On Pure and (approximate) Strong Equilibria of Facility Location Games
Hansen, Thomas Dueholm
2008-01-01
We study social cost losses in Facility Location games, where n selfish agents install facilities over a network and connect to them, so as to forward their local demand (expressed by a non-negative weight per agent). Agents using the same facility share fairly its installation cost, but every agent pays individually a (weighted) connection cost to the chosen location. We study the Price of Stability (PoS) of pure Nash equilibria and the Price of Anarchy of strong equilibria (SPoA), that generalize pure equilibria by being resilient to coalitional deviations. A special case of recently studied network design games, Facility Location merits separate study as a classic model with numerous applications and individual characteristics: our analysis for unweighted agents on metric networks reveals constant upper and lower bounds for the PoS, while an O(ln n) upper bound implied by previous work is tight for non-metric networks. Strong equilibria do not always exist, even for the unweighted metric case. For this cas...
On Pure and (approximate) Strong Equilibria of Facility Location Games
DEFF Research Database (Denmark)
Hansen, Thomas Dueholm; Telelis, Orestis A.
2008-01-01
We study social cost losses in Facility Location games, where n selfish agents install facilities over a network and connect to them, so as to forward their local demand (expressed by a non-negative weight per agent). Agents using the same facility share fairly its installation cost, but every...... networks we prove upper and lower bounds on PoS, while an O(ln n) upper bound implied by previous work is tight for non-metric networks. We also prove a constant upper bound for the SPoA of metric networks when strong equilibria exist. For the weighted game on general networks we prove existence of e...
Approximation of stochastic equilibria for dynamic systems with colored noise
Energy Technology Data Exchange (ETDEWEB)
Bashkirtseva, Irina [Ural Federal University, Lenina 51, Ekaterinburg, 620083 (Russian Federation)
2015-03-10
We consider nonlinear dynamic systems forced by colored noise. Using first approximation systems, we study dynamics of deviations of stochastic solutions from stable deterministic equilibria. Equations for the stationary second moments of deviations of random states are derived. An application of the elaborated theory to Van der Pol system driven by colored noise is given. A dependence of the dispersion on the time correlation of the colored noise is studied.
Strong washout approximation to resonant leptogenesis
Energy Technology Data Exchange (ETDEWEB)
Garbrecht, Bjoern; Gautier, Florian; Klaric, Juraj [Physik Department T70, James-Franck-Strasse, Techniche Universitaet Muenchen, 85748 Garching (Germany)
2016-07-01
We study resonant Leptogenesis with two sterile neutrinos with masses M{sub 1} and M{sub 2}, Yukawa couplings Y{sub 1} and Y{sub 2}, and a single active flavor. Specifically, we focus on the strong washout regime, where the decay width dominates the mass splitting of the two sterile neutrinos. We show that one can approximate the effective decay asymmetry by it's late time limit ε = X sin(2 φ)/(X{sup 2}+sin{sup 2}φ), where X=8 π Δ/(vertical stroke Y{sub 1} vertical stroke {sup 2}+ vertical stroke Y{sub 2} vertical stroke {sup 2}), Δ=4(M{sub 1}-M{sub 2})/(M{sub 1}+M{sub 2}), and φ=arg(Y{sub 2}/Y{sub 1}), and establish criteria for the validity of this approximation. We compare the approximate results with numerical ones, obtained by solving the mixing and oscillations of the sterile neutrinos. We generalize the formula to the case of several active flavors, and demonstrate how it can be used to calculate the lepton asymmetry in phenomenological scenarios which are in agreement with the neutrino oscillation data. We find that that using the late time limit is an applicable approximation throughout the phenomenologically viable parameter space.
Gutzwiller approximation in strongly correlated electron systems
Li, Chunhua
Gutzwiller wave function is an important theoretical technique for treating local electron-electron correlations nonperturbatively in condensed matter and materials physics. It is concerned with calculating variationally the ground state wave function by projecting out multi-occupation configurations that are energetically costly. The projection can be carried out analytically in the Gutzwiller approximation that offers an approximate way of calculating expectation values in the Gutzwiller projected wave function. This approach has proven to be very successful in strongly correlated systems such as the high temperature cuprate superconductors, the sodium cobaltates, and the heavy fermion compounds. In recent years, it has become increasingly evident that strongly correlated systems have a strong propensity towards forming inhomogeneous electronic states with spatially periodic superstrutural modulations. A good example is the commonly observed stripes and checkerboard states in high- Tc superconductors under a variety of conditions where superconductivity is weakened. There exists currently a real challenge and demand for new theoretical ideas and approaches that treats strongly correlated inhomogeneous electronic states, which is the subject matter of this thesis. This thesis contains four parts. In the first part of the thesis, the Gutzwiller approach is formulated in the grand canonical ensemble where, for the first time, a spatially (and spin) unrestricted Gutzwiller approximation (SUGA) is developed for studying inhomogeneous (both ordered and disordered) quantum electronic states in strongly correlated electron systems. The second part of the thesis applies the SUGA to the t-J model for doped Mott insulators which led to the discovery of checkerboard-like inhomogeneous electronic states competing with d-wave superconductivity, consistent with experimental observations made on several families of high-Tc superconductors. In the third part of the thesis, new
Energy Technology Data Exchange (ETDEWEB)
McNamara, B.
1984-04-01
Tandem and stellarator equilibria at high ..beta.. have proved hard to compute and the relaxation methods of Bauer et al., Chodura and Schluter, Hirshman, Strauss, and Pearlstein et al. have been slow to converge. This paper reports an extension of the low-..beta.. analytic method of Pearlstein, Kaiser, and Newcomb to arbitrary ..beta.. for tandem mirrors which converges in 10 to 20 iterations. Extensions of the method to stellarator equilibria are proposed and are very close to the analytic method of Johnson and Greene - the stellarator expansion. Most of the results of all these calculations can be adequately described by low-..beta.. approximations since the MHD stability limits occur at low ..beta... The tandem mirror, having weak curvature and a long central cell, allows finite Larmor radius effects to eliminate most ballooning modes and offers the possibility of really high average ..beta... This is the interest in developing such three-dimensional numerical algorithms.
On Eulerian equilibria in K-order approximation of the gyrostat in the three-body problem
Directory of Open Access Journals (Sweden)
J. A. Vera
2006-01-01
the main result of this work, the number of Eulerian equilibria in an approximate dynamics of order k for k≥1 is independent of the order of truncation of the potential if the gyrostat S0 is close to the sphere. The instability of Eulerian equilibria is proven for any approximate dynamics if the gyrostat is close to the sphere. In this way, we generalize the classical results on equilibria of the three-body problem and many of those obtained by other authors using more classic techniques for the case of rigid bodies.
Tokamak equilibria with strong toroidal current density reversal
Ludwig, G. O.; Rodrigues, Paulo; Bizarro, João P. S.
2013-05-01
The equilibrium of large magnetic islands in the core of a tokamak under conditions of strong toroidal current density reversal is investigated by a new method. The method uses distinct spectral representations to describe each simply connected region as well as the containing shell geometry. This ideal conducting shell may substitute for the plasma edge region or take a virtual character representing the external equilibrium field effect. The internal equilibrium of the islands is solved within the framework of the variational moment method. Equivalent surface current densities are defined on the boundaries of the islands and on the thin containing shell, giving a straightforward formulation to the interaction between regions. The equilibrium of the island-shell system is determined by matching moments of the Dirichlet boundary conditions. Finally, the macroscopic stability against a class of tilting displacements is examined by means of an energy principle. It is found out that the up-down symmetric islands are stable to this particular perturbation and geometry but the asymmetric system presents a bifurcation in the equilibrium.
Directory of Open Access Journals (Sweden)
Lu-Chuan Ceng
2014-01-01
Full Text Available We first introduce and analyze one iterative algorithm by using the composite shrinking projection method for finding a solution of the system of generalized equilibria with constraints of several problems: a generalized mixed equilibrium problem, finitely many variational inequalities, and the common fixed point problem of an asymptotically strict pseudocontractive mapping in the intermediate sense and infinitely many nonexpansive mappings in a real Hilbert space. We prove a strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another iterative algorithm involving no shrinking projection method and derive its weak convergence under mild assumptions. Our results improve and extend the corresponding results in the earlier and recent literature.
Approximations for strongly-coupled supersymmetric quantum mechanics
Kabat, D; Kabat, Daniel; Lifschytz, Gilad
2000-01-01
We advocate a set of approximations for studying the finite temperature behavior of strongly-coupled theories in 0+1 dimensions. The approximation consists of expanding about a Gaussian action, with the width of the Gaussian determined by a set of gap equations. The approximation can be applied to supersymmetric systems, provided that the gap equations are formulated in superspace. It can be applied to large-N theories, by keeping just the planar contribution to the gap equations. We analyze several models of scalar supersymmetric quantum mechanics, and show that the Gaussian approximation correctly distinguishes between a moduli space, mass gap, and supersymmetry breaking at strong coupling. Then we apply the approximation to a bosonic large-N gauge theory, and argue that a Gross-Witten transition separates the weak-coupling and strong-coupling regimes. A similar transition should occur in a generic large-N gauge theory, in particular in 0-brane quantum mechanics.
Generalized eikonal approximation for strong-field ionization
Vélez, F Cajiao; Kamiński, J Z
2015-01-01
We develop the eikonal perturbation theory to describe the strong-field ionization by finite laser pulses. This approach in the first order with respect to the binding potential (the so-called generalized eikonal approximation) avoids a singularity at the potential center. Thus, in contrast to the ordinary eikonal approximation, it allows to treat rescattering phenomena in terms of quantum trajectories. We demonstrate how the first Born approximation and its domain of validity follow from eikonal perturbation theory. Using this approach, we study the coherent diffraction patterns in photoelectron energy spectra and their modifications induced by the interaction of photoelectrons with the atomic potential. Along with these first results, we discuss the prospects of using the generalized eikonal approximation to study strong-field ionization from multi-centered atomic systems and to study other strong-field phenomena.
Energy Method to Obtain Approximate Solutions of Strongly Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Alex Elías-Zúñiga
2013-01-01
Full Text Available We introduce a nonlinearization procedure that replaces the system potential energy by an equivalent representation form that is used to derive analytical solutions of strongly nonlinear conservative oscillators. We illustrate the applicability of this method by finding the approximate solutions of two strongly nonlinear oscillators and show that this procedure provides solutions that follow well the numerical integration solutions of the corresponding equations of motion.
STRONG APPROXIMATION FOR MOVING AVERAGE PROCESSES UNDER DEPENDENCE ASSUMPTIONS
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Let {Xt, t ≥ 1} be a moving average process defined by Xt = ∞Σk=0akξt-k,where {ak,k ≥ 0} is a sequence of real numbers and {ξt,-∞＜ t ＜∞} is a doubly infinite sequence of strictly stationary dependent random variables. Under the conditions of {ak, k ≥ 0} which entail that {Xt, t ≥ 1} is either a long memory process or a linear process, the strong approximation of {Xt, t ≥ 1} to a Gaussian process is studied. Finally,the results are applied to obtain the strong approximation of a long memory process to a fractional Brownian motion and the laws of the iterated logarithm for moving average processes.
Properties of strongly dipolar Bose gases beyond the Born approximation
Ołdziejewski, Rafał
2016-01-01
Strongly dipolar Bose gases can form liquid droplets stabilized by quantum fluctuations. In theoretical description of this phenomenon, low energy scattering amplitude is utilized as an effective potential. We show that for magnetic atoms corrections with respect to Born approximation arise, and derive modified pseudopotential using realistic interaction model. We discuss the resulting changes in collective mode frequencies and droplet stability diagram. Our results are relevant for recent experiments with erbium and dysprosium atoms.
Strong swirl approximation and intensive vortices in the atmosphere
Klimenko, A Y
2014-01-01
This work investigates intensive vortices, which are characterised by the existence of a converging radial flow that significantly intensifies the flow rotation. Evolution and amplification of the vorticity present in the flow play important roles in the formation of the vortex. When rotation in the flow becomes sufficiently strong - and this implies validity of the strong swirl approximation developed by Einstein and Li (1951), Lewellen (1962), Turner (1966) and Lundgren (1985) - the analysis of Klimenko (2001a-c) and of the present work determine that further amplification of vorticity is moderated by interactions of vorticity and velocity. This imposes physical constraints on the flow resulting in the so-called compensating regime, where the radial distribution of the axial vorticity is characterised by the 4/3 and 3/2 power laws. This asymptotic treatment of a strong swirl is based on vorticity equations and involves higher order terms. This treatment incorporates multiscale analysis indicating downstream...
Strong semiclassical approximation of Wigner functions for the Hartree dynamics
Athanassoulis, Agissilaos
2011-01-01
We consider the Wigner equation corresponding to a nonlinear Schrödinger evolution of the Hartree type in the semiclassical limit h → 0. Under appropriate assumptions on the initial data and the interaction potential, we show that the Wigner function is close in L 2 to its weak limit, the solution of the corresponding Vlasov equation. The strong approximation allows the construction of semiclassical operator-valued observables, approximating their quantum counterparts in Hilbert-Schmidt topology. The proof makes use of a pointwise-positivity manipulation, which seems necessary in working with the L 2 norm and the precise form of the nonlinearity. We employ the Husimi function as a pivot between the classical probability density and the Wigner function, which - as it is well known - is not pointwise positive in general.
Breakdown of the Dipole Approximation in Strong-Field Ionization
Ludwig, A; Mayer, B W; Phillips, C R; Gallmann, L; Keller, U
2014-01-01
We report the breakdown of the electric dipole approximation in the long-wavelength limit in strong-field ionization with linearly polarized few-cycle mid-infrared laser pulses at intensities on the order of 10$^{13}$ W/cm$^2$. Photoelectron momentum distributions were recorded by velocity map imaging and projected onto the beam propagation axis. We observe an increasing shift of the peak of this projection opposite to the beam propagation direction with increasing laser intensities. From a comparison with semi-classical simulations, we identify the combined action of the magnetic field of the laser pulse and the Coulomb potential as origin of our observations.
Strong-field ionization via high-order Coulomb corrected strong-field approximation
Klaiber, Michael; Yakaboylu, Enderalp; Hatsagortsyan, Karen Z; Keitel, Christoph H
2016-01-01
Signatures of the Coulomb corrections in the photoelectron momentum distribution during laser-induced ionization of atoms or ions in tunneling and multiphoton regimes are investigated analytically in the case of an one-dimensional problem. High-order Coulomb corrected strong-field approximation is applied, where the exact continuum state in the S-matrix is approximated by the eikonal Coulomb-Volkov state including the second-order corrections to the eikonal. Although, without high-order corrections our theory coincides with the known analytical R-matrix (ARM) theory, we propose a simplified procedure for the matrix element derivation. Rather than matching the eikonal Coulomb-Volkov wave function with the bound state as in the ARM-theory to remove the Coulomb singularity, we calculate the matrix element via the saddle-point integration method as by time as well as by coordinate, and in this way avoiding the Coulomb singularity. The momentum shift in the photoelectron momentum distribution with respect to the A...
Strong Convergence of Stochastic Approximation Without Lyapunov Functions
1995-01-01
We prove convergence with probability one of a multivariate Markov stochastic approximation procedure of the Robbins-Monro type with several roots. The argument exploits convergence of the corresponding system of ordinary differential equations to its stationary points. If the points are either linearly stable or linearly unstable, we prove convergence with probability 1 of the procedure to a random vector whose distribution concentrates on the set of stable stationary points. This generalize...
The method of secondary quantization in the strong bond approximation
Directory of Open Access Journals (Sweden)
O.A. Anikeenok
2015-12-01
Full Text Available Expressions for the calculation of the Fourier transform of the direct Coulomb interaction of electrons have been derived in the method of strong bond. It was shown that in the elaborated method it is not necessary to spread out nuclear charges over the crystal as it is done in the case of delocalized electrons.
Embedding Relations Connected with Strong Approximation of Fourier Series
Indian Academy of Sciences (India)
Bogdan Szal
2010-11-01
We consider the embedding relation between the class $W^q H^_$, including only odd functions and a set of functions defined via the strong means of Fourier series of odd continuous functions. We establish an improvement of a recent theorem of Le and Zhou [Math. Inequal. Appl. 11(4)(2008) 749--756] which is a generalization of Tikhonov’s results [Anal. Math. 31(2005) 183--194]. We also extend the Leindler theorem [Anal. Math. 31(2005) 175--182] concerning sequences of Fourier coefficients.
Strong Approximations of Martingale Vectors and Their Applications in Markov-Chain Adaptive Designs
Institute of Scientific and Technical Information of China (English)
Li-xin Zhang
2004-01-01
The strong approximations of a class of Rd-valued martingales are considered. The conditions usedin this paper are easier to check than those used in [3] and [9]. As an application, the strong approximation ofa class of non-homogenous Markov chains is established, and the asymptotic properties are established for themulti-treatment Markov chain adaptive designs in clinical trials.
T.V. Hvozd; Y.V. Kalyuzhnyi
2016-01-01
Phase behavior of the Yukawa hard-sphere polydisperse mixture with high degree of polydispersity is studied using high temperature approximation (HTA) and mean spherical approximation (MSA). We have extended and applied the scheme developed to calculate the phase diagrams of polydisperse mixtures described by the truncatable free energy models, i.e., the models with Helmholtz free energy defined by the finite number of the moments of the species distribution function. At high degree of polydi...
Reformulation of the strong field approximation for light-matter interactions
Galstyan, A; Hamido, A; Popov, Yu V; Mota-Furtado, F; O'Mahony, P F; Janssens, N; Catoire, F; Piraux, B
2015-01-01
We consider the interaction of hydrogen-like atoms with a strong laser field and show that the strong field approximation and all its variants may be grouped into a set of families of approximation schemes. This is done by introducing an ansatz describing the electron wave packet as the sum of the initial state wave function times a phase factor and a function which is the perturbative solution in the Coulomb potential of an inhomogeneous time-dependent Schr\\"odinger equation. It is the phase factor that characterizes a given family. In each of these families, the velocity and length gauge version of the approximation scheme lead to the same results at each order in the Coulomb potential. By contrast, irrespective of the gauge, approximation schemes belonging to different families give different results. Furthermore, this new formulation of the strong field approximations allows us to gain deeper insight into the validity of the strong field approximation schemes. In particular, we address two important quest...
Applications of Adiabatic Approximation to One- and Two-electron Phenomena in Strong Laser Fields
Bondar, Denys
2010-01-01
The adiabatic approximation is a natural approach for the description of phenomena induced by low frequency laser radiation because the ratio of the laser frequency to the characteristic frequency of an atom or a molecule is a small parameter. Since the main aim of this work is the study of ionization phenomena, the version of the adiabatic approximation that can account for the transition from a bound state to the continuum must be employed. Despite much work in this topic, a universally accepted adiabatic approach of bound-free transitions is lacking. Hence, based on Savichev's modified adiabatic approximation [Sov. Phys. JETP 73, 803 (1991)], we first of all derive the most convenient form of the adiabatic approximation for the problems at hand. Connections of the obtained result with the quasiclassical approximation and other previous investigations are discussed. Then, such an adiabatic approximation is applied to single-electron ionization and non-sequential double ionization of atoms in a strong low fr...
Strong approximations and sequential change-point analysis for diffusion processes
DEFF Research Database (Denmark)
Mihalache, Stefan-Radu
2012-01-01
In this paper ergodic diffusion processes depending on a parameter in the drift are considered under the assumption that the processes can be observed continuously. Strong approximations by Wiener processes for a stochastic integral and for the estimator process constructed by the one-step proced......-step procedure of Le Cam are obtained. Applying these approximations, a CUSUM-type procedure is developed for the sequential testing of changes in the parameter....
Directory of Open Access Journals (Sweden)
Jianping Cai
2003-01-01
Full Text Available A method of approximate potential is presented for the study of certain kinds of strongly nonlinear oscillators. This method is to express the potential for an oscillatory system by a polynomial of degree four such that the leading approximation may be derived in terms of elliptic functions. The advantage of present method is that it is valid for relatively large oscillations. As an application, the elapsed time of periodic motion of a strongly nonlinear oscillator with slowly varying parameters is studied in detail. Comparisons are made with other methods to assess the accuracy of the present method.
Approximating Curve and Strong Convergence of the CQ Algorithm for the Split Feasibility Problem
Directory of Open Access Journals (Sweden)
Xu Hong-Kun
2010-01-01
Full Text Available Using the idea of Tikhonov's regularization, we present properties of the approximating curve for the split feasibility problem (SFP and obtain the minimum-norm solution of SFP as the strong limit of the approximating curve. It is known that in the infinite-dimensional setting, Byrne's CQ algorithm (Byrne, 2002 has only weak convergence. We introduce a modification of Byrne's CQ algorithm in such a way that strong convergence is guaranteed and the limit is also the minimum-norm solution of SFP.
The strong field approximation within a Faddeev-like formalism for laser-matter interactions
Popov, Yu; Mota-Furtado, F; O'Mahony, P F; Piraux, B
2016-01-01
We consider the interaction of atomic hydrogen with an intense laser field within the strong-field approximation. By using a Faddeev-like formalism, we introduce a new perturbative series in the binding potential of the atom. As a first test of this new approach, we calculate the electron energy spectrum in the very simple case of a photon energy higher than the ionisation potential. We show that by contrast to the standard perturbative series in the binding potential obtained within the strong field approximation, the first terms of the new series converge rapidly towards the results we get by solving the corresponding time-dependent Schroedinger equation.
New approximate solutions for the strongly nonlinear cubic-quintic duffing oscillators
Karahan, M. M. Fatih; Pakdemirli, Mehmet
2016-06-01
Strongly nonlinear cubic-quintic Duffing oscillator is considered. Approximate solutions are derived using the multiple scales Lindstedt Poincare method (MSLP), a relatively new method developed for strongly nonlinear oscillators. The free undamped oscillator is considered first. Approximate analytical solutions of the MSLP are contrasted with the classical multiple scales (MS) method and numerical simulations. It is found that contrary to the classical MS method, the MSLP can provide acceptable solutions for the case of strong nonlinearities. Next, the forced and damped case is treated. Frequency response curves of both the MS and MSLP methods are obtained and contrasted with the numerical solutions. The MSLP method and numerical simulations are in good agreement while there are discrepancies between the MS and numerical solutions.
ON THE UNIFORM STRONG APPROXIMATION OF MARCINKIEWICZ TYPE FOR MULTIVARIABLE CONTINUOUS FUNCTIONS
Institute of Scientific and Technical Information of China (English)
Yujun Zhang; Xiaoyuan He
2005-01-01
The rate of uniform strong approximation of Marcinkiewicz type for multivariable continuous func-tions is obtained in this paper as follows:‖1/k+1 k∑j=0|Sj(f)- f|q‖≤C/k +1 k∑j=0 Eqj(f),where Sj (f) denotes the square partial Fourier sum of f and Ej (f) denotes the square best approximation of f by trigonometric polynomials of degree (j, j, … ,j),j = 0,1, 2,….
Prat, Vincent; Lignières, François; Ballot, Jérôme; Culpin, Pierre-Marie
2016-01-01
Context. As of today, asteroseismology mainly allows us to probe internal rotation of stars when modes are only weakly affected by rotation using perturbative methods. Such methods cannot be applied to rapidly rotating stars, which exhibit complex oscillation spectra. In this context, the so-called traditional approximation, which neglects the terms associated with the latitudinal component of the rotation vector, describes modes that are strongly affected by rotation and is sometimes used for interpreting asteroseismic data. However, its domain of validity is not established yet. Aims. We aim at deriving analytical prescriptions for period spacings of low-frequency gravity modes strongly affected by rotation through the full Coriolis acceleration that can be used to probe stellar internal structure and rotation. Methods. The asymptotic theory of gravito-inertial waves in uniformly rotating stars using ray theory described by Prat et al. (2016, A&A, 587, A110) is approximated in the low-frequency regime, ...
Bauer, J H
2010-01-01
In the recent work of Vanne and Saenz [Phys. Rev. A 75, 063403 (2007)] the quasistatic limit of the velocity gauge strong-field approximation describing the ionization rate of atomic or molecular systems exposed to linearly polarized laser fields was derived. It was shown that in the low-frequency limit the ionization rate is proportional to the laser frequency (for a constant intensity of the laser field). In the present work I show that for circularly polarized laser fields the ionization rate is proportional to higher powers of the laser frequency for hydrogenic atoms. The new analytical expressions for asymptotic ionization rates (which become accurate in the quasistatic limit) contain no summations over multiphoton contributions. For very low laser frequencies (optical or infrared), these expressions usually remain with an order-of-magnitude agreement with the velocity gauge strong-field approximation.
Zhang, Liangsheng; Zhao, Bo; Devakul, Trithep; Huse, David A.
2016-06-01
We present a simplified strong-randomness renormalization group (RG) that captures some aspects of the many-body localization (MBL) phase transition in generic disordered one-dimensional systems. This RG can be formulated analytically and is mathematically equivalent to a domain coarsening model that has been previously solved. The critical fixed-point distribution and critical exponents (that satisfy the Chayes inequality) are thus obtained analytically or to numerical precision. This reproduces some, but not all, of the qualitative features of the MBL phase transition that are indicated by previous numerical work and approximate RG studies: our RG might serve as a "zeroth-order" approximation for future RG studies. One interesting feature that we highlight is that the rare Griffiths regions are fractal. For thermal Griffiths regions within the MBL phase, this feature might be qualitatively correctly captured by our RG. If this is correct beyond our approximations, then these Griffiths effects are stronger than has been previously assumed.
Prat, V.; Mathis, S.; Lignières, F.; Ballot, J.; Culpin, P.-M.
2017-02-01
Context. As of today, asteroseismology mainly allows us to probe the internal rotation of stars when modes are only weakly affected by rotation using perturbative methods. Such methods cannot be applied to rapidly rotating stars, which exhibit complex oscillation spectra. In this context, the so-called traditional approximation, which neglects the terms associated with the latitudinal component of the rotation vector, describes modes that are strongly affected by rotation. This approximation is sometimes used for interpreting asteroseismic data, however, its domain of validity is not established yet. Aims: We aim at deriving analytical prescriptions for period spacings of low-frequency gravity modes strongly affected by rotation through the full Coriolis acceleration (i.e. without neglecting any component of the rotation vector), which can be used to probe stellar internal structure and rotation. Methods: We approximated the asymptotic theory of gravito-inertial waves in uniformly rotating stars using ray theory described in a previous paper in the low-frequency regime, where waves are trapped near the equatorial plane. We put the equations of ray dynamics into a separable form and used the Einstein-Brillouin-Keller (EBK) quantisation method to compute modes frequencies from rays. Results: Two spectral patterns that depend on stratification and rotation are predicted within this new approximation: one for axisymmetric modes and one for non-axisymmetric modes. Conclusions: The detection of the predicted patterns in observed oscillation spectra would give constraints on internal rotation and chemical stratification of rapidly rotating stars exhibiting gravity modes, such as γ Doradus, SPB, or Be stars. The obtained results have a mathematical form that is similar to that of the traditional approximation, but the new approximation takes the full Coriolis, which allows for propagation near the centre, and centrifugal accelerations into account.
Analytical approximate technique for strongly nonlinear oscillators problem arising in engineering
Directory of Open Access Journals (Sweden)
Y. Khan
2012-12-01
Full Text Available In this paper, a novel method called generalized of the variational iteration method is presented to obtain an approximate analytical solution for strong nonlinear oscillators problem associated in engineering phenomena. This approach resulted in the frequency of the motion as a function of the amplitude of oscillation. It is determined that the method works very well for the whole range of parameters and an excellent agreement is demonstrated and discussed between the approximate frequencies and the exact one. The most significant features of this method are its simplicity and excellent accuracy for the whole range of oscillation amplitude values. Also, the results reveal that this technique is very effective and convenient for solving conservative oscillatory systems with complex nonlinearities. Results obtained by the proposed method are compared with Energy Balance Method (EBM and exact solution showed that, contrary to EBM, simply one or two iterations are enough for obtaining highly accurate results.
Strongly Convergent Approximations to Fixed Points of Total Asymptotically Nonexpansive Mappings
Institute of Scientific and Technical Information of China (English)
Yakov ALBER; Rafa ESP ′ INOLA Pepa LORENZO
2008-01-01
In this work we prove a new strong convergence result of the regularized successive ap-proximation method given by y n +1 = q n z 0 +(1 -q n )n y n ,n =1 2 ..., where lim n →∞ q n = 0 and ∞ n =1 q n = ∞, for T a total asymptotically nonexpansive mapping, I.e., T is such that T N x -T n y ≤x -y + k (1) n φ ( x -y )+k (2)n , where k 1 n and k2 n are real null convergent sequences and φ : R +→R+ is continuous such that φ (0) = 0 and lim →∞φ (t) t ≤C for a certain constant C>0. Among other features, our results essentially generalize existing results on strong convergence for T nonexpansive and asymptotically nonexpansive. The convergence and stability analysis is given for both self- and nonself-mappings.
Collective-field-corrected strong field approximation for laser-irradiated metal clusters
Keil, Th
2013-01-01
The strong field approximation (SFA) formulated in terms of so-called "quantum orbits" led to much insight into intense-laser driven ionization dynamics. In plain SFA, the emitted electron is treated as a free electron in the laser field alone. However, with improving experimental techniques and more advanced numerical simulations it becomes more and more obvious that the plain SFA misses interesting effects even on a qualitative level. Examples are holographic side lobes, the low-energy structure, radial patterns in photoelectron spectra at low kinetic energies, and strongly rotated angular distributions. For this reason increasing effort has been recently devoted to Coulomb corrections of the SFA. In the current paper, we follow a similar line but consider ionization of metal clusters. It is known that photoelectrons from clusters can be much more energetic than those emitted from atoms or small molecules, especially if the Mie resonance of the expanding cluster is evoked. We develop a SFA that takes the co...
On function classes related pertaining to strong approximation of double Fourier series
Baituyakova, Zhuldyz
2015-09-01
The investigation of embedding of function classes began a long time ago. After Alexits [1], Leindler [2], and Gogoladze[3] investigated estimates of strong approximation by Fourier series in 1965, G. Freud[4] raised the corresponding saturation problem in 1969. The list of the authors dealing with embedding problems partly is also very long. It suffices to mention some names: V. G. Krotov, W. Lenski, S. M. Mazhar, J. Nemeth, E. M. Nikisin, K. I. Oskolkov, G. Sunouchi, J. Szabados, R. Taberski and V. Totik. Study on this topic has since been carried on over a decade, but it seems that most of the results obtained are limited to the case of one dimension. In this paper, embedding results are considered which arise in the strong approximation by double Fourier series. We prove theorem on the interrelation between the classes Wr1,r2HS,M ω and H(λ, p, r1, r2, ω(δ1, δ2)), in the one-dimensional case proved by L. Leindler.
Nematic Equilibria on a Two-Dimensional Annulus
Lewis, A. H.
2017-01-16
We study planar nematic equilibria on a two-dimensional annulus with strong and weak tangent anchoring, in the Oseen–Frank theoretical framework. We analyze a radially invariant defect-free state and compute analytic stability criteria for this state in terms of the elastic anisotropy, annular aspect ratio, and anchoring strength. In the strong anchoring case, we define and characterize a new spiral-like equilibrium which emerges as the defect-free state loses stability. In the weak anchoring case, we compute stability diagrams that quantify the response of the defect-free state to radial and azimuthal perturbations. We study sector equilibria on sectors of an annulus, including the effects of weak anchoring and elastic anisotropy, giving novel insights into the correlation between preferred numbers of boundary defects and the geometry. We numerically demonstrate that these sector configurations can approximate experimentally observed equilibria with boundary defects.
Chaaban, Anas
2016-03-01
The symmetric K-user interference channel is studied with the goal of characterizing its capacity region in the strong interference regime within a constant gap. The achievable rate region of a scheme combining rate-splitting at the transmitters and interference alignment and successive decoding/computation at the receivers is derived. Next it is shown that this scheme achieves the so-called greedy-max corner points of the capacity region within a constant gap. By combining this result with previous results by Ordentlich et al. on the sum-capacity of the symmetric interference channel, a constant gap characterization of the capacity region for the strong interference regime is obtained. This leads to the first approximate characterization of the capacity region of the symmetric K-user IC. Furthermore, a new scheme that achieves the sum-capacity of the channel in the strong interference regime within a constant gap is also proposed, and the corresponding gap is calculated. The advantage of the new scheme is that it leads to a characterization within a constant gap without leaving an outage set contrary to the scheme by Ordentlich et al..
Strong-field-approximation theory of high-order harmonic generation by polyatomic molecules
Odžak, S.; Hasović, E.; Milošević, D. B.
2016-04-01
A theory of high-order harmonic generation by arbitrary polyatomic molecules is introduced. A polyatomic molecule is modeled by an (N +1 ) -particle system, which consists of N heavy atomic (ionic) centers and an electron. After the separation of the center-of-mass coordinate, the dynamics of this system is reduced to the relative electronic and nuclear coordinates. Various versions (with or without the dressing of the initial and/or final molecular state) of the molecular strong-field approximation are introduced. For neutral polyatomic molecules the derived expression for the T -matrix element takes a simple form. The interference minima in the harmonic spectrum are explained as a multiple-slit type of interference. This is illustrated by numerical examples for the ozone (O3) and carbon dioxide (CO2) molecules.
Thygesen, Uffe Høgsbro
2016-03-01
We consider organisms which use a renewal strategy such as run-tumble when moving in space, for example to perform chemotaxis in chemical gradients. We derive a diffusion approximation for the motion, applying a central limit theorem due to Anscombe for renewal-reward processes; this theorem has not previously been applied in this context. Our results extend previous work, which has established the mean drift but not the diffusivity. For a classical model of tumble rates applied to chemotaxis, we find that the resulting chemotactic drift saturates to the swimming velocity of the organism when the chemical gradients grow increasingly steep. The dispersal becomes anisotropic in steep gradients, with larger dispersal across the gradient than along the gradient. In contrast to one-dimensional settings, strong bias increases dispersal. We next include Brownian rotation in the model and find that, in limit of high chemotactic sensitivity, the chemotactic drift is 64% of the swimming velocity, independent of the magnitude of the Brownian rotation. We finally derive characteristic timescales of the motion that can be used to assess whether the diffusion limit is justified in a given situation. The proposed technique for obtaining diffusion approximations is conceptually and computationally simple, and applicable also when statistics of the motion is obtained empirically or through Monte Carlo simulation of the motion.
Quasi-Localized Charge Approximation for Strongly Correlated Plasmas in Traps
Kählert, Hanno; Bonitz, Michael; Kalman, Gabor
2012-10-01
Over the last two decades, the Quasi-Localized Charge Approximation (QLCA) has been successfully applied to investigate the dielectric properties of various strongly coupled systems [1]. While these earlier studies focused on bulk properties, we are concerned with the application of the QLCA to finite inhomogeneous systems. These situations are commonly encountered in ion trap plasmas, ultra-cold neutral plasmas, or dusty plasmas. Starting from the microscopic Lagrangian, we derive an equation for the fluid displacement field and compare our results with previous calculations [2] and a theory for strongly correlated ion plasmas [3]. Since the QLCA accounts for correlation effects, it improves upon so-called ``cold-fluid'' theories and should allow to reduce the discrepancies between the latter and molecular dynamics simulations in a confined Yukawa plasma [4]. Here, we present our first results.[3pt] [1] K. I. Golden and G. J. Kalman, Phys. Plasmas 7, 14 (2000)[0pt] [2] C.-J. Lee and G. J. Kalman, J. Korean Phys. Soc. 58, 448 (2011)[0pt] [3] D. H. E. Dubin and J. P. Schiffer, Phys. Rev. E 53, 5249 (1996), D. H. E. Dubin, Phys. Rev. E 53, 5268 (1996)[0pt] [4] H. K"ahlert and M. Bonitz, Phys. Rev. E 83, 056401 (2011)
Jump conditions in transonic equilibria
Energy Technology Data Exchange (ETDEWEB)
Guazzotto, L.; Betti, R. [Department of Mechanical Engineering, University of Rochester, Rochester, New York 14627 (United States); Jardin, S. C. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08540 (United States)
2013-04-15
In the present paper, the numerical calculation of transonic equilibria, first introduced with the FLOW code in Guazzotto et al.[Phys. Plasmas 11, 604 (2004)], is critically reviewed. In particular, the necessity and effect of imposing explicit jump conditions at the transonic discontinuity are investigated. It is found that 'standard' (low-{beta}, large aspect ratio) transonic equilibria satisfy the correct jump condition with very good approximation even if the jump condition is not explicitly imposed. On the other hand, it is also found that high-{beta}, low aspect ratio equilibria require the correct jump condition to be explicitly imposed. Various numerical approaches are described to modify FLOW to include the jump condition. It is proved that the new methods converge to the correct solution even in extreme cases of very large {beta}, while they agree with the results obtained with the old implementation of FLOW in lower-{beta} equilibria.
Strong approximation for the general Kesten-Spitzer random walk in independent random scenery
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper is to prove that, if a one-dimensional random wa lkcan be approximated by a Brownian motion, then the related random walk in a g eneral independent scenery can be approximated by a Brownian motion in Brownian scenery.
Dreissigacker, Ingo; Lein, Manfred
2014-05-01
Motivated by recent experiments on circular dichroism in the photoelectron momentum distributions from strong-field ionization of chiral molecules [C. Lux et al., Angew. Chem. Int. Ed. 51, 5001 (2012), 10.1002/anie.201109035; C. S. Lehmann et al., J. Chem. Phys. 139, 234307 (2013), 10.1063/1.4844295], we investigate the origin of this effect theoretically. We show that it is not possible to describe photoelectron circular dichroism with the commonly used strong-field approximation due to its plane-wave nature. We therefore apply the Born approximation to the scattering state and use this as a continuum-state correction in the strong-field approximation. We obtain electron distributions for the molecules camphor and fenchone. In order to gain physical insight into the process, we study the contributions of individual molecular orientations.
An approximation theory or strongly stabilizing solutions to the operator LQ Riccati equation
Oostveen, JC; Curtain, RF; Ito, K
2000-01-01
The linear-quadratic (LQ) control problem is considered for a class of infinite-dimensional systems with bounded input and output operators, that are not exponentially stabilizable, but only strongly stabilizable. A sufficient condition for the existence of a minimizing control and of a stabilizing
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper, the Dirichlet problem of Stokes approximate of non-homogeneous incompressible Navier-Stokes equations is studied. It is shown that there exist global weak solutions as well as global and unique strong solution for this problem, under the assumption that initial density ρ0(x) is bounded away from 0 and other appropriate assumptions (see Theorem 1 and Theorem 2). The semi-Galerkin method is applied to construct the approximate solutions and a prior estimates are made to elaborate upon the compactness of the approximate solutions.
Analytical Approximation of the Deconvolution of Strongly Overlapping Broad Fluorescence Bands
Dubrovkin, J. M.; Tomin, V. I.; Ushakou, D. V.
2016-09-01
A method for deconvoluting strongly overlapping spectral bands into separate components that enables the uniqueness of the deconvolution procedure to be monitored was proposed. An asymmetric polynomial-modified function subjected to Fourier filtering (PMGFS) that allowed more accurate and physically reasonable band shapes to be obtained and also improved significantly the deconvolution convergence was used as the band model. The method was applied to the analysis of complexation in solutions of the molecular probe 4'-(diethylamino)-3-hydroxyflavone with added LiCl. Two-band fluorescence of the probe in such solutions was the result of proton transfer in an excited singlet state and overlapped strongly with stronger spontaneous emission of complexes with the ions. Physically correct deconvolutions of overlapping bands could not always be obtained using available software.
The set of badly approximable vectors is strongly $C^1$ incompressible
Broderick, Ryan; Kleinbock, Dmitry; Reich, Asaf; Weiss, Barak
2011-01-01
We prove that the countable intersection of $C^1$-diffeomorphic images of certain Diophantine sets has full Hausdorff dimension. For example, we show this for the set of badly approximable vectors in $\\mathbb{R}^d$, improving earlier results of Schmidt and Dani. To prove this, inspired by ideas of McMullen, we define a new variant of Schmidt's $(\\alpha, \\beta)$-game and show that our sets are hyperplane absolute winning (HAW), which in particular implies winning in the original game. The HAW property passes automatically to games played on certain fractals, thus our sets intersect a large class of fractals in a set of positive dimension. This extends earlier results of Fishman to a more general set-up, with simpler proofs.
DEFF Research Database (Denmark)
Thygesen, Uffe Høgsbro
2016-01-01
not previously been applied in this context. Our results extend previous work, which has established the mean drift but not the diffusivity. For a classical model of tumble rates applied to chemotaxis, we find that the resulting chemotactic drift saturates to the swimming velocity of the organism when......We consider organisms which use a renewal strategy such as run–tumble when moving in space, for example to perform chemotaxis in chemical gradients. We derive a diffusion approximation for the motion, applying a central limit theorem due to Anscombe for renewal-reward processes; this theorem has......, in limit of high chemotactic sensitivity, the chemotactic drift is 64 % of the swimming velocity, independent of the magnitude of the Brownian rotation. We finally derive characteristic timescales of the motion that can be used to assess whether the diffusion limit is justified in a given situation...
Weak and strong field approximations and circular orbits of Kehagias-Sfetsos space-time
Dwornik, M; Gergely, L Á
2013-01-01
The Kehagias-Sfetsos asymptotically flat black hole and naked singularity solutions of Ho\\v{r}ava-Lifshitz gravity are investigated both in the weak-field and strong-field regimes. In the weak-field limit the gravitational field generated by the Kehagias-Sfetsos spherically symmetric solution is weaker then in the case of the Schwarzschild black hole of general relativity. In the strong-field regime naked singularities with $\\omega_{0} \\ll 1 $ display an unusual distance dependence: gravity becomes weaker when approaching the singularity. The stability of circular orbits is also analyzed. While in the black hole case the square of the angular momentum should be larger than a certain finite, non-zero minimal value, in the naked singularity case there are stable circular orbits for any non-zero value of the angular momentum. In this regime we prove the existence of an infimum of the allowed radii of circular orbits (corresponding to vanishing angular momentum).
STRONG CONVERGENCE OF APPROXIMATED SEQUENCES FOR NONEXPANSIVE MAPPINGS IN BANACH SPACES
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This paper studies the convergence of the sequence defined by x0∈C,xn+1=αnu+(1-αn)Txn,n=0,1,2,…, where 0 ≤αn ≤ 1, limn→∞αn = 0, ∑∞n=0 αn = ∞, and T is a nonexpansive mapping from a nonempty closed convex subset C of a Banach space X into itself. The iterative sequence {xn} converges strongly to a fixed point of T in the case when X is a uniformly convex Banach space with a uniformly Gateaux differentiable norm or a uniformly smooth Banach space only. The results presented in this paper extend and improve some recent results.
Existence of Multiagent Equilibria with Limited Agents
Bowling, M; 10.1613/jair.1332
2011-01-01
Multiagent learning is a necessary yet challenging problem as multiagent systems become more prevalent and environments become more dynamic. Much of the groundbreaking work in this area draws on notable results from game theory, in particular, the concept of Nash equilibria. Learners that directly learn an equilibrium obviously rely on their existence. Learners that instead seek to play optimally with respect to the other players also depend upon equilibria since equilibria are fixed points for learning. From another perspective, agents with limitations are real and common. These may be undesired physical limitations as well as self-imposed rational limitations, such as abstraction and approximation techniques, used to make learning tractable. This article explores the interactions of these two important concepts: equilibria and limitations in learning. We introduce the question of whether equilibria continue to exist when agents have limitations. We look at the general effects limitations can have on agent b...
Directory of Open Access Journals (Sweden)
Yun Wang
2016-01-01
Full Text Available Gamma Gaussian inverse Wishart cardinalized probability hypothesis density (GGIW-CPHD algorithm was always used to track group targets in the presence of cluttered measurements and missing detections. A multiple models GGIW-CPHD algorithm based on best-fitting Gaussian approximation method (BFG and strong tracking filter (STF is proposed aiming at the defect that the tracking error of GGIW-CPHD algorithm will increase when the group targets are maneuvering. The best-fitting Gaussian approximation method is proposed to implement the fusion of multiple models using the strong tracking filter to correct the predicted covariance matrix of the GGIW component. The corresponding likelihood functions are deduced to update the probability of multiple tracking models. From the simulation results we can see that the proposed tracking algorithm MM-GGIW-CPHD can effectively deal with the combination/spawning of groups and the tracking error of group targets in the maneuvering stage is decreased.
Prayogi, A.; Majidi, M. A.
2017-07-01
In condensed-matter physics, strongly-correlated systems refer to materials that exhibit variety of fascinating properties and ordered phases, depending on temperature, doping, and other factors. Such unique properties most notably arise due to strong electron-electron interactions, and in some cases due to interactions involving other quasiparticles as well. Electronic correlation effects are non-trivial that one may need a sufficiently accurate approximation technique with quite heavy computation, such as Quantum Monte-Carlo, in order to capture particular material properties arising from such effects. Meanwhile, less accurate techniques may come with lower numerical cost, but the ability to capture particular properties may highly depend on the choice of approximation. Among the many-body techniques derivable from Feynman diagrams, we aim to formulate algorithmic implementation of the Ladder Diagram approximation to capture the effects of electron-electron interactions. We wish to investigate how these correlation effects influence the temperature-dependent properties of strongly-correlated metals and semiconductors. As we are interested to study the temperature-dependent properties of the system, the Ladder diagram method needs to be applied in Matsubara frequency domain to obtain the self-consistent self-energy. However, at the end we would also need to compute the dynamical properties like density of states (DOS) and optical conductivity that are defined in the real frequency domain. For this purpose, we need to perform the analytic continuation procedure. At the end of this study, we will test the technique by observing the occurrence of metal-insulator transition in strongly-correlated metals, and renormalization of the band gap in strongly-correlated semiconductors.
Hvozd, Taras V; Kalyuzhnyi, Yurij V
2017-02-15
We have studied the phase behavior of polydisperse Yukawa hard-sphere fluid confined in random porous media using extension and combination of high temperature approximation and scaled particle theory. The porous media are represented by the matrix of randomly placed hard-sphere obstacles. Due to the confinement, polydispersity effects are substantially enhanced. At an intermediate degree of fluid polydispersity and low density of the matrix, we observe two-phase coexistence with two critical points, and cloud and shadow curves forming closed loops of ellipsoidal shape. With the increase of the matrix density and the constant degree of polydispersity, these two critical points merge and disappear, and at lower temperatures the system fractionates into three coexisting phases. A similar phase behavior was observed in the absence of the porous media caused, however, by the increase of the polydispersity.
高维Wiener sausage 的强逼近%Strong approximation of high dimensional Wiener sausage
Institute of Scientific and Technical Information of China (English)
王艳清
2011-01-01
本文研究了四维及四维以上的Wiener sausage的体积,得到它们可以由一维Brown运动强逼近.作为应用,推出了弱收敛和重对数率.%In this paper, we study the volume of Wiener sausage in Rd ford ≥ 4. We obtain that it can be strongly approximated by a one-dimensional standard Brownian motion. As an application, we give the weak convergence and laws of the iterated logarithm.
Network Connection Games with Disconnected Equilibria
Brandes, Ulrik; Nick, Bobo
2008-01-01
In this paper we extend a popular non-cooperative network creation game (NCG) to allow for disconnected equilibrium networks. There are n players, each is a vertex in a graph, and a strategy is a subset of players to build edges to. For each edge a player must pay a cost, and the utility is a trade-off between edge costs and shortest path lengths to all other players. We extend the model to a penalized game (PCG), for which we reduce the penalty counted towards the utility for a pair of disconnected players to a finite value. Our analysis concentrates on existence, structure, and cost of disconnected regular and strong Nash equilibria. Although the PCG is not a potential game, pure Nash equilibria always and pure strong equilibria very often exist. We provide tight conditions under which disconnected (strong) Nash equilibria can evolve. Components of these equilibria must be (strong) Nash equilibria of a smaller NCG. However, in contrast to the NCG, for almost all parameter values no tree is a stable componen...
Braided magnetic fields: equilibria, relaxation and heating
Pontin, D I; Russell, A J B; Hornig, G
2015-01-01
We examine the dynamics of magnetic flux tubes containing non-trivial field line braiding (or linkage), using mathematical and computational modelling. The key results obtained from recent modelling efforts are summarised, in the context of testable predictions for the laboratory. We discuss the existence of braided force-free equilibria, and demonstrate that for a field anchored at perfectly-conducting plates, these equilibria exist and contain current sheets whose thickness scales inversely with the braid complexity - as measured for example by the topological entropy. By contrast, for a periodic domain braided exact equilibria typically do not exist, while approximate equilibria contain thin current sheets. In the presence of resistivity, reconnection is triggered at the current sheets and a turbulent relaxation ensues. We discuss the properties of this relaxation, and in particular the existence of constraints that may mean that the final state is not the linear force-free field predicted by Taylor's hypo...
Mathematical Model for Multicomponent Adsorption Equilibria Using Only Pure Component Data
DEFF Research Database (Denmark)
Marcussen, Lis
2000-01-01
A mathematical model for nonideal adsorption equilibria in multicomponent mixtures is developed. It is applied with good results for pure substances and for prediction of strongly nonideal multicomponent equilibria using only pure component data. The model accounts for adsorbent...
Milošević, D. B.; Becker, W.
2016-06-01
A theory of above-threshold ionization of atoms by a strong laser field is formulated. Two versions of the strong-field approximation (SFA) are considered, the direct SFA and the improved SFA, which do not and do, respectively, take into account rescattering of the freed electron off the parent ion. The atomic bound state is included in two different ways: as an expansion in terms of Slater-type orbitals or as an asymptotic wave function. Even though we are using the single-active-electron approximation, multielectron effects are taken into account in two ways: by a proper choice of the ground state and by an adequate definition of the ionization rate. For the case of the asymptotic bound-state wave functions, using the saddle-point method, a simple expression for the T -matrix element is derived for both the direct and the improved SFA. The theory is applied to ionization by a bicircular field, which consists of two coplanar counterrotating circularly polarized components with frequencies that are integer multiples of a fundamental frequency ω . Special emphasis is on the ω -2 ω case. In this case, the threefold rotational symmetry of the field carries over to the velocity map of the liberated electrons, for both the direct and the improved SFA. The results obtained are analyzed in detail using the quantum-orbit formalism, which gives good physical insight into the above-threshold ionization process. For this purpose, a specific classification of the saddle-point solutions is introduced for both the backward-scattered and the forward-scattered electrons. The high-energy backward-scattering quantum orbits are similar to those discovered for high-order harmonic generation. The short forward-scattering quantum orbits for a bicircular field are similar to those of a linearly polarized field. The conclusion is that these orbits are universal, i.e., they do not depend much on the shape of the laser field.
Vanne, Y V; Saenz, Alejandro; Vanne, Yulian V.
2006-01-01
In recent articles [Mishima et al., Phys. Rev. A, 66, 033401(2002); Chao, Phys. Rev. A, 72, 053414 (2005)] it was proposed to use the residue theorem for the exact calculation of the transition amplitude describing strong-field ionization of atomic systems within Keldysh theory. This should avoid the necessity to apply the method of steepest descent (saddle-point approximation). Comparing the results of both approaches for atomic hydrogen a difference by a factor of 2 was found for the 1s, and an even more drastic deviation for the 2s state. Thus it was concluded that the use of the saddle-point approximation is problematic. In this work the deviations are explained and it is shown that the previous conclusion is based on an unjustified neglect of an important contribution occurring in the application of the residue theorem. Furthermore, the applicability of the method of steepest descent for the ionization of Rydberg states is discussed and an improvement of the standard result is suggested that successfully...
Energy Technology Data Exchange (ETDEWEB)
Cao, X [Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen, 361005 (China); You, J Q; Nori, F [Advanced Science Institute, RIKEN, Wako-shi 351-0198 (Japan); Zheng, H, E-mail: xfcao@xmu.edu.cn [Department of Physics, Shanghai Jiao Tong University, Shanghai 200240 (China)
2011-07-15
We investigate the spontaneous emission (SE) spectrum of a qubit in a lossy resonant cavity. We use neither the rotating-wave approximation nor the Markov approximation. For the weak-coupling case, the SE spectrum of the qubit is a single peak, with its location depending on the spectral density of the qubit environment. Then, the asymmetry (of the location and heights of the two peaks) of the two SE peaks (which are related to the vacuum Rabi splitting) changes as the qubit-cavity coupling increases. Explicitly, for a qubit in a low-frequency intrinsic bath, the height asymmetry of the splitting peaks is enhanced as the qubit-cavity coupling strength increases. However, for a qubit in an Ohmic bath, the height asymmetry of the spectral peaks is inverted compared to the low-frequency bath case. With further increasing the qubit-cavity coupling to the ultra-strong regime, the height asymmetry of the left and right peaks is slightly inverted, which is consistent with the corresponding case of a low-frequency bath. This inversion of the asymmetry arises from the competition between the Ohmic bath and the cavity bath. Therefore, after considering the anti-rotating terms, our results explicitly show how the height asymmetry in the SE spectrum peaks depends on the qubit-cavity coupling and the type of intrinsic noise experienced by the qubit.
Adsorption equilibria of dimethylnaphthalene isomers
Energy Technology Data Exchange (ETDEWEB)
Rota, R.; Morbidelli, M. [Politecnico di Milano (Italy). Dipt. di Chimica Fisica Applicata; Rombi, E.; Monaci, R.; Ferino, I.; Solinas, V. [Univ. di Cagliari (Italy). Dipt. di Scienze Chimiche
1996-01-01
Commercial sources of DMNs are the aromatic petroleum fraction of the appropriate boiling range and the coal liquefaction products. Adsorption processes for separating mixtures of dimethylnaphthalene (DMN) isomers are of potential interest for the production of 2,6-DMN. In this work, the adsorption equilibria of liquid mixtures of DMN isomers on zeolites have been investigated experimentally. The separation factors between the various isomers have been found to depend strongly on the composition of the fluid phase. A suitable equilibrium model, based on the adsorbed solution theory, has been developed to describe the multicomponent adsorption equilibria in the entire range of interest. Its performance has been tested using binary and ternary equilibrium data.
Phase Equilibria Diagrams Database
SRD 31 NIST/ACerS Phase Equilibria Diagrams Database (PC database for purchase) The Phase Equilibria Diagrams Database contains commentaries and more than 21,000 diagrams for non-organic systems, including those published in all 21 hard-copy volumes produced as part of the ACerS-NIST Phase Equilibria Diagrams Program (formerly titled Phase Diagrams for Ceramists): Volumes I through XIV (blue books); Annuals 91, 92, 93; High Tc Superconductors I & II; Zirconium & Zirconia Systems; and Electronic Ceramics I. Materials covered include oxides as well as non-oxide systems such as chalcogenides and pnictides, phosphates, salt systems, and mixed systems of these classes.
Learning efficient correlated equilibria
Borowski, Holly P.
2014-12-15
The majority of distributed learning literature focuses on convergence to Nash equilibria. Correlated equilibria, on the other hand, can often characterize more efficient collective behavior than even the best Nash equilibrium. However, there are no existing distributed learning algorithms that converge to specific correlated equilibria. In this paper, we provide one such algorithm which guarantees that the agents\\' collective joint strategy will constitute an efficient correlated equilibrium with high probability. The key to attaining efficient correlated behavior through distributed learning involves incorporating a common random signal into the learning environment.
Energy Technology Data Exchange (ETDEWEB)
Jemai, M
2004-07-01
In the present thesis we have applied the self consistent random phase approximation (SCRPA) to the Hubbard model with a small number of sites (a chain of 2, 4, 6,... sites). Earlier SCRPA had produced very good results in other models like the pairing model of Richardson. It was therefore interesting to see what kind of results the method is able to produce in the case of a more complex model like the Hubbard model. To our great satisfaction the case of two sites with two electrons (half-filling) is solved exactly by the SCRPA. This may seem a little trivial but the fact is that other respectable approximations like 'GW' or the approach with the Gutzwiller wave function yield results still far from exact. With this promising starting point, the case of 6 sites at half filling was considered next. For that case, evidently, SCRPA does not any longer give exact results. However, they are still excellent for a wide range of values of the coupling constant U, covering for instance the phase transition region towards a state with non zero magnetisation. We consider this as a good success of the theory. Non the less the case of 4 sites (a plaquette), as indeed all cases with 4n sites at half filling, turned out to have a problem because of degeneracies at the Hartree Fock level. A generalisation of the present method, including in addition to the pairs, quadruples of Fermions operators (called second RPA) is proposed to also include exactly the plaquette case in our approach. This is therefore a very interesting perspective of the present work. (author)
Energy Technology Data Exchange (ETDEWEB)
Schaefer, B.; Lambert, S.M.; Song, Y.; Prausnitz, J.M.
1994-10-01
Goal of this work is the extension of a Perturbed-Hard-Sphere-Chain equation of state (PHSC EOS) to systems containing strong polar components. Three different types of association models (ten Brinke/Karasz, SAFI, modified Veytsman) were used to calculate the contribution of specific interactions like hydrogen bonding to thermodynamic quantities. Pure component parameters obtained from regression of temperature dependent density and vapor pressure data allow the prediction of VLE and LLE data. The results of simple fluids and polymer solutions were compared with experimental data. The SAFT and the modified Veytsman extension give similar results for pure fluids and mixtures with components of similar segment size. Differences increase with increasing difference of segment size.
Computational Aspects of Equilibria
Yannakakis, Mihalis
Equilibria play a central role in game theory and economics. They characterize the possible outcomes in the interaction of rational, optimizing agents: In a game between rational players that want to optimize their payoffs, the only solutions in which no player has any incentive to switch his strategy are the Nash equilibria. Price equilibria in markets give the prices that allow the market to clear (demand matches supply) while the traders optimize their preferences (utilities). Fundamental theorems of Nash [34] and Arrow-Debreu [2] established the existence of the respective equilibria (under suitable conditions in the market case). The proofs in both cases use a fixed point theorem (relying ultimately on a compactness argument), and are non-constructive, i.e., do not yield an algorithm for constructing an equilibrium. We would clearly like to compute these predicted outcomes. This has led to extensive research since the 60’s in the game theory and mathematical economics literature, with the development of several methods for computation of equilibria, and more generally fixed points. More recently, equilibria problems have been studied intensively in the computer science community, from the point of view of modern computation theory. While we still do not know definitely whether equilibria can be computed in general efficiently or not, these investigations have led to a better understanding of the computational complexity of equilibria, the various issues involved, and the relationship with other open problems in computation. In this talk we will discuss some of these aspects and our current understanding of the relevant problems. We outline below the main points and explain some of the related issues.
Olano, C. A.
2009-11-01
Context: Using certain simplifications, Kompaneets derived a partial differential equation that states the local geometrical and kinematical conditions that each surface element of a shock wave, created by a point blast in a stratified gaseous medium, must satisfy. Kompaneets could solve his equation analytically for the case of a wave propagating in an exponentially stratified medium, obtaining the form of the shock front at progressive evolutionary stages. Complete analytical solutions of the Kompaneets equation for shock wave motion in further plane-parallel stratified media were not found, except for radially stratified media. Aims: We aim to analytically solve the Kompaneets equation for the motion of a shock wave in different plane-parallel stratified media that can reflect a wide variety of astrophysical contexts. We were particularly interested in solving the Kompaneets equation for a strong explosion in the interstellar medium of the Galactic disk, in which, due to intense winds and explosions of stars, gigantic gaseous structures known as superbubbles and supershells are formed. Methods: Using the Kompaneets approximation, we derived a pair of equations that we call adapted Kompaneets equations, that govern the propagation of a shock wave in a stratified medium and that permit us to obtain solutions in parametric form. The solutions provided by the system of adapted Kompaneets equations are equivalent to those of the Kompaneets equation. We solved the adapted Kompaneets equations for shock wave propagation in a generic stratified medium by means of a power-series method. Results: Using the series solution for a shock wave in a generic medium, we obtained the series solutions for four specific media whose respective density distributions in the direction perpendicular to the stratification plane are of an exponential, power-law type (one with exponent k=-1 and the other with k =-2) and a quadratic hyperbolic-secant. From these series solutions, we deduced
Instability of Magnetic Equilibria in Barotropic Stars
Mitchell, J P; Reisenegger, A; Spruit, H; Valdivia, J A; Langer, N
2014-01-01
In stably stratified stars, numerical magneto-hydrodynamics simulations have shown that arbitrary initial magnetic fields evolve into stable equilibrium configurations, usually containing nearly axisymmetric, linked poloidal and toroidal fields that stabilize each other. In this work, we test the hypothesis that stable stratification is a requirement for the existence of such stable equilibria. For this purpose, we follow numerically the evolution of magnetic fields in barotropic (and thus neutrally stable) stars, starting from two different types of initial conditions, namely random disordered magnetic fields, as well as linked poloidal-toroidal configurations resembling the previously found equilibria. With many trials, we always find a decay of the magnetic field over a few Alfv\\'en times, never a stable equilibrium. This strongly suggests that there are no stable equilibria in barotropic stars, thus clearly invalidating the assumption of barotropic equations of state often imposed on the search of magneti...
MHD equilibria with diamagnetic effects
Tessarotto, M.; Zorat, R.; Johnson, J. L.; White, R. B.
1997-11-01
An outstanding issue in magnetic confinement is the establishment of MHD equilibria with enhanced flow shear profiles for which turbulence (and transport) may be locally effectively suppressed or at least substantially reduced with respect to standard weak turbulence models. Strong flows develop in the presence of equilibrium E× B-drifts produced by a strong radial electric field, as well as due to diamagnetic contributions produced by steep equilibrium radial profiles of number density, temperature and the flow velocity itself. In the framework of a kinetic description, this generally requires the construction of guiding-center variables correct to second order in the relevant expansion parameter. For this purpose, the Lagrangian approach developed recently by Tessarotto et al. [1] is adopted. In this paper the conditions of existence of such equilibria are analyzed and their basic physical properties are investigated in detail. 1 - M. Pozzo, M. Tessarotto and R. Zorat, in Theory of fusion Plasmas, E.Sindoni et al. eds. (Societá Italiana di Fisica, Editrice Compositori, Bologna, 1996), p.295.
Directory of Open Access Journals (Sweden)
Yan Tang
2013-01-01
Full Text Available Suppose that C is a nonempty closed convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. A viscosity iterative process is constructed in this paper. A strong convergence theorem is proved for a common element of the set of fixed points of a finite family of pseudocontractive mappings and the set of solutions of a finite family of monotone mappings. And the common element is the unique solution of certain variational inequality. The results presented in this paper extend most of the results that have been proposed for this class of nonlinear mappings.
Galaktionov, E. V.; Galaktionova, N. E.; Tropp, E. A.
2016-12-01
Variational formulations of the problems of sessile and pendent drops are given taking into account the force of gravity in the axially symmetric case. Approximate expressions that describe the surface profiles of these drops by the asymptotic method for small Bond numbers have been obtained by the linearization method in the case of strong wetting.
Institute of Scientific and Technical Information of China (English)
Feng Jing-Jing; Zhang Qi-Chang; Wang Wei
2011-01-01
In this paper,the extended Pad6 approximant is used to construct the homoclinic and the heteroclinic trajectories in nonlinear dynamical systems that are asymmetric at origin. Meanwhile,the conservative system,the autonomous systern,and the nonautonomous system equations with quadratic and cubic nonlinearities are considered. The disturbanceparameter εis not limited to being small. The ranges of the values of the linear and the nonlinear term parameters,which are variables,can be determined when the boundary values are satisfied. New conditions for the potentiality and the convergence are posed to make it possible to solve the boundary-value problems formulated for the orbitals and to evaluate the initial amplitude values.
Resurrecting Equilibria Through Cycles
DEFF Research Database (Denmark)
Barnett, Richard C.; Bhattacharya, Joydeep; Bunzel, Helle
In an overlapping generations model, momentary equilibria are defined as points that lie on the intergenerational offer curve, i.e., they satisfy agents' optimality conditions and market clearing at any date. However, some dynamic sequences commencing from such points may not be considered valid ...
Equilibria with Coordination Failures
Herings, P.J.J.; van der Laan, G.; Talman, A.J.J.
2004-01-01
This paper extends the recent literature on equilibria with coordination failures to arbitrary convex sets of admissible prices.We introduce a new equilibrium concept, called quantity constrained equilibrium (QCE), giving a uni.ed treatment to all cases considered in the literature so far.At a QCE
Shambayati, Shervin
2001-01-01
In order to evaluate performance of strong channel codes in presence of imperfect carrier phase tracking for residual carrier BPSK modulation in this paper an approximate 'brick wall' model is developed which is independent of the channel code type for high data rates. It is shown that this approximation is reasonably accurate (less than 0.7dB for low FERs for (1784,1/6) code and less than 0.35dB for low FERs for (5920,1/6) code). Based on the approximation's accuracy, it is concluded that the effects of imperfect carrier tracking are more or less independent of the channel code type for strong channel codes. Therefore, the advantage that one strong channel code has over another with perfect carrier tracking translates to nearly the same advantage under imperfect carrier tracking conditions. This will allow the link designers to incorporate projected channel code performance of strong channel codes into their design tables without worrying about their behavior in the face of imperfect carrier phase tracking.
Phase equilibria in model surfactants forming Langmuir monolayers.
Ramírez, E; Santana, A; Cruz, A; López, G E
2007-12-14
The study of Langmuir monolayers has generated the attention of researchers because of their unique properties and their not well understood phase equilibrium. These monolayers exhibit interesting phase diagrams where the unusual liquid-liquid equilibrium can be observed for a single component monolayer. Monte Carlo computer simulations in the virtual Gibbs ensemble were used to obtain the phase diagram of Langmuir monolayers. The liquid-vapor and liquid-liquid phase equilibria were considered by constructing the Cailletet-Mathias phase diagrams. By using the Ising model and the rectilinear approximations the identification of the critical properties for both equilibria was determined. These critical parameters were calculated as a function of the strength of the interaction between the surfactant molecules and the aqueous subphase. As a result, we have identified the coexistence between a liquid expanded state (LES)-vapor and the liquid condensed state-LES, in agreement with experimental and theoretical evidence in the literature. We obtained a clear separation of phases and a strong dependence on the strength of the solvent used. Namely, as the interaction between the solvent and the head of the surfactant increases, the critical properties also increase. Equilibrium states were characterized by computing thermodynamic quantities as a function of temperature and solvent strength.
Equilibria of Generalized Cut and Choose Protocols
DEFF Research Database (Denmark)
Branzei, Simina; Caragiannis, Ioannis; Kurokawa, David
Classic cake cutting protocols — which fairly allocate a divisible good among agents with heterogeneous preferences — are susceptible to manipulation. Do their strategic outcomes still guarantee fairness? To answer this question we adopt a novel algo rithmic approach, proposing a concrete computa...... the stronger fairness notion of envy-freeness. Finally, we show that under an obliviousness restriction, which still allows the computation of approximately envy-free allocations, GCC protocols are guaranteed to have exact subgame perfect Nash equilibria...
Instability of magnetic equilibria in barotropic stars
Mitchell, J. P.; Braithwaite, J.; Reisenegger, A.; Spruit, H.; Valdivia, J. A.; Langer, N.
2015-02-01
In stably stratified stars, numerical magnetohydrodynamics simulations have shown that arbitrary initial magnetic fields evolve into stable equilibrium configurations, usually containing nearly axisymmetric, linked poloidal and toroidal fields that stabilize each other. In this work, we test the hypothesis that stable stratification is a requirement for the existence of such stable equilibria. For this purpose, we follow numerically the evolution of magnetic fields in barotropic (and thus neutrally stable) stars, starting from two different types of initial conditions, namely random disordered magnetic fields, as well as linked poloidal-toroidal configurations resembling the previously found equilibria. With many trials, we always find a decay of the magnetic field over a few Alfvén times, never a stable equilibrium. This strongly suggests that there are no stable equilibria in barotropic stars, thus clearly invalidating the assumption of barotropic equations of state often imposed on the search of magnetic equilibria. It also supports the hypothesis that, as dissipative processes erode the stable stratification, they might destabilize previously stable magnetic field configurations, leading to their decay.
The freedom to choose neutron star magnetic field equilibria
Glampedakis, Kostas
2016-01-01
Our ability to interpret and glean useful information from the large body of observations of strongly magnetised neutron stars rests largely on our theoretical understanding of magnetic field equilibria. We answer the following question: is one free to arbitrarily prescribe magnetic equilibria such that fluid degrees of freedom can balance the equilibrium equations? We examine this question for various models for neutron star matter; from the simplest single-fluid barotrope to more realistic non-barotropic multifluid models with superfluid/superconducting components, muons and entropy. We do this for both axi- and non-axisymmetric equilibria, and in Newtonian gravity and general relativity. We show that, in axisymmetry, the most realistic model allows complete freedom in choosing a magnetic field equilibrium whereas non-axisymmetric equilibria are never completely arbitrary.
Adsorption analysis equilibria and kinetics
Do, Duong D
1998-01-01
This book covers topics of equilibria and kinetics of adsorption in porous media. Fundamental equilibria and kinetics are dealt with for homogeneous as well as heterogeneous particles. Five chapters of the book deal with equilibria and eight chapters deal with kinetics. Single component as well as multicomponent systems are discussed. In kinetics analysis, we deal with the various mass transport processes and their interactions inside a porous particle. Conventional approaches as well as the new approach using Maxwell-Stefan equations are presented. Various methods to measure diffusivity, such
Quantum equilibria for macroscopic systems
Energy Technology Data Exchange (ETDEWEB)
Grib, A [Department of Theoretical Physics and Astronomy, Russian State Pedagogical University, St. Petersburg (Russian Federation); Khrennikov, A [Centre for Mathematical Modelling in Physics and Cognitive Sciences Vaexjoe University (Sweden); Parfionov, G [Department of Mathematics, St. Petersburg State University of Economics and Finances (Russian Federation); Starkov, K [Department of Mathematics, St. Petersburg State University of Economics and Finances (Russian Federation)
2006-06-30
Nash equilibria are found for some quantum games with particles with spin-1/2 for which two spin projections on different directions in space are measured. Examples of macroscopic games with the same equilibria are given. Mixed strategies for participants of these games are calculated using probability amplitudes according to the rules of quantum mechanics in spite of the macroscopic nature of the game and absence of Planck's constant. A possible role of quantum logical lattices for the existence of macroscopic quantum equilibria is discussed. Some examples for spin-1 cases are also considered.
Tokamak-like Vlasov equilibria
Tasso, H
2014-01-01
Vlasov equilibria of axisymmetric plasmas with vacuum toroidal magnetic field can be reduced, up to a selection of ions and electrons distributions functions, to a Grad-Shafranov-like equation. Quasineutrality narrow the choice of the distributions functions. In contrast to two-dimensional translationally symmetric equilibria whose electron distribution function consists of a displaced Maxwellian, the toroidal equilibria need deformed Maxwellians. In order to be able to carry through the calculations, this deformation is produced by means of either a Heaviside step function or an exponential function. The resulting Grad-Shafranov-like equations are established explicitly.
Institutions, Equilibria and Efficiency
DEFF Research Database (Denmark)
Competition and efficiency is at the core of economic theory. This volume collects papers of leading scholars, which extend the conventional general equilibrium model in important ways. Efficiency and price regulation are studied when markets are incomplete and existence of equilibria...... membership are evaluated. Core equivalence is shown for bargaining economies. The theory of risk aversion is extended and the relation between risk taking and wealth is experimentally investigated. Other topics include: determinacy in OLG with cash-in-advance constraints, income distribution and democracy...... in such settings is proven under very general preference assumptions. The model is extended to include geographical location choice, a commodity space incorporating manufacturing imprecision and preferences for club-membership, schools and firms. Inefficiencies arising from household externalities or group...
Protolytic equilibria of bromazepam
Directory of Open Access Journals (Sweden)
DUSAN M. SLADIC
2002-03-01
Full Text Available The protolytic equilibria of bromazepam, an ampholyte sparingly soluble in water, in homogeneous and heterogeneous systems were studied in the pH range 014 at 25 ?C and at ionic strength of 0.1 mol/dm3 (NaCl. On the basis of 13C-NMR spectra, the protonation site was predicted in acidic media the pyridine nitrogen of bormazepam is protonated. The acidity constants of bromazepam were determined spectrophotometrically (pKa1 2.83 and pKa2 11.60 and potentiometrically (pKa1 2.99. In the heterogeneous system the following equilibrium constants were determined: Ks0 = [HA] (pKs0 3.44, Ks1 = [H2A+]/[H3O+] (pKs1 0.61, and Ks2 = [A-][H3O+] (pKs2 15.04.
Information Anatomy of Stochastic Equilibria
Directory of Open Access Journals (Sweden)
Sarah Marzen
2014-08-01
Full Text Available A stochastic nonlinear dynamical system generates information, as measured by its entropy rate. Some—the ephemeral information—is dissipated and some—the bound information—is actively stored and so affects future behavior. We derive analytic expressions for the ephemeral and bound information in the limit of infinitesimal time discretization for two classical systems that exhibit dynamical equilibria: first-order Langevin equations (i where the drift is the gradient of an analytic potential function and the diffusion matrix is invertible and (ii with a linear drift term (Ornstein–Uhlenbeck, but a noninvertible diffusion matrix. In both cases, the bound information is sensitive to the drift and diffusion, while the ephemeral information is sensitive only to the diffusion matrix and not to the drift. Notably, this information anatomy changes discontinuously as any of the diffusion coefficients vanishes, indicating that it is very sensitive to the noise structure. We then calculate the information anatomy of the stochastic cusp catastrophe and of particles diffusing in a heat bath in the overdamped limit, both examples of stochastic gradient descent on a potential landscape. Finally, we use our methods to calculate and compare approximations for the time-local predictive information for adaptive agents.
Social Interactions under Incomplete Information: Games, Equilibria, and Expectations
Yang, Chao
Interactions under Incomplete Information", is an application of the first chapter to censored outcomes, corresponding to the situation when agents" behaviors are subjected to some binding restrictions. In an interesting empirical analysis for property tax rates set by North Carolina municipal governments, it is found that there is a significant positive correlation among near-by municipalities. Additionally, some private information about its own residents is used by a municipal government to predict others' tax rates, which enriches current empirical work about tax competition. The third chapter, "Social Interactions under Incomplete Information with Multiple Equilibria", extends the first chapter by investigating effective estimation methods when the condition for a unique equilibrium may not be satisfied. With multiple equilibria, the previous model is incomplete due to the unobservable equilibrium selection. Neither conventional likelihoods nor moment conditions can be used to estimate parameters without further specifications. Although there are some solutions to this issue in the current literature, they are based on strong assumptions such as agents with the same observable characteristics play the same strategy. This paper relaxes those assumptions and extends the all-solution method used to estimate discrete choice games to a setting with both discrete and continuous choices, bounded and unbounded outcomes, and a general form of incomplete information, where the existence of a pure strategy equilibrium has been an open question for a long time. By the use of differential topology and functional analysis, it is found that when all exogenous characteristics are public information, there are a finite number of equilibria. With privately known exogenous characteristics, the equilbria can be represented by a compact set in a Banach space and be approximated by a finite set. As a result, a finite-state probability mass function can be used to specify a probability measure
On Uniqueness of coalitional equilibria
Finus, M.; Mouche, van P.H.M.; Rundshagen, B.
2014-01-01
For the so-called "new approach" of coalitio formation it is important that coalitional equilibria are unique. Uniqueness comes down to existene and to semi-uniqueness, i.e.\\\\that there exists at most one equilibrium. Although conditions for existence are not problematic, conditions for semi-uniquen
Correct Representation of Conformational Equilibria.
Fulop, F.; And Others
1983-01-01
In representing conformational equilibria of compounds having only one chiral center, erroneous formulas showing different antipodes on the two sides of the equilibrium are rare. In contrast, with compounds having two or more chiral centers especially with saturated heterocycles, this erroneous representation occurs frequently in the chemical…
DEFF Research Database (Denmark)
Marchukov, O. V.; Eriksen, E. H.; Midtgaard, J. M.
2016-01-01
-trivial geometric factors that depend solely on the geometry of the confinement through the single-particle eigenstates of the external potential. To obtain accurate effective Hamiltonians to describe such systems one needs to be able to compute these geometric factors with high precision which is difficult due...... to the computational complexity of the high-dimensional integrals involved. An approach using the local density approximation would therefore be a most welcome approximation due to its simplicity. Here we assess the accuracy of the local density approximation by going beyond the simple harmonic oscillator that has...
Equilibria in Load Balancing Games
Institute of Scientific and Technical Information of China (English)
Bo Chen
2009-01-01
A Nash equilibrium (NE) in a multi-agent game is a strategy profile that is resilient to unilateral deviations.A strong Nash equilibrium (SE) is one that is stable against coordinated deviations of any coalition.We show that,in the load balancing games,NEs approximate SEs in the sense that the benefit of each member of any coalition from coordinated deviations is well limited.Furthermore,we show that an easily recognizable special subset of NEs exhibit even better approximation of SEs.
Equilibria, Fixed Points, and Complexity Classes
Yannakakis, Mihalis
2008-01-01
Many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind. Examples include Nash equilibria in games; market equilibria; computing optimal strategies and the values of competitive games (stochastic and other games); stable configurations of neural networks; analysing basic stochastic models for evolution like branching processes and for language like stochastic context-free grammars; and models that incorporate the basic primitives of probability and recursion like recursive Markov chains. It is not known whether these problems can be solved in polynomial time. There are certain common computational principles underlying different types of equilibria, which are captured by the complexity classes PLS, PPAD, and FIXP. Representative complete problems for these classes are respectively, pure Nash equilibria in games where they are guaranteed to exist, (mixed) Nash equilibria in 2-player normal form games, and (mixed) Nash equilibria in normal form games with 3 (or ...
Phase equilibria basic principles, applications, experimental techniques
Reisman, Arnold
2013-01-01
Phase Equilibria: Basic Principles, Applications, Experimental Techniques presents an analytical treatment in the study of the theories and principles of phase equilibria. The book is organized to afford a deep and thorough understanding of such subjects as the method of species model systems; condensed phase-vapor phase equilibria and vapor transport reactions; zone refining techniques; and nonstoichiometry. Physicists, physical chemists, engineers, and materials scientists will find the book a good reference material.
The freedom to choose neutron star magnetic field equilibria: Table 1.
Glampedakis, Kostas; Lasky, Paul D.
2016-12-01
Our ability to interpret and glean useful information from the large body of observations of strongly magnetized neutron stars rests largely on our theoretical understanding of magnetic field equilibria. We answer the following question: is one free to arbitrarily prescribe magnetic equilibria such that fluid degrees of freedom can balance the equilibrium equations? We examine this question for various models for neutron star matter; from the simplest single-fluid barotrope to more realistic non-barotropic multifluid models with superfluid/superconducting components, muons and entropy. We do this for both axi- and non-axisymmetric equilibria, and in Newtonian gravity and general relativity. We show that, in axisymmetry, the most realistic model allows complete freedom in choosing a magnetic field equilibrium whereas non-axisymmetric equilibria are never completely arbitrary.
Sentic, Stipo; Sessions, Sharon
2012-10-01
In the tropics, gravity waves quickly redistribute buoyancy anomalies, which leads to approximately weak temperature gradients (WTG) in the horizontal. In our cloud resolving model (CRM), the WTG approximation is enforced by relaxing potential temperature perturbations to a reference profile which represents the mean state of the atmosphere. To obtain reference profiles, the model is run in a non-WTG mode until radiative convective equilibrium (RCE). RCE vertical profiles of temperature and moisture are then used as reference profiles for WTG simulations. Continuing the work of Sessions et al (2010), we investigate the sensitivity of multiple equilibria in a CRM to changes in sea surface temperatures (SST). Multiple equilibria refers to a precipitating or non-precipitating steady state under identical forcing conditions. Specifically, we run RCE simulations for different SSTs to generate reference profiles representing different large scale environments for WTG simulations. We then perform WTG experiments for each SST with varying surface wind speeds. The model domain is initialized either with a completely dry troposphere, or with a RCE moisture profile. We find that the range of wind speeds maintaining both a dry and a precipitating steady state is strongly dependent on SST.
Phase Equilibria of Stored Chemical Energy Reactants.
1984-07-25
The reaction of lithium aluminum alloy with water at high temperature is considered in terms of phase equilibria in the system Li-A1-0-H. A...thermodynamic analysis of the system reveals the potential importance of lithium hydride as a reaction product. Major needs for experimental phase equilibria data
Inefficiency of Nash Equilibria. I
1982-03-12
continuously for U’ near csEA a’ This also shows that for il close to , D6?’)(X) fl (IW’, f ) - * for a a hence we may assume U0 open.all * 6 A A Furthermore...34 Journal of Economic Theory 22 (1980), 363-376. 14] P. Dubey, A. as-Colell and M. Shubik, "Efficiency Properties of Strategic Market Games: An...Axiomatic Approach," Journal of Economic Theory 22 (1980), 339-362. [5] P. Dubey and J. D. Rogsvski, "Inefficiency of Nash Equilibria: II," forthcoming
Motion Control along Relative Equilibria
DEFF Research Database (Denmark)
Nordkvist, Nikolaj
2008-01-01
The subject of this thesis is control of mechanical systems as they evolve along the steady motions called relative equilibria. These trajectories are of interest in theory and applications and have the characterizing property that the system's body-fixed velocity is constant. For example, constant...... on a Lie group is locally controllable along a relative equilibrium. These conditions subsume the well-known local controllability conditions for equilibrium points. Second, for systems that have fewer controls than degrees of freedom, we present a novel algorithm to control simple mechanical control...
Comparison of electron drift waves in numerical and analytical tokamak equilibria
Energy Technology Data Exchange (ETDEWEB)
Rafiq, T; Anderson, J; Persson, M [Department of Electromagnetics and Euratom/VR Association, Chalmers University of Technology, S-41296 Goeteborg (Sweden)
2004-01-01
In this paper, we demonstrate the importance of the details of the equilibria on the stability of electron drift waves. A comparison of electrostatic electron drift waves in numerical and analytical tokamak equilibria is presented in fully three-dimensional circular and non-circular tokamaks. The numerical equilibria are obtained using the variational moments equilibrium code and the analytical equilibria used is the generalized s-alpha model. An eigenvalue equation for the model is derived using the ballooning mode formalism and solved numerically using a standard shooting technique. The stability and the localization of the electron drift wave is found to be strongly dependent on the local shear of the magnetic field. Large values of the local shear are found to be stabilizing. A disagreement in the results is found between analytical and numerical equilibria at aspect ratios of typical tokamaks, suggesting that the latter approach should be used in the transport calculations. The effects of the local shaping of the magnetic surfaces are complicated and can be both stabilizing and destabilizing, depending on the details of the equilibria.
Solution influence on biomolecular equilibria - Nucleic acid base associations
Pohorille, A.; Pratt, L. R.; Burt, S. K.; Macelroy, R. D.
1984-01-01
Various attempts to construct an understanding of the influence of solution environment on biomolecular equilibria at the molecular level using computer simulation are discussed. First, the application of the formal statistical thermodynamic program for investigating biomolecular equilibria in solution is presented, addressing modeling and conceptual simplications such as perturbative methods, long-range interaction approximations, surface thermodynamics, and hydration shell. Then, Monte Carlo calculations on the associations of nucleic acid bases in both polar and nonpolar solvents such as water and carbon tetrachloride are carried out. The solvent contribution to the enthalpy of base association is positive (destabilizing) in both polar and nonpolar solvents while negative enthalpies for stacked complexes are obtained only when the solute-solute in vacuo energy is added to the total energy. The release upon association of solvent molecules from the first hydration layer around a solute to the bulk is accompanied by an increase in solute-solvent energy and decrease in solvent-solvent energy. The techniques presented are expectd to displace less molecular and more heuristic modeling of biomolecular equilibria in solution.
On the topological stability of magnetostatic equilibria
Tsinganos, K. C.; Rosner, R.; Distler, J.
1984-01-01
The topological stability of MHD equilibria is investigated by exploring the formal analogy, in the ideal MHD limit, between the topology of magnetic lines of force in coordinate space and the topology of integral surfaces of one- and two-dimensional Hamiltonian systems in phase space. It is demonstrated that in an astrophysical setting, symmetric magnetostatic equilibria satisfying the ideal MHD equations are exceptional. The principal result of the study is that previous infinitesimal perturbation theory calculations can be generalized to include finite-amplitude and symmetry-breaking effects. The effect of the ergodicity of perturbed symmetric equilibria on heat dispersal in magnetically dominated plasmas is discussed.
Equilibria in Dynamic Selfish Routing
Anshelevich, Elliot; Ukkusuri, Satish
In both transportation and communication networks we are faced with “selfish flows”, where every agent sending flow over the network desires to get it to its destination as soon as possible. Such flows have been well studied in time-invariant networks in the last few years. A key observation that must be taken into account in defining and studying selfish flow, however, is that a flow can take a non-negligible amount of time to travel across the network from the source to destination, and that network states like traffic load and congestion can vary during this period. Such flows are called dynamic flows (a.k.a. flows over time). This variation in network state as the flow progresses through the network results in the fundamentally different and significantly more complex nature of dynamic flow equilibria, as compared to those defined in static network settings.
Inefficient equilibria in transition economy
Directory of Open Access Journals (Sweden)
Sergei Guriev
1999-01-01
Full Text Available The paper studies a general equilibrium in an economy where all market participants face a bid-ask spread. The spread may be caused by indirect business taxes, middlemen rent-seeking, delays in payments or liquidity constraints or price uncertainty. Wherever it comes from the spread causes inefficiency of the market equilibrium. We discuss some institutions that can decrease the inefficiency. One is second currency (barter exchange in the inter-firm transactions. It is shown that the general equilibrium in an economy with second currency is effective though is still different from Arrow–Debreu equilibrium. Another solution can be introduction of mutual trade credit. In the economy with trade credit there are multiple equilibria that are more efficient than original bid-ask spread but still not as efficient as Arrow–Debreu one, too. The implications for firms' integration and applicability to Russian economy are discussed.
Symmetry transforms for ideal magnetohydrodynamics equilibria.
Bogoyavlenskij, Oleg I
2002-11-01
A method for constructing ideal magnetohydrodynamics (MHD) equilibria is introduced. The method consists of the application of symmetry transforms to any known MHD equilibrium [ O. I. Bogoyavlenskij, Phys. Rev. E. 62, 8616, (2000)]. The transforms break the geometrical symmetries of the field-aligned solutions and produce continuous families of the nonsymmetric MHD equilibria. The method of symmetry transforms also allows to obtain MHD equilibria with current sheets and exact solutions with noncollinear vector fields B and V. A model of the nonsymmetric astrophysical jets outside of their accretion disks is developed. The total magnetic and kinetic energy of the jet is finite in any layer c(1)
Nash equilibria via duality and homological selection
Indian Academy of Sciences (India)
Arnab Basu; Samik Basu; Mahan MJ
2014-11-01
Given a multifunction from to the -fold symmetric product Sym$_{k}(X)$, we use the Dold–Thom theorem to establish a homological selection theorem. This is used to establish existence of Nash equilibria. Cost functions in problems concerning the existence of Nash equilibria are traditionally multilinear in the mixed strategies. The main aim of this paper is to relax the hypothesis of multilinearity. We use basic intersection theory, Poincaré duality in addition to the Dold–Thom theorem.
On multicomponent adsorption equilibria of xylene mixtures on zeolites
Energy Technology Data Exchange (ETDEWEB)
Paludetto, R.; Storti, G.; Gamba, G.; Carra, S.; Morbidelli, M.
1987-11-01
Adsorption equilibria of two ternary systems involving m-xylene, p-xylene, and either toluene or isopropylbenzene on zeolite K-Y have been studied. Due to nonideal behavior of the adsorbed phase, m- and p-xylene selectivity is strongly dependent upon composition. In particular, it is found that the addition of a third component can either enhance or depress such selectivity values. Ternary experimental data are well predicted by the developed equilibrium model, whose parameters can be estimated based only on experimental data relative to pure and binary mixtures. Finally, the role of these nonidealities in the equilibrium behavior on the dynamics of adsorption separation columns is discussed.
Non-existence of Normal Tokamak Equilibria with Negative Central Current
Energy Technology Data Exchange (ETDEWEB)
G.W. Hammett; S.C. Jardin; B.C. Stratton
2003-02-18
Recent tokamak experiments employing off-axis, non-inductive current drive have found that a large central current hole can be produced. The current density is measured to be approximately zero in this region, though in principle there was sufficient current-drive power for the central current density to have gone significantly negative. Recent papers have used a large aspect-ratio expansion to show that normal MHD equilibria (with axisymmetric nested flux surfaces, non-singular fields, and monotonic peaked pressure profiles) can not exist with negative central current. We extend that proof here to arbitrary aspect ratio, using a variant of the virial theorem to derive a relatively simple integral constraint on the equilibrium. However, this constraint does not, by itself, exclude equilibria with non-nested flux surfaces, or equilibria with singular fields and/or hollow pressure profiles that may be spontaneously generated.
Lagrangian relative equilibria for a gyrostat in the three-body problem: bifurcations and stability
Energy Technology Data Exchange (ETDEWEB)
Guirao, Juan L G; Vera, Juan A, E-mail: juan.garcia@upct.e, E-mail: juanantonio.vera@upct.e [Departamento de Matematica Aplicada y EstadIstica, Universidad Politecnica de Cartagena, Hospital de Marina, 30203 Cartagena, Region de Murcia (Spain)
2010-05-14
In this paper we consider the non-canonical Hamiltonian dynamics of a gyrostat in the frame of the three-body problem. Using geometric/mechanic methods we study the approximate dynamics of the truncated Legendre series representation of the potential of an arbitrary order. Working in the reduced problem, we study the existence of relative equilibria that we refer to as Lagrange type following the analogy with the standard techniques. We provide necessary and sufficient conditions for the linear stability of Lagrangian relative equilibria if the gyrostat morphology form is close to a sphere. Thus, we generalize the classical results on equilibria of the three-body problem and many results on them obtained by the classic approach for the case of rigid bodies.
Gell-Mann, Murray; Gell-Mann, Murray; Hartle, James B
1997-01-01
We introduce a condition for the strong decoherence of a set of alternative histories of a closed quantum-mechanical system such as the universe. The condition applies, for a pure initial state, to sets of homogeneous histories that are chains of projections, generally branch-dependent. Strong decoherence implies the consistency of probability sum rules but not every set of consistent or even medium decoherent histories is strongly decoherent. Two conditions characterize a strongly decoherent set of histories: (1) At any time the operators that effectively commute with generalized records of history up to that moment provide the pool from which --- with suitable adjustment for elapsed time --- the chains of projections extending history to the future may be drawn. (2) Under the adjustment process, generalized record operators acting on the initial state of the universe are approximately unchanged. This expresses the permanence of generalized records. The strong decoherence conditions (1) and (2) guarantee wha...
Computation of two-fluid, flowing equilibria
Steinhauer, Loren; Kanki, Takashi; Ishida, Akio
2006-10-01
Equilibria of flowing two-fluid plasmas are computed for realistic compact-toroid and spherical-tokamak parameters. In these examples the two-fluid parameter ɛ (ratio of ion inertial length to overall plasma size) is small, ɛ ˜ 0.03 -- 0.2, but hardly negligible. The algorithm is based on the nearby-fluids model [1] which avoids a singularity that otherwise occurs for small ɛ. These representative equilibria exhibit significant flows, both toroidal and poloidal. Further, the flow patterns display notable flow shear. The importance of two-fluid effects is demonstrated by comparing with analogous equilibria (e.g. fixed toroidal and poloidal current) for a static plasma (Grad-Shafranov solution) and a flowing single-fluid plasma. Differences between the two-fluid, single-fluid, and static equilibria are highlighted: in particular with respect to safety factor profile, flow patterns, and electrical potential. These equilibria are computed using an iterative algorithm: it employs a successive-over-relaxation procedure for updating the magnetic flux function and a Newton-Raphson procedure for updating the density. The algorithm is coded in Visual Basic in an Excel platform on a personal computer. The computational time is essentially instantaneous (seconds). [1] L.C. Steinhauer and A. Ishida, Phys. Plasmas 13, 052513 (2006).
Settling the Complexity of Computing Two-Player Nash Equilibria
Chen, Xi; Teng, Shang-Hua
2007-01-01
We settle a long-standing open question in algorithmic game theory. We prove that Bimatrix, the problem of finding a Nash equilibrium in a two-player game, is complete for the complexity class PPAD Polynomial Parity Argument, Directed version) introduced by Papadimitriou in 1991. This is the first of a series of results concerning the complexity of Nash equilibria. In particular, we prove the following theorems: Bimatrix does not have a fully polynomial-time approximation scheme unless every problem in PPAD is solvable in polynomial time. The smoothed complexity of the classic Lemke-Howson algorithm and, in fact, of any algorithm for Bimatrix is not polynomial unless every problem in PPAD is solvable in randomized polynomial time. Our results demonstrate that, even in the simplest form of non-cooperative games, equilibrium computation and approximation are polynomial-time equivalent to fixed point computation. Our results also have two broad complexity implications in mathematical economics and operations res...
Three-dimensional magnetotail equilibria by numerical relaxation techniques
Hesse, Michael; Birn, Joachim
1993-01-01
Consideration is given to a numerical method to iteratively approach 3D magnetostatic force equilibria, with modeling emphasis on the development of a suitable model of the earth's magnetotail, including a portion of the inner magnetosphere, i.e., on models which violate the 'tail approximation' commonly employed in analytical models. The numerical approach is compared to methods developed for laboratory plasma physics. The method is applied to the magnetotail outside of 10 R(E), using Tsyganenko's (1987) model for the quiet magnetosphere as an initial condition. The changes of the magnetic field necessary to yield an equilibrium configuration and the resulting distribution of the self-consistently derived pressure are discussed. It is shown that a self-consistent magnetotail equilibrium based on a close approximation to Tsyganenko's requires a region 1 type current system, which is not present in the initial configuration.
Multiple Equilibria in Noisy Rational Expectations Economies
DEFF Research Database (Denmark)
Palvolgyi, Domotor; Venter, Gyuri
This paper studies equilibrium uniqueness in standard noisy rational expectations economies with asymmetric or differential information a la Grossman and Stiglitz (1980) and Hellwig (1980). We show that the standard linear equilibrium of Grossman and Stiglitz (1980) is the unique equilibrium......-sloping” demand curves, (iv) higher prices leading to future returns that are higher in expectation (price drift) and (v) more positively skewed. Discontinuous equilibria can be arbitrarily close to being fully-revealing. Finally, discontinuous equilibria with the same construction also exist in Hellwig (1980)....
Institute of Scientific and Technical Information of China (English)
Lei DENG; Ming Ge YANG
2006-01-01
Some new coincidence theorems involving admissible set-valued mappings are proved in general noncompact topological spaces. As applications, some new minimax inequalities, section theorem, best approximation theorem, existence theorems of weighted Nash equilibria and Pareto equilibria for multiobjective games are given in general topological spaces.
Boric acid equilibria in near-critical and supercritical water
Energy Technology Data Exchange (ETDEWEB)
Wofford, W.T.; Gloyna, E.F.; Johnston, K.P. [Univ. of Texas, Austin, TX (United States)
1998-05-01
Greater knowledge of acid-base equilibria is crucial to understanding the chemistry of hydrothermal processes including oxidation of organics, corrosion, catalysis, hydrolysis reactions, crystal growth and formation, precipitation of metal complexes and steam power cycles. The pH values of aqueous solutions of boric acid and KOH were measured with the optical indicator 2-naphthol at temperatures from 300 to 380 C. The equilibrium constant K{sub b}{sup {minus}1} for the reaction B(OH){sub 3} + OH{sup {minus}} = B(OH){sub 4}{sup {minus}} was determined from the pH measurements and correlated with a modified Born model. The titration curve for the addition of HCl to sodium borate exhibits strong acid-strong base behavior even at 350 C and 24.1 MPa. At these conditions, aqueous solutions of sodium borate buffer the pH at 9.6 {+-} 0.25.
Binary Solid-Liquid Phase Equilibria
Ellison, Herbert R.
1978-01-01
Indicates some of the information that may be obtained from a binary solid-liquid phase equilibria experiment and a method to write a computer program that will plot an ideal phase diagram to which the experimental results may be compared. (Author/CP)
Phase equilibria of carbohydrates in polar solvents
DEFF Research Database (Denmark)
Jonsdottir, Svava Osk; Rasmussen, Peter
1999-01-01
A method for calculating interaction energies and interaction parameters with molecular mechanics methods is extended to predict solid-liquid equilibria (SLE) for saccharides in aqueous solution, giving results in excellent agreement with experimental values. Previously, the method has been shown...
Intermediates and Generic Convergence to Equilibria
DEFF Research Database (Denmark)
Freitas, Michael Marcondes de; Wiuf, Carsten; Feliu, Elisenda
2016-01-01
Known graphical conditions for the generic or global convergence to equilibria of the dynamical system arising from a reaction network are shown to be invariant under the so-called successive removal of intermediates, a systematic procedure to simplify the network, making the graphical conditions...
Phase equilibria of carbohydrates in polar solvents
DEFF Research Database (Denmark)
Jonsdottir, Svava Osk; Rasmussen, Peter
1999-01-01
A method for calculating interaction energies and interaction parameters with molecular mechanics methods is extended to predict solid-liquid equilibria (SLE) for saccharides in aqueous solution, giving results in excellent agreement with experimental values. Previously, the method has been shown...
Stability of Hall equilibria in neutron star crusts
Marchant, Pablo; Valdivia, Juan Alejandro; Hoyos, Jaime H
2014-01-01
In the solid crusts of neutron stars, the advection of the magnetic field by the current-carrying electrons, an effect known as Hall drift, should play a very important role as the ions remain essentially fixed (as long as the solid does not break). Although Hall drift preserves the magnetic field energy, it has been argued that it may drive a turbulent cascade to scales at which Ohmic dissipation becomes effective, allowing a much faster decay in objects with very strong fields. On the other hand, it has been found that there are "Hall equilibria", i.e., field configurations that are unaffected by Hall drift. Here, we address the crucial question of the stability of these equilibria through axially symmetric (2D) numerical simulations of Hall drift and Ohmic diffusion, with the simplifying assumption of uniform electron density and conductivity. We demonstrate the 2D-stability of a purely poloidal equilibrium, for which Ohmic dissipation makes the field evolve towards an attractor state through adjacent stab...
State-of-the-art review of phase equilibria
Energy Technology Data Exchange (ETDEWEB)
Prausnitz, J.M.
1980-03-01
High-pressure phase-equilibrium calculations using an equation of state are more sensitive to the mixing rules than to details in the effect of density or temperature on pressure. Attention must be given to the problem of how to extend equations of state to mixtures. One possible technique is provided by perturbation theory; another by superposition of chemical equilibria. At low or moderate pressures, vapor-phase corrections are often important. When specific intermolecular forces produce formation of molecular aggregates, strong deviations from ideal-gas behavior can be significant even at pressures well below 1 bar. When vapor-liquid equilibrium data are reduced using conventional expressions for the excess Gibbs energy, the resulting binary parameters tend to be partially correlated, it difficult, but no impossible, to calculate ternary liquid-liquid equilibria using binary parameters only. New models for calculating properties of liquid-phase mixtures mist allow for changes in free volume to give consideration to the effect of mixing on changes in rotational and vibrational degrees of freedom. Liquid-phase volumetric effects are also important in describing the solubilities of gases in solvent mixtures. Therefore, future liquid-phase models should incorporate a liquid-phase equation of state, either of the van der Waals type or, perhaps, as given by the direct-correlation function theory of liquids.
Variational approximation of molecular kinetics from short off-equilibrium simulations
Wu, Hao; Paul, Fabian; Klus, Stefan; Koltai, Peter; Noé, Frank
2016-01-01
Markov state models (MSMs) and Master equation models are popular approaches to approximate molecular kinetics, equilibria, metastable states, and reaction coordinates in terms of a state space discretization usually obtained by clustering. Recently, a powerful generalization of MSMs has been introduced, the variational approach of conformation dynamics (VAC) and its special case the time-lagged independent component analysis (TICA), which allow us to approximate molecular kinetics and reaction coordinates by linear combinations of smooth basis functions or order parameters. While MSMs can be learned from trajectories whose starting points are not sampled from an equilibrium ensemble, TICA and VAC have as yet not enjoyed this property, and thus previous TICA/VAC estimates have been strongly biased when used with ensembles of short trajectories. Here, we employ Koopman operator theory and ideas from dynamic mode decomposition (DMD) to show how TICA/VAC can be used to estimate the unbiased equilibrium distribut...
Institute of Scientific and Technical Information of China (English)
陈崇钧; 罗根祥; 金军; 王好平
2001-01-01
When surface potential of the particles,ψ ,is high,sinh y can be approximated by ≈ ey/2 in the nonlinear Poisson-Boltzmann equation.Thus,we present a simple method of calculating the interaction force and energy per unit area between two dissimilar plates with high potentials at constant surface potential.These formulae could be applicable to the case of repulsive case,in which the derivative of y must vanish at an interior point,and a minimum ymin=u always exists.A turning point at ～ κ h≈ 2(π － 1)e－ y1/2 for the repulsion or attraction between dissimilar planar surfaces.These formulae are divergent at κ h ∞ ,and zero point at κ h≈ 2π .This means that they can only be used at κ h Agreement of the approximation for force,Eq.（ 13） ,is good with the exact numerical values of the interaction of dissimilar plates given by Devereux [6] for high surface potentials.For y1 ≥ 5κ h ≤ 3.0 the relative errors of Eq.(13) are less than 5％ ,and for κ h ≤ 3.5 relative errors are less than 10％ .For the interaction energy,Eq.(15),the applicable range extends to κ h=4.0.Beyond this range the error increases rapidly.The higher surface potential is the better the precision of Eq.（ 13） and Eq.( 15).The condition of the strong interaction has been satisfied.
Dąbrowska, Barbara
2000-03-01
The Deiters equation of state and the Redlich-Kwong equation of state were used for calculations of low-temperature vapour-liquid phase equilibria and related thermodynamic properties in binary systems containing halogenhydrocarbons. In all calculations, standard mixing rules for the Deiters equation of state as well as the modified mixing rules (including the repulsion function and density-dependent weight factors or the repulsion function and modified mean density approximation with density-dependent weight factors) were used. The calculations were done for the following systems: CF 4/CHF 3, CF 3Cl/CF 2Cl 2, CH 4/CHF 2Cl, CH 4/CF 2Cl 2, CHF 3/CFCl 3, N 2/CF 2Cl 2. The best results were achieved with the Deiters equation of state, especially with modified mixing rules. For higher pressures and lower temperatures the Redlich-Kwong equation of state is not able to predict the phase equilibria in halogenhydrocarbon systems accurately. It fails too in the case of strongly polar substances. The best parameter sets for the Redlich-Kwong equation of state and the Deiters equation of state for the systems investigated were collected.
Multiple Equilibria in a Single-Column Model of the Tropical Atmosphere
Sobel, Adam H; Bacmeister, Julio T
2007-01-01
A single-column model run under the weak temperature gradient approximation, a parameterization of large-scale dynamics appropriate for the tropical atmosphere, is shown to have multiple stable equilibria. Under conditions permitting persistent deep convection, the model has a statistically steady state in which such convection occurs, as well as an extremely dry state in which convection does not occur. Which state is reached depends on the initial moisture profile.
Energy Technology Data Exchange (ETDEWEB)
Chen, J.; Nakajima, N.; Okamoto, M.
1998-12-01
By means of a global mode analysis of ideal MHD modes for Mercier-unstable equilibria in a planar axis L=2/M=10 heliotron/torsatron system with an inherently large Shafranov shift, the conjecture from local mode analysis for Mercier-unstable equilibria given in [N. Nakajima, Phys. Plasmas 3, 4556 (1996)] has been confirmed and the properties of pressure-driven modes, namely, ballooning modes and interchange modes, inherent to such three-dimensional systems have been clarified. The change of the local magnetic shear due to the Shafranov shift, which is related to toroidicity, reduces the field line bending stabilizing effects on ballooning modes. According to the degree of the reduction of the local magnetic shear by the Shafranov shift, the Mercier-unstable equilibria are categorized into toroidicity-dominant (strong reduction) and helicity-dominant (weak reduction) Mercier-unstable equilibria. Since the local magnetic curvature due to helicity has the same period M in the toroidal direction as the toroidal field period of the equilibria, the characteristics of the pressure-driven modes in such Mercier-unstable equilibria dramatically change, both according to the reduction of the local magnetic shear by the Shafranov shift and also according to the relative magnitude of the typical toroidal mode number n of the perturbation compared with the toroidal field period of the equilibria M. In the toroidicity-dominant Mercier-unstable equilibria, the pressure-driven modes change from interchange modes for low toroidal mode numbers n < M, to tokamak-like poloidally localized ballooning modes with a weak toroidal mode coupling for moderate toroidal mode numbers n - M, and finally to both poloidally and toroidally localized ballooning modes purely inherent to three-dimensional systems for fairly high toroidal mode numbers n >> M. In the helicity-dominant Mercier-unstable equilibria, the pressure-driven modes change from interchange modes for n < M or n - M, directly to both
Computing Equilibria of Two Player Games
DEFF Research Database (Denmark)
Sørensen, Troels Bjerre
with computing equilibria of game theoretic models where only two agents are involved. The work described ranges from the theoretical development of algorithms for computing refined equilibria, which satisfy additional constraints beyond being an equilibrium, to the practical solving of real life games. Part I...... Theory. The application areas of Game Theory fathoms most academic disciplines, all the way from Political Science and Economics through Biology to Computer Science. It also has played an important role in areas Philosophy and Ethics. It has even been used to politically justify military conflicts...... to the prediction. Predicting behavior of rational agents has many application areas. The phrasing of the last paragraph was vague for sole purpose of not implying any restriction on what agents are and in what context they act. The whole area of reasoning about rational interaction of agents is known as Game...
The pressure tensor in tangential equilibria
Directory of Open Access Journals (Sweden)
F. Mottez
2004-09-01
Full Text Available The tangential equilibria are characterized by a bulk plasma velocity and a magnetic field that are perpendicular to the gradient direction. Such equilibria can be spatially periodic (like waves, or they can separate two regions with asymptotic uniform conditions (like MHD tangential discontinuities. It is possible to compute the velocity moments of the particle distribution function. Even in very simple cases, the pressure tensor is not isotropic and not gyrotropic. The differences between a scalar pressure and the pressure tensor derived in the frame of the Maxwell-Vlasov theory are significant when the gradient scales are of the order of the Larmor radius; they concern mainly the ion pressure tensor.
Multiple equilibria in a simple elastocapillary system
Taroni, Michele
2012-09-28
We consider the elastocapillary interaction of a liquid drop placed between two elastic beams, which are both clamped at one end to a rigid substrate. This is a simple model system relevant to the problem of surface-tension-induced collapse of flexible micro-channels that has been observed in the manufacture of microelectromechanical systems (MEMS). We determine the conditions under which the beams remain separated, touch at a point, or stick along a portion of their length. Surprisingly, we show that in many circumstances multiple equilibrium states are possible. We develop a lubrication-type model for the flow of liquid out of equilibrium and thereby investigate the stability of the multiple equilibria. We demonstrate that for given material properties two stable equilibria may exist, and show via numerical solutions of the dynamic model that it is the initial state of the system that determines which stable equilibrium is ultimately reached. © 2012 Cambridge University Press.
Approximate Representations and Approximate Homomorphisms
Moore, Cristopher
2010-01-01
Approximate algebraic structures play a defining role in arithmetic combinatorics and have found remarkable applications to basic questions in number theory and pseudorandomness. Here we study approximate representations of finite groups: functions f:G -> U_d such that Pr[f(xy) = f(x) f(y)] is large, or more generally Exp_{x,y} ||f(xy) - f(x)f(y)||^2$ is small, where x and y are uniformly random elements of the group G and U_d denotes the unitary group of degree d. We bound these quantities in terms of the ratio d / d_min where d_min is the dimension of the smallest nontrivial representation of G. As an application, we bound the extent to which a function f : G -> H can be an approximate homomorphism where H is another finite group. We show that if H's representations are significantly smaller than G's, no such f can be much more homomorphic than a random function. We interpret these results as showing that if G is quasirandom, that is, if d_min is large, then G cannot be embedded in a small number of dimensi...
Approximate Fixed Point Theorems in Banach Spaces with Applications in Game Theory
Brânzei, R.; Morgan, J.; Scalzo, V.; Tijs, S.H.
2002-01-01
In this paper some new approximate fixed point theorems for multifunctions in Banach spaces are presented and a method is developed indicating how to use approximate fixed point theorems in proving the existence of approximate Nash equilibria for non-cooperative games.
Relative Equilibria in the Spherical, Finite Density 3-Body Problem
Scheeres, D J
2016-01-01
The relative equilibria for the spherical, finite density 3 body problem are identified. Specifically, there are 28 distinct relative equilibria in this problem which include the classical 5 relative equilibria for the point-mass 3-body problem. None of the identified relative equilibria exist or are stable over all values of angular momentum. The stability and bifurcation pathways of these relative equilibria are mapped out as the angular momentum of the system is increased. This is done under the assumption that they have equal and constant densities and that the entire system rotates about its maximum moment of inertia. The transition to finite density greatly increases the number of relative equilibria in the 3-body problem and ensures that minimum energy configurations exist for all values of angular momentum.
CERN. Geneva
2015-01-01
Most physics results at the LHC end in a likelihood ratio test. This includes discovery and exclusion for searches as well as mass, cross-section, and coupling measurements. The use of Machine Learning (multivariate) algorithms in HEP is mainly restricted to searches, which can be reduced to classification between two fixed distributions: signal vs. background. I will show how we can extend the use of ML classifiers to distributions parameterized by physical quantities like masses and couplings as well as nuisance parameters associated to systematic uncertainties. This allows for one to approximate the likelihood ratio while still using a high dimensional feature vector for the data. Both the MEM and ABC approaches mentioned above aim to provide inference on model parameters (like cross-sections, masses, couplings, etc.). ABC is fundamentally tied Bayesian inference and focuses on the “likelihood free” setting where only a simulator is available and one cannot directly compute the likelihood for the dat...
Self-consistent equilibria in cylindrical reversed-field pinch
Energy Technology Data Exchange (ETDEWEB)
Lo Surdo, C. [ENEA, Centro Ricerche Frascati, Rome (Italy). Dip. di Energia; Paccagnella, R.; Guo, S. [CNR, Padua (Italy). Istituto Gas Ionizzati
1995-07-01
The object of this work is to study the self-consistent magnetofluidstatic equilibria of a 2-region (plasma + gas) reversed-field pinch (RFP) in cylindrical approximation (namely, with vanishing inverse aspect ratio). Differently from what happens in a tokamak, in a RFP a significant part of the plasma current is driven by a dynamo electric field (DEF), in its turn mainly due to plasma turbulence. So, it is worked out a reasonable mathematical model of the above self-consistent equilibria under the following main points it has been: (a) to the lowest order, and according to a standard ansatz, the turbulent DEF say {epsilon}{sup t}, is expressed as a homogeneous transform of the magnetic field B of degree 1, {epsilon}{sup t}=({alpha}) (B), with {alpha}{identical_to}a given 2-nd rank tensor, homogeneous of degree 0 in B and generally depending on the plasma state; (b) {epsilon}{sup t} does not explicitly appear in the plasma energy balance, as it were produced by a Maxwell demon able of extract the corresponding Joule power from the plasma. In particular, it is showed that, if both {alpha} and the resistivity tensor {eta} are isotropic and constant, the magnetic field is force-free with abnormality equal to {alpha}{eta}{sub 0}/{eta}, in the limit of vanishing {beta}; that is, the well-known J.B. Taylor`result is recovered, in this particular conditions, starting from ideas quite different from the usual ones (minimization of total magnetic energy under constrained total elicity). Finally, the general problem is solved numerically under circular (besides cylindrical) symmetry, for simplicity neglecting the existence of gas region (i.e., assuming the plasma in direct contact with the external wall).
Dudebout, Nicolas
2014-12-15
This paper proves that exogenous empirical-evidence equilibria (xEEEs) in perfect-monitoring repeated games induce correlated equilibria of the associated one-shot game. An empirical-evidence equilibrium (EEE) is a solution concept for stochastic games. At equilibrium, agents\\' strategies are optimal with respect to models of their opponents. These models satisfy a consistency condition with respect to the actual behavior of the opponents. As such, EEEs replace the full-rationality requirement of Nash equilibria by a consistency-based bounded-rationality one. In this paper, the framework of empirical evidence is summarized, with an emphasis on perfect-monitoring repeated games. A less constraining notion of consistency is introduced. The fact that an xEEE in a perfect-monitoring repeated game induces a correlated equilibrium on the underlying one-shot game is proven. This result and the new notion of consistency are illustrated on the hawk-dove game. Finally, a method to build specific correlated equilibria from xEEEs is derived.
Transport and phase equilibria of benzene in FAU type zeolites
Saravanan, Chandra
We have studied lattice models for self-diffusion of benzene in FAU type zeolites, to explore the effect of the thermodynamics of confined fluids on the transport properties of molecules in zeolites. Our model assumes that benzene molecules are located near Na+ ions in supercages, and in 12-ring windows separating adjacent supercages, respectively. The study was performed in three stages. First, to disentangle the effect of a vapor-liquid phase equilibria on diffusion in zeolites, the transport of benzene in Na-Y is modeled in the absence of attractive guest-guest interactions. The loading dependence of diffusion coefficient, Dtheta, at a constant temperature, referred to as a diffusion isotherm, is modeled with site-blocking effects using a mean field theory (MFT) that yields, Dq=16kq a2q, where atheta ≅ 11 A is the mean intercage jump length and 1/ktheta is the mean supercage residence time. A completely analytical expression is derived to calculate ktheta. The MFT is tested using a mean field approximation (MFA) where ktheta and atheta are calculated from kinetic Monte Carlo simulations yielding excellent qualitative agreement. Further calculations are performed to test MFA by calculating "exact" diffusion coefficients from mean square displacement (MSD) calculations also yielding excellent qualitative agreement. Next, by including guest-guest attractive interactions, we have performed lattice grand canonical Monte Carlo simulations of benzene adsorption in Na-X zeolite to determine whether strongly confined benzene molecules exhibit subcritical properties. We observe a phase transition from low to high density of adsorbed benzene, analogous to vapor-liquid equilibrium, at temperatures as high as 300 K and above. By performing thermodynamic integration to construct the coexistence curve, we obtain a critical point for benzene in Na-X at Tc = 370 +/- 20 K, thetac = 0.45 +/- 0.05 fractional coverage. We suggest that careful adsorption experiments should be
Correlated Equilibria of Classical Strategic Games with Quantum Signals
La Mura, P
2003-01-01
Correlated equilibria are sometimes more efficient than the Nash equilibria of a game without signals. We investigate whether the availability of quantum signals in the context of a classical strategic game may allow the players to achieve even better efficiency than in any correlated equilibrium with classical signals, and find the answer to be positive.
A unifying approach to existence of Nash equilibria
Balder, E.J.
2001-01-01
An approach initiated in [4] is shown to unify results about the existence of (i) Nash equilibria in games with at most countably many players, (ii) Cournot-Nash equilibrium distributions for large, anonymous games, and (iii) Nash equilibria (both mixed and pure) for continuum games. A new, central
Cycles and Multiple Equilibria in the Market for Durable Lemons
M.C.W. Janssen (Maarten); V.A. Karamychev (Vladimir)
2000-01-01
textabstractWe investigate the nature of market failure in a dynamic version of Akerlof (1970) where identical cohorts of a durable good enter the market over time. In the dynamic model, equilibria with qualitatively different properties emerge. Typically, in equilibria of the dynamic model, sellers
High temperature phase equilibria and phase diagrams
Kuo, Chu-Kun; Yan, Dong-Sheng
2013-01-01
High temperature phase equilibria studies play an increasingly important role in materials science and engineering. It is especially significant in the research into the properties of the material and the ways in which they can be improved. This is achieved by observing equilibrium and by examining the phase relationships at high temperature. The study of high temperature phase diagrams of nonmetallic systems began in the early 1900s when silica and mineral systems containing silica were focussed upon. Since then technical ceramics emerged and more emphasis has been placed on high temperature
Entropy and Equilibria in Competitive Systems
Directory of Open Access Journals (Sweden)
A. Y. Klimenko
2013-12-01
Full Text Available This paper investigates the applicability of thermodynamic concepts and principles to competitive systems. We show that Tsallis entropies are suitable for the characterisation of systems with transitive competition when mutations deviate from Gibbs mutations. Different types of equilibria in competitive systems are considered and analysed. As competition rules become more and more intransitive, thermodynamic analogies are eroded, and the behaviour of the system can become complex. This work analyses the phenomenon of punctuated evolution in the context of the competitive risk/benefit dilemma.
Navrotsky, Alexandra; Ma, Chengcheng; Lilova, Kristina; Birkner, Nancy
2010-10-08
Knowing the thermodynamic stability of transition metal oxide nanoparticles is important for understanding and controlling their role in a variety of industrial and environmental systems. Using calorimetric data on surface energies for cobalt, iron, manganese, and nickel oxide systems, we show that surface energy strongly influences their redox equilibria and phase stability. Spinels (M(3)O(4)) commonly have lower surface energies than metals (M), rocksalt oxides (MO), and trivalent oxides (M(2)O(3)) of the same metal; thus, the contraction of the stability field of the divalent oxide and expansion of the spinel field appear to be general phenomena. Using tabulated thermodynamic data for bulk phases to calculate redox phase equilibria at the nanoscale can lead to errors of several orders of magnitude in oxygen fugacity and of 100 to 200 kelvin in temperature.
Mass-Radius Relation of Strongly Magnetized White Dwarfs
Bera, P.; Bhattacharya, D.
2017-03-01
We study the strongly magnetized white dwarf configurations in a self-consistent manner as a progenitor of the over-luminous type-Ia supernovae. We compute static equilibria of white dwarf stars containing a strong magnetic field and present the modification of the white dwarf mass-radius relation caused by the magnetic field. From a static equilibrium study, we find that a maximum white dwarf mass of about 1.9 M⊙ may be supported if the interior poloidal field is as strong as approximately 1010 T. On the other hand if the field is purely toroidal the maximum mass can be more than 5 M⊙. All these modifications are mainly from the presence of the Lorenz force. The effects of i) modification of the equation of state due to Landau quantization, ii) electrostatic interaction due to ions, iii) general relativistic calculation on the stellar structure and, iv) field geometry are also considered. These strongly magnetised configurations are sensitive to magnetic instabilities where the perturbations grow at the corresponding Alfven time scales.
Mass-radius relation of strongly magnetized white dwarfs
Bera, Prasanta; Bhattacharya, Dipankar
2016-07-01
We study the strongly magnetized white dwarf configurations in a self-consistent manner as a progenitor of the over-luminous type-Ia supernovae. We compute static equilibria of white dwarf stars containing a strong magnetic field and present the modification of white dwarf mass-radius relation caused by the magnetic field. From a static equilibrium study, we find that a maximum white dwarf mass of about 1.9 M_{⊙} may be supported if the interior poloidal field is as strong as approximately 10^{10} T. On the other hand, if the field is purely toroidal the maximum mass can be more than 5 M_⊙. All these modifications are mainly from the presence of Lorenz force. The effects of i) modification of equation of state due to Landau quantization ii) electrostatic interaction due to ions, ii) general relativistic calculation on the stellar structure and, iii) field geometry are also considered. These strongly magnetised configurations are sensitive to magnetic instabilities where the perturbations grow at the corresponding Alfven time scales.
TOKAMAK EQUILIBRIA WITH CENTRAL CURRENT HOLES AND NEGATIVE CURRENT DRIVE
Energy Technology Data Exchange (ETDEWEB)
CHU, M.S.; PARKS, P.B.
2002-06-01
OAK B202 TOKAMAK EQUILIBRIA WITH CENTRAL CURRENT HOLES AND NEGATIVE CURRENT DRIVE. Several tokamak experiments have reported the development of a central region with vanishing currents (the current hole). Straightforward application of results from the work of Greene, Johnson and Weimer [Phys. Fluids, 3, 67 (1971)] on tokamak equilibrium to these plasmas leads to apparent singularities in several physical quantities including the Shafranov shift and casts doubts on the existence of this type of equilibria. In this paper, the above quoted equilibrium theory is re-examined and extended to include equilibria with a current hole. It is shown that singularities can be circumvented and that equilibria with a central current hole do satisfy the magnetohydrodynamic equilibrium condition with regular behavior for all the physical quantities and do not lead to infinitely large Shafranov shifts. Isolated equilibria with negative current in the central region could exist. But equilibria with negative currents in general do not have neighboring equilibria and thus cannot have experimental realization, i.e. no negative currents can be driven in the central region.
Close pairs of relative equilibria for identical point vortices
DEFF Research Database (Denmark)
Dirksen, Tobias; Aref, Hassan
2011-01-01
Numerical solution of the classical problem of relative equilibria for identical point vortices on the unbounded plane reveals configurations that are very close to the analytically known, centered, symmetrically arranged, nested equilateral triangles. New numerical solutions of this kind are found...... also has this property, and new relative equilibria close to the nested, symmetrically arranged, regular heptagons have been found. The centered regular nonagon is also marginally stable. Again, a new family of close relative equilibria has been found. The closest relative equilibrium pairs occur...
CONSTRUCTING EXAMPLES WITH 5 EQUILIBRIA FOR SYMMETRIC 3 × 2 CES / LES PURE EXCHANGE ECONOMIES
Institute of Scientific and Technical Information of China (English)
Huang Hui; Shi Xiaojun; Zhang Shunming
2012-01-01
This paper explores the existence of multiple equilibria for symmetric 3 individual,2 good CES / LES pure exchange economies.Analytically,we show that there are no more than 5 equilibria in such economies.The number of equilibria varies from 5 to 3 then to 1.We generalize our analytical results of existence of 1,3,5 equilibria for a wide range of parametrizations.We also provide concrete examples of 1,3,5 equilibria with parameter zones specified.
An Algorithm for Computing All Berge Equilibria
Directory of Open Access Journals (Sweden)
H. W. Corley
2015-01-01
Full Text Available An algorithm is presented in this note for determining all Berge equilibria for an n-person game in normal form. This algorithm is based on the notion of disappointment, with the payoff matrix (PM being transformed into a disappointment matrix (DM. The DM has the property that a pure strategy profile of the PM is a BE if and only if (0,…,0 is the corresponding entry of the DM. Furthermore, any (0,…,0 entry of the DM is also a more restrictive Berge-Vaisman equilibrium if and only if each player’s BE payoff is at least as large as the player’s maximin security level.
New Thermodynamic Paradigm of Chemical Equilibria
Zilbergleyt, B
2011-01-01
The paper presents new thermodynamic paradigm of chemical equilibrium, setting forth comprehensive basics of Discrete Thermodynamics of Chemical Equilibria (DTd). Along with previous results by the author during the last decade, this work contains also some new developments of DTd. Based on the Onsager's constitutive equations, reformulated by the author thermodynamic affinity and reaction extent, and Le Chatelier's principle, DTd brings forward a notion of chemical equilibrium as a balance of internal and external thermodynamic forces (TdF), acting against a chemical system. Basic expression of DTd is the chemical system logistic map of thermodynamic states that ties together energetic characteristics of chemical reaction, occurring in the system, the system shift from "true" thermodynamic equilibrium (TdE), and causing that shift external thermodynamic forces. Solutions to the basic map are pitchfork bifurcation diagrams in coordinates "shift from TdE - growth factor (or TdF)"; points, corresponding to the ...
Magnetic equilibria for X-Diverted plasmas
Pekker, M.; Valanju, P.; Kotschenreuther, M.; Wiley, J.; Mahajan, S.
2006-10-01
The X-divertor has been proposed to solve heat exhaust problems for reactors beyond ITER. By generating an extra X-point downstream from the main X-point, the X-divertor greatly expands magnetic flux at the divertor plates. As a result, the heat is distributed over a larger area and the line length is greatly increased. We have developed coil sets for X-diverted magnetic equilibria for many devices (NSTX, PEGASUS, EAST, HL-2A, CREST, and a CTF). These demonstrate that the XD configuration can be created for highly shaped plasmas using moderate coil currents. For reactors, all coils can be placed behind 1 m of shielding. We have also shown that XD configurations are robust to modest plasma perturbations and VDEs; this is in contrast to the sensitivity of highly tilted divertor plates.
One-dimensional Vlasov-Maxwell equilibria
Greene, John M.
1993-06-01
The purpose of this paper is to show that the Vlasov equilibrium of a plasma of charged particles in an electromagnetic field is closely related to a fluid equilibrium, where only a few moments of the velocity distribution of the plasma are considered. In this fluid equilibrium the electric field should be calculated from Ohm's law, rather than the Poisson equation. In practice, only one-dimensional equilibria are treated, because the symmetry makes this case tractable. The emphasis here is on gaining a better understanding of the subject, but an alternate way of doing the calculations is suggested. It is shown that particle distributions can be found that are consistent with any reasonable electromagnetic field profile.
Global approximation of convex functions
Azagra, D
2011-01-01
We show that for every (not necessarily bounded) open convex subset $U$ of $\\R^n$, every (not necessarily Lipschitz or strongly) convex function $f:U\\to\\R$ can be approximated by real analytic convex functions, uniformly on all of $U$. In doing so we provide a technique which transfers results on uniform approximation on bounded sets to results on uniform approximation on unbounded sets, in such a way that not only convexity and $C^k$ smoothness, but also local Lipschitz constants, minimizers, order, and strict or strong convexity, are preserved. This transfer method is quite general and it can also be used to obtain new results on approximation of convex functions defined on Riemannian manifolds or Banach spaces. We also provide a characterization of the class of convex functions which can be uniformly approximated on $\\R^n$ by strongly convex functions.
Ion, Anca Veronica
2010-01-01
The paper is devoted to the study of stability of equilibrium solutions of a delay differential equation that models leukemia. The equation was previously studied in [5] and [6], where the emphasis is put on the numerical study of periodic solutions. Some stability results for the equilibria are also presented in these works, but they are incomplete and contain some errors. Our work aims to complete and to bring corrections to those results. Both Lyapunov first order approximation method and second Lyapunov method are used.
system and the mutual solubilities between carbide and boride phases are small. The solid state sections (C) are characterized by two- phase ... equilibria existing between the phase pairs W2B + W2C, W2B + WC, WC + WB, WB + C, W2B5 + C, W2B5 + B4C, and WB approximately 4 + B4C. The two-phase
Learning Equilibria with Partial Information in Decentralized Wireless Networks
Rose, Luca; Lasaulce, Samson; Debbah, Mérouane
2011-01-01
In this article, a survey of several important equilibrium concepts for decentralized networks is presented. The term decentralized is used here to refer to scenarios where decisions (e.g., choosing a power allocation policy) are taken autonomously by devices interacting with each other (e.g., through mutual interference). The iterative long-term interaction is characterized by stable points of the wireless network called equilibria. The interest in these equilibria stems from the relevance of network stability and the fact that they can be achieved by letting radio devices to repeatedly interact over time. To achieve these equilibria, several learning techniques, namely, the best response dynamics, fictitious play, smoothed fictitious play, reinforcement learning algorithms, and regret matching, are discussed in terms of information requirements and convergence properties. Most of the notions introduced here, for both equilibria and learning schemes, are illustrated by a simple case study, namely, an interfe...
Stable equilibria of elliptic roly-poly toys
Hong, Seok-In
2016-11-01
As an instructive (gravitational potential) energy approach, we show that the elliptic roly-poly has a richer and more useful profile (including the tilted configuration) of stable equilibria than conventional spherical or cylindrical roly-polys.
Existence of General Competitive Equilibria: A Variational Approach
Directory of Open Access Journals (Sweden)
G. Anello
2016-01-01
Full Text Available We study the existence of general competitive equilibria in economies with agents and goods in a finite number. We show that there exists a Walras competitive equilibrium in all ownership private economies such that, for all consumers, initial endowments do not contain free goods and utility functions are locally Lipschitz quasiconcave. The proof of the existence of competitive equilibria is based on variational methods by applying a theoretical existence result for Generalized Quasi Variational Inequalities.
Directory of Open Access Journals (Sweden)
Lu-Chuan Ceng
2014-01-01
Full Text Available We first introduce and analyze one multistep iterative algorithm by hybrid shrinking projection method for finding a solution of the system of generalized equilibria with constraints of several problems: the generalized mixed equilibrium problem, finitely many variational inclusions, the minimization problem for a convex and continuously Fréchet differentiable functional, and the fixed-point problem of an asymptotically strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another multistep iterative algorithm involving no shrinking projection method and derive its weak convergence under mild assumptions.
Unifying dynamical and structural stability of equilibria
Arnoldi, Jean-François; Haegeman, Bart
2016-09-01
We exhibit a fundamental relationship between measures of dynamical and structural stability of linear dynamical systems-e.g. linearized models in the vicinity of equilibria. We show that dynamical stability, quantified via the response to external perturbations (i.e. perturbation of dynamical variables), coincides with the minimal internal perturbation (i.e. perturbations of interactions between variables) able to render the system unstable. First, by reformulating a result of control theory, we explain that harmonic external perturbations reflect the spectral sensitivity of the Jacobian matrix at the equilibrium, with respect to constant changes of its coefficients. However, for this equivalence to hold, imaginary changes of the Jacobian's coefficients have to be allowed. The connection with dynamical stability is thus lost for real dynamical systems. We show that this issue can be avoided, thus recovering the fundamental link between dynamical and structural stability, by considering stochastic noise as external and internal perturbations. More precisely, we demonstrate that a linear system's response to white-noise perturbations directly reflects the intensity of internal white-noise disturbance that it can accommodate before becoming stochastically unstable.
PARALLEL ASSAY OF OXYGEN EQUILIBRIA OF HEMOGLOBIN
Lilly, Laura E.; Blinebry, Sara K.; Viscardi, Chelsea M.; Perez, Luis; Bonaventura, Joe; McMahon, Tim J.
2013-01-01
Methods to systematically analyze in parallel the function of multiple protein or cell samples in vivo or ex vivo (i.e. functional proteomics) in a controlled gaseous environment have thus far been limited. Here we describe an apparatus and procedure that enables, for the first time, parallel assay of oxygen equilibria in multiple samples. Using this apparatus, numerous simultaneous oxygen equilibrium curves (OECs) can be obtained under truly identical conditions from blood cell samples or purified hemoglobins (Hbs). We suggest that the ability to obtain these parallel datasets under identical conditions can be of immense value, both to biomedical researchers and clinicians who wish to monitor blood health, and to physiologists studying non-human organisms and the effects of climate change on these organisms. Parallel monitoring techniques are essential in order to better understand the functions of critical cellular proteins. The procedure can be applied to human studies, wherein an OEC can be analyzed in light of an individual’s entire genome. Here, we analyzed intraerythrocytic Hb, a protein that operates at the organism’s environmental interface and then comes into close contact with virtually all of the organism’s cells. The apparatus is theoretically scalable, and establishes a functional proteomic screen that can be correlated with genomic information on the same individuals. This new method is expected to accelerate our general understanding of protein function, an increasingly challenging objective as advances in proteomic and genomic throughput outpace the ability to study proteins’ functional properties. PMID:23827235
The CHEASE code for toroidal MHD equilibria
Energy Technology Data Exchange (ETDEWEB)
Luetjens, H. [Ecole Polytechnique, 91 - Palaiseau (France). Centre de Physique Theorique; Bondeson, A. [Chalmers Univ. of Technology, Goeteborg (Sweden). Inst. for Electromagnetic Field Theory and Plasma Physics; Sauter, O. [ITER-San Diego, La Jolla, CA (United States)
1996-03-01
CHEASE solves the Grad-Shafranov equation for the MHD equilibrium of a Tokamak-like plasma with pressure and current profiles specified by analytic forms or sets of data points. Equilibria marginally stable to ballooning modes or with a prescribed fraction of bootstrap current can be computed. The code provides a mapping to magnetic flux coordinates, suitable for MHD stability calculations or global wave propagation studies. The code computes equilibrium quantities for the stability codes ERATO, MARS, PEST, NOVA-W and XTOR and for the global wave propagation codes LION and PENN. The two-dimensional MHD equilibrium (Grad-Shafranov) equation is solved in variational form. The discretization uses bicubic Hermite finite elements with continuous first order derivates for the poloidal flux function {Psi}. The nonlinearity of the problem is handled by Picard iteration. The mapping to flux coordinates is carried out with a method which conserves the accuracy of the cubic finite elements. The code uses routines from the CRAY libsci.a program library. However, all these routines are included in the CHEASE package itself. If CHEASE computes equilibrium quantities for MARS with fast Fourier transforms, the NAG library is required. CHEASE is written in standard FORTRAN-77, except for the use of the input facility NAMELIST. CHEASE uses variable names with up to 8 characters, and therefore violates the ANSI standard. CHEASE transfers plot quantities through an external disk file to a plot program named PCHEASE using the UNIRAS or the NCAR plot package. (author) figs., tabs., 34 refs.
Bilinear Relative Equilibria of Identical Point Vortices
DEFF Research Database (Denmark)
Aref, H.; Beelen, Peter; Brøns, Morten
2012-01-01
-axis and n on the x-axis. We define generating polynomials q(z) and p(z), respectively, for each set of vortices. A second-order, linear ODE for p(z) given q(z) is derived. Several results relating the general solution of the ODE to relative equilibrium configurations are established. Our strongest result......A new class of bilinear relative equilibria of identical point vortices in which the vortices are constrained to be on two perpendicular lines, conveniently taken to be the x- and y-axes of a Cartesian coordinate system, is introduced and studied. In the general problem we have m vortices on the y......, obtained using Sturm’s comparison theorem, is that if p(z) satisfies the ODE for a given q(z) with its imaginary zeros symmetric relative to the x-axis, then it must have at least n−m+2 simple, real zeros. For m=2 this provides a complete characterization of all zeros, and we study this case in some detail...
First principles calculation of L2{sub 1}+A2 coherent equilibria in the Fe-Al-Ti system
Energy Technology Data Exchange (ETDEWEB)
Alonso, Paula R., E-mail: pralonso@cnea.gov.a [Departamento de Materiales (GIDAT-CAC), Comision Nacional de Energia Atomica, Avda. General Paz 1499, B1650KNA San Martin, Pcia. Buenos Aires (Argentina); Instituto Sabato, Universidad Nacional de San Martin, Avda. General Paz 1499, B1650KNA San Martin, Pcia. Buenos Aires (Argentina); Gargano, Pablo H. [Departamento de Materiales (GIDAT-CAC), Comision Nacional de Energia Atomica, Avda. General Paz 1499, B1650KNA San Martin, Pcia. Buenos Aires (Argentina); Instituto Sabato, Universidad Nacional de San Martin, Avda. General Paz 1499, B1650KNA San Martin, Pcia. Buenos Aires (Argentina); Ramirez-Caballero, Gustavo E.; Balbuena, Perla B. [Department of Chemical Engineering, Texas A and M University, College Station, TX 77843 (United States); Rubiolo, Gerardo H. [Departamento de Materiales (GIDAT-CAC), Comision Nacional de Energia Atomica, Avda. General Paz 1499, B1650KNA San Martin, Pcia. Buenos Aires (Argentina); Instituto Sabato, Universidad Nacional de San Martin, Avda. General Paz 1499, B1650KNA San Martin, Pcia. Buenos Aires (Argentina); Consejo Nacional de Investigaciones Cientificas y Tecnologicas (CONICET), Avda Rivadavia 1917, C1033AAJ Ciudad Autonoma de Buenos Aires (Argentina)
2009-10-01
By combining first-principles density functional total energy calculations and statistical mechanics the ground state and the phase equilibria at finite temperatures of the ternary system Fe-Al-Ti have been investigated. Total energy calculations have been performed by means of the Wien 2k code to establish the ground state energetic. A cluster expansion method was therewith used to describe solid solutions. At several chosen finite temperatures the cluster variation method in the irregular tetrahedron approximation was employed in order to calculate the iron rich ternary bcc equilibria. It is confirmed that there are two kinds of phase separations of the bcc phase, A2+L2{sub 1} and B2+L2{sub 1}.
Weighted approximation with varying weight
Totik, Vilmos
1994-01-01
A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.
Without the strong force, there could be no life. The carbon in living matter is synthesised in stars via the strong force. Lighter atomic nuclei become bound together in a process called nuclear fusion. A minor change in this interaction would make life impossible. As its name suggests, the strong force is the most powerful of the 4 forces, yet its sphere of influence is limited to within the atomic nucleus. Indeed it is the strong force that holds together the quarks inside the positively charged protons. Without this glue, the quarks would fly apart repulsed by electromagnetism. In fact, it is impossible to separate 2 quarks : so much energy is needed, that a second pair of quarks is produced. Text for the interactive: Can you pull apart the quarks inside a proton?
The mechanics of rocking stones: equilibria on separated scales
Domokos, Gábor; Szabó, Tímea
2011-01-01
Rocking stones, balanced in counter-intuitive positions have always intrigued geologists. In our paper we explain this phenomenon based on high-precision scans of pebbles which exhibit similar behavior. We construct their convex hull and the heteroclinic graph carrying their equilibrium points. By systematic simplification of the arising Morse-Smale complex in a one-parameter process we show that equilibria occur typically in highly localized groups (flocks), the number of the latter can be reliably observed and determined by hand experiments. Both local and global (micro and macro) equilibria can be either stable or unstable. Most commonly, rocks and pebbles are balanced on stable local equilibria belonging to stable flocks. However, it is possible to balance a convex body on a stable local equilibrium belonging to an unstable flock and this is the intriguing mechanical scenario corresponding to rocking stones. Since outside observers can only reliably perceive flocks, the last described situation will appea...
Recent progress in the relative equilibria of point vortices — In memoriam Hassan Aref
DEFF Research Database (Denmark)
Beelen, Peter; Brøns, Morten; Krishnamurthy, Vikas S.;
2013-01-01
Hassan Aref, who sadly passed away in 2011, was one of the world's leading researchers in the dynamics and equilibria of point vortices. We review two problems on the subject of point vortex relative equilibria in which he was engaged at the time of his death: bilinear relative equilibria and the...
It takes two to tango: Equilibria in a model of sales
M.R. Baye (Michael); D. Kovenock (Dan); C.G. de Vries (Casper)
1992-01-01
textabstractWe show that the Varian model of sales with more than two firms has two types of equilibria: a unique symmetric equilibrium, and a continuum of asymmetric equilibria. In contrast, the 2-firm game has a unique equilibrium that is symmetric. For the n-firm case the asymmetric equilibria im
On the existence and convergence of price equilibria for random economies
Nummelin, Esa
2000-01-01
We study an exchange economy comprising $n$ agents,where the excess demands by the agents are random variables. We show that under certain conditions the set of price equilibria is nonempty. We also prove a theorem concerning the convergence of the random price equilibria toward the price equilibria of an associated “expectation economy.”
Strong approximation of continuous local martingales by simple random walks
Szekely, Balazs
2010-01-01
The aim of this paper is to represent any continuous local martingale as an almost sure limit of a nested sequence of simple, symmetric random walks, time changed by a discrete quadratic variation process. One basis of this is a similar construction of Brownian motion. The other major tool is a representation of continuous local martingales given by Dambis, Dubins and Schwarz (DDS) in terms of Brownian motion time-changed by the quadratic variation. Rates of convergence (which are conjectured to be nearly optimal in the given setting) are also supplied. A necessary and sufficient condition for the independence of the random walks and the discrete time changes or, equivalently, for the independence of the DDS Brownian motion and the quadratic variation is proved to be the symmetry of increments of the martingale given the past, which is a reformulation of an earlier result by Ocone.
Effective bounds on strong unicity in L1-approximation
DEFF Research Database (Denmark)
Kohlenbach, Ulrich; Oliva, Paulo B.
In this paper we present another case study in the general project of Proof Mining which means the logical analysis of prima facie non-effective proofs with the aim of extracting new computationally relevant data. We use techniques based on monotone functional interpretation (developed in [17]) t...
An Analytical Approximation Method for Strongly Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Wang Shimin
2012-01-01
Full Text Available An analytical method is proposed to get the amplitude-frequency and the phase-frequency characteristics of free/forced oscillators with nonlinear restoring force. The nonlinear restoring force is expressed as a spring with varying stiffness that depends on the vibration amplitude. That is, for stationary vibration, the restoring force linearly depends on the displacement, but the stiffness of the spring varies with the vibration amplitude for nonstationary oscillations. The varied stiffness is constructed by means of the first and second averaged derivatives of the restoring force with respect to the displacement. Then, this stiffness gives the amplitude frequency and the phase frequency characteristics of the oscillator. Various examples show that this method can be applied extensively to oscillators with nonlinear restoring force, and that the solving process is extremely simple.
Ideal MHD beta-limits of poloidally asymmetric equilibria
Energy Technology Data Exchange (ETDEWEB)
Todd, A.M.M.; Miller, A.E.; Grimm, R.C.; Okabayashi, M.; Dalhed, H.E. Jr.
1981-05-01
The ideal MHD stability of poloidally asymmetric equilibria, which are typical of a tokamak reactor design with a single-null poloidal divertor is examined. As with symmetric equilibria, stability to non-axisymmetric modes improves with increasing triangularity and ellipticity, and with lower edge safety factor. Pressure profiles optimized with respect to ballooning stability are obtained for an asymmetric shape, resulting in ..beta../sub critical/ approx. = 5.7%. The corresponding value for an equivalent symmetric shape is ..beta../sub critical/ approx. = 6.5%.
Long-range correlations and coherent structures in magnetohydrodynamic equilibria.
Weichman, Peter B
2012-12-01
The equilibrium theory of the 2D magnetohydrodynamic equations is derived, accounting for the full infinite hierarchies of conserved integrals. An exact description in terms of two coupled elastic membranes emerges, producing long-ranged correlations between the magnetic and velocity fields. This is quite different from the results of previous variational treatments, which relied on a local product ansatz for the thermodynamic Gibbs distribution. The equilibria display the same type of coherent structures, such as compact eddies and zonal jets, previously found in pure fluid equilibria. Possible consequences of this for recent simulations of the solar tachocline are discussed.
A method of computational magnetohydrodynamics defining stable Scyllac equilibria.
Betancourt, O; Garabedian, P
1977-02-01
A computer code has been developed for the numerical calculation of sharp boundary equilibria of a toroidal plasma with diffuse pressure profile. This generalizes earlier work that was done separately on the sharp boundary and diffuse models, and it allows for large amplitude distortions of the plasma in three-dimensional space. By running the code, equilibria that are stable to the so-called m = 1, k = 0 mode have been found for Scyllac, which is a high beta toroidal confinement device of very large aspect ratio.
Nanoscale effects on thermodynamics and phase equilibria in oxide systems.
Navrotsky, Alexandra
2011-08-22
Because different solid materials (phases) have different surface energies, equilibria among them will be significantly affected by particle size. This Minireview summarizes experimental (calorimetric) data for the surface energies of oxides and discusses shifts in the stability of polymorphs, the thermodynamics of hydration, and oxidation-reduction reactions in nanoscale oxide systems.
Should Elliptical Galaxies Be Idealised as Collisionless Equilibria?
Kandrup, Henry E.
2000-01-01
This talk summarises several different lines of argument suggesting that one should not expect cuspy nonaxisymmetric galaxies to exist as robust, long-lived collisionless equilibria, i.e., that such objects should not be idealised as time-independent solutions to the collisionless Boltzmann equation.
Shallow-water vortex equilibria and their stability
Płotka, H.; Dritschel, D. G.
2011-12-01
We first describe the equilibrium form and stability of steadily-rotating simply-connected vortex patches in the single-layer quasi-geostrophic model of geophysical fluid dynamics. This model, valid for rotating shallow-water flow in the limit of small Rossby and Froude numbers, has an intrinsic length scale LD called the "Rossby deformation length" relating the strength of stratification to that of the background rotation rate. Specifically, LD = c/f where is a characteristic gravity-wave speed, g is gravity (or "reduced" gravity in a two-layer context where one layer is infinitely deep), H is the mean active layer depth, and f is the Coriolis frequency (here constant). We next introduce ageostrophic effects by using the full shallow-water model to generate what we call "quasi-equilibria". These equilibria are not strictly steady, but radiate such weak gravity waves that they are steady for all practical purposes. Through an artificial ramping procedure, we ramp up the potential vorticity anomaly of the fluid particles in our quasi-geostrophic equilibria to obtain shallow-water quasi-equilibria at finite Rossby number. We show a few examples of these states in this paper.
Deep water periodic waves as Hamiltonian relative equilibria
van Groesen, Embrecht W.C.; Lie She Liam, L.S.L.; Lakhturov, I.; Andonowati, A.; Biggs, N.
2007-01-01
We use a recently derived KdV-type of equation for waves on deep water to study Stokes waves as relative equilibria. Special attention is given to investigate the cornered Stokes-120 degree wave as a singular solution in the class of smooth steady wave profiles.
Computation of Stackelberg Equilibria of Finite Sequential Games
DEFF Research Database (Denmark)
Bosanski, Branislav; Branzei, Simina; Hansen, Kristoffer Arnsfelt
2015-01-01
The Stackelberg equilibrium is a solution concept that describes optimal strategies to commit to: Player~1 (the leader) first commits to a strategy that is publicly announced, then Player~2 (the follower) plays a best response to the leader's choice. We study Stackelberg equilibria in finite...
QUASI-EQUILIBRIA IN MARKETS WITH NON-CONVEX PREFERENCES.
An upper bound is placed on social divergence from general equilibrium , due to non-convexity of the traders’ preference relations. Existence and significance of certain quasi-equilibria are investigated. If there is a sufficiently large number of traders in the market, the existence of a configuration arbitrarily close to equilibrium is demonstrated. (Author)
Asset pricing puzzles explained by incomplete Brownian equilibria
DEFF Research Database (Denmark)
Christensen, Peter Ove; Larsen, Kasper
We examine a class of Brownian based models which produce tractable incomplete equilibria. The models are based on finitely many investors with heterogeneous exponential utilities over intermediate consumption who receive partially unspanned income. The investors can trade continuously on a finit...... markets. Consequently, our model can simultaneously help explaining the risk-free rate and equity premium puzzles....
Shallow-water vortex equilibria and their stability
Energy Technology Data Exchange (ETDEWEB)
Plotka, H; Dritschel, D G, E-mail: hanna@mcs.st-andrews.ac.uk, E-mail: dgd@mcs.st-andrews.ac.uk [School of Mathematics and Statistics, University of St Andrews, North Haugh, St. Andrews KY16 9SS (United Kingdom)
2011-12-22
We first describe the equilibrium form and stability of steadily-rotating simply-connected vortex patches in the single-layer quasi-geostrophic model of geophysical fluid dynamics. This model, valid for rotating shallow-water flow in the limit of small Rossby and Froude numbers, has an intrinsic length scale L{sub D} called the 'Rossby deformation length' relating the strength of stratification to that of the background rotation rate. Specifically, L{sub D} = c/f where c={radical}gH is a characteristic gravity-wave speed, g is gravity (or 'reduced' gravity in a two-layer context where one layer is infinitely deep), H is the mean active layer depth, and f is the Coriolis frequency (here constant). We next introduce ageostrophic effects by using the full shallow-water model to generate what we call 'quasi-equilibria'. These equilibria are not strictly steady, but radiate such weak gravity waves that they are steady for all practical purposes. Through an artificial ramping procedure, we ramp up the potential vorticity anomaly of the fluid particles in our quasi-geostrophic equilibria to obtain shallow-water quasi-equilibria at finite Rossby number. We show a few examples of these states in this paper.
From Singularity Theory to Finiteness of Walrasian Equilibria
DEFF Research Database (Denmark)
Castro, Sofia B.S.D.; Dakhlia, Sami F.; Gothen, Peter
The paper establishes that for an open and dense subset of smooth exchange economies, the number of Walrasian equilibria is finite. In particular, our results extend to non-regular economies; it even holds when restricted to the subset of critical ones. The proof rests on concepts from singularity...
Stable bootstrap-current driven equilibria for low aspect ratio tokamaks
Energy Technology Data Exchange (ETDEWEB)
Miller, R.L.; Lin-Liu, Y.R.; Turnbull, A.D.; Chan, V.S. [General Atomics, San Diego, CA (United States); Pearlstein, L.D. [Lawrence Livermore National Lab., CA (United States); Sauter, O.; Villard, L. [Ecole Polytechnique Federale, Lausanne (Switzerland). Centre de Recherche en Physique des Plasma (CRPP)
1996-09-01
Low aspect ratio tokamaks can potentially provide a high ratio of plasma pressure to magnetic pressure {beta} and high plasma current I at a modest size, ultimately leading to a high power density compact fusion power plant. For the concept to be economically feasible, bootstrap current must be a major component of the plasma. A high value of the Troyon factor {beta}{sub N} and strong shaping are required to allow simultaneous operation at high {beta} and high bootstrap current fraction. Ideal magnetohydrodynamic stability of a range of equilibria at aspect 1.4 is systematically explored by varying the pressure profile and shape. The pressure and current profiles are constrained in such a way as to assure complete bootstrap current alignment. Both {beta}{sub N} and {beta} are defined in terms of the vacuum toroidal field. Equilibria with {beta} {sub N}{>=}8 and {beta} {approx_equal}35% to 55% exist which are stable to n = {infinity} ballooning modes, and stable to n = 0,1,2,3 kink modes with a conducting wall. The dependence of {beta} and {beta}{sub N} with respect to aspect ratio is also considered. (author) 9 figs., 14 refs.
High-pressure fluid-phase equilibria: Experimental methods and systems investigated (2005-2008)
DEFF Research Database (Denmark)
Fonseca, José; Dohrn, Ralf; Peper, Stephanie
2011-01-01
A review of systems is given, for which experimental high-pressure phase-equilibrium data were published in the period between 2005 and 2008, continuing a series of reviews. To find candidates for articles that are of interest for this survey a three-stage search strategy was used including...... a systematic search of the contents of the 17 most important journals of the field. Experimental methods for the investigation of high-pressure phase equilibria were classified, described and illustrated using examples from articles of the period between 2005 and 2008. For the systems investigated......, the reference, the temperature and pressure range of the data, and the experimental method used for the measurements is given in 54 tables. Vapor–liquid equilibria, liquid–liquid equilibria, vapor–liquid–liquid equilibria, solid–liquid equilibria, solid–vapor equilibria, solid–vapor–liquid equilibria, critical...
Diophantine approximation and badly approximable sets
DEFF Research Database (Denmark)
Kristensen, S.; Thorn, R.; Velani, S.
2006-01-01
Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X. The clas......Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X....... The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...
Postperovskite phase equilibria in the MgSiO3-Al2O3 system.
Tsuchiya, Jun; Tsuchiya, Taku
2008-12-09
We investigate high-P,T phase equilibria of the MgSiO(3)-Al(2)O(3) system by means of the density functional ab initio computation methods with multiconfiguration sampling. Being different from earlier studies based on the static substitution properties with no consideration of Rh(2)O(3)(II) phase, present calculations demonstrate that (i) dissolving Al(2)O(3) tends to decrease the postperovskite transition pressure of MgSiO(3) but the effect is not significant ( approximately -0.2 GPa/mol% Al(2)O(3)); (ii) Al(2)O(3) produces the narrow perovskite+postperovskite coexisting P,T area (approximately 1 GPa) for the pyrolitic concentration (x(Al2O3) approximately 6 mol%), which is sufficiently responsible to the deep-mantle D'' seismic discontinuity; (iii) the transition would be smeared (approximately 4 GPa) for the basaltic Al-rich composition (x(Al2O3) approximately 20 mol%), which is still seismically visible unless iron has significant effects; and last (iv) the perovskite structure spontaneously changes to the Rh(2)O(3)(II) with increasing the Al concentration involving small displacements of the Mg-site cations.
Two Point Pade Approximants and Duality
Banks, Tom
2013-01-01
We propose the use of two point Pade approximants to find expressions valid uniformly in coupling constant for theories with both weak and strong coupling expansions. In particular, one can use these approximants in models with a strong/weak duality, when the symmetries do not determine exact expressions for some quantity.
DEFF Research Database (Denmark)
Krøll, Annette Elisabeth; Marcussen, Lis
1997-01-01
An equilibrium equation for pure component adsorption is compared to experiments and to the vacancy solution theory. The investigated equilibrium equation is a special case of a model for prediction of multicomponent adsorption equilibria.The vacancy solution theory for multicomponent systems req...
Rytov approximation in electron scattering
Krehl, Jonas; Lubk, Axel
2017-06-01
In this work we introduce the Rytov approximation in the scope of high-energy electron scattering with the motivation of developing better linear models for electron scattering. Such linear models play an important role in tomography and similar reconstruction techniques. Conventional linear models, such as the phase grating approximation, have reached their limits in current and foreseeable applications, most importantly in achieving three-dimensional atomic resolution using electron holographic tomography. The Rytov approximation incorporates propagation effects which are the most pressing limitation of conventional models. While predominately used in the weak-scattering regime of light microscopy, we show that the Rytov approximation can give reasonable results in the inherently strong-scattering regime of transmission electron microscopy.
Estimation of Fluid Properties and Phase Equilibria.
Herskowitz, M.
1985-01-01
Describes a course (given to junior/senior students with strong background in thermodynamics and transport phenomena) that covers the theoretical and practical aspects of properties estimation. An outline for the course is included. (JN)
Leike, Reimar H
2016-01-01
In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a ranking function that quantifies how "embarrassing" it is to communicate a given approximation. We show that there is only one ranking under the requirements that (1) the best ranked approximation is the non-approximated belief and (2) that the ranking judges approximations only by their predictions for actual outcomes. We find that this ranking is equivalent to the Kullback-Leibler divergence that is frequently used in the literature. However, there seems to be confusion about the correct order in which its functional arguments, the approximated and non-approximated beliefs, should be used. We hope that our elementary derivation settles the apparent confusion. We show for example that when approximating beliefs with Gaussian distributions the optimal approximation is given by moment matching. This is in contrast to many su...
Fisicaro, E; Braibanti, A; Sambasiva Rao, R; Compari, C; Ghiozzi, A; Nageswara Rao, G
1998-04-01
An algorithm is proposed for the estimation of binding parameters for the interaction of biologically important macromolecules with smaller ones from electrometric titration data. The mathematical model is based on the representation of equilibria in terms of probability concepts of statistical molecular thermodynamics. The refinement of equilibrium concentrations of the components and estimation of binding parameters (log site constant and cooperativity factor) is performed using singular value decomposition, a chemometric technique which overcomes the general obstacles due to near singularity. The present software is validated with a number of biochemical systems of varying number of sites and cooperativity factors. The effect of random errors of realistic magnitude in experimental data is studied using the simulated primary data for some typical systems. The safe area within which approximate binding parameters ensure convergence has been reported for the non-self starting optimization algorithms.
DEFF Research Database (Denmark)
Katajainen, Jyrki
2008-01-01
In this project the goal is to develop the safe * family of containers for the CPH STL. The containers to be developed should be safer and more reliable than any of the existing implementations. A special focus should be put on strong exception safety since none of the existing prototypes available...... at the CPH STL can give this guarantee for all operations. In spite of the safety requirements, the strict running-time requirements specified in the C++ standard, and additional requirements specified in the CPH STL design documents, must be fulfilled....
Rašin, Andrija
1994-01-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
On Element SDD Approximability
Avron, Haim; Toledo, Sivan
2009-01-01
This short communication shows that in some cases scalar elliptic finite element matrices cannot be approximated well by an SDD matrix. We also give a theoretical analysis of a simple heuristic method for approximating an element by an SDD matrix.
Paek, Min-Kyu; Do, Kyung-Hyo; Kang, Youn-Bae; Jung, In-Ho; Pak, Jong-Jin
2016-10-01
Deoxidation equilibria in high-Mn- and high-Al-alloyed liquid steels were studied over the entire Fe-Mn-Al composition range by both experiments and thermodynamic modeling. Effect of Mn on the Al deoxidation equilibria in liquid iron was measured by the different experimental techniques depending on the Al content. In order to confirm the reproducibility of the experimental results, the deoxidation experiments were carried out reversibly from high oxygen state by addition of Al as a deoxidizer, and from low oxygen state by addition of Fe2O3 or MnO as an oxygen source. For the Al-rich side, CaO flux was added on top of liquid iron in order to remove suspended Al2O3 inclusions in the melt. Based on the present experimental result and available critically evaluated literature data, the Al deoxidation equilibria in Fe-Mn-Al-O liquid alloy were thermodynamically modeled. The Modified Quasichemical Model was used in order to take into account a strong short-range ordering of atoms in molten state. Deoxidation equilibria and inclusion stability diagram for entire Fe-Mn-Al melt were successfully reproduced by the present model.
Approximate iterative algorithms
Almudevar, Anthony Louis
2014-01-01
Iterative algorithms often rely on approximate evaluation techniques, which may include statistical estimation, computer simulation or functional approximation. This volume presents methods for the study of approximate iterative algorithms, providing tools for the derivation of error bounds and convergence rates, and for the optimal design of such algorithms. Techniques of functional analysis are used to derive analytical relationships between approximation methods and convergence properties for general classes of algorithms. This work provides the necessary background in functional analysis a
Approximation of distributed delays
Lu, Hao; Eberard, Damien; Simon, Jean-Pierre
2010-01-01
We address in this paper the approximation problem of distributed delays. Such elements are convolution operators with kernel having bounded support, and appear in the control of time-delay systems. From the rich literature on this topic, we propose a general methodology to achieve such an approximation. For this, we enclose the approximation problem in the graph topology, and work with the norm defined over the convolution Banach algebra. The class of rational approximates is described, and a constructive approximation is proposed. Analysis in time and frequency domains is provided. This methodology is illustrated on the stabilization control problem, for which simulations results show the effectiveness of the proposed methodology.
Diophantine approximation and badly approximable sets
DEFF Research Database (Denmark)
Kristensen, S.; Thorn, R.; Velani, S.
2006-01-01
Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X. The clas......Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X...
EFFECT OF PROFILES AND SHAPE ON IDEAL STABILITY OF ADVANCED TOKAMAK EQUILIBRIA
Energy Technology Data Exchange (ETDEWEB)
MAKOWSKI,MA; CASPER,TA; FERRON,JR; TAYLOR,TS; TURNBULL,AD
2003-08-01
OAK-B135 The pressure profile and plasma shape, parameterized by elongation ({kappa}), triangularity ({delta}), and squareness ({zeta}), strongly influence stability. In this study, ideal stability of single null and symmetric, double-null, advanced tokamak (AT) configurations is examined. All the various shapes are bounded by a common envelope and can be realized in the DIII-D tokamak. The calculated AT equilibria are characterized by P{sub 0}/
{approx} 2.0-4.5, weak negative central shear, high q{sub min} (> 2.0), high bootstrap fraction, an H-mode pedestal, and varying shape parameters. The pressure profile is modeled by various polynomials together with a hyperbolic tangent pedestal, consistent with experimental observations. Stability is calculated with the DCON code and the resulting stability boundary is corroborated by GATO runs.
Sparse approximation with bases
2015-01-01
This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...
Experimental methods for phase equilibria at high pressures.
Dohrn, Ralf; Fonseca, José M S; Peper, Stephanie
2012-01-01
Knowledge of high-pressure phase equilibria is crucial in many fields, e.g., for the design and optimization of high-pressure chemical and separation processes, carbon capture and storage, hydrate formation, applications of ionic liquids, and geological processes. This review presents the variety of methods to measure phase equilibria at high pressures and, following a classification, discusses the measurement principles, advantages, challenges, and error sources. Examples of application areas are given. A detailed knowledge and understanding of the different methods is fundamental not only for choosing the most suitable method for a certain task but also for the evaluation of experimental data. The discrepancy between the (sometimes low) true accuracy of published experimental data and the (high) accuracy claimed by authors is addressed. Some essential requirements for the generation of valuable experimental results are summarized.
Vlasov tokamak equilibria with shearad toroidal flow and anisotropic pressure
Kuiroukidis, Ap; Tasso, H
2015-01-01
By choosing appropriate deformed Maxwellian ion and electron distribution functions depending on the two particle constants of motion, i.e. the energy and toroidal angular momentum, we reduce the Vlasov axisymmetric equilibrium problem for quasineutral plasmas to a transcendental Grad-Shafranov-like equation. This equation is then solved numerically under the Dirichlet boundary condition for an analytically prescribed boundary possessing a lower X-point to construct tokamak equilibria with toroidal sheared ion flow and anisotropic pressure. Depending on the deformation of the distribution functions these steady states can have toroidal current densities either peaked on the magnetic axis or hollow. These two kinds of equilibria may be regarded as a bifurcation in connection with symmetry properties of the distribution functions on the magnetic axis.
Phase diagrams and heterogeneous equilibria a practical introduction
Predel, Bruno; Pool, Monte
2004-01-01
This graduate-level textbook provides an introduction to the practical application of phase diagrams. It is intended for students and researchers in chemistry, metallurgy, mineralogy, and materials science as well as in engineering and physics. Heterogeneous equilibria are described by a minimum of theory illustrated by practical examples and realistic case discussions from the different fields of application. The treatment of the physical and energetic background of phase equilibria leads to the discussion of the thermodynamics of mixtures and the correlation between energetics and composition. Thus, tools for the prediction of energetic, structural, and physical quantities are provided. The authors treat the nucleation of phase transitions, the production and stability of technologically important metastable phases, and metallic glasses. Furthermore, the text also concisely presents the thermodynamics and composition of polymer systems.
Bifurcation Analysis of Equilibria in Competitive Logistic Networks with Adaptation
Raimondi, A.; Tebaldi, C.
2008-04-01
A general n-node network is considered for which, in absence of interactions, each node is governed by a logistic equation. Interactions among the nodes take place in the form of competition, which also includes adaptive abilities through a (short term) memory effect. As a consequence the dynamics of the network is governed by a system of n2 nonlinear ordinary differential equations. As a first step, equilibria and their stability are investigated analytically for the general network in dependence of the relevant parameters, namely the strength of competition, the adaptation rate and the network size. The existence of classes of invariant subspaces, related to symmetries, allows the introduction of a reduced model, four dimensional, where n appears as a parameter, which give full account of existence and stability for the equilibria in the network.
A Novel Formulation of Baroclinic Rotational Equilibria
Yasutake, Nobutoshi
2014-01-01
We have developed a new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. It is applicable not only to barotropic equations of state but also to baroclinic ones, for which angular momentum distributions are not cylindrical. The formulation is based on the Lagrangian variational principle. Some test calculations are presented, in which we have achieved an error of $O(10^{-4})$ in the Virial relation. We believe that this method could be a major break-through in stellar evolution theory, in which it is a common practice that rotation is included only approximately in one dimensional models.
Generalized statistical model for multicomponent adsorption equilibria on zeolites
Energy Technology Data Exchange (ETDEWEB)
Rota, R.; Gamba, G.; Paludetto, R.; Carra, S.; Morbidelli, M. (Dipartimento di Chimica Fisica Applicata, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano (IT))
1988-05-01
The statistical thermodynamic approach to multicomponent adsorption equilibria on zeolites has been extended to nonideal systems, through the correction of cross coefficients characterizing the interaction between unlike molecules. Estimation of the model parameters requires experimental binary equilibrium data. Comparisons with the classical model based on adsorbed solution theory are reported for three nonideal ternary systems. The two approaches provide comparable results in the simulation of binary and ternary adsorption equilibrium data at constant temperature and pressure.
Generalized Thermodynamics of Phase Equilibria in Scalar Active Matter
Solon, Alexandre P.; Stenhammar, Joakim; Cates, Michael E.; Kafri, Yariv; Tailleur, Julien
2016-01-01
Motility-induced phase separation (MIPS) arises generically in fluids of self-propelled particles when interactions lead to a kinetic slowdown at high density. Starting from a continuum description of diffusive scalar active matter, we give a general prescription for phase equilibria that amounts, at a hydrodynamics scale, to extremalizing a generalized free energy. We illustrate our approach on two well known models: self-propelled particles interacting either through a density-dependent pro...
Correlated Equilibria in Continuous Games: Characterization and Computation
2008-12-22
Annals of Mathematics Studies, pages 75 – 86. Princeton University Press, Princeton, NJ, 1953. [9] M. Dresher, S. Karlin, and L. S. Shapley. Polynomial...games. In H. W. Kuhn and A. W. Tucker, editors, Contributions to the Theory of Games I, number 24 in Annals of Mathematics Studies, pages 161 – 180...J. Lipton and E. Markakis. Nash equilibria via polynomial equations. In Proceedings of LATIN, 2004. [18] J. F. Nash. Non-cooperative games. Annals of Mathematics , 54
Liquid equilibria in the Fe-Ni-Mn system
Energy Technology Data Exchange (ETDEWEB)
Schuermann, E. [Technische Univ. Clausthal, Clausthal-Zellerfeld (Germany). Inst. fuer Eisenhuettenkunde und Giessereiwesen; Djurdjevic, M.; Nedeljkovic, L. [Belgrade Univ. (Yugoslavia). Faculty of Technology and Metallurgy
1997-12-01
New literature results on the liquid equilibria in the three edge binary systems make necessary a reconsideration and correction of liquidus surfaces of the {gamma} and {delta} solid solutions hitherto outlined in the literature. Therefore, with respect to the critically reinterpreted edge binary systems, the shape of the stable liquidus surface of the {gamma} and {delta} solid solutions has been newly outlined. (orig.) 7 refs.
Directory of Open Access Journals (Sweden)
Pongsakorn Sunthrayuth
2012-01-01
Full Text Available We introduce a new general system of generalized nonlinear mixed composite-type equilibria and propose a new iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a general system of generalized nonlinear mixed composite-type equilibria, and the set of fixed points of a countable family of strict pseudocontraction mappings. Furthermore, we prove the strong convergence theorem of the purposed iterative scheme in a real Hilbert space. As applications, we apply our results to solve a certain minimization problem related to a strongly positive bounded linear operator. Finally, we also give a numerical example which supports our results. The results obtained in this paper extend the recent ones announced by many others.
Relative Equilibria in the Spherical, Finite Density Three-Body Problem
Scheeres, D. J.
2016-10-01
The relative equilibria for the spherical, finite density three-body problem are identified. Specifically, there are 28 distinct relative equilibria in this problem which include the classical five relative equilibria for the point-mass three-body problem. None of the identified relative equilibria exist or are stable over all values of angular momentum. The stability and bifurcation pathways of these relative equilibria are mapped out as the angular momentum of the system is increased. This is done under the assumption that they have equal and constant densities and that the entire system rotates about its maximum moment of inertia. The transition to finite density greatly increases the number of relative equilibria in the three-body problem and ensures that minimum energy configurations exist for all values of angular momentum.
Nash equilibria in multi-agent motor interactions.
Directory of Open Access Journals (Sweden)
Daniel A Braun
2009-08-01
Full Text Available Social interactions in classic cognitive games like the ultimatum game or the prisoner's dilemma typically lead to Nash equilibria when multiple competitive decision makers with perfect knowledge select optimal strategies. However, in evolutionary game theory it has been shown that Nash equilibria can also arise as attractors in dynamical systems that can describe, for example, the population dynamics of microorganisms. Similar to such evolutionary dynamics, we find that Nash equilibria arise naturally in motor interactions in which players vie for control and try to minimize effort. When confronted with sensorimotor interaction tasks that correspond to the classical prisoner's dilemma and the rope-pulling game, two-player motor interactions led predominantly to Nash solutions. In contrast, when a single player took both roles, playing the sensorimotor game bimanually, cooperative solutions were found. Our methodology opens up a new avenue for the study of human motor interactions within a game theoretic framework, suggesting that the coupling of motor systems can lead to game theoretic solutions.
On the complexity of Nash dynamics and Sink Equilibria
Mirrokni, Vahab
2009-01-01
Studying Nash dynamics is an important approach for analyzing the outcome of games with repeated selfish behavior of self-interested agents. Sink equilibria has been introduced by Goemans, Mirrokni, and Vetta for studying social cost on Nash dynamics over pure strategies in games. However, they do not address the complexity of sink equilibria in these games. Recently, Fabrikant and Papadimitriou initiated the study of the complexity of Nash dynamics in two classes of games. In order to completely understand the complexity of Nash dynamics in a variety of games, we study the following three questions for various games: (i) given a state in game, can we verify if this state is in a sink equilibrium or not? (ii) given an instance of a game, can we verify if there exists any sink equilibrium other than pure Nash equilibria? and (iii) given an instance of a game, can we verify if there exists a pure Nash equilibrium (i.e, a sink equilibrium with one state)? In this paper, we almost answer all of the above question...
2011-01-01
Modeling the Thermodynamic and Transport Properties of Decahydronaphthalene/Propane Mixtures: Phase Equilibria , Density, and Viscosity Nathaniel...Decahydronaphthalene/Propane Mixtures: Phase Equilibria , Density, And Viscosity 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d...Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 Keywords: phase equilibria ; modified Sanchez-Lacombe equation of state
Approximation techniques for engineers
Komzsik, Louis
2006-01-01
Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you''re looking for approximate solutions to engineering problems, everything you need is nestled between the covers of this book. Now you can benefit from Louis Komzsik''s years of industrial experience to gain a working knowledge of a vast array of approximation techniques through this complete and self-contained resource.
Achieser, N I
2004-01-01
A pioneer of many modern developments in approximation theory, N. I. Achieser designed this graduate-level text from the standpoint of functional analysis. The first two chapters address approximation problems in linear normalized spaces and the ideas of P. L. Tchebysheff. Chapter III examines the elements of harmonic analysis, and Chapter IV, integral transcendental functions of the exponential type. The final two chapters explore the best harmonic approximation of functions and Wiener's theorem on approximation. Professor Achieser concludes this exemplary text with an extensive section of pr
Strong convergence theorems for strongly relatively nonexpansive sequences and applications
Aoyama, Koji; Kohsaka, Fumiaki
2012-01-01
The aim of this paper is to establish strong convergence theorems for a strongly relatively nonexpansive sequence in a smooth and uniformly convex Banach space. Then we employ our results to approximate solutions of the zero point problem for a maximal monotone operator and the fixed point problem for a relatively nonexpansive mapping.
Electroconvective instability of self-similar equilibria
Demekhin, E; Shtemler, Yury
2010-01-01
Stability of electro-hydrodynamic processes between ion-exchange membranes is investigated. Solutions of the equilibrium problem which represents the balance between diffusion and electro-migration are commonly described in an one-dimensional (1D) steady-state approximation. In the present work a novel class of the 1D unsteady self-similar equilibrium solution is developed asymptotically in small Debye length, epsilon, and large distance between membranes (both made dimensionless with the diffusion-layer thickness). First, the 1D unsteady family of self-similar equilibrium solutions is developed. Then, a linear stability of the self-similar solutions slowly varied with time is investigated in the limit of small epsilonand the marginal stability curves are obtained. Method of matched asymptotics is applied provided that only the outer solution is considered, ignoring the inner solutions. The success of the analysis is provided by transforming the equations to the divergent type (nabla G=0) with the patching co...
Stability and attractive basins of multiple equilibria in delayed two-neuron networks
Institute of Scientific and Technical Information of China (English)
Huang Yu-Jiao; Zhang Hua-Guang; Wang Zhan-Shan
2012-01-01
Multiple stability for two-dimensional delayed recurrent neural networks with piecewise linear activation functions of 2r (r ≥ 1) corner points is studied.Sufficient conditions are established for checking the existence of (2r + 1)2 equilibria in delayed recurrent neural networks.Under these conditions,(r + 1)2 equilibria are locally exponentially stable,and (2r + 1)2 - (r + 1)2 - r2 equilibria are unstable.Attractive basins of stable equilibria are estimated,which are larger than invariant sets derived by decomposing state space.One example is provided to illustrate the effectiveness of our results.
Expectation Consistent Approximate Inference
DEFF Research Database (Denmark)
Opper, Manfred; Winther, Ole
2005-01-01
We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood from replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability dis...
Ordered cones and approximation
Keimel, Klaus
1992-01-01
This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.
Approximate Modified Policy Iteration
Scherrer, Bruno; Ghavamzadeh, Mohammad; Geist, Matthieu
2012-01-01
Modified policy iteration (MPI) is a dynamic programming (DP) algorithm that contains the two celebrated policy and value iteration methods. Despite its generality, MPI has not been thoroughly studied, especially its approximation form which is used when the state and/or action spaces are large or infinite. In this paper, we propose three approximate MPI (AMPI) algorithms that are extensions of the well-known approximate DP algorithms: fitted-value iteration, fitted-Q iteration, and classification-based policy iteration. We provide an error propagation analysis for AMPI that unifies those for approximate policy and value iteration. We also provide a finite-sample analysis for the classification-based implementation of AMPI (CBMPI), which is more general (and somehow contains) than the analysis of the other presented AMPI algorithms. An interesting observation is that the MPI's parameter allows us to control the balance of errors (in value function approximation and in estimating the greedy policy) in the fina...
Pressure, Chaotic Magnetic Fields and MHD Equilibria
Energy Technology Data Exchange (ETDEWEB)
S.R. Hudson & N. Nakajima
2010-05-12
Analyzes of plasma behavior often begin with a description of the ideal magnetohydrodynamic equilibrium, this being the simplest model capable of approximating macroscopic force balance. Ideal force balance is when the pressure gradient is supported by the Lorentz force, ∇p = j x B. We discuss the implications of allowing for a chaotic magnetic field on the solutions to this equation. We argue that the solutions are pathological and not suitable for numerical calculations. If the pressure and magnetic Field are continuous, the only non-trivial solutions have an uncountable infinity of discontinuities in the pressure gradient and current. The problems arise from the arbitrarily small length scales in the structure of the field, and the consequence of ideal force balance that the pressure is constant along the Field-lines, B • ∇p = 0. A simple method to ameliorate the singularities is to include a small but Finite perpendicular diffusion. A self-consistent set of equilibrium equations is described and some algorithmic approaches aimed at solving these equations are discussed.
Spectroscopic studies on U(VI)-salicylate complex formation with multiple equilibria
Energy Technology Data Exchange (ETDEWEB)
Cha, W.; Cho, H.R.; Jung, E.C.; Park, K.K.; Kim, W.H.; Song, K. [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of). Nuclear Chemistry Research Div.
2012-07-01
This study investigates multiple equilibria related to the formation of the U(VI)-salicylate complex in a pH range of 3.0-5.5 using UV-Vis absorption and fluorescence measurement techniques. The absorbance changes at the characteristic charge-transfer bands of the complex were monitored, and the results indicated the presence of multiple equilibria and the formation of both 1:1 and 1:2 (U(VI):salicylate) complexes possessing bi-dentate chelate structures. The determined step-wise formation constants (log K{sub 1:1} and log K{sub 1:2}) are as follows: 12.5 {+-} 0.1 and 11.4 {+-} 0.2 for salicylate, 11.2 {+-} 0.1 and 10.1 {+-} 0.2 for 5-sulfosalicylate, and 12.4 {+-} 0.1 and 11.4 {+-} 0.1 for 2,6-dihydroxybenzoate, respectively. The molar absorptivities of the complexes are also provided. Furthermore, time-resolved laser-induced luminescence spectra of U(VI) species demonstrate the presence of both a dynamic and static quenching process upon the addition of a salicylate ligand. Particularly for the luminescent hydroxouranyl species, a strong static quenching effect is observed. The results suggest that both the UO{sub 2}(HSal){sup +} and the U(VI)-Sal chelate complexes serve as ground-state complexes that induce static quenching. The Stern-Volmer parameters were derived based on the measured luminescent intensity and lifetime data. The static quenching constants (log K{sub S}) obtained are 3.3 {+-} 0.1, 4.9 {+-} 0.1, and 4.4 {+-} 0.1 for UO{sub 2}{sup 2+}, (UO{sub 2}){sub 2}(OH){sub 2}{sup 2+} and (UO{sub 2}){sub 3}(OH){sub 5}{sup +}, respectively. (orig.)
Approximate calculation of integrals
Krylov, V I
2006-01-01
A systematic introduction to the principal ideas and results of the contemporary theory of approximate integration, this volume approaches its subject from the viewpoint of functional analysis. In addition, it offers a useful reference for practical computations. Its primary focus lies in the problem of approximate integration of functions of a single variable, rather than the more difficult problem of approximate integration of functions of more than one variable.The three-part treatment begins with concepts and theorems encountered in the theory of quadrature. The second part is devoted to t
Approximate and renormgroup symmetries
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, Nail H. [Blekinge Institute of Technology, Karlskrona (Sweden). Dept. of Mathematics Science; Kovalev, Vladimir F. [Russian Academy of Sciences, Moscow (Russian Federation). Inst. of Mathematical Modeling
2009-07-01
''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)
Approximating Stationary Statistical Properties
Institute of Scientific and Technical Information of China (English)
Xiaoming WANG
2009-01-01
It is well-known that physical laws for large chaotic dynamical systems are revealed statistically. Many times these statistical properties of the system must be approximated numerically. The main contribution of this manuscript is to provide simple and natural criterions on numerical methods (temporal and spatial discretization) that are able to capture the stationary statistical properties of the underlying dissipative chaotic dynamical systems asymptotically. The result on temporal approximation is a recent finding of the author, and the result on spatial approximation is a new one. Applications to the infinite Prandtl number model for convection and the barotropic quasi-geostrophic model are also discussed.
Approximation of the Inverse -Frame Operator
Indian Academy of Sciences (India)
M R Abdollahpour; A Najati
2011-05-01
In this paper, we introduce the concept of (strong) projection method for -frames which works for all conditional -Riesz frames. We also derive a method for approximation of the inverse -frame operator which is efficient for all -frames. We show how the inverse of -frame operator can be approximated as close as we like using finite-dimensional linear algebra.
Directory of Open Access Journals (Sweden)
Malvina Baica
1985-01-01
Full Text Available The author uses a new modification of Jacobi-Perron Algorithm which holds for complex fields of any degree (abbr. ACF, and defines it as Generalized Euclidean Algorithm (abbr. GEA to approximate irrationals.
Approximations in Inspection Planning
DEFF Research Database (Denmark)
Engelund, S.; Sørensen, John Dalsgaard; Faber, M. H.
2000-01-01
Planning of inspections of civil engineering structures may be performed within the framework of Bayesian decision analysis. The effort involved in a full Bayesian decision analysis is relatively large. Therefore, the actual inspection planning is usually performed using a number of approximations....... One of the more important of these approximations is the assumption that all inspections will reveal no defects. Using this approximation the optimal inspection plan may be determined on the basis of conditional probabilities, i.e. the probability of failure given no defects have been found...... by the inspection. In this paper the quality of this approximation is investigated. The inspection planning is formulated both as a full Bayesian decision problem and on the basis of the assumption that the inspection will reveal no defects....
The Karlqvist approximation revisited
Tannous, C
2015-01-01
The Karlqvist approximation signaling the historical beginning of magnetic recording head theory is reviewed and compared to various approaches progressing from Green, Fourier, Conformal mapping that obeys the Sommerfeld edge condition at angular points and leads to exact results.
Approximations in Inspection Planning
DEFF Research Database (Denmark)
Engelund, S.; Sørensen, John Dalsgaard; Faber, M. H.
2000-01-01
Planning of inspections of civil engineering structures may be performed within the framework of Bayesian decision analysis. The effort involved in a full Bayesian decision analysis is relatively large. Therefore, the actual inspection planning is usually performed using a number of approximations....... One of the more important of these approximations is the assumption that all inspections will reveal no defects. Using this approximation the optimal inspection plan may be determined on the basis of conditional probabilities, i.e. the probability of failure given no defects have been found...... by the inspection. In this paper the quality of this approximation is investigated. The inspection planning is formulated both as a full Bayesian decision problem and on the basis of the assumption that the inspection will reveal no defects....
Gautschi, Walter; Rassias, Themistocles M
2011-01-01
Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovia, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational alg
Approximation Behooves Calibration
DEFF Research Database (Denmark)
da Silva Ribeiro, André Manuel; Poulsen, Rolf
2013-01-01
Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009.......Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009....
Thermodynamic assessment of hydrothermal alkali feldspar-mica-aluminosilicate equilibria
Sverjensky, Dimitri A.; Hemley, J. J.; D'angelo, W. M.
1991-04-01
The thermodynamic properties of minerals retrieved from consideration of solid-solid and dehydration equilibria with calorimetric reference values, and those of aqueous species derived from studies of electrolytes, are not consistent with experimentally measured high-temperature solubilities in the systems K 2O- and Na 2O-Al 2O 3-SiO 2-H 2O-HCl (e.g., K-fs - Ms - Qtz - K + - H +). This introduces major inaccuracies into the computation of ionic activity ratios and the acidities of diagenetic, metamorphic, and magmatic hydrothermal fluids buffered by alkali silicate-bearing assemblages. We report a thermodynamic analysis of revised solubility equilibria in these systems that integrates the thermodynamic properties of minerals obtained from phase equilibria studies ( BERMAN, 1988) with the properties of aqueous species calculated from a calibrated equation of state ( SHOCK and HELGESON, 1988). This was achieved in two separate steps. First, new values of the free energies and enthalpies of formation at 25°C and 1 bar for the alkali silicates muscovite and albite were retrieved from the experimental solubility equilibria at 300°C and P sat. Because the latter have stoichiometric reaction coefficients different from those for solid-solid and dehydration equilibria, our procedure preserves exactly the relative thermodynamic properties of the alkali-bearing silicates ( BERMAN, 1988). Only simple arithmetic adjustments of -1,600 and -1,626 ( ±500) cal/mol to all the K- and Na-bearing silicates, respectively, in BERMAN (1988) are required. In all cases, the revised values are within ±0.2% of calorimetric values. Similar adjustments were derived for the properties of minerals from HELGESON et al. (1978). Second, new values of the dissociation constant of HCl were retrieved from the solubility equilibria at temperatures and pressures from 300-600°C and 0.5-2.0 kbars using a simple model for aqueous speciation. The results agree well with the conductance
Approximate kernel competitive learning.
Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang
2015-03-01
Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches.
Directory of Open Access Journals (Sweden)
Maksim Duškin
2015-11-01
Full Text Available Approximation and supposition This article compares exponents of approximation (expressions like Russian около, примерно, приблизительно, более, свыше and the words expressing supposition (for example Russian скорее всего, наверное, возможно. These words are often confused in research, in particular researchers often mention exponents of supposition in case of exponents of approximation. Such approach arouses some objections. The author intends to demonstrate in this article a notional difference between approximation and supposition, therefore the difference between exponents of these two notions. This difference could be described by specifying different attitude of approximation and supposition to the notion of knowledge. Supposition implies speaker’s ignorance of the exact number, while approximation does not mean such ignorance. The article offers examples proving this point of view.
Phase equilibria in the In–Sb–Bi system at 300 ºC
Directory of Open Access Journals (Sweden)
DUSKO MINIC
2006-07-01
Full Text Available Binary thermodynamic data, successfully used for phase diagram calculations of the binary systems In–Sb, Bi–Sb and In–Bi, were used fort the prediction of phase equilibria in the ternary system In–Sb–Bi at 300 ºC. The predicted equilibria were compared with the results of SEM–EDX analysis.
Looking for multiple equilibria when geography matters : German city growth and the WWII shock
Bosker, Maarten; Brakman, Steven; Garretsen, Harry; Schramm, Marc
2007-01-01
Based on the methodology of Davis and Weinstein, we look for multiple equilibria in German city growth. Bytaking the bombing of Germany during WWII as an example of a large, temporary shock, we analyze whether German city growth is characterized by multiple equilibria. In doing so, we allow for spat
Liquid-liquid equilibria for ternary polymer mixtures
Oh, Suk Yung; Bae, Young Chan
2011-01-01
A molecular thermodynamic model for multicomponent systems based on a closed-packed lattice model is presented based on two contributions; entropy and energy contribution. The calculated liquid-liquid equilibria of ternary chainlike mixtures agreed with Monte Carlo simulation results. The proposed model can satisfactorily predict Types 0, 1, 2 and 3 phase separations of the Treybal classification. The model parameters obtained from the binary systems were used to directly predict real ternary systems and the calculated results correlated well with experimental data using few adjustable parameters. Specific interactions in associated binary systems were considered using a secondary lattice.
Anomeric and tautomeric equilibria in D-2-glucosamine Schiff bases
Kołodziej, B.; Grech, E.; Schilf, W.; Kamieński, B.; Makowski, M.; Rozwadowski, Z.; Dziembowska, T.
2007-11-01
The structure of some glucosamine Schiff bases has been studied by means of ab initio RHF and DFT calculation and CP/MAS 13C and 15N NMR measurements. The anomeric and tautomeric equilibria in a DMSO solution have been studied by 1H, 13C and 15N NMR spectroscopy. The anomeric composition of D-2-glucosamine Schiff bases in the solid state and in DMSO solution has been shown to depends on the tautomeric form of Schiff bases and electronic properties of substituents on the aromatic ring.
Application of conformal solution theory to gas-gas equilibria
Energy Technology Data Exchange (ETDEWEB)
Tan, P.Y.; Luks, K.D.; Kozak, J.J.
1971-08-01
The conformal solution theory (CST) is applied to the problem of gas-gas immiscibility. It is found that the occurrence of this phenomena can be predicted in the system He-Xe; in particular, the calculated critical locus is in satisfactory agreement with the experimental data of de Swaan Arons and Diepen, provided a suitable reference is chosen. Furthermore, using CST as a guide, it was found that criteria could be developed, related to Temkin's criteria, which permit the prediction and classification of the 3 types of gas-gas equilibria known to occur in mixtures of nonpolar molecules. (10 refs.)
Cryptographically Blinded Games: Leveraging Players' Limitations for Equilibria and Profit
DEFF Research Database (Denmark)
Hubacek, Pavel; Park, Sunoo
2014-01-01
In this work we apply methods from cryptography to enable mutually distrusting players to implement broad classes of mediated equilibria of strategic games without trusted mediation. Our implementation uses a pre-play 'cheap talk' phase, consisting of non- binding communication between players pr...... prior to play in the original game. In the cheap talk phase, the players run a secure multi-party computation protocol to sample from an equilibrium of a "cryptographically blinded" version of the game, in which actions are encrypted...
Solitonlike solutions of magnetostatic equilibria: Plane-symmetric case
Yoshino, Hirotaka
2008-01-01
We present the plane-symmetric solitonlike solutions of magnetostatic equilibria by solving the nonlinear Grad-Shafranov (GS) equation numerically. The solutions have solitonlike and periodic structures in the $x$ and $y$ directions, respectively, and $z$ is the direction of plane symmetry. Although such solutions are unstable against the numerical iteration, we give the procedure to realize the sufficient convergence. Our result provides the definite answer for the existence of the solitonlike solutions that was questioned in recent years. The method developed in this paper will make it possible to study the axisymmetric solitonlike solutions of the nonlinear GS equation, which could model astrophysical jets with knotty structures.
Nas-Walras equilibria of a large economy.
Minelli, E; Polemarchakis, H M
2000-05-09
Individuals exchange contracts for the delivery of commodities in competitive markets and, simultaneously, act strategically; actions affect utilities across individuals directly or through the payoffs of contracts. This encompasses economies with asymmetric information. Nash-Walras equilibria exist for large economies, even if utility functions are not quasi-concave and choice sets are not convex, which is the case in standard settings; the separation of the purchase from the sale of contracts and the pooling of the deliveries on contracts guarantee that the markets for commodities clear.
Energy Technology Data Exchange (ETDEWEB)
Baseri, Hadi [School of Chemical, Gas and Petroleum Engineering, Semnan University, Semnan 35196-45399 (Iran, Islamic Republic of); Lotfollahi, Mohammad Nader, E-mail: mnlotfollahi@semnan.ac.ir [School of Chemical, Gas and Petroleum Engineering, Semnan University, Semnan 35196-45399 (Iran, Islamic Republic of)
2011-10-15
Highlights: > Extended PR-EOS was presented for VLE of H{sub 2}O/Salt/CO{sub 2} systems at high pressure. > The proposed EPR-EOS is based upon contributions to the Helmholtz energy. > Born, Margules, and Debye-Huckel or mean spherical approximation terms were used. > Two different mixing rules Panagiotopoulos and Reid and Kwak and Mansoori (KM) were used. > A combination of KM mixing rule with DH term results more accurate VLE results. - Abstract: A modification of the extended Peng-Robinson equation of state (PR-EOS) is presented to describe the (vapour + liquid) equilibria of systems containing water and salts. The modification employs three additional terms including a Born term, a Margules term and two terms separately used for estimation of the long-range electrostatic interactions (the Debye-Huckel (DH) or the mean spherical approximation (MSA) terms). Effects of two mixing rules, first, the Panagiotopoulos and Reid mixing rule (PR) and, second, the Kwak and Mansoori mixing rule (KM), on the final values of VLE calculations are also investigated. The results show that the KM mixing rule is more appropriate than the PR mixing rule. The proposed equation of state is used to calculate the (vapour + liquid) equilibrium (VLE) of the systems containing (water + sodium sulphate + carbon dioxide) and (water + sodium chloride + carbon dioxide) at high pressure. The comparison of calculated results with the experimental data shows that a combination of KM mixing rule with the DH term results a more accurate VLE values.
Quasi-Leontief utility functions on partially ordered sets II: Nash equilibria
Briec, Walter; Horvath, Charles
2011-01-01
We prove that, under appropriate conditions, an abstract game with quasi-Leontief payoff functions $u_i : \\prod_{j=1}^nX_j\\to\\mathbb{R}$ has a Nash equilibria. When all the payoff functions are globally quasi-Leontief, the existence and the characterization of efficient Nash equilibria mainly follows from the analysis carried out in part I. When the payoff functions are individually quasi-Leontief functions the matter is somewhat more complicated. We assume that all the strategy spaces are compact topological semilattices, and under appropriate continuity conditions on the payoff functions, we show that there exists an efficient Nash equilibria using the Eilenberg-Montgomery Fixed Point Theorem for acyclic valued upper semicontinuous maps defined on an absolute retract and some non trivial properties of topological semilattices. The map in question is defined on the set of Nash equilibria and its fixed points are exactly the efficient Nash equilibria.
Directory of Open Access Journals (Sweden)
Christiansen Ditte G
2009-06-01
Full Text Available Abstract Background Triploid individuals often play a key role in speciation by hybridization. An understanding of the gamete types (ploidy and genomic content and stability of hybrid populations with triploid individuals is therefore of importance for exploring the role of hybridization in evolution. The all-hybrid populations of the edible frog, Pelophylax esculentus, are unique in their composition and genetic dynamics: Diploid (genotype LR and triploid (LLR and LRR hybrids depend on each other's different gamete contributions for successful reproduction and maintenance of the populations, as the parental genotypes P. lessonae (LL and P. ridibundus (RR are absent among adults. This study provides data and interpretations on gamete types and sex determination that are essential for understanding the function, evolutionary potential and threats of this intriguing system. Results Dissection of metamorphs from a crossing experiment confirmed that sex determination is an XX-XY system with the Y confined to the L genome. From microsatellite analysis of parents and offspring from the crossings, gamete frequencies could be deduced: Triploids of both sexes mostly made haploid gametes with the genome they had in double dose, however LLR females also made approximately 10% LL gametes by automixis. LR frogs showed much variation in their gamete production. In LRR-rich populations, their LR sperm production was sufficiently high (22% to explain the observed proportion of LRR males, the formation of which has not previously been understood. A model was constructed to calculate equilibrium genotype proportions for different population types on the basis of the gamete proportions found. These equilibria agreed well with empirical literature data. Conclusion If population differentiation with respect to genotype proportions is really driven by gamete patterns, as strongly suggested by the present study, all-hybrid populations constitute not one, but several
Christiansen, Ditte G
2009-01-01
Background Triploid individuals often play a key role in speciation by hybridization. An understanding of the gamete types (ploidy and genomic content) and stability of hybrid populations with triploid individuals is therefore of importance for exploring the role of hybridization in evolution. The all-hybrid populations of the edible frog, Pelophylax esculentus, are unique in their composition and genetic dynamics: Diploid (genotype LR) and triploid (LLR and LRR) hybrids depend on each other's different gamete contributions for successful reproduction and maintenance of the populations, as the parental genotypes P. lessonae (LL) and P. ridibundus (RR) are absent among adults. This study provides data and interpretations on gamete types and sex determination that are essential for understanding the function, evolutionary potential and threats of this intriguing system. Results Dissection of metamorphs from a crossing experiment confirmed that sex determination is an XX-XY system with the Y confined to the L genome. From microsatellite analysis of parents and offspring from the crossings, gamete frequencies could be deduced: Triploids of both sexes mostly made haploid gametes with the genome they had in double dose, however LLR females also made approximately 10% LL gametes by automixis. LR frogs showed much variation in their gamete production. In LRR-rich populations, their LR sperm production was sufficiently high (22%) to explain the observed proportion of LRR males, the formation of which has not previously been understood. A model was constructed to calculate equilibrium genotype proportions for different population types on the basis of the gamete proportions found. These equilibria agreed well with empirical literature data. Conclusion If population differentiation with respect to genotype proportions is really driven by gamete patterns, as strongly suggested by the present study, all-hybrid populations constitute not one, but several intrinsically different
Covariant approximation averaging
Shintani, Eigo; Blum, Thomas; Izubuchi, Taku; Jung, Chulwoo; Lehner, Christoph
2014-01-01
We present a new class of statistical error reduction techniques for Monte-Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in $N_f=2+1$ lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte-Carlo calculations over conventional methods for the same cost.
Diophantine approximations on fractals
Einsiedler, Manfred; Shapira, Uri
2009-01-01
We exploit dynamical properties of diagonal actions to derive results in Diophantine approximations. In particular, we prove that the continued fraction expansion of almost any point on the middle third Cantor set (with respect to the natural measure) contains all finite patterns (hence is well approximable). Similarly, we show that for a variety of fractals in [0,1]^2, possessing some symmetry, almost any point is not Dirichlet improvable (hence is well approximable) and has property C (after Cassels). We then settle by similar methods a conjecture of M. Boshernitzan saying that there are no irrational numbers x in the unit interval such that the continued fraction expansions of {nx mod1 : n is a natural number} are uniformly eventually bounded.
Monotone Boolean approximation
Energy Technology Data Exchange (ETDEWEB)
Hulme, B.L.
1982-12-01
This report presents a theory of approximation of arbitrary Boolean functions by simpler, monotone functions. Monotone increasing functions can be expressed without the use of complements. Nonconstant monotone increasing functions are important in their own right since they model a special class of systems known as coherent systems. It is shown here that when Boolean expressions for noncoherent systems become too large to treat exactly, then monotone approximations are easily defined. The algorithms proposed here not only provide simpler formulas but also produce best possible upper and lower monotone bounds for any Boolean function. This theory has practical application for the analysis of noncoherent fault trees and event tree sequences.
First-principles calculation of phase equilibria and phase separation of the Fe-Ni alloy system
Institute of Scientific and Technical Information of China (English)
Ying Chen; Shuichi Iwata; Tetsuo Mohri
2006-01-01
Theoretical investigation of the phase equilibria of the Fe-Ni alloy has been performed by combining the FLAPW total energy calculations and the Cluster Variation Method through the Cluster Expansion Method. The calculations have proved the stabilization of the L12 phase at 1:3 stoichiometry, which is in agreement with the experimental result,and predicted the existence of L10 as a stable phase below 550 K; this L10 phase has been missing in the conventional phasediagram. The calculations are extended to the Fe-rich region that is characterized by a wide range phase separation and has drawn considerable attention because of the intriguing Invar property associated with a Fe concentration of 65%. To reveal the origin of the phase separation, a P-V curve in an entire concentration range is derived by the second derivative of free energy functional of the disordered phase with respect to the volume. The calculation confirmed that the phase separation is caused by the breakdown of the mechanical-stability criterion. The newly calculated phase separation line combined with the L10 and L12 order-disordered phase boundaries provides phase equilibria in the wider concentration range of the system. Furthermore, a coefficient of thermal expansion (CTE) is attempted by incorporating the thermal vibration effect through harmonic approximation of the Debye-Gruneisen model. The Invar behavior has been reproduced, and the origin of this anomalous volume change has been discussed.
Phase equilibria in polydisperse nonadditive hard-sphere systems.
Paricaud, Patrice
2008-08-01
Colloidal particles naturally exhibit a size polydispersity that can greatly influence their phase behavior in solution. Nonadditive hard-sphere (NAHS) mixtures are simple and well-suited model systems to represent phase transitions in colloid systems. Here, we propose an analytical equation of state (EOS) for NAHS fluid mixtures, which can be straightforwardly applied to polydisperse systems. For positive values of the nonadditivity parameter Delta the model gives accurate predictions of the simulated fluid-fluid coexistence curves and compressibility factors. NPT Monte Carlo simulations of the mixing properties of the NAHS symmetric binary mixture with Delta>0 are reported. It is shown that the enthalpy of mixing is largely positive and overcomes the positive entropy of mixing when the pressure is increased, leading to a fluid-fluid phase transition with a lower critical solution pressure. Phase equilibria in polydisperse systems are predicted with the model by using the density moment formalism [P. Sollich, Adv. Chem. Phys. 116, 265 (2001)]. We present predictions of the cloud and shadow curves for polydisperse NAHS systems composed of monodisperse spheres and polydisperse colloid particles. A fixed nonadditivity parameter Delta > 0 is assumed between the monodisperse and polydisperse spheres, and a Schulz distribution is used to represent the size polydispersity. Polydispersity is found to increase the extent of the immiscibility region. The predicted cloud and shadow curves depend dramatically on the upper cutoff diameter sigmac of the Schulz distribution, and three-phase equilibria can occur for large values of sigmac.
Conformational equilibria and intrinsic affinities define integrin activation.
Li, Jing; Su, Yang; Xia, Wei; Qin, Yan; Humphries, Martin J; Vestweber, Dietmar; Cabañas, Carlos; Lu, Chafen; Springer, Timothy A
2017-03-01
We show that the three conformational states of integrin α5β1 have discrete free energies and define activation by measuring intrinsic affinities for ligand of each state and the equilibria linking them. The 5,000-fold higher affinity of the extended-open state than the bent-closed and extended-closed states demonstrates profound regulation of affinity. Free energy requirements for activation are defined with protein fragments and intact α5β1 On the surface of K562 cells, α5β1 is 99.8% bent-closed. Stabilization of the bent conformation by integrin transmembrane and cytoplasmic domains must be overcome by cellular energy input to stabilize extension. Following extension, headpiece opening is energetically favored. N-glycans and leg domains in each subunit that connect the ligand-binding head to the membrane repel or crowd one another and regulate conformational equilibria in favor of headpiece opening. The results suggest new principles for regulating signaling in the large class of receptors built from extracellular domains in tandem with single-span transmembrane domains.
Prestack wavefield approximations
Alkhalifah, Tariq
2013-09-01
The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
Norton, Andrew H.
1991-01-01
Local spline approximants offer a means for constructing finite difference formulae for numerical solution of PDEs. These formulae seem particularly well suited to situations in which the use of conventional formulae leads to non-linear computational instability of the time integration. This is explained in terms of frequency responses of the FDