluctuations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lei, Huan; Baker, Nathan A.; Wu, Lei

2016-08-05

Thermal fluctuations cause perturbations of fluid-fluid interfaces and highly nonlinear hydrodynamics in multiphase flows. In this work, we develop a novel multiphase smoothed dissipative particle dynamics model. This model accounts for both bulk hydrodynamics and interfacial fluctuations. Interfacial surface tension is modeled by imposing a pairwise force between SDPD particles. We show that the relationship between the model parameters and surface tension, previously derived under the assumption of zero thermal fluctuation, is accurate for fluid systems at low temperature but overestimates the surface tension for intermediate and large thermal fluctuations. To analyze the effect of thermal fluctuations on surface tension,more » we construct a coarse-grained Euler lattice model based on the mean field theory and derive a semi-analytical formula to directly relate the surface tension to model parameters for a wide range of temperatures and model resolutions. We demonstrate that the present method correctly models the dynamic processes, such as bubble coalescence and capillary spectra across the interface.« less

Electron transfer statistics and thermal fluctuations in molecular junctions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goswami, Himangshu Prabal; Harbola, Upendra

2015-02-28

We derive analytical expressions for probability distribution function (PDF) for electron transport in a simple model of quantum junction in presence of thermal fluctuations. Our approach is based on the large deviation theory combined with the generating function method. For large number of electrons transferred, the PDF is found to decay exponentially in the tails with different rates due to applied bias. This asymmetry in the PDF is related to the fluctuation theorem. Statistics of fluctuations are analyzed in terms of the Fano factor. Thermal fluctuations play a quantitative role in determining the statistics of electron transfer; they tend tomore » suppress the average current while enhancing the fluctuations in particle transfer. This gives rise to both bunching and antibunching phenomena as determined by the Fano factor. The thermal fluctuations and shot noise compete with each other and determine the net (effective) statistics of particle transfer. Exact analytical expression is obtained for delay time distribution. The optimal values of the delay time between successive electron transfers can be lowered below the corresponding shot noise values by tuning the thermal effects.« less

Stabilization of composition fluctuations in mixed membranes by hybrid lipids

NASA Astrophysics Data System (ADS)

Safran, Samuel; Palmieri, Benoit

2013-03-01

A ternary mixture model is proposed to describe composition fluctuations in mixed membranes composed of saturated, unsaturated and hybrid lipids. The asymmetric hybrid lipid has one saturated and one unsaturated hydrocarbon chain and it can reduce the packing incompatibility between saturated and unsaturated lipids. A methodology to recast the free-energy of the lattice in terms of a continuous isotropic field theory is proposed and used to analyze composition fluctuations above the critical temperature. The effect of hybrid lipids on fluctuations domains rich in saturated/unsaturated lipids is predicted. The correlation length of such fluctuations decreases significantly with increasing amounts of hybrids even if the temperature is maintained close to the critical temperature. This provides an upper bound for the domain sizes expected in rafts stabilized by hybrids, above the critical temperature. When the hybrid composition of the membrane is increased further, a crossover value is found above which ``stripe-like'' fluctuations are observed. The wavelength of these fluctuations decreases with increasing hybrid fraction and tends toward a molecular size in a membrane that contains only hybrids.

Self-reproduction in k-inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Helmer, Ferdinand; Winitzki, Sergei

2006-09-15

We study cosmological self-reproduction in models of inflation driven by a scalar field {phi} with a noncanonical kinetic term (k-inflation). We develop a general criterion for the existence of attractors and establish conditions selecting a class of k-inflation models that admit a unique attractor solution. We then consider quantum fluctuations on the attractor background. We show that the correlation length of the fluctuations is of order c{sub s}H{sup -1}, where c{sub s} is the speed of sound. By computing the magnitude of field fluctuations, we determine the coefficients of Fokker-Planck equations describing the probability distribution of the spatially averaged fieldmore » {phi}. The field fluctuations are generally large in the inflationary attractor regime; hence, eternal self-reproduction is a generic feature of k-inflation. This is established more formally by demonstrating the existence of stationary solutions of the relevant Fokker-Planck equations. We also show that there exists a (model-dependent) range {phi}{sub R}<{phi}<{phi}{sub max} within which large fluctuations are likely to drive the field towards the upper boundary {phi}={phi}{sub max}, where the semiclassical consideration breaks down. An exit from inflation into reheating without reaching {phi}{sub max} will occur almost surely (with probability 1) only if the initial value of {phi} is below {phi}{sub R}. In this way, strong self-reproduction effects constrain models of k-inflation.« less

White noise and synchronization shaping the age structure of the human population

NASA Astrophysics Data System (ADS)

Cebrat, Stanislaw; Biecek, Przemyslaw; Bonkowska, Katarzyna; Kula, Mateusz

2007-06-01

We have modified the standard diploid Penna model of ageing in such a way that instead of threshold of defective loci resulting in genetic death of individuals, the fluctuation of environment and "personal" fluctuations of individuals were introduced. The sum of the both fluctuations describes the health status of the individual. While environmental fluctuations are the same for all individuals in the population, the personal component of fluctuations is composed of fluctuations corresponding to each physiological function (gene, genetic locus). It is rather accepted hypothesis that physiological parameters of any organism fluctuate highly nonlinearly. Transition to the synchronized behaviors could be a very strong diagnostic signal of the life threatening disorder. Thus, in our model, mutations of genes change the chaotic fluctuations representing the function of a wild gene to the synchronized signals generated by mutated genes. Genes are switched on chronologically, like in the standard Penna model. Accumulation of defective genes predicted by Medawar's theory of ageing leads to the replacement of uncorrelated white noise corresponding to the healthy organism by the correlated signals of defective functions. As a result we have got the age distribution of population corresponding to the human demographic data.

Collisionless Isotropization of the Solar-wind Protons by Compressive Fluctuations and Plasma Instabilities

NASA Astrophysics Data System (ADS)

Verscharen, Daniel; Chandran, Benjamin D. G.; Klein, Kristopher G.; Quataert, Eliot

2016-11-01

Compressive fluctuations are a minor yet significant component of astrophysical plasma turbulence. In the solar wind, long-wavelength compressive slow-mode fluctuations lead to changes in {β }\\parallel {{p}}\\equiv 8π {n}{{p}}{k}{{B}}{T}\\parallel {{p}}/{B}2 and in {R}{{p}}\\equiv {T}\\perp {{p}}/{T}\\parallel {{p}}, where {T}\\perp {{p}} and {T}\\parallel {{p}} are the perpendicular and parallel temperatures of the protons, B is the magnetic field strength, and {n}{{p}} is the proton density. If the amplitude of the compressive fluctuations is large enough, {R}{{p}} crosses one or more instability thresholds for anisotropy-driven microinstabilities. The enhanced field fluctuations from these microinstabilities scatter the protons so as to reduce the anisotropy of the pressure tensor. We propose that this scattering drives the average value of {R}{{p}} away from the marginal stability boundary until the fluctuating value of {R}{{p}} stops crossing the boundary. We model this “fluctuating-anisotropy effect” using linear Vlasov-Maxwell theory to describe the large-scale compressive fluctuations. We argue that this effect can explain why, in the nearly collisionless solar wind, the average value of {R}{{p}} is close to unity.

A theory of how active behavior stabilises neural activity: Neural gain modulation by closed-loop environmental feedback

PubMed Central

2018-01-01

During active behaviours like running, swimming, whisking or sniffing, motor actions shape sensory input and sensory percepts guide future motor commands. Ongoing cycles of sensory and motor processing constitute a closed-loop feedback system which is central to motor control and, it has been argued, for perceptual processes. This closed-loop feedback is mediated by brainwide neural circuits but how the presence of feedback signals impacts on the dynamics and function of neurons is not well understood. Here we present a simple theory suggesting that closed-loop feedback between the brain/body/environment can modulate neural gain and, consequently, change endogenous neural fluctuations and responses to sensory input. We support this theory with modeling and data analysis in two vertebrate systems. First, in a model of rodent whisking we show that negative feedback mediated by whisking vibrissa can suppress coherent neural fluctuations and neural responses to sensory input in the barrel cortex. We argue this suppression provides an appealing account of a brain state transition (a marked change in global brain activity) coincident with the onset of whisking in rodents. Moreover, this mechanism suggests a novel signal detection mechanism that selectively accentuates active, rather than passive, whisker touch signals. This mechanism is consistent with a predictive coding strategy that is sensitive to the consequences of motor actions rather than the difference between the predicted and actual sensory input. We further support the theory by re-analysing previously published two-photon data recorded in zebrafish larvae performing closed-loop optomotor behaviour in a virtual swim simulator. We show, as predicted by this theory, that the degree to which each cell contributes in linking sensory and motor signals well explains how much its neural fluctuations are suppressed by closed-loop optomotor behaviour. More generally we argue that our results demonstrate the dependence of neural fluctuations, across the brain, on closed-loop brain/body/environment interactions strongly supporting the idea that brain function cannot be fully understood through open-loop approaches alone. PMID:29342146

A theory of how active behavior stabilises neural activity: Neural gain modulation by closed-loop environmental feedback.

PubMed

Buckley, Christopher L; Toyoizumi, Taro

2018-01-01

During active behaviours like running, swimming, whisking or sniffing, motor actions shape sensory input and sensory percepts guide future motor commands. Ongoing cycles of sensory and motor processing constitute a closed-loop feedback system which is central to motor control and, it has been argued, for perceptual processes. This closed-loop feedback is mediated by brainwide neural circuits but how the presence of feedback signals impacts on the dynamics and function of neurons is not well understood. Here we present a simple theory suggesting that closed-loop feedback between the brain/body/environment can modulate neural gain and, consequently, change endogenous neural fluctuations and responses to sensory input. We support this theory with modeling and data analysis in two vertebrate systems. First, in a model of rodent whisking we show that negative feedback mediated by whisking vibrissa can suppress coherent neural fluctuations and neural responses to sensory input in the barrel cortex. We argue this suppression provides an appealing account of a brain state transition (a marked change in global brain activity) coincident with the onset of whisking in rodents. Moreover, this mechanism suggests a novel signal detection mechanism that selectively accentuates active, rather than passive, whisker touch signals. This mechanism is consistent with a predictive coding strategy that is sensitive to the consequences of motor actions rather than the difference between the predicted and actual sensory input. We further support the theory by re-analysing previously published two-photon data recorded in zebrafish larvae performing closed-loop optomotor behaviour in a virtual swim simulator. We show, as predicted by this theory, that the degree to which each cell contributes in linking sensory and motor signals well explains how much its neural fluctuations are suppressed by closed-loop optomotor behaviour. More generally we argue that our results demonstrate the dependence of neural fluctuations, across the brain, on closed-loop brain/body/environment interactions strongly supporting the idea that brain function cannot be fully understood through open-loop approaches alone.

Fluctuation relations between hierarchical kinetically equivalent networks with Arrhenius-type transitions and their roles in systems and structural biology.

PubMed

Deng, De-Ming; Lu, Yi-Ta; Chang, Cheng-Hung

2017-06-01

The legality of using simple kinetic schemes to determine the stochastic properties of a complex system depends on whether the fluctuations generated from hierarchical equivalent schemes are consistent with one another. To analyze this consistency, we perform lumping processes on the stochastic differential equations and the generalized fluctuation-dissipation theorem and apply them to networks with the frequently encountered Arrhenius-type transition rates. The explicit Langevin force derived from those networks enables us to calculate the state fluctuations caused by the intrinsic and extrinsic noises on the free energy surface and deduce their relations between kinetically equivalent networks. In addition to its applicability to wide classes of network related systems, such as those in structural and systems biology, the result sheds light on the fluctuation relations for general physical variables in Keizer's canonical theory.

Order parameter fluctuations at a buried quantum critical point

PubMed Central

Feng, Yejun; Wang, Jiyang; Jaramillo, R.; van Wezel, Jasper; Haravifard, S.; Srajer, G.; Liu, Y.; Xu, Z.-A.; Littlewood, P. B.; Rosenbaum, T. F.

2012-01-01

Quantum criticality is a central concept in condensed matter physics, but the direct observation of quantum critical fluctuations has remained elusive. Here we present an X-ray diffraction study of the charge density wave (CDW) in 2H-NbSe2 at high pressure and low temperature, where we observe a broad regime of order parameter fluctuations that are controlled by proximity to a quantum critical point. X-rays can track the CDW despite the fact that the quantum critical regime is shrouded inside a superconducting phase; and in contrast to transport probes, allow direct measurement of the critical fluctuations of the charge order. Concurrent measurements of the crystal lattice point to a critical transition that is continuous in nature. Our results confirm the long-standing expectations of enhanced quantum fluctuations in low-dimensional systems, and may help to constrain theories of the quantum critical Fermi surface. PMID:22529348

Hydrated Electron Transfer to Nucleobases in Aqueous Solutions Revealed by Ab Initio Molecular Dynamics Simulations.

PubMed

Zhao, Jing; Wang, Mei; Fu, Aiyun; Yang, Hongfang; Bu, Yuxiang

2015-08-03

We present an ab initio molecular dynamics (AIMD) simulation study into the transfer dynamics of an excess electron from its cavity-shaped hydrated electron state to a hydrated nucleobase (NB)-bound state. In contrast to the traditional view that electron localization at NBs (G/A/C/T), which is the first step for electron-induced DNA damage, is related only to dry or prehydrated electrons, and a fully hydrated electron no longer transfers to NBs, our AIMD simulations indicate that a fully hydrated electron can still transfer to NBs. We monitored the transfer dynamics of fully hydrated electrons towards hydrated NBs in aqueous solutions by using AIMD simulations and found that due to solution-structure fluctuation and attraction of NBs, a fully hydrated electron can transfer to a NB gradually over time. Concurrently, the hydrated electron cavity gradually reorganizes, distorts, and even breaks. The transfer could be completed in about 120-200 fs in four aqueous NB solutions, depending on the electron-binding ability of hydrated NBs and the structural fluctuation of the solution. The transferring electron resides in the π*-type lowest unoccupied molecular orbital of the NB, which leads to a hydrated NB anion. Clearly, the observed transfer of hydrated electrons can be attributed to the strong electron-binding ability of hydrated NBs over the hydrated electron cavity, which is the driving force, and the transfer dynamics is structure-fluctuation controlled. This work provides new insights into the evolution dynamics of hydrated electrons and provides some helpful information for understanding the DNA-damage mechanism in solution. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Application of a renormalization-group treatment to the statistical associating fluid theory for potentials of variable range (SAFT-VR).

PubMed

Forte, Esther; Llovell, Felix; Vega, Lourdes F; Trusler, J P Martin; Galindo, Amparo

2011-04-21

An accurate prediction of phase behavior at conditions far and close to criticality cannot be accomplished by mean-field based theories that do not incorporate long-range density fluctuations. A treatment based on renormalization-group (RG) theory as developed by White and co-workers has proven to be very successful in improving the predictions of the critical region with different equations of state. The basis of the method is an iterative procedure to account for contributions to the free energy of density fluctuations of increasing wavelengths. The RG method has been combined with a number of versions of the statistical associating fluid theory (SAFT), by implementing White's earliest ideas with the improvements of Prausnitz and co-workers. Typically, this treatment involves two adjustable parameters: a cutoff wavelength L for density fluctuations and an average gradient of the wavelet function Φ. In this work, the SAFT-VR (variable range) equation of state is extended with a similar crossover treatment which, however, follows closely the most recent improvements introduced by White. The interpretation of White's latter developments allows us to establish a straightforward method which enables Φ to be evaluated; only the cutoff wavelength L then needs to be adjusted. The approach used here begins with an initial free energy incorporating only contributions from short-wavelength fluctuations, which are treated locally. The contribution from long-wavelength fluctuations is incorporated through an iterative procedure based on attractive interactions which incorporate the structure of the fluid following the ideas of perturbation theories and using a mapping that allows integration of the radial distribution function. Good agreement close and far from the critical region is obtained using a unique fitted parameter L that can be easily related to the range of the potential. In this way the thermodynamic properties of a square-well (SW) fluid are given by the same number of independent intermolecular model parameters as in the classical equation. Far from the critical region the approach provides the correct limiting behavior reducing to the classical equation (SAFT-VR). In the critical region the β critical exponent is calculated and is found to take values close to the universal value. In SAFT-VR the free energy of an associating chain fluid is obtained following the thermodynamic perturbation theory of Wertheim from the knowledge of the free energy and radial distribution function of a reference monomer fluid. By determining L for SW fluids of varying well width a unique equation of state is obtained for chain and associating systems without further adjustment of critical parameters. We use computer simulation data of the phase behavior of chain and associating SW fluids to test the accuracy of the new equation.

Theory of dynamic barriers, activated hopping, and the glass transition in polymer melts

NASA Astrophysics Data System (ADS)

Schweizer, Kenneth S.; Saltzman, Erica J.

2004-07-01

A statistical mechanical theory of collective dynamic barriers, slow segmental relaxation, and the glass transition of polymer melts is developed by combining, and in some aspects extending, methods of mode coupling, density functional, and activated hopping transport theories. A coarse-grained description of polymer chains is adopted and the melt is treated as a liquid of segments. The theory is built on the idea that collective density fluctuations on length scales considerably longer than the local cage scale are of primary importance in the deeply supercooled regime. The barrier hopping or segmental relaxation time is predicted to be a function primarily of a single parameter that is chemical structure, temperature, and pressure dependent. This parameter depends on the material-specific dimensionless amplitude of thermal density fluctuations (compressibility) and a reduced segmental density determined by the packing length and backbone characteristic ratio. Analytic results are derived for a crossover temperature Tc, collective barrier, and glass transition temperature Tg. The relation of these quantities to structural and thermodynamic properties of the polymer melt is established. A universal power-law scaling behavior of the relaxation time below Tc is predicted based on identification of a reduced temperature variable that quantifies the breadth of the supercooled regime. Connections between the ratio Tc/Tg, two measures of dynamic fragility, and the magnitude of the local relaxation time at Tg logically follow. Excellent agreement with experiment is found for these generic aspects, and the crucial importance of the experimentally observed near universality of the dynamic crossover time is established. Extensions of the theory to treat the full chain dynamics, heterogeneity, barrier fluctuations, and nonpolymeric thermal glass forming liquids are briefly discussed.

Fermionic Spinon Theory of Square Lattice Spin Liquids near the Néel State

NASA Astrophysics Data System (ADS)

Thomson, Alex; Sachdev, Subir

2018-01-01

Quantum fluctuations of the Néel state of the square lattice antiferromagnet are usually described by a CP1 theory of bosonic spinons coupled to a U(1) gauge field, and with a global SU(2) spin rotation symmetry. Such a theory also has a confining phase with valence bond solid (VBS) order, and upon including spin-singlet charge-2 Higgs fields, deconfined phases with Z2 topological order possibly intertwined with discrete broken global symmetries. We present dual theories of the same phases starting from a mean-field theory of fermionic spinons moving in π flux in each square lattice plaquette. Fluctuations about this π -flux state are described by (2 +1 )-dimensional quantum chromodynamics (QCD3 ) with a SU(2) gauge group and Nf=2 flavors of massless Dirac fermions. It has recently been argued by Wang et al. [Deconfined Quantum Critical Points: Symmetries and Dualities, Phys. Rev. X 7, 031051 (2017)., 10.1103/PhysRevX.7.031051] that this QCD3 theory describes the Néel-VBS quantum phase transition. We introduce adjoint Higgs fields in QCD3 and obtain fermionic dual descriptions of the phases with Z2 topological order obtained earlier using the bosonic CP1 theory. We also present a fermionic spinon derivation of the monopole Berry phases in the U(1) gauge theory of the VBS state. The global phase diagram of these phases contains multicritical points, and our results imply new boson-fermion dualities between critical gauge theories of these points.

Wave fluctuations in the system with some Yang-Mills condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prokhorov, G., E-mail: zhoraprox@yandex.ru; Pasechnik, R., E-mail: Roman.Pasechnik@thep.lu.se; Vereshkov, G., E-mail: gveresh@gmail.com

2016-12-15

Self-consistent dynamics of non-homogeneous fluctuations and homogeneous and isotropic condensate of Yang–Mills fields was investigated in zero, linear and quasilinear approximations over the wave modes in the framework of N = 4 supersymmetric model in Hamilton gauge in quasiclassical theory. The models with SU(2), SU(3) and SU(4) gauge groups were considered. Particle production effect and effect of generation of longitudinal oscillations were obtained.

Derivation and precision of mean field electrodynamics with mesoscale fluctuations

NASA Astrophysics Data System (ADS)

Zhou, Hongzhe; Blackman, Eric G.

2018-06-01

Mean field electrodynamics (MFE) facilitates practical modelling of secular, large scale properties of astrophysical or laboratory systems with fluctuations. Practitioners commonly assume wide scale separation between mean and fluctuating quantities, to justify equality of ensemble and spatial or temporal averages. Often however, real systems do not exhibit such scale separation. This raises two questions: (I) What are the appropriate generalized equations of MFE in the presence of mesoscale fluctuations? (II) How precise are theoretical predictions from MFE? We address both by first deriving the equations of MFE for different types of averaging, along with mesoscale correction terms that depend on the ratio of averaging scale to variation scale of the mean. We then show that even if these terms are small, predictions of MFE can still have a significant precision error. This error has an intrinsic contribution from the dynamo input parameters and a filtering contribution from differences in the way observations and theory are projected through the measurement kernel. Minimizing the sum of these contributions can produce an optimal scale of averaging that makes the theory maximally precise. The precision error is important to quantify when comparing to observations because it quantifies the resolution of predictive power. We exemplify these principles for galactic dynamos, comment on broader implications, and identify possibilities for further work.

Cointegration as a data normalization tool for structural health monitoring applications

NASA Astrophysics Data System (ADS)

Harvey, Dustin Y.; Todd, Michael D.

2012-04-01

The structural health monitoring literature has shown an abundance of features sensitive to various types of damage in laboratory tests. However, robust feature extraction in the presence of varying operational and environmental conditions has proven to be one of the largest obstacles in the development of practical structural health monitoring systems. Cointegration, a technique adapted from the field of econometrics, has recently been introduced to the SHM field as one solution to the data normalization problem. Response measurements and feature histories often show long-run nonstationarity due to fluctuating temperature, load conditions, or other factors that leads to the occurrence of false positives. Cointegration theory allows nonstationary trends common to two or more time series to be modeled and subsequently removed. Thus, the residual retains sensitivity to damage with dependence on operational and environmental variability removed. This study further explores the use of cointegration as a data normalization tool for structural health monitoring applications.

Simulated pressure denaturation thermodynamics of ubiquitin.

PubMed

Ploetz, Elizabeth A; Smith, Paul E

2017-12-01

Simulations of protein thermodynamics are generally difficult to perform and provide limited information. It is desirable to increase the degree of detail provided by simulation and thereby the potential insight into the thermodynamic properties of proteins. In this study, we outline how to analyze simulation trajectories to decompose conformation-specific, parameter free, thermodynamically defined protein volumes into residue-based contributions. The total volumes are obtained using established methods from Fluctuation Solution Theory, while the volume decomposition is new and is performed using a simple proximity method. Native and fully extended ubiquitin are used as the test conformations. Changes in the protein volumes are then followed as a function of pressure, allowing for conformation-specific protein compressibility values to also be obtained. Residue volume and compressibility values indicate significant contributions to protein denaturation thermodynamics from nonpolar and coil residues, together with a general negative compressibility exhibited by acidic residues. Copyright © 2017 Elsevier B.V. All rights reserved.

Radiative-photochemical response of the mesosphere to dynamical forcing

NASA Technical Reports Server (NTRS)

Frederick, J. E.

1981-01-01

Combination of the chemical continuity equation for odd oxygen with the second law of thermodynamics yields analytic solutions which describe the coupled behavior of temperature and ozone perturbations in response to an externally specified forcing. The results appear in a form which allows easy physical interpretation of the coupling between radiative and photochemical processes. When the forcing is chosen to mimic a planetary scale wave, the theory shows that photochemical acceleration of radiative damping reduces the amplitude of the temperature perturbation by an amount which increases with the wave period. Although ozone fluctuations are anti-correlated with those in temperature, minima in ozone do not coincide exactly in longitude with temperature maxima. The percentage variation in ozone increases upward and is always larger than that in temperature at the same pressure. This demonstrates that variations in ozone on constant pressure surfaces may serve as a sensitive indicator of wave activity in the mesosphere.

A gravitational wave observatory operating beyond the quantum shot-noise limit

NASA Astrophysics Data System (ADS)

Ligo Scientific Collaboration; Abadie, J.; Abbott, B. P.; Abbott, R.; Abbott, T. D.; Abernathy, M.; Adams, C.; Adhikari, R.; Affeldt, C.; Allen, B.; Allen, G. S.; Amador Ceron, E.; Amariutei, D.; Amin, R. S.; Anderson, S. B.; Anderson, W. G.; Arai, K.; Arain, M. A.; Araya, M. C.; Aston, S. M.; Atkinson, D.; Aufmuth, P.; Aulbert, C.; Aylott, B. E.; Babak, S.; Baker, P.; Ballmer, S.; Barker, D.; Barr, B.; Barriga, P.; Barsotti, L.; Barton, M. A.; Bartos, I.; Bassiri, R.; Bastarrika, M.; Batch, J.; Bauchrowitz, J.; Behnke, B.; Bell, A. S.; Belopolski, I.; Benacquista, M.; Berliner, J. M.; Bertolini, A.; Betzwieser, J.; Beveridge, N.; Beyersdorf, P. T.; Bilenko, I. A.; Billingsley, G.; Birch, J.; Biswas, R.; Black, E.; Blackburn, J. K.; Blackburn, L.; Blair, D.; Bland, B.; Bock, O.; Bodiya, T. P.; Bogan, C.; Bondarescu, R.; Bork, R.; Born, M.; Bose, S.; Brady, P. R.; Braginsky, V. B.; Brau, J. E.; Breyer, J.; Bridges, D. O.; Brinkmann, M.; Britzger, M.; Brooks, A. F.; Brown, D. A.; Brummitt, A.; Buonanno, A.; Burguet-Castell, J.; Burmeister, O.; Byer, R. L.; Cadonati, L.; Camp, J. B.; Campsie, P.; Cannizzo, J.; Cannon, K.; Cao, J.; Capano, C. D.; Caride, S.; Caudill, S.; Cavagliá, M.; Cepeda, C.; Chalermsongsak, T.; Chalkley, E.; Charlton, P.; Chelkowski, S.; Chen, Y.; Christensen, N.; Cho, H.; Chua, S. S. Y.; Chung, S.; Chung, C. T. Y.; Ciani, G.; Clara, F.; Clark, D. E.; Clark, J.; Clayton, J. H.; Conte, R.; Cook, D.; Corbitt, T. R.; Cordier, M.; Cornish, N.; Corsi, A.; Costa, C. A.; Coughlin, M.; Couvares, P.; Coward, D. M.; Coyne, D. C.; Creighton, J. D. E.; Creighton, T. D.; Cruise, A. M.; Cumming, A.; Cunningham, L.; Cutler, R. M.; Dahl, K.; Danilishin, S. L.; Dannenberg, R.; Danzmann, K.; Daudert, B.; Daveloza, H.; Davies, G.; Daw, E. J.; Dayanga, T.; Debra, D.; Degallaix, J.; Dent, T.; Dergachev, V.; Derosa, R.; Desalvo, R.; Dhurandhar, S.; Diguglielmo, J.; di Palma, I.; Díaz, M.; Donovan, F.; Dooley, K. L.; Dorsher, S.; Drever, R. W. P.; Driggers, J. C.; Du, Z.; Dumas, J.-C.; Dwyer, S.; Eberle, T.; Edgar, M.; Edwards, M.; Effler, A.; Ehrens, P.; Engel, R.; Etzel, T.; Evans, K.; Evans, M.; Evans, T.; Factourovich, M.; Fairhurst, S.; Fan, Y.; Farr, B. F.; Farr, W.; Fazi, D.; Fehrmann, H.; Feldbaum, D.; Finn, L. S.; Fisher, R. P.; Flanigan, M.; Foley, S.; Forsi, E.; Fotopoulos, N.; Frede, M.; Frei, M.; Frei, Z.; Freise, A.; Frey, R.; Fricke, T. T.; Friedrich, D.; Fritschel, P.; Frolov, V. V.; Fulda, P. J.; Fyffe, M.; Ganija, M. R.; Garcia, J.; Garofoli, J. A.; Geng, R.; Gergely, L. Á.; Gholami, I.; Ghosh, S.; Giaime, J. A.; Giampanis, S.; Giardina, K. D.; Gill, C.; Goetz, E.; Goggin, L. M.; González, G.; Gorodetsky, M. L.; Goßler, S.; Graef, C.; Grant, A.; Gras, S.; Gray, C.; Gray, N.; Greenhalgh, R. J. S.; Gretarsson, A. M.; Grosso, R.; Grote, H.; Grunewald, S.; Guido, C.; Gupta, R.; Gustafson, E. K.; Gustafson, R.; Ha, T.; Hage, B.; Hallam, J. M.; Hammer, D.; Hammond, G.; Hanks, J.; Hanna, C.; Hanson, J.; Harms, J.; Harry, G. M.; Harry, I. W.; Harstad, E. D.; Hartman, M. T.; Haughian, K.; Hayama, K.; Heefner, J.; Heintze, M. C.; Hendry, M. A.; Heng, I. S.; Heptonstall, A. W.; Herrera, V.; Hewitson, M.; Hild, S.; Hoak, D.; Hodge, K. A.; Holt, K.; Hong, T.; Hooper, S.; Hosken, D. J.; Hough, J.; Howell, E. J.; Hughey, B.; Huynh-Dinh, T.; Husa, S.; Huttner, S. H.; Ingram, D. R.; Inta, R.; Isogai, T.; Ivanov, A.; Izumi, K.; Jacobson, M.; Jang, H.; Johnson, W. W.; Jones, D. I.; Jones, G.; Jones, R.; Ju, L.; Kalmus, P.; Kalogera, V.; Kamaretsos, I.; Kandhasamy, S.; Kang, G.; Kanner, J. B.; Katsavounidis, E.; Katzman, W.; Kaufer, H.; Kawabe, K.; Kawamura, S.; Kawazoe, F.; Kells, W.; Keppel, D. G.; Keresztes, Z.; Khalaidovski, A.; Khalili, F. Y.; Khazanov, E. A.; Kim, B.; Kim, C.; Kim, D.; Kim, H.; Kim, K.; Kim, N.; Kim, Y.-M.; King, P. J.; Kinsey, M.; Kinzel, D. L.; Kissel, J. S.; Klimenko, S.; Kokeyama, K.; Kondrashov, V.; Kopparapu, R.; Koranda, S.; Korth, W. Z.; Kozak, D.; Kringel, V.; Krishnamurthy, S.; Krishnan, B.; Kuehn, G.; Kumar, R.; Kwee, P.; Lam, P. K.; Landry, M.; Lang, M.; Lantz, B.; Lastzka, N.; Lawrie, C.; Lazzarini, A.; Leaci, P.; Lee, C. H.; Lee, H. M.; Leindecker, N.; Leong, J. R.; Leonor, I.; Li, J.; Lindquist, P. E.; Lockerbie, N. A.; Lodhia, D.; Lormand, M.; Luan, J.; Lubinski, M.; Lück, H.; Lundgren, A. P.; MacDonald, E.; Machenschalk, B.; Macinnis, M.; MacLeod, D. M.; Mageswaran, M.; Mailand, K.; Mandel, I.; Mandic, V.; Marandi, A.; Márka, S.; Márka, Z.; Markosyan, A.; Maros, E.; Martin, I. W.; Martin, R. M.; Marx, J. N.; Mason, K.; Matichard, F.; Matone, L.; Matzner, R. A.; Mavalvala, N.; Mazzolo, G.; McCarthy, R.; McClelland, D. E.; McGuire, S. C.; McIntyre, G.; McIver, J.; McKechan, D. J. A.; Meadors, G. D.; Mehmet, M.; Meier, T.; Melatos, A.; Melissinos, A. C.; Mendell, G.; Menendez, D.; Mercer, R. A.; Meshkov, S.; Messenger, C.; Meyer, M. S.; Miao, H.; Miller, J.; Mitrofanov, V. P.; Mitselmakher, G.; Mittleman, R.; Miyakawa, O.; Moe, B.; Moesta, P.; Mohanty, S. D.; Moraru, D.; Moreno, G.; Mori, T.; Mossavi, K.; Mow-Lowry, C. M.; Mueller, C. L.; Mueller, G.; Mukherjee, S.; Mullavey, A.; Müller-Ebhardt, H.; Munch, J.; Murphy, D.; Murray, P. G.; Mytidis, A.; Nash, T.; Nawrodt, R.; Necula, V.; Nelson, J.; Newton, G.; Nishizawa, A.; Nolting, D.; Nuttall, L.; O'Dell, J.; O'Reilly, B.; O'Shaughnessy, R.; Ochsner, E.; Oelker, E.; Oh, J. J.; Oh, S. H.; Ogin, G. H.; Oldenburg, R. G.; Osthelder, C.; Ott, C. D.; Ottaway, D. J.; Ottens, R. S.; Overmier, H.; Owen, B. J.; Page, A.; Pan, Y.; Pankow, C.; Papa, M. A.; Ajith, P.; Patel, P.; Pedraza, M.; Peiris, P.; Pekowsky, L.; Penn, S.; Peralta, C.; Perreca, A.; Phelps, M.; Pickenpack, M.; Pinto, I. M.; Pitkin, M.; Pletsch, H. J.; Plissi, M. V.; Pöld, J.; Postiglione, F.; Predoi, V.; Price, L. R.; Prijatelj, M.; Principe, M.; Privitera, S.; Prix, R.; Prokhorov, L.; Puncken, O.; Quetschke, V.; Raab, F. J.; Radkins, H.; Raffai, P.; Rakhmanov, M.; Ramet, C. R.; Rankins, B.; Mohapatra, S. R. P.; Raymond, V.; Redwine, K.; Reed, C. M.; Reed, T.; Reid, S.; Reitze, D. H.; Riesen, R.; Riles, K.; Robertson, N. A.; Robinson, C.; Robinson, E. L.; Roddy, S.; Rodriguez, C.; Rodruck, M.; Rollins, J.; Romano, J. D.; Romie, J. H.; Röver, C.; Rowan, S.; Rüdiger, A.; Ryan, K.; Ryll, H.; Sainathan, P.; Sakosky, M.; Salemi, F.; Samblowski, A.; Sammut, L.; Sancho de La Jordana, L.; Sandberg, V.; Sankar, S.; Sannibale, V.; Santamaría, L.; Santiago-Prieto, I.; Santostasi, G.; Sathyaprakash, B. S.; Sato, S.; Saulson, P. R.; Savage, R. L.; Schilling, R.; Schlamminger, S.; Schnabel, R.; Schofield, R. M. S.; Schulz, B.; Schutz, B. F.; Schwinberg, P.; Scott, J.; Scott, S. M.; Searle, A. C.; Seifert, F.; Sellers, D.; Sengupta, A. S.; Sergeev, A.; Shaddock, D. A.; Shaltev, M.; Shapiro, B.; Shawhan, P.; Shoemaker, D. H.; Sibley, A.; Siemens, X.; Sigg, D.; Singer, A.; Singer, L.; Sintes, A. M.; Skelton, G.; Slagmolen, B. J. J.; Slutsky, J.; Smith, R. J. E.; Smith, J. R.; Smith, M. R.; Smith, N. D.; Somiya, K.; Sorazu, B.; Soto, J.; Speirits, F. C.; Stein, A. J.; Steinert, E.; Steinlechner, J.; Steinlechner, S.; Steplewski, S.; Stefszky, M.; Stochino, A.; Stone, R.; Strain, K. A.; Strigin, S.; Stroeer, A. S.; Stuver, A. L.; Summerscales, T. Z.; Sung, M.; Susmithan, S.; Sutton, P. J.; Talukder, D.; Tanner, D. B.; Tarabrin, S. P.; Taylor, J. R.; Taylor, R.; Thomas, P.; Thorne, K. A.; Thorne, K. S.; Thrane, E.; Thüring, A.; Titsler, C.; Tokmakov, K. V.; Torres, C.; Torrie, C. I.; Traylor, G.; Trias, M.; Tseng, K.; Ugolini, D.; Urbanek, K.; Vahlbruch, H.; Vallisneri, M.; van Veggel, A. A.; Vass, S.; Vaulin, R.; Vecchio, A.; Veitch, J.; Veitch, P. J.; Veltkamp, C.; Villar, A. E.; Vitale, S.; Vorvick, C.; Vyatchanin, S. P.; Wade, A.; Waldman, S. J.; Wallace, L.; Wan, Y.; Wanner, A.; Wang, X.; Wang, Z.; Ward, R. L.; Wei, P.; Weinert, M.; Weinstein, A. J.; Weiss, R.; Wen, L.; Wen, S.; Wessels, P.; West, M.; Westphal, T.; Wette, K.; Whelan, J. T.; Whitcomb, S. E.; White, D.; Whiting, B. F.; Wilkinson, C.; Willems, P. A.; Williams, H. R.; Williams, L.; Willke, B.; Winkelmann, L.; Winkler, W.; Wipf, C. C.; Wittel, H.; Wiseman, A. G.; Woan, G.; Wooley, R.; Worden, J.; Yablon, J.; Yakushin, I.; Yamamoto, K.; Yamamoto, H.; Yang, H.; Yeaton-Massey, D.; Yoshida, S.; Yu, P.; Zanolin, M.; Zhang, L.; Zhang, W.; Zhang, Z.; Zhao, C.; Zotov, N.; Zucker, M. E.; Zweizig, J.

2011-12-01

Around the globe several observatories are seeking the first direct detection of gravitational waves (GWs). These waves are predicted by Einstein's general theory of relativity and are generated, for example, by black-hole binary systems. Present GW detectors are Michelson-type kilometre-scale laser interferometers measuring the distance changes between mirrors suspended in vacuum. The sensitivity of these detectors at frequencies above several hundred hertz is limited by the vacuum (zero-point) fluctuations of the electromagnetic field. A quantum technology--the injection of squeezed light--offers a solution to this problem. Here we demonstrate the squeezed-light enhancement of GEO600, which will be the GW observatory operated by the LIGO Scientific Collaboration in its search for GWs for the next 3-4 years. GEO600 now operates with its best ever sensitivity, which proves the usefulness of quantum entanglement and the qualification of squeezed light as a key technology for future GW astronomy.

A prospectus for a theory of variable variability

NASA Technical Reports Server (NTRS)

Childress, S.; Spiegel, E. A.

1981-01-01

It is proposed that the kind of stellar variability exhibited by the Sun in its magnetic activity cycle should be considered as a prototype of a class of stellar variability. The signature includes long 'periods' (compared to that of the radial fundamental model), erratic behavior, and intermittency. As other phenomena in the same variability class we nominate the liminosity fluctuations of ZZ Ceti stars and the solar 160 m oscillation. We discuss the possibility that analogous physical mechanisms are at work in all these cases, namely instabilities driven in a thin layer. These instabilities should be favorable to grave modes (in angle) and should arise in conditions that may allow more than one kind of instability to occur at once. The interaction of these competing instabilities produces complicated temporal variations. Given suitable idealizations, it is shown how to begin to compute solutions of small, but finite, amplitude.

Formulating viscous hydrodynamics for large velocity gradients

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pratt, Scott

2008-02-15

Viscous corrections to relativistic hydrodynamics, which are usually formulated for small velocity gradients, have recently been extended from Navier-Stokes formulations to a class of treatments based on Israel-Stewart equations. Israel-Stewart treatments, which treat the spatial components of the stress-energy tensor {tau}{sub ij} as dynamical objects, introduce new parameters, such as the relaxation times describing nonequilibrium behavior of the elements {tau}{sub ij}. By considering linear response theory and entropy constraints, we show how the additional parameters are related to fluctuations of {tau}{sub ij}. Furthermore, the Israel-Stewart parameters are analyzed for their ability to provide stable and physical solutions for sound waves.more » Finally, it is shown how these parameters, which are naturally described by correlation functions in real time, might be constrained by lattice calculations, which are based on path-integral formulations in imaginary time.« less

A resource-based game theoretical approach for the paradox of the plankton.

PubMed

Huang, Weini; de Araujo Campos, Paulo Roberto; Moraes de Oliveira, Viviane; Fagundes Ferrreira, Fernando

2016-01-01

The maintenance of species diversity is a central focus in ecology. It is not rare to observe more species than the number of limiting resources, especially in plankton communities. However, such high species diversity is hard to achieve in theory under the competitive exclusion principles, known as the plankton paradox. Previous studies often focus on the coexistence of predefined species and ignore the fact that species can evolve. We model multi-resource competitions using evolutionary games, where the number of species fluctuates under extinction and the appearance of new species. The interspecific and intraspecific competitions are captured by a dynamical payoff matrix, which has a size of the number of species. The competition strength (payoff entries) is obtained from comparing the capability of species in consuming resources, which can change over time. This allows for the robust coexistence of a large number of species, providing a possible solution to the plankton paradox.

A resource-based game theoretical approach for the paradox of the plankton

PubMed Central

de Araujo Campos, Paulo Roberto; Moraes de Oliveira, Viviane

2016-01-01

The maintenance of species diversity is a central focus in ecology. It is not rare to observe more species than the number of limiting resources, especially in plankton communities. However, such high species diversity is hard to achieve in theory under the competitive exclusion principles, known as the plankton paradox. Previous studies often focus on the coexistence of predefined species and ignore the fact that species can evolve. We model multi-resource competitions using evolutionary games, where the number of species fluctuates under extinction and the appearance of new species. The interspecific and intraspecific competitions are captured by a dynamical payoff matrix, which has a size of the number of species. The competition strength (payoff entries) is obtained from comparing the capability of species in consuming resources, which can change over time. This allows for the robust coexistence of a large number of species, providing a possible solution to the plankton paradox. PMID:27602293

Stochastic theory of polarized light in nonlinear birefringent media: An application to optical rotation

NASA Astrophysics Data System (ADS)

Tsuchida, Satoshi; Kuratsuji, Hiroshi

2018-05-01

A stochastic theory is developed for the light transmitting the optical media exhibiting linear and nonlinear birefringence. The starting point is the two-component nonlinear Schrödinger equation (NLSE). On the basis of the ansatz of “soliton” solution for the NLSE, the evolution equation for the Stokes parameters is derived, which turns out to be the Langevin equation by taking account of randomness and dissipation inherent in the birefringent media. The Langevin equation is converted to the Fokker-Planck (FP) equation for the probability distribution by employing the technique of functional integral on the assumption of the Gaussian white noise for the random fluctuation. The specific application is considered for the optical rotation, which is described by the ellipticity (third component of the Stokes parameters) alone: (i) The asymptotic analysis is given for the functional integral, which leads to the transition rate on the Poincaré sphere. (ii) The FP equation is analyzed in the strong coupling approximation, by which the diffusive behavior is obtained for the linear and nonlinear birefringence. These would provide with a basis of statistical analysis for the polarization phenomena in nonlinear birefringent media.

One dimensionalization in the spin-1 Heisenberg model on the anisotropic triangular lattice

NASA Astrophysics Data System (ADS)

Gonzalez, M. G.; Ghioldi, E. A.; Gazza, C. J.; Manuel, L. O.; Trumper, A. E.

2017-11-01

We investigate the effect of dimensional crossover in the ground state of the antiferromagnetic spin-1 Heisenberg model on the anisotropic triangular lattice that interpolates between the regime of weakly coupled Haldane chains (J'≪J ) and the isotropic triangular lattice (J'=J ). We use the density-matrix renormalization group (DMRG) and Schwinger boson theory performed at the Gaussian correction level above the saddle-point solution. Our DMRG results show an abrupt transition between decoupled spin chains and the spirally ordered regime at (J'/J) c˜0.42 , signaled by the sudden closing of the spin gap. Coming from the magnetically ordered side, the computation of the spin stiffness within Schwinger boson theory predicts the instability of the spiral magnetic order toward a magnetically disordered phase with one-dimensional features at (J'/J) c˜0.43 . The agreement of these complementary methods, along with the strong difference found between the intra- and the interchain DMRG short spin-spin correlations for sufficiently large values of the interchain coupling, suggests that the interplay between the quantum fluctuations and the dimensional crossover effects gives rise to the one-dimensionalization phenomenon in this frustrated spin-1 Hamiltonian.

Spatial inhomogeneities in ionic liquids, charged proteins, and charge stabilized colloids from collective variables theory.

PubMed

Patsahan, O; Ciach, A

2012-09-01

Effects of size and charge asymmetry between oppositely charged ions or particles on spatial inhomogeneities are studied for a large range of charge and size ratios. We perform a stability analysis of the primitive model of ionic systems with respect to periodic ordering using the collective variables-based theory. We extend previous studies [Ciach et al., Phys. Rev. E 75, 051505 (2007)] in several ways. First, we employ a nonlocal approximation for the reference hard-sphere fluid which leads to the Percus-Yevick pair direct correlation functions for the uniform case. Second, we use the Weeks-Chandler-Anderson regularization scheme for the Coulomb potential inside the hard core. We determine the relevant order parameter connected with the periodic ordering and analyze the character of the dominant fluctuations along the λ lines. We show that the above-mentioned modifications produce large quantitative and partly qualitative changes in the phase diagrams obtained previously. We discuss possible scenarios of the periodic ordering for the whole range of size and charge ratios of the two ionic species, covering electrolytes, ionic liquids, charged globular proteins or nanoparticles in aqueous solutions, and charge-stabilized colloids.

Time-dependent Gutzwiller theory of magnetic excitations in the Hubbard model

NASA Astrophysics Data System (ADS)

Seibold, G.; Becca, F.; Rubin, P.; Lorenzana, J.

2004-04-01

We use a spin-rotational invariant Gutzwiller energy functional to compute random-phase-approximation-like (RPA) fluctuations on top of the Gutzwiller approximation (GA). The method can be viewed as an extension of the previously developed GA+RPA approach for the charge sector [G. Seibold and J. Lorenzana, Phys. Rev. Lett. 86, 2605 (2001)] with respect to the inclusion of the magnetic excitations. Unlike the charge case, no assumptions about the time evolution of the double occupancy are needed in this case. Interestingly, in a spin-rotational invariant system, we find the correct degeneracy between triplet excitations, showing the consistency of both computations. Since no restrictions are imposed on the symmetry of the underlying saddle-point solution, our approach is suitable for the evaluation of the magnetic susceptibility and dynamical structure factor in strongly correlated inhomogeneous systems. We present a detailed study of the quality of our approach by comparing with exact diagonalization results and show its much higher accuracy compared to the conventional Hartree-Fock+RPA theory. In infinite dimensions, where the GA becomes exact for the Gutzwiller variational energy, we evaluate ferromagnetic and antiferromagnetic instabilities from the transverse magnetic susceptibility. The resulting phase diagram is in complete agreement with previous variational computations.

The Need for a Kinetics for Biological Transport

PubMed Central

Schindler, A. M.; Iberall, A. S.

1973-01-01

The traditional theory of transport across capillary membranes via a laminar Poiseuille flow is shown to be invalid. It is demonstrated that the random, diffusive nature of the molecular flow and interactions with the “pore” walls play an important role in the transport process. Neither the continuum Navier-Stokes theory nor the equivalent theory of irreversible thermodynamics is adequate to treat the problem. Combination of near-continuum hydrodynamic theory, noncontinuum kinetic theory, and the theory of fluctuations provides a first step toward modeling both liquid processes in general and membrane transport processes as a specific application. PMID:4726880

Exact solutions of massive gravity in three dimensions

NASA Astrophysics Data System (ADS)

Chakhad, Mohamed

In recent years, there has been an upsurge in interest in three-dimensional theories of gravity. In particular, two theories of massive gravity in three dimensions hold strong promise in the search for fully consistent theories of quantum gravity, an understanding of which will shed light on the problems of quantum gravity in four dimensions. One of these theories is the "old" third-order theory of topologically massive gravity (TMG) and the other one is a "new" fourth-order theory of massive gravity (NMG). Despite this increase in research activity, the problem of finding and classifying solutions of TMG and NMG remains a wide open area of research. In this thesis, we provide explicit new solutions of massive gravity in three dimensions and suggest future directions of research. These solutions belong to the Kundt class of spacetimes. A systematic analysis of the Kundt solutions with constant scalar polynomial curvature invariants provides a glimpse of the structure of the spaces of solutions of the two theories of massive gravity. We also find explicit solutions of topologically massive gravity whose scalar polynomial curvature invariants are not all constant, and these are the first such solutions. A number of properties of Kundt solutions of TMG and NMG, such as an identification of solutions which lie at the intersection of the full nonlinear and linearized theories, are also derived.

Observational limitations of Bose-Einstein photon statistics and radiation noise in thermal emission

NASA Astrophysics Data System (ADS)

Lee, Y.-J.; Talghader, J. J.

2018-01-01

For many decades, theory has predicted that Bose-Einstein statistics are a fundamental feature of thermal emission into one or a few optical modes; however, the resulting Bose-Einstein-like photon noise has never been experimentally observed. There are at least two reasons for this: (1) Relationships to describe the thermal radiation noise for an arbitrary mode structure have yet to be set forth, and (2) the mode and detector constraints necessary for the detection of such light is extremely hard to fulfill. Herein, photon statistics and radiation noise relationships are developed for systems with any number of modes and couplings to an observing space. The results are shown to reproduce existing special cases of thermal emission and are then applied to resonator systems to discuss physically realizable conditions under which Bose-Einstein-like thermal statistics might be observed. Examples include a single isolated cavity and an emitter cavity coupled to a small detector space. Low-mode-number noise theory shows major deviations from solely Bose-Einstein or Poisson treatments and has particular significance because of recent advances in perfect absorption and subwavelength structures both in the long-wave infrared and terahertz regimes. These microresonator devices tend to utilize a small volume with few modes, a regime where the current theory of thermal emission fluctuations and background noise, which was developed decades ago for free-space or single-mode cavities, has no derived solutions.

Consistent compactification of double field theory on non-geometric flux backgrounds

NASA Astrophysics Data System (ADS)

Hassler, Falk; Lüst, Dieter

2014-05-01

In this paper, we construct non-trivial solutions to the 2 D-dimensional field equations of Double Field Theory (DFT) by using a consistent Scherk-Schwarz ansatz. The ansatz identifies 2( D - d) internal directions with a twist U M N which is directly connected to the covariant fluxes ABC . It exhibits 2( D - d) linear independent generalized Killing vectors K I J and gives rise to a gauged supergravity in d dimensions. We analyze the covariant fluxes and the corresponding gauged supergravity with a Minkowski vacuum. We calculate fluctuations around such vacua and show how they gives rise to massive scalars field and vectors field with a non-abelian gauge algebra. Because DFT is a background independent theory, these fields should directly correspond the string excitations in the corresponding background. For ( D - d) = 3 we perform a complete scan of all allowed covariant fluxes and find two different kinds of backgrounds: the single and the double elliptic case. The later is not T-dual to a geometric background and cannot be transformed to a geometric setting by a field redefinition either. While this background fulfills the strong constraint, it is still consistent with the Killing vectors depending on the coordinates and the winding coordinates, thereby giving a non-geometric patching. This background can therefore not be described in Supergravity or Generalized Geometry.

Stationary to nonstationary transition in crossed-field devices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marini, Samuel; Rizzato, Felipe B.; Pakter, Renato

2016-03-15

The previous results based on numerical simulations showed that a cold electron beam injected in a crossed field gap does not reach a time independent stationary state in the space charge limited regime [P. J. Christenson and Y. Y. Lau, Phys. Plasmas 1, 3725 (1994)]. In this work, the effect of finite injection temperature in the transition from stationary to nonstationary states is investigated. A fully kinetic model for the electron flow is derived and used to determine the possible stationary states of the system. It is found that although there is always a stationary solution for any set ofmore » parameters, depending on the injection temperature the electron flow becomes very sensitive to fluctuations and the stationary state is never reached. By investigating the nonlinear dynamics of a characteristic electron, a theory based on a single free parameter is constructed to predict when the transition between stationary and nonstationary states occurs. In agreement with the previous numerical results, the theory indicates that for vanishing temperatures the system never reaches the time independent stationary state in the space charge limited regime. Nevertheless, as the injection temperature is raised it is found a broad range of system parameters for which the stationary state is indeed attained. By properly adjusting the free parameter in the theory, one can be able to describe, to a very good accuracy, when the transition occurs.« less

Charge-induced fluctuation forces in graphitic nanostructures

DOE PAGES

Drosdoff, D.; Bondarev, Igor V.; Widom, Allan; ...

2016-01-21

Charge fluctuations in nanocircuits with capacitor components are shown to give rise to a novel type of long-ranged interaction, which coexist with the regular Casimir–van derWaals force. The developed theory distinguishes between thermal and quantum mechanical effects, and it is applied to capacitors involving graphene nanostructures. The charge fluctuations mechanism is captured via the capacitance of the system with geometrical and quantum mechanical components. The dependence on the distance separation, temperature, size, and response properties of the system shows that this type of force can have a comparable and even dominant effect to the Casimir interaction. Lastly, our results stronglymore » indicate that fluctuation-induced interactions due to various thermodynamic quantities can have important thermal and quantum mechanical contributions at the microscale and the nanoscale.« less

The effect of the dynamic wet troposphere on radio interferometric measurements

NASA Technical Reports Server (NTRS)

Treuhaft, R. N.; Lanyi, G. E.

1987-01-01

A statistical model of water vapor fluctuations is used to describe the effect of the dynamic wet troposphere on radio interferometric measurements. It is assumed that the spatial structure of refractivity is approximated by Kolmogorov turbulence theory, and that the temporal fluctuations are caused by spatial patterns moved over a site by the wind, and these assumptions are examined for the VLBI delay and delay rate observables. The results suggest that the delay rate measurement error is usually dominated by water vapor fluctuations, and water vapor induced VLBI parameter errors and correlations are determined as a function of the delay observable errors. A method is proposed for including the water vapor fluctuations in the parameter estimation method to obtain improved parameter estimates and parameter covariances.

An investigation of combustion and entropy noise

NASA Technical Reports Server (NTRS)

Strahle, W. C.

1977-01-01

The relative importance of entropy and direct combustion noise in turbopropulsion systems and the parameters upon which these noise sources depend were studied. Theory and experiment were employed to determine that at least with the apparatus used here, entropy noise can dominate combustion noise if there is a sufficient pressure gradient terminating the combustor. Measurements included combustor interior fluctuating pressure, near and far field fluctuating pressure, and combustor exit plane fluctuating temperatures, as well as mean pressures and temperatures. Analysis techniques included spectral, cross-correlation, cross power spectra, and ordinary and partial coherence analysis. Also conducted were combustor liner modification experiments to investigate the origin of the frequency content of combustion noise. Techniques were developed to extract nonpropagational pseudo-sound and the heat release fluctuation spectra from the data.

Intermittency in heavy ion collisions

NASA Astrophysics Data System (ADS)

Murray, Michael; HELIOS Collaboration

1991-04-01

This paper describes a study of multiplicity and transverse energy fluctuations using factorial moments for sulphur collisions with silver — bromide emulsion and platinium targets at 200 GeV/A. The data were taken with the HELIOS experiment at CERN. Bialas and Peschanski [1] predicted a power law dependence of the moments on the rapidity bin size if the fluctuations are invariant over a range of scales. This pattern is known as intermittency in the theory of turbulence, and indicates a fractal structure. Fluctuations were studied for a range of pseudorapidity scales using scaled factorial moments. Correlated fluctuations were studied using correlated scaled factorial moments. For peripheral collisions the data are weakly intermittent and consistent with a simple cascading mechanism, the a model. For central collisions no clear signal of intermittency was seen.

Intermittency in heavy ion collisions

NASA Astrophysics Data System (ADS)

1991-04-01

This paper describes a study of multiplicity and transverse energy fluctuations using factorial moments for sulphur collisions with silver - bromide emulsion and platinium targets at 200 GeV/A. The data were taken with the HELIOS experiment at CERN. Bialas and Peschanski [1] predicted a power law dependence of the moments on the rapidity bin size if the fluctuations are invariant over a range of scales. This pattern is known as intermittency in the theory of turbulence, and indicates a fractal structure. Fluctuations were studied for a range of pseudorapidity scales using scaled factorial moments. Correlated fluctuations were studied using correlated scaled factorial moments. For peripheral collisions the data are weakly intermittent and consistent with a simple cascading mechanism, the a model. For central collisions no clear signal of intermittency was seen.

Nonequilibrium thermodynamic potentials for continuous-time Markov chains.

PubMed

Verley, Gatien

2016-01-01

We connect the rare fluctuations of an equilibrium (EQ) process and the typical fluctuations of a nonequilibrium (NE) stationary process. In the framework of large deviation theory, this observation allows us to introduce NE thermodynamic potentials. For continuous-time Markov chains, we identify the relevant pairs of conjugated variables and propose two NE ensembles: one with fixed dynamics and fluctuating time-averaged variables, and another with fixed time-averaged variables, but a fluctuating dynamics. Accordingly, we show that NE processes are equivalent to conditioned EQ processes ensuring that NE potentials are Legendre dual. We find a variational principle satisfied by the NE potentials that reach their maximum in the NE stationary state and whose first derivatives produce the NE equations of state and second derivatives produce the NE Maxwell relations generalizing the Onsager reciprocity relations.

First-order reactant in homogeneous turbulence before the final period of decay. [contaminant fluctuations in chemical reaction

NASA Technical Reports Server (NTRS)

Kumar, P.; Patel, S. R.

1974-01-01

A method is described for studying theoretically the concentration fluctuations of a dilute contaminate undergoing a first-order chemical reaction. The method is based on Deissler's (1958) theory for homogeneous turbulence for times before the final period, and it follows the approach used by Loeffler and Deissler (1961) to study temperature fluctuations in homogeneous turbulence. Four-point correlation equations are obtained; it is assumed that terms containing fifth-order correlation are very small in comparison with those containing fourth-order correlations, and can therefore be neglected. A spectrum equation is obtained in a form which can be solved numerically, yielding the decay law for the concentration fluctuations in homogeneous turbulence for the period much before the final period of decay.

Fluctuations in turbulent Rayleigh-Benard convection: The role of plumes

NASA Astrophysics Data System (ADS)

Lohse, Detlef

2004-03-01

Our unifying theory of turbulent thermal convection (Grossmann and Lohse, J. Fluid Mech. 407, 27 (2000); Phys. Rev. Lett. 86, 3316 (2001); Phys. Rev. E 66, 016305 (2002)) is revisited, stressing the role of the thermal plumes for the thermal dissipation rate and solving a problem on the local distribution of the thermal dissipation rate, which had been addressed by Verzicco and Camussi. We moreover make predictions for temperature and velocity fluctuation as function of Rayleigh and Prandtl number and show that the thermal plumes also play an important role for the fluctuations. We conclude with a list of detailed suggestions for measurements to verify or falsify our present understanding of heat transport and fluctuation in turbulent thermal convection. -- This is joint work with Siegfried Grossmann, Marburg.

Dynamical properties of nematic liquid crystals subjected to shear flow and magnetic fields: tumbling instability and nonequilibrium fluctuations.

PubMed

Fatriansyah, Jaka Fajar; Orihara, Hiroshi

2013-07-01

We investigate the dynamical properties of monodomain nematic liquid crystals under shear flow and magnetic fields on the basis of the Ericksen-Leslie theory. Stable and unstable states appear depending on the magnetic field and the shear rate. The trajectory of the unstable state shows tumbling motion. The phase diagram of these states is plotted as a function of the three components of the magnetic field at a constant shear rate. The phase diagram changes depending on the viscous properties of different types of nematic liquid crystals. In this nonequilibrium steady state, we calculate the correlation function of director fluctuations and the response function, and discuss the nonequilibrium fluctuations and the modified fluctuation-dissipation relation in connection with nonconservative forces due to shear flow.

Recent Developments in Non-Fermi Liquid Theory

NASA Astrophysics Data System (ADS)

Lee, Sung-Sik

2018-03-01

Non-Fermi liquids are unconventional metals whose physical properties deviate qualitatively from those of noninteracting fermions due to strong quantum fluctuations near Fermi surfaces. They arise when metals are subject to singular interactions mediated by soft collective modes. In the absence of well-defined quasiparticles, universal physics of non-Fermi liquids is captured by interacting field theories which replace Landau Fermi liquid theory. However, it has been difficult to understand their universal low-energy physics due to a lack of theoretical methods that take into account strong quantum fluctuations in the presence of abundant low-energy degrees of freedom. In this review, we discuss two approaches that have been recently developed for non-Fermi liquid theory with emphasis on two space dimensions. The first is a perturbative scheme based on a dimensional regularization, which achieves a controlled access to the low-energy physics by tuning the codimension of Fermi surface. The second is a nonperturbative approach which treats the interaction ahead of the kinetic term through a non-Gaussian scaling called interaction-driven scaling. Examples of strongly coupled non-Fermi liquids amenable to exact treatments through the interaction-driven scaling are discussed.

Turbulence and Global Properties of the Solar Wind

NASA Technical Reports Server (NTRS)

Goldstein, Melvyn L.

2007-01-01

The solar wind shows striking characteristics that suggest that it is a turbulent magnetofluid, but the picture is not altogether simple. From the earliest observations, a strong correlation between magnetic fluctuations and plasma velocity fluctuations as noted. The high corrections suggest that the fluctuations are Alven waves. In addition, the power spectrum of the magnetic fluctuation showed evidence of an inertial range that resembled that seen in fully-developed fluid turbulence. Alfven waves, however, are exact solutions of the equations of an incompressible magnetohydrodynamics. Thus, there was a puzzle: how can a magnetofluid consisting of Alfven waves be turbulent? The answer lay in the role of velocity shears in the solar wind that could drive turbulent evolution. Puzzles remain: for example, the power spectrum of the velocity fluctuations is less steep than the slope of the magnetic fluctuations. The plasma in the magnetic tail of Earth's magnetosphere also shows aspects of turbulence, as does the plasma in the dayside magnetosphere near the poles--the so-called dayside cusps.

Dynamics of Large-Scale Fluctuations in Native Proteins.

NASA Astrophysics Data System (ADS)

Erman, Burak; Erkip, Albert

2003-03-01

The fluctuations of residues of proteins about their equilibrium configurations are analyzed by Langevin dynamics. Residue pairs that are within a given cutoff distance of each other are assumed to be connected by linear springs. The action of the solvent and intramolecular interactions on each residue are treated as random noise. The correlations of fluctuations resulting from the solution of the Langevin equation are observed to be identical to those obtained by the Gaussian Network Model based on equilibrium statistical mechanics. The time delayed correlations of fluctuations, and the response of the protein to a given frequency and to a window of frequencies are determined. The fluctuations of the residues resulting from a given fixed externally applied frequency are evaluated for different modes of the system. Synchronous and asynchronous components of correlations for different modes are formulated. The results of the present study are applied to study the fluctuation dynamics of the 241 residue protein S. marcescens endonuclease (1QL0).

Influence of the Solar Cycle on Turbulence Properties and Cosmic-Ray Diffusion

NASA Astrophysics Data System (ADS)

Zhao, L.-L.; Adhikari, L.; Zank, G. P.; Hu, Q.; Feng, X. S.

2018-04-01

The solar cycle dependence of various turbulence quantities and cosmic-ray (CR) diffusion coefficients is investigated by using OMNI 1 minute resolution data over 22 years. We employ Elsässer variables z ± to calculate the magnetic field turbulence energy and correlation lengths for both the inwardly and outwardly directed interplanetary magnetic field (IMF). We present the temporal evolution of both large-scale solar wind (SW) plasma variables and small-scale magnetic fluctuations. Based on these observed quantities, we study the influence of solar activity on CR parallel and perpendicular diffusion using quasi-linear theory and nonlinear guiding center theory, respectively. We also evaluate the radial evolution of the CR diffusion coefficients by using the boundary conditions for different solar activity levels. We find that in the ecliptic plane at 1 au (1), the large-scale SW temperature T, velocity V sw, Alfvén speed V A , and IMF magnitude B 0 are positively related to solar activity; (2) the fluctuating magnetic energy density < {{z}+/- }2> , residual energy E D , and corresponding correlation functions all have an obvious solar cycle dependence. The residual energy E D is always negative, which indicates that the energy in magnetic fluctuations is larger than the energy in kinetic fluctuations, especially at solar maximum; (3) the correlation length λ for magnetic fluctuations does not show significant solar cycle variation; (4) the temporally varying shear source of turbulence, which is most important in the inner heliosphere, depends on the solar cycle; (5) small-scale fluctuations may not depend on the direction of the background magnetic field; and (6) high levels of SW fluctuations will increase CR perpendicular diffusion and decrease CR parallel diffusion, but this trend can be masked if the background IMF changes in concert with turbulence in response to solar activity. These results provide quantitative inputs for both turbulence transport models and CR diffusion models, and also provide valuable insight into the long-term modulation of CRs in the heliosphere.

Chaotic Calculations.

ERIC Educational Resources Information Center

Chenery, Gordon

1991-01-01

Uses chaos theory to investigate the nonlinear phenomenon of population growth fluctuation. Illustrates the use of computers and computer programs to make calculations in a nonlinear difference equation system. (MDH)

Statistical physics of multicomponent alloys using KKR-CPA

DOE PAGES

Khan, Suffian N.; Staunton, Julie B.; Stocks, George Malcolm

2016-02-16

We apply variational principles from statistical physics and the Landau theory of phase transitions to multicomponent alloys using the multiple-scattering theory of Korringa-Kohn-Rostoker (KKR) and the coherent potential approximation (CPA). This theory is a multicomponent generalization of the S( 2) theory of binary alloys developed by G. M. Stocks, J. B. Staunton, D. D. Johnson and others. It is highly relevant to the chemical phase stability of high-entropy alloys as it predicts the kind and size of finite-temperature chemical fluctuations. In doing so it includes effects of rearranging charge and other electronics due to changing site occupancies. When chemical fluctuationsmore » grow without bound an absolute instability occurs and a second-order order-disorder phase transition may be inferred. The S( 2) theory is predicated on the fluctuation-dissipation theorem; thus we derive the linear response of the CPA medium to perturbations in site-dependent chemical potentials in great detail. The theory lends itself to a natural interpretation in terms of competing effects: entropy driving disorder and favorable pair interactions driving atomic ordering. Moreover, to further clarify interpretation we present results for representative ternary alloys CuAgAu, NiPdPt, RhPdAg, and CoNiCu within a frozen charge (or band-only) approximation. These results include the so-called Onsager mean field correction that extends the temperature range for which the theory is valid.« less

Self-sustained oscillations of a shock wave interacting with a boundary layer on a supercritical airfoil

NASA Technical Reports Server (NTRS)

Ventres, C. S.; Howe, M. S.

1984-01-01

A theory is proposed of the self-sustaining oscillations of a weak shock on an airfoi in steady, transonic flow. The interaction of the shock with the boundary layer on the airfoil produces displacement thickness fluctuations which convect downstream and generate sound by interaction with the trailing edge. A feedback loop is established when this sound impinges on the shock wave, resulting in the production of further fluctuations in the displacement thickness. The details are worked out for an idealized mean boundary layer velocity profile, but strong support for the basic hypotheses of the theory is provided by a comparison with recent experiments involving the generation of acoustic 'tone bursts' by a supercritical airfoil section.

Self-sustained oscillations of a shock wave interacting with a boundary layer on a supercritical airfoil

NASA Technical Reports Server (NTRS)

Ventres, C. S.; Howe, M. S.

1983-01-01

A theory is proposed of the self-sustaining oscillations of a weak shock on an airfoil in steady, transonic flow. The interaction of the shock with the boundary layer on the airfoil produces displacement thickness fluctuations which convect downstream and generate sound by interaction with the trailing edge. A feedback loop is established when this sound impinges on the shock wave, resulting in the production of further fluctuations in the displacement thickness. The details are worked out for an idealized mean boundary layer velocity profile, but strong support for the basic hypotheses of the theory is provided by a comparison with recent experiments involving the generation of acoustic "tone bursts' by a supercritical airfoil section.

Amoeba-inspired nanoarchitectonic computing implemented using electrical Brownian ratchets.

PubMed

Aono, M; Kasai, S; Kim, S-J; Wakabayashi, M; Miwa, H; Naruse, M

2015-06-12

In this study, we extracted the essential spatiotemporal dynamics that allow an amoeboid organism to solve a computationally demanding problem and adapt to its environment, thereby proposing a nature-inspired nanoarchitectonic computing system, which we implemented using a network of nanowire devices called 'electrical Brownian ratchets (EBRs)'. By utilizing the fluctuations generated from thermal energy in nanowire devices, we used our system to solve the satisfiability problem, which is a highly complex combinatorial problem related to a wide variety of practical applications. We evaluated the dependency of the solution search speed on its exploration parameter, which characterizes the fluctuation intensity of EBRs, using a simulation model of our system called 'AmoebaSAT-Brownian'. We found that AmoebaSAT-Brownian enhanced the solution searching speed dramatically when we imposed some constraints on the fluctuations in its time series and it outperformed a well-known stochastic local search method. These results suggest a new computing paradigm, which may allow high-speed problem solving to be implemented by interacting nanoscale devices with low power consumption.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xia, Zhenwei; Yang, Weihong, E-mail: whyang@ustc.edu.cn

By using analytical method, the exact solutions of the incompressible dissipative Hall magnetohydrodynamics (MHD) equations are derived. It is found that a phase difference may occur between the velocity and magnetic field fluctuations when the kinetic and magnetic Reynolds numbers are both very large. Since velocity and magnetic field fluctuations are both circular polarized, the phase difference makes them no longer parallel or anti-parallel like that in the incompressible ideal Hall MHD.

Asymptotics of QCD traveling waves with fluctuations and running coupling effects

NASA Astrophysics Data System (ADS)

Beuf, Guillaume

2008-09-01

Extending the Balitsky-Kovchegov (BK) equation independently to running coupling or to fluctuation effects due to pomeron loops is known to lead in both cases to qualitative changes of the traveling-wave asymptotic solutions. In this paper we study the extension of the forward BK equation, including both running coupling and fluctuations effects, extending the method developed for the fixed coupling case [E. Brunet, B. Derrida, A.H. Mueller, S. Munier, Phys. Rev. E 73 (2006) 056126, cond-mat/0512021]. We derive the exact asymptotic behavior in rapidity of the probabilistic distribution of the saturation scale.

Nonadiabatic fluctuation in the measured geometric phase

NASA Astrophysics Data System (ADS)

Ai, Qing; Huo, Wenyi; Long, Gui Lu; Sun, C. P.

2009-08-01

We study how the nonadiabatic effect causes the observable fluctuation in the “geometric phase” for a two-level system, which is defined as the experimentally measurable quantity in the adiabatic limit. From the Rabi exact solution to this model, we give a reasonable explanation to the experimental discovery of phase fluctuation in the superconducting circuit system [P. J. Leek, J. M. Fink, A. Blais, R. Bianchetti, M. Göppl, J. M. Gambetta, D. I. Schuster, L. Frunzio, R. J. Schoelkopf, and A. Wallraf, Science 318, 1889 (2007)], which seemed to be regarded as the conventional experimental error.

A computer program for calculating laminar and turbulent boundary layers for two-dimensional time-dependent flows

NASA Technical Reports Server (NTRS)

Cebeci, T.; Carr, L. W.

1978-01-01

A computer program is described which provides solutions of two dimensional equations appropriate to laminar and turbulent boundary layers for boundary conditions with an external flow which fluctuates in magnitude. The program is based on the numerical solution of the governing boundary layer equations by an efficient two point finite difference method. An eddy viscosity formulation was used to model the Reynolds shear stress term. The main features of the method are briefly described and instructions for the computer program with a listing are provided. Sample calculations to demonstrate its usage and capabilities for laminar and turbulent unsteady boundary layers with an external flow which fluctuated in magnitude are presented.

Time evolution of linearized gauge field fluctuations on a real-time lattice

NASA Astrophysics Data System (ADS)

Kurkela, A.; Lappi, T.; Peuron, J.

2016-12-01

Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Due to instabilities, small quantum fluctuations on top of the classical background may significantly affect the dynamics of the system. In this paper we argue for the need for a numerical calculation of a system of classical gauge fields and small linearized fluctuations in a way that keeps the separation between the two manifest. We derive and test an explicit algorithm to solve these equations on the lattice, maintaining gauge invariance and Gauss' law.

Derivation of dynamo current drive in a closed-current volume and stable current sustainment in the HIT-SI experiment

NASA Astrophysics Data System (ADS)

Hossack, A. C.; Sutherland, D. A.; Jarboe, T. R.

2017-02-01

A derivation is given showing that the current inside a closed-current volume can be sustained against resistive dissipation by appropriately phased magnetic perturbations. Imposed-dynamo current drive theory is used to predict the toroidal current evolution in the helicity injected torus with steady inductive helicity injection (HIT-SI) experiment as a function of magnetic fluctuations at the edge. Analysis of magnetic fields from a HIT-SI discharge shows that the injector-imposed fluctuations are sufficient to sustain the measured toroidal current without instabilities whereas the small, plasma-generated magnetic fluctuations are not sufficiently large to sustain the current.

The alpha dynamo parameter and measurability of helicities in magnetohydrodynamic turbulence

NASA Technical Reports Server (NTRS)

Matthaeus, W. H.; Goldstein, M. L.; Lantz, S. R.

1986-01-01

Alpha, an important parameter in dynamo theory, is shown to be proportional to either the kinetic, current, magnetic, or velocity helicities of the fluctuating magnetic field and fluctuating velocity field. The particular helicity to which alpha is proportional depends on the assumptions used in deriving the first-order smoothed equations that describe the alpha effect. In two cases, viz., when alpha is proportional to either the magnetic helicity or velocity helicity, alpha can be determined experimentally from two-point measurements of the fluctuating fields in incompressible, homogeneous turbulence with arbitrary rotational symmetry. For the other two possibilities, alpha can be determined if the turbulence is isotropic.

Nonlinear dynamics of mushy layers induced by external stochastic fluctuations.

PubMed

Alexandrov, Dmitri V; Bashkirtseva, Irina A; Ryashko, Lev B

2018-02-28

The time-dependent process of directional crystallization in the presence of a mushy layer is considered with allowance for arbitrary fluctuations in the atmospheric temperature and friction velocity. A nonlinear set of mushy layer equations and boundary conditions is solved analytically when the heat and mass fluxes at the boundary between the mushy layer and liquid phase are induced by turbulent motion in the liquid and, as a result, have the corresponding convective form. Namely, the 'solid phase-mushy layer' and 'mushy layer-liquid phase' phase transition boundaries as well as the solid fraction, temperature and concentration (salinity) distributions are found. If the atmospheric temperature and friction velocity are constant, the analytical solution takes a parametric form. In the more common case when they represent arbitrary functions of time, the analytical solution is given by means of the standard Cauchy problem. The deterministic and stochastic behaviour of the phase transition process is analysed on the basis of the obtained analytical solutions. In the case of stochastic fluctuations in the atmospheric temperature and friction velocity, the phase transition interfaces (mushy layer boundaries) move faster than in the deterministic case. A cumulative effect of these noise contributions is revealed as well. In other words, when the atmospheric temperature and friction velocity fluctuate simultaneously due to the influence of different external processes and phenomena, the phase transition boundaries move even faster. This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'.This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'. © 2018 The Author(s).

Structural changes and fluctuations of proteins. I. A statistical thermodynamic model.

PubMed

Ikegami, A

1977-01-01

A general theory of the structural changes and fluctuations of proteins has been proposed based on statistical thermodynamic considerations at the chain level. The "structure" of protein was assumed to be characterized by the state of secondary bonds between unique pairs of specific sites on peptide chains. Every secondary bond changes between the bonded and unbonded states by thermal agitation and the "structure" is continuously fluctuating. The free energy of the "structural state" that is defined by the fraction of secondary bonds in the bonded state has been expressed by the bond energy, the cooperative interaction between bonds, the mixing entropy of bonds, and the entropy of polypeptide chains. The most probable "structural state" can be simply determined by graphical analysis and the effect of temperature or solvent composition on it is discussed. The temperature dependence of the free energy, the probability distribution of structural states and the specific heat have been calculted for two examples of structural change. The theory predicts two different types of structural changes from the ordered to disorderd state, a "structured transition" and a "gradual structural change" with rising temperature. In the "structural transition", the probability distribution has two maxima in the temperature range of transition. In the "gradual structural change", the probabilty distribution has only one maximum during the change. A considerable fraction of secondary bonds is in the unbounded state and is always fluctuating even in the ordered state at room temperature. Such structural flucutations in a single protein molecule have been discussed quantitatively. The theory is extended to include small molecules which bind to the protein molecule and affect the structural state. The changes of structural state caused by specific and non-specific binding and allosteric effects are explained in a unified manner.

A new mathematical approach for shock-wave solution in a dusty plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Das, G.C.; Dwivedi, C.B.; Talukdar, M.

1997-12-01

The problem of nonlinear Burger equation in a plasma contaminated with heavy dust grains has been revisited. As discussed earlier [C. B. Dwivedi and B. P. Pandey, Phys. Plasmas {bold 2}, 9 (1995)], the Burger equation originates due to dust charge fluctuation dynamics. A new alternate mathematical approach based on a simple traveling wave formalism has been applied to find out the solution of the derived Burger equation, and the method recovers the known shock-wave solution. This technique, although having its own limitation, predicts successfully the salient features of the weak shock-wave structure in a dusty plasma with dust chargemore » fluctuation dynamics. It is emphasized that this approach of the traveling wave formalism is being applied for the first time to solve the nonlinear wave equation in plasmas. {copyright} {ital 1997 American Institute of Physics.}« less

Apparent dispersion in transient groundwater flow

USGS Publications Warehouse

Goode, Daniel J.; Konikow, Leonard F.

1990-01-01

This paper investigates the effects of large-scale temporal velocity fluctuations, particularly changes in the direction of flow, on solute spreading in a two-dimensional aquifer. Relations for apparent longitudinal and transverse dispersivity are developed through an analytical solution for dispersion in a fluctuating, quasi-steady uniform flow field, in which storativity is zero. For transient flow, spatial moments are evaluated from numerical solutions. Ignored or unknown transients in the direction of flow primarily act to increase the apparent transverse dispersivity because the longitudinal dispersivity is acting in a direction that is not the assumed flow direction. This increase is a function of the angle between the transient flow vector and the assumed steady state flow direction and the ratio of transverse to longitudinal dispersivity. The maximum effect on transverse dispersivity occurs if storativity is assumed to be zero, such that the flow field responds instantly to boundary condition changes.

Charging and Screening in Nonpolar Solutions of Nonionizable Surfactants

NASA Astrophysics Data System (ADS)

Behrens, Sven

2010-03-01

Nonpolar liquids do not easily accommodate electric charges, but surfactant additives are often found to dramatically increase the solution conductivity and promote surface charging of suspended colloid particles. Such surfactant-mediated electrostatic effects have been associated with equilibrium charge fluctuations among reverse surfactant micelles and in some cases with the statistically rare ionization of individual surfactant molecules. Here we present experimental evidence that even surfactants without any ionizable group can mediate charging and charge screening in nonpolar oils, and that they can do so at surfactant concentrations well below the critical micelle concentration (cmc). Precision conductometry, light scattering, and Karl-Fischer titration of sorbitan oleate solutions in hexane, paired with electrophoretic mobility measurements on suspended polymer particles, reveal a distinctly electrostatic action of the surfactant. We interpret our observations in terms of a charge fluctuation model and argue that the observed charging processes are likely facilitated, but not limited, by the presence of ionizable impurities.

Motor-mediated microtubule self-organization in dilute and semi-dilute filament solutions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Swaminathan, S.; Ziebert, F.; Aranson, I. S.

We study molecular motor-induced microtubule self-organization in dilute and semi-dilute filament solutions. In the dilute case, we use a probabilistic model of microtubule interaction via molecular motors to investigate microtubule bundle dynamics. Microtubules are modeled as polar rods interacting through fully inelastic, binary collisions. Our model indicates that initially disordered systems of interacting rods exhibit an orientational instability resulting in spontaneous ordering. We study the existence and dynamic interaction of microtubule bundles analytically and numerically. Our results reveal a long term attraction and coalescing of bundles indicating a clear coarsening in the system; microtubule bundles concentrate into fewer orientations onmore » a slow logarithmic time scale. In semi-dilute filament solutions, multiple motors can bind a filament to several others and, for a critical motor density, induce a transition to an ordered phase with a nonzero mean orientation. Motors attach to a pair of filaments and walk along the pair bringing them into closer alignment. We develop a spatially homogenous, mean-field theory that explicitly accounts for a force-dependent detachment rate of motors, which in turn affects the mean and the fluctuations of the net force acting on a filament. We show that the transition to the oriented state can be both continuous and discontinuous when the force-dependent detachment of motors is important.« less

Weakly inhomogeneous MHD turbulence and transport of solar wind fluctuations

NASA Technical Reports Server (NTRS)

Matthaeus, W. H.; Zhou, Y.; Oughton, S.; Zank, G. P.

1992-01-01

An evaluation is conducted of recent theories of small-scale MHD turbulence transport in an inhomogeneous background that are pertinent to the evolution of solar wind turbulence. Attention is given to the WKB formalism that has been used in many solar wind-related physics applications, with a view to its shortcomings. Also discussed are the structure of two-scale transport theories, and their relationship to WKB theory in light of multiple-scales analysis.

Concentration fluctuations and dilution in aquifers

NASA Astrophysics Data System (ADS)

Kapoor, Vivek; Kitanidis, Peter K.

1998-05-01

The concentration of solute undergoing advection and local dispersion in a random hydraulic conductivity field is analyzed to quantify its variability and dilution. Detailed numerical evaluations of the concentration variance σc2 are compared to an approximate analytical description, which is based on a characteristic variance residence time (VRT), over which local dispersion destroys concentration fluctuations, and effective dispersion coefficients that quantify solute spreading rates. Key features of the analytical description for a finite size impulse input of solute are (1) initially, the concentration fields become more irregular with time, i.e., coefficient of variation, CV=σc/, increases with time ( being the mean concentration); (2) owing to the action of local dispersion, at large times (t > VRT), σc2 is a linear combination of 2 and (∂/∂xi)2, and the CV decreases with time (at the center, CV ≅ (N)1/2 VRT/t, N being the macroscopic dimensionality of the plume); (3) at early time, dilution and spreading can be severely disconnected; however, at large time the volume occupied by solute approaches that apparent from its spatial second moments; and (4) in contrast to the advection-local dispersion case, under advection alone, the CV grows unboundedly with time (at the center, CV ∝ tN/4), and spatial second moment is increasingly disconnected from dilution, as time progresses. The predicted large time evolution of dilution and concentration fluctuation measures is observed in the numerical simulations.

Break-up dynamics of fluctuating liquid threads

PubMed Central

Petit, Julien; Rivière, David; Kellay, Hamid; Delville, Jean-Pierre

2012-01-01

The thinning dynamics of a liquid neck before break-up, as may happen when a drop detaches from a faucet or a capillary, follows different rules and dynamic scaling laws depending on the importance of inertia, viscous stresses, or capillary forces. If now the thinning neck reaches dimensions comparable to the thermally excited interfacial fluctuations, as for nanojet break-up or the fragmentation of thermally annealed nanowires, these fluctuations should play a dominant role according to recent theory and observations. Using near-critical interfaces, we here fully characterize the universal dynamics of this thermal fluctuation-dominated regime and demonstrate that the cross-over from the classical two-fluid pinch-off scenario of a liquid thread to the fluctuation-dominated regime occurs at a well-defined neck radius proportional to the thermal length scale. Investigating satellite drop formation, we also show that at the level of the cross-over between these two regimes it is more probable to produce monodisperse droplets because fluctuation-dominated pinch-off may allow the unique situation where satellite drop formation can be inhibited. Nonetheless, the interplay between the evolution of the neck profiles from the classical to the fluctuation-dominated regime and the satellites’ production remains to be clarified. PMID:23090994

Cosmic bubble and domain wall instabilities II: fracturing of colliding walls

DOE Office of Scientific and Technical Information (OSTI.GOV)

Braden, Jonathan; Bond, J. Richard; Mersini-Houghton, Laura, E-mail: j.braden@ucl.ac.uk, E-mail: bond@cita.utoronto.ca, E-mail: mersini@physics.unc.edu

2015-08-01

We study collisions between nearly planar domain walls including the effects of small initial nonplanar fluctuations. These perturbations represent the small fluctuations that must exist in a quantum treatment of the problem. In a previous paper, we demonstrated that at the linear level a subset of these fluctuations experience parametric amplification as a result of their coupling to the planar symmetric background. Here we study the full three-dimensional nonlinear dynamics using lattice simulations, including both the early time regime when the fluctuations are well described by linear perturbation theory as well as the subsequent stage of fully nonlinear evolution. Wemore » find that the nonplanar fluctuations have a dramatic effect on the overall evolution of the system. Specifically, once these fluctuations begin to interact nonlinearly the split into a planar symmetric part of the field and the nonplanar fluctuations loses its utility. At this point the colliding domain walls dissolve, with the endpoint of this being the creation of a population of oscillons in the collision region. The original (nearly) planar symmetry has been completely destroyed at this point and an accurate study of the system requires the full three-dimensional simulation.« less

Cosmic bubble and domain wall instabilities II: fracturing of colliding walls

DOE Office of Scientific and Technical Information (OSTI.GOV)

Braden, Jonathan; Department of Physics, University of Toronto,60 St. George Street, Toronto, ON, M5S 3H8; Department of Physics and Astronomy, University College London,Gower Street, London, WC1E 6BT

2015-08-26

We study collisions between nearly planar domain walls including the effects of small initial nonplanar fluctuations. These perturbations represent the small fluctuations that must exist in a quantum treatment of the problem. In a previous paper, we demonstrated that at the linear level a subset of these fluctuations experience parametric amplification as a result of their coupling to the planar symmetric background. Here we study the full three-dimensional nonlinear dynamics using lattice simulations, including both the early time regime when the fluctuations are well described by linear perturbation theory as well as the subsequent stage of fully nonlinear evolution. Wemore » find that the nonplanar fluctuations have a dramatic effect on the overall evolution of the system. Specifically, once these fluctuations begin to interact nonlinearly the split into a planar symmetric part of the field and the nonplanar fluctuations loses its utility. At this point the colliding domain walls dissolve, with the endpoint of this being the creation of a population of oscillons in the collision region. The original (nearly) planar symmetry has been completely destroyed at this point and an accurate study of the system requires the full three-dimensional simulation.« less

Thermal modulation voltammetry with laser heating at an aqueous|nitrobenzene solution microinterface: determination of the standard entropy changes of transfer for tetraalkylammonium ions.

PubMed

Hinoue, Teruo; Ikeda, Eiji; Watariguchi, Shigeru; Kibune, Yasuyuki

2007-01-01

Thermal modulation voltammetry (TMV) with laser heating was successfully performed at an aqueous|nitrobenzene (NB) solution microinterface, by taking advantage of the fact that laser light with a wavelength of 325.0 nm is optically transparent to the aqueous solution but opaque to the NB solution. When the laser beam impinges upon the interface from the aqueous solution side, a temperature is raised around the interface through the thermal diffusion subsequent to the light-to-heat conversion following the optical absorption by the NB solution near the interface. Based on such a principle, we achieved a fluctuating temperature perturbation around the interface for TMV by periodically irradiating the interface with the laser beam. On the other hand, the fluctuating temperature perturbation has influence on currents for transfer of an ion across the interface to produce fluctuating currents synchronized with the perturbation through temperature coefficients of several variables concerning the transfer, such as the standard transfer potential and the diffusion coefficient of the ion. Consequently, TMV has the possibility of providing information about the standard entropy change of transfer corresponding to a temperature coefficient of the standard transfer potential and a temperature coefficient of the diffusion coefficient. In this work, the aqueous|NB solution interface of 30 microm in diameter was irradiated with the laser beam at 10 Hz, and the currents synchronized with the periodical irradiation were recorded as a function of the potential difference across the interface in order to construct a TM voltammogram. TM voltammograms were measured for transfer of tetramethylammonium, tetraethylammonium, tetrapropylammonium, and tetra-n-butylammonium ions from the aqueous solution to the NB solution, and the standard entropy change of transfer was determined for each ion, according to an analytical procedure based on a mathematical expression of the TM voltammogram. Comparison of the values obtained in this work with the literature values has proved that TMV with laser heating is available for the determination of the standard entropy change of transfer for an ion.

Quantum statistical effects in the mass transport of interstitial solutes in a crystalline solid

NASA Astrophysics Data System (ADS)

Woo, C. H.; Wen, Haohua

2017-09-01

The impact of quantum statistics on the many-body dynamics of a crystalline solid at finite temperatures containing an interstitial solute atom (ISA) is investigated. The Mori-Zwanzig theory allows the many-body dynamics of the crystal to be formulated and solved analytically within a pseudo-one-particle approach using the Langevin equation with a quantum fluctuation-dissipation relation (FDR) based on the Debye model. At the same time, the many-body dynamics is also directly solved numerically via the molecular dynamics approach with a Langevin heat bath based on the quantum FDR. Both the analytical and numerical results consistently show that below the Debye temperature of the host lattice, quantum statistics significantly impacts the ISA transport properties, resulting in major departures from both the Arrhenius law of diffusion and the Einstein-Smoluchowski relation between the mobility and diffusivity. Indeed, we found that below one-third of the Debye temperature, effects of vibrations on the quantum mobility and diffusivity are both orders-of-magnitude larger and practically temperature independent. We have shown that both effects have their physical origin in the athermal lattice vibrations derived from the phonon ground state. The foregoing theory is tested in quantum molecular dynamics calculation of mobility and diffusivity of interstitial helium in bcc W. In this case, the Arrhenius law is only valid in a narrow range between ˜300 and ˜700 K. The diffusivity becomes temperature independent on the low-temperature side while increasing linearly with temperature on the high-temperature side.

Prediction of HR/BP response to the spontaneous breathing trial by fluctuation dissipation theory

NASA Astrophysics Data System (ADS)

Chen, Man

2014-03-01

We applied the non-equilibrium fluctuation dissipation theorem to predict how critically-ill patients respond to treatment, based on both heart rate data and blood pressure data collected by standard hospital monitoring devices. The non-equilibrium fluctuation dissipation theorem relates the response of a system to a perturbation to the fluctuations in the stationary state of the system. It is shown that the response of patients to a standard procedure performed on patients, the spontaneous breathing trial (SBT), can be predicted by the non-equilibrium fluctuation dissipation approach. We classify patients into different groups according to the patients' characteristics. For each patient group, we extend the fluctuation dissipation theorem to predict interactions between blood pressure and beat-to-beat dynamics of heart rate in response to a perturbation (SBT), We also extract the form of the perturbation function directly from the physiological data, which may help to reduce the prediction error. We note this method is not limited to the analysis of the heart rate dynamics, but also can be applied to analyze the response of other physiological signals to other clinical interventions.

An improved car-following model considering velocity fluctuation of the immediately ahead car

NASA Astrophysics Data System (ADS)

Yu, Shaowei; Huang, Mengxing; Ren, Jia; Shi, Zhongke

2016-05-01

To better describe car-following behaviors in the adaptive cruise control strategy and further increase roadway traffic mobility and reduce fuel consumptions, the linkage between velocity fluctuation of the immediately ahead car and the following car's acceleration or deceleration is explored with respect to the measured car-following data by employing the gray correlation analysis theory and then an improved car-following model considering velocity fluctuation of the immediately ahead car on basis of the full velocity difference model is proposed. Numerical simulations are carried out and the effects of velocity fluctuation of the immediately ahead car on each car's velocity, acceleration, vehicular gap, fuel consumptions and the total fuel consumptions of the whole car-following system with different time window lengths are investigated in detail. The results show that velocity fluctuation of the immediately ahead car has significant effects on car-following behaviors and fuel consumptions, and that considering velocity fluctuation of the immediately ahead car in designing the adaptive cruise control system can improve traffic flow stability and reduce fuel consumptions.

Stochastic Acceleration of Galactic Cosmic Rays by Compressible Plasma Fluctuations in Supernova Shells

NASA Astrophysics Data System (ADS)

Zhang, Ming

2015-10-01

A theory of 2-stage acceleration of Galactic cosmic rays in supernova remnants is proposed. The first stage is accomplished by the supernova shock front, where a power-law spectrum is established up to a certain cutoff energy. It is followed by stochastic acceleration with compressible waves/turbulence in the downstream medium. With a broad \\propto {k}-2 spectrum for the compressible plasma fluctuations, the rate of stochastic acceleration is constant over a wide range of particle momentum. In this case, the stochastic acceleration process extends the power-law spectrum cutoff energy of Galactic cosmic rays to the knee without changing the spectral slope. This situation happens as long as the rate of stochastic acceleration is faster than 1/5 of the adiabatic cooling rate. A steeper spectrum of compressible plasma fluctuations that concentrate their power in long wavelengths will accelerate cosmic rays to the knee with a small bump before its cutoff in the comic-ray energy spectrum. This theory does not require a strong amplification of the magnetic field in the upstream interstellar medium in order to accelerate cosmic rays to the knee energy.

Temperature dependent structural properties and bending rigidity of pristine and defective hexagonal boron nitride

NASA Astrophysics Data System (ADS)

Thomas, Siby; Ajith, K. M.; Chandra, Sharat; Valsakumar, M. C.

2015-08-01

Structural and thermodynamical properties of monolayer pristine and defective boron nitride sheets (h-BN) have been investigated in a wide temperature range by carrying out atomistic simulations using a tuned Tersoff-type inter-atomic empirical potential. The temperature dependence of lattice parameter, radial distribution function, specific heat at constant volume, linear thermal expansion coefficient and the height correlation function of the thermally excited ripples on pristine as well as defective h-BN sheet have been investigated. Specific heat shows considerable increase beyond the Dulong-Petit limit at high temperatures, which is interpreted as a signature of strong anharmonicity present in h-BN. Analysis of the height fluctuations, < {{h}2}> , shows that the bending rigidity and variance of height fluctuations are strongly temperature dependent and this is explained using the continuum theory of membranes. A detailed study of the height-height correlation function shows deviation from the prediction of harmonic theory of membranes as a consequence of the strong anharmonicity in h-BN. It is also seen that the variance of the height fluctuations increases with defect concentration.

The spectrum of random magnetic fields in the mean field dynamo theory of the Galactic magnetic field

NASA Technical Reports Server (NTRS)

Kulsrud, Russell M.; Anderson, Stephen W.

1992-01-01

The fluctuation spectrum that must arise in a mean field dynamo generation of galactic fields if the initial field is weak is considered. A kinetic equation for its evolution is derived and solved. The spectrum evolves by transfer of energy from one magnetic mode to another by interaction with turbulent velocity modes. This kinetic equation is valid in the limit that the rate of evolution of the magnetic modes is slower than the reciprocal decorrelation time of the turbulent modes. This turns out to be the case by a factor greater than 3. Most of the fluctuation energy concentrates on small scales, shorter than the hydrodynamic turbulent scales. The fluctuation energy builds up to equipartition with the turbulent energy in times that are short compared to the e-folding time of the mean field. The turbulence becomes strongly modified before the dynamo amplification starts. Thus, the kinematic assumption of the mean dynamo theory is invalid. Thus, the galactic field must have a primordial origin, although it may subsequently be modified by dynamo action.

Self-consistent phonons revisited. I. The role of thermal versus quantum fluctuations on structural transitions in large Lennard-Jones clusters.

PubMed

Georgescu, Ionuţ; Mandelshtam, Vladimir A

2012-10-14

The theory of self-consistent phonons (SCP) was originally developed to address the anharmonic effects in condensed matter systems. The method seeks a harmonic, temperature-dependent Hamiltonian that provides the "best fit" for the physical Hamiltonian, the "best fit" being defined as the one that optimizes the Helmholtz free energy at a fixed temperature. The present developments provide a scalable O(N) unified framework that accounts for anharmonic effects in a many-body system, when it is probed by either thermal (ℏ → 0) or quantum fluctuations (T → 0). In these important limits, the solution of the nonlinear SCP equations can be reached in a manner that requires only the multiplication of 3N × 3N matrices, with no need of diagonalization. For short range potentials, such as Lennard-Jones, the Hessian, and other related matrices are highly sparse, so that the scaling of the matrix multiplications can be reduced from O(N(3)) to ~O(N). We investigate the role of quantum effects by continuously varying the de-Boer quantum delocalization parameter Λ and report the N-Λ (T = 0), and also the classical N-T (Λ = 0) phase diagrams for sizes up to N ~ 10(4). Our results demonstrate that the harmonic approximation becomes inadequate already for such weakly quantum systems as neon clusters, or for classical systems much below the melting temperatures.

One-dimensional analytical solution for hydraulic head and numerical solution for solute transport through a horizontal fracture for submarine groundwater discharge.

PubMed

He, Cairong; Wang, Tongke; Zhao, Zhixue; Hao, Yonghong; Yeh, Tian-Chyi J; Zhan, Hongbin

2017-11-01

Submarine groundwater discharge (SGD) has been recognized as a major pathway of groundwater flow to coastal oceanic environments. It could affect water quality and marine ecosystems due to pollutants and trace elements transported through groundwater. Relations between different characteristics of aquifers and SGD have been investigated extensively before, but the role of fractures in SGD still remains unknown. In order to better understand the mechanism of groundwater flow and solute transport through fractures in SGD, one-dimensional analytical solutions of groundwater hydraulic head and velocity through a synthetic horizontal fracture with periodic boundary conditions were derived using a Laplace transform technique. Then, numerical solutions of solute transport associated with the given groundwater velocity were developed using a finite-difference method. The results indicated that SGD associated with groundwater flow and solute transport was mainly controlled by sea level periodic fluctuations, which altered the hydraulic head and the hydraulic head gradient in the fracture. As a result, the velocity of groundwater flow associated with SGD also fluctuated periodically. We found that the pollutant concentration associated with SGD oscillated around a constant value, and could not reach a steady state. This was particularly true at locations close to the seashore. This finding of the role of fracture in SGD will assist pollution remediation and marine conservation in coastal regions. Copyright © 2017 Elsevier B.V. All rights reserved.

One-dimensional analytical solution for hydraulic head and numerical solution for solute transport through a horizontal fracture for submarine groundwater discharge

NASA Astrophysics Data System (ADS)

He, Cairong; Wang, Tongke; Zhao, Zhixue; Hao, Yonghong; Yeh, Tian-Chyi J.; Zhan, Hongbin

2017-11-01

Submarine groundwater discharge (SGD) has been recognized as a major pathway of groundwater flow to coastal oceanic environments. It could affect water quality and marine ecosystems due to pollutants and trace elements transported through groundwater. Relations between different characteristics of aquifers and SGD have been investigated extensively before, but the role of fractures in SGD still remains unknown. In order to better understand the mechanism of groundwater flow and solute transport through fractures in SGD, one-dimensional analytical solutions of groundwater hydraulic head and velocity through a synthetic horizontal fracture with periodic boundary conditions were derived using a Laplace transform technique. Then, numerical solutions of solute transport associated with the given groundwater velocity were developed using a finite-difference method. The results indicated that SGD associated with groundwater flow and solute transport was mainly controlled by sea level periodic fluctuations, which altered the hydraulic head and the hydraulic head gradient in the fracture. As a result, the velocity of groundwater flow associated with SGD also fluctuated periodically. We found that the pollutant concentration associated with SGD oscillated around a constant value, and could not reach a steady state. This was particularly true at locations close to the seashore. This finding of the role of fracture in SGD will assist pollution remediation and marine conservation in coastal regions.

Fluctuating Selection in the Moran

PubMed Central

Dean, Antony M.; Lehman, Clarence; Yi, Xiao

2017-01-01

Contrary to classical population genetics theory, experiments demonstrate that fluctuating selection can protect a haploid polymorphism in the absence of frequency dependent effects on fitness. Using forward simulations with the Moran model, we confirm our analytical results showing that a fluctuating selection regime, with a mean selection coefficient of zero, promotes polymorphism. We find that increases in heterozygosity over neutral expectations are especially pronounced when fluctuations are rapid, mutation is weak, the population size is large, and the variance in selection is big. Lowering the frequency of fluctuations makes selection more directional, and so heterozygosity declines. We also show that fluctuating selection raises dn/ds ratios for polymorphism, not only by sweeping selected alleles into the population, but also by purging the neutral variants of selected alleles as they undergo repeated bottlenecks. Our analysis shows that randomly fluctuating selection increases the rate of evolution by increasing the probability of fixation. The impact is especially noticeable when the selection is strong and mutation is weak. Simulations show the increase in the rate of evolution declines as the rate of new mutations entering the population increases, an effect attributable to clonal interference. Intriguingly, fluctuating selection increases the dn/ds ratios for divergence more than for polymorphism, a pattern commonly seen in comparative genomics. Our model, which extends the classical neutral model of molecular evolution by incorporating random fluctuations in selection, accommodates a wide variety of observations, both neutral and selected, with economy. PMID:28108586

Measures of three-dimensional anisotropy and intermittency in strong Alfvénic turbulence

NASA Astrophysics Data System (ADS)

Mallet, A.; Schekochihin, A. A.; Chandran, B. D. G.; Chen, C. H. K.; Horbury, T. S.; Wicks, R. T.; Greenan, C. C.

2016-06-01

We measure the local anisotropy of numerically simulated strong Alfvénic turbulence with respect to two local, physically relevant directions: along the local mean magnetic field and along the local direction of one of the fluctuating Elsasser fields. We find significant scaling anisotropy with respect to both these directions: the fluctuations are `ribbon-like' - statistically, they are elongated along both the mean magnetic field and the fluctuating field. The latter form of anisotropy is due to scale-dependent alignment of the fluctuating fields. The intermittent scalings of the nth-order conditional structure functions in the direction perpendicular to both the local mean field and the fluctuations agree well with the theory of Chandran, Schekochihin & Mallet, while the parallel scalings are consistent with those implied by the critical-balance conjecture. We quantify the relationship between the perpendicular scalings and those in the fluctuation and parallel directions, and find that the scaling exponent of the perpendicular anisotropy (I.e. of the aspect ratio of the Alfvénic structures in the plane perpendicular to the mean magnetic field) depends on the amplitude of the fluctuations. This is shown to be equivalent to the anticorrelation of fluctuation amplitude and alignment at each scale. The dependence of the anisotropy on amplitude is shown to be more significant for the anisotropy between the perpendicular and fluctuation-direction scales than it is between the perpendicular and parallel scales.

Nonequilibrium fluctuations in a frictional granular motor: Experiments and kinetic theory

NASA Astrophysics Data System (ADS)

Gnoli, Andrea; Sarracino, Alessandro; Puglisi, Andrea; Petri, Alberto

2013-05-01

We report the study of an experimental granular Brownian motor, inspired by the one published in Eshuis [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.104.248001 104, 248001 (2010)], but different in some ingredients. As in that previous work, the motor is constituted by a rotating blade, the surfaces of which break the rotation-inversion symmetry through alternated patches of different inelasticity, immersed in a gas of granular particles. The main difference of our experimental setup is in the orientation of the main axis, which is parallel to the (vertical) direction of shaking of the granular fluid, guaranteeing an isotropic distribution for the velocities of colliding grains, characterized by a variance v02. We also keep the granular system diluted, in order to compare with Boltzmann-equation-based kinetic theory. In agreement with theory, we observe the crucial role of Coulomb friction which induces two main regimes: (i) rare collisions, with an average angular velocity <ω>˜v03, and (ii) frequent collisions (FC), with <ω>˜v0. We also study the fluctuations of the angle spanned in a large-time interval Δθ, which in the FC regime is proportional to the work done upon the motor. We observe that the fluctuation relation is satisfied with a slope which weakly depends on the relative collision frequency.

Bouncing cosmological solutions from f(R,T) gravity

NASA Astrophysics Data System (ADS)

Shabani, Hamid; Ziaie, Amir Hadi

2018-05-01

In this work we study classical bouncing solutions in the context of f(R,T)=R+h(T) gravity in a flat FLRW background using a perfect fluid as the only matter content. Our investigation is based on introducing an effective fluid through defining effective energy density and pressure; we call this reformulation as the " effective picture". These definitions have been already introduced to study the energy conditions in f(R,T) gravity. We examine various models to which different effective equations of state, corresponding to different h(T) functions, can be attributed. It is also discussed that one can link between an assumed f(R,T) model in the effective picture and the theories with generalized equation of state ( EoS). We obtain cosmological scenarios exhibiting a nonsingular bounce before and after which the Universe lives within a de-Sitter phase. We then proceed to find general solutions for matter bounce and investigate their properties. We show that the properties of bouncing solution in the effective picture of f(R,T) gravity are as follows: for a specific form of the f(R,T) function, these solutions are without any future singularities. Moreover, stability analysis of the nonsingular solutions through matter density perturbations revealed that except two of the models, the parameters of scalar-type perturbations for the other ones have a slight transient fluctuation around the bounce point and damp to zero or a finite value at late times. Hence these bouncing solutions are stable against scalar-type perturbations. It is possible that all energy conditions be respected by the real perfect fluid, however, the null and the strong energy conditions can be violated by the effective fluid near the bounce event. These solutions always correspond to a maximum in the real matter energy density and a vanishing minimum in the effective density. The effective pressure varies between negative values and may show either a minimum or a maximum.

Numerical methods for the stochastic Landau-Lifshitz Navier-Stokes equations.

PubMed

Bell, John B; Garcia, Alejandro L; Williams, Sarah A

2007-07-01

The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several computational fluid dynamics approaches are considered (including MacCormack's two-step Lax-Wendroff scheme and the piecewise parabolic method) and are found to give good results for the variance of momentum fluctuations. However, neither of these schemes accurately reproduces the fluctuations in energy or density. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce fluctuations in density, energy, and momentum. A variety of numerical tests, including the random walk of a standing shock wave, are considered and results from the stochastic LLNS solver are compared with theory, when available, and with molecular simulations using a direct simulation Monte Carlo algorithm.

Effect of reduction in the density of states on fluctuation conductivity in Bi 2Sr 2CaCu 2O 8+ x single crystals

NASA Astrophysics Data System (ADS)

Chowdhury, P.; Bhatia, S. N.

1999-06-01

The in-plane ( ρab) and out-of-plane ( ρc) resistivities of BSCCO single crystals have been measured by six terminals technique. The ρab and ρc are well described by the fluctuation theory developed by Dorin et al. The main effect of these fluctuations is to cause a reduction in the quasi-particle density of states (DOS), leading to a negative contribution in the fluctuation conductivity Lawrence-Doniach (LD) and Maki-Thompson (MT) contributions. We have analyzed paraconductivity by adding this DOS contribution to LD and MT contributions. The analysis shows that approaches based on the conventional LD model alone cannot explain the paraconductivity along ab-plane and c-axis, even when the MT contribution is included.

Buckling of stiff polymers: Influence of thermal fluctuations

NASA Astrophysics Data System (ADS)

Emanuel, Marc; Mohrbach, Hervé; Sayar, Mehmet; Schiessel, Helmut; Kulić, Igor M.

2007-12-01

The buckling of biopolymers is a frequently studied phenomenon The influence of thermal fluctuations on the buckling transition is, however, often ignored and not completely understood. A quantitative theory of the buckling of a wormlike chain based on a semiclassical approximation of the partition function is presented. The contribution of thermal fluctuations to the force-extension relation that allows one to go beyond the classical Euler buckling is derived in the linear and nonlinear regimes as well. It is shown that the thermal fluctuations in the nonlinear buckling regime increase the end-to-end distance of the semiflexible rod if it is confined to two dimensions as opposed to the three-dimensional case. The transition to a buckled state softens at finite temperature. We derive the scaling behavior of the transition shift with increasing ratio of contour length versus persistence length.

Ubiquitous signatures of nematic quantum criticality in optimally doped Fe-based superconductors

DOE PAGES

Kuo, H. -H.; Chu, J. -H.; Palmstrom, J. C.; ...

2016-05-19

A key actor in the conventional theory of superconductivity is the induced interaction between electrons mediated by the exchange of virtual collective fluctuations (phonons in the case of conventional s-wave superconductors). Other collective modes that can play the same role, especially spin fluctuations, have been widely discussed in the context of high-temperature and heavy Fermion superconductors. The strength of such collective fluctuations is measured by the associated susceptibility. Here we use differential elastoresistance measurements from five optimally doped iron-based superconductors to show that divergent nematic susceptibility appears to be a generic feature in the optimal doping regime of these materials.more » This observation motivates consideration of the effects of nematic fluctuations on the superconducting pairing interaction in this family of compounds and possibly beyond.« less

Origin of the multiple configurations that drive the response of δ-plutonium’s elastic moduli to temperature

DOE PAGES

Migliori, Albert; Söderlind, Per; Landa, Alexander; ...

2016-09-19

The electronic and thermodynamic complexity of plutonium has resisted a fundamental understanding for this important elemental metal. critical test of any theory is the unusual softening of the bulk modulus with increasing temperature, a result that is counterintuitive because no or very little change in the atomic volume is observed upon heating. This unexpected behavior has in the past been attributed to competing but never-observed electronic states with different bonding properties similar to the scenario with magnetic states in Invar alloys. When using the recent observation of plutonium dynamic magnetism, we construct a theory for plutonium that agrees with relevantmore » measurements by using density-functional-theory (DFT) calculations with no free parameters to compute the effect of longitudinal spin fluctuations on the temperature dependence of the bulk moduli in δ-Pu. We also show that the softening with temperature can be understood in terms of a continuous distribution of thermally activated spin fluctuations.« less

A general solution strategy of modified power method for higher mode solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Peng; Lee, Hyunsuk; Lee, Deokjung, E-mail: deokjung@unist.ac.kr

2016-01-15

A general solution strategy of the modified power iteration method for calculating higher eigenmodes has been developed and applied in continuous energy Monte Carlo simulation. The new approach adopts four features: 1) the eigen decomposition of transfer matrix, 2) weight cancellation for higher modes, 3) population control with higher mode weights, and 4) stabilization technique of statistical fluctuations using multi-cycle accumulations. The numerical tests of neutron transport eigenvalue problems successfully demonstrate that the new strategy can significantly accelerate the fission source convergence with stable convergence behavior while obtaining multiple higher eigenmodes at the same time. The advantages of the newmore » strategy can be summarized as 1) the replacement of the cumbersome solution step of high order polynomial equations required by Booth's original method with the simple matrix eigen decomposition, 2) faster fission source convergence in inactive cycles, 3) more stable behaviors in both inactive and active cycles, and 4) smaller variances in active cycles. Advantages 3 and 4 can be attributed to the lower sensitivity of the new strategy to statistical fluctuations due to the multi-cycle accumulations. The application of the modified power method to continuous energy Monte Carlo simulation and the higher eigenmodes up to 4th order are reported for the first time in this paper. -- Graphical abstract: -- Highlights: •Modified power method is applied to continuous energy Monte Carlo simulation. •Transfer matrix is introduced to generalize the modified power method. •All mode based population control is applied to get the higher eigenmodes. •Statistic fluctuation can be greatly reduced using accumulated tally results. •Fission source convergence is accelerated with higher mode solutions.« less

Enhancement of large fluctuations to extinction in adaptive networks

NASA Astrophysics Data System (ADS)

Hindes, Jason; Schwartz, Ira B.; Shaw, Leah B.

2018-01-01

During an epidemic, individual nodes in a network may adapt their connections to reduce the chance of infection. A common form of adaption is avoidance rewiring, where a noninfected node breaks a connection to an infected neighbor and forms a new connection to another noninfected node. Here we explore the effects of such adaptivity on stochastic fluctuations in the susceptible-infected-susceptible model, focusing on the largest fluctuations that result in extinction of infection. Using techniques from large-deviation theory, combined with a measurement of heterogeneity in the susceptible degree distribution at the endemic state, we are able to predict and analyze large fluctuations and extinction in adaptive networks. We find that in the limit of small rewiring there is a sharp exponential reduction in mean extinction times compared to the case of zero adaption. Furthermore, we find an exponential enhancement in the probability of large fluctuations with increased rewiring rate, even when holding the average number of infected nodes constant.

Intrinsic fluctuations of the proton saturation momentum scale in high multiplicity p+p collisions

DOE PAGES

McLerran, Larry; Tribedy, Prithwish

2015-11-02

High multiplicity events in p+p collisions are studied using the theory of the Color Glass Condensate. Here, we show that intrinsic fluctuations of the proton saturation momentum scale are needed in addition to the sub-nucleonic color charge fluctuations to explain the very high multiplicity tail of distributions in p+p collisions. It is presumed that the origin of such intrinsic fluctuations is non-perturbative in nature. Classical Yang Mills simulations using the IP-Glasma model are performed to make quantitative estimations. Furthermore, we find that fluctuations as large as O(1) of the average values of the saturation momentum scale can lead to raremore » high multiplicity events seen in p+p data at RHIC and LHC energies. Using the available data on multiplicity distributions we try to constrain the distribution of the proton saturation momentum scale and make predictions for the multiplicity distribution in 13 TeV p+p collisions.« less

Noncommutative gauge theories and Kontsevich's formality theorem

NASA Astrophysics Data System (ADS)

Jurčo, B.; Schupp, P.; Wess, J.

2001-09-01

The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten map.) Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups; as a byproduct we obtain a "Mini Seiberg-Witten map" that explicitly relates ordinary abelian and nonabelian gauge fields. All constructions are also valid for non-constant B-field, and even more generally for any Poisson tensor.

Dust in magnetised plasmas - Basic theory and some applications. [to planetary rings

NASA Technical Reports Server (NTRS)

Northrop, T. G.; Morfill, G. E.

1984-01-01

In this paper the theory of charged test particle motion in magnetic fields is reviewed. This theory is then extended to charged dust particles, for which gravity and charge fluctuations play an important role. It is shown that systematic drifts perpendicular to the magnetic field and stochastic transport effects may then have to be considered none of which occur in the case of atomic particles (with the exception of charge exchange reactions). Some applications of charged dust particle transport theory to planetary rings are then briefly discussed.

Emergent "Quantum" Theory in Complex Adaptive Systems.

PubMed

Minic, Djordje; Pajevic, Sinisa

2016-04-30

Motivated by the question of stability, in this letter we argue that an effective quantum-like theory can emerge in complex adaptive systems. In the concrete example of stochastic Lotka-Volterra dynamics, the relevant effective "Planck constant" associated with such emergent "quantum" theory has the dimensions of the square of the unit of time. Such an emergent quantum-like theory has inherently non-classical stability as well as coherent properties that are not, in principle, endangered by thermal fluctuations and therefore might be of crucial importance in complex adaptive systems.

Emergent “Quantum” Theory in Complex Adaptive Systems

PubMed Central

Minic, Djordje; Pajevic, Sinisa

2017-01-01

Motivated by the question of stability, in this letter we argue that an effective quantum-like theory can emerge in complex adaptive systems. In the concrete example of stochastic Lotka-Volterra dynamics, the relevant effective “Planck constant” associated with such emergent “quantum” theory has the dimensions of the square of the unit of time. Such an emergent quantum-like theory has inherently non-classical stability as well as coherent properties that are not, in principle, endangered by thermal fluctuations and therefore might be of crucial importance in complex adaptive systems. PMID:28890591

Cosmological perturbations in inflation and in de Sitter space

NASA Astrophysics Data System (ADS)

Pimentel, Guilherme Leite

This thesis focuses on various aspects of inflationary fluctuations. First, we study gravitational wave fluctuations in de Sitter space. The isometries of the spacetime constrain to a few parameters the Wheeler-DeWitt wavefunctional of the universe, to cubic order in fluctuations. At cubic order, there are three independent terms in the wavefunctional. From the point of view of the bulk action, one term corresponds to Einstein gravity, and a new term comes from a cubic term in the curvature tensor. The third term is a pure phase and does not give rise to a new shape for expectation values of graviton fluctuations. These results can be seen as the leading order non-gaussian contributions in a slow-roll expansion for inflationary observables. We also use the wavefunctional approach to explain a universal consistency condition of n-point expectation values in single field inflation. This consistency condition relates a soft limit of an n-point expectation value to ( n-1)-point expectation values. We show how these conditions can be easily derived from the wavefunctional point of view. Namely, they follow from the momentum constraint of general relativity, which is equivalent to the constraint of spatial diffeomorphism invariance. We also study expectation values beyond tree level. We show that subhorizon fluctuations in loop diagrams do not generate a mass term for superhorizon fluctuations. Such a mass term could spoil the predictivity of inflation, which is based on the existence of properly defined field variables that become constant once their wavelength is bigger than the size of the horizon. Such a mass term would be seen in the two point expectation value as a contribution that grows linearly with time at late times. The absence of this mass term is closely related to the soft limits studied in previous chapters. It is analogous to the absence of a mass term for the photon in quantum electrodynamics, due to gauge symmetry. Finally, we use the tools of holography and entanglement entropy to study superhorizon correlations in quantum field theories in de Sitter space. The entropy has interesting terms that have no equivalent in flat space field theories. These new terms are due to particle creation in an expanding universe. The entropy is calculated directly for free massive scalar theories. For theories with holographic duals, it is determined by the area of some extremal surface in the bulk geometry. We calculate the entropy for different classes of holographic duals. For one of these classes, the holographic dual geometry is an asymptotically Anti-de Sitter space that decays into a crunching cosmology, an open Friedmann-Robertson-Walker universe. The extremal surface used in the calculation of the entropy lies almost entirely on the slice of maximal scale factor of the crunching cosmology.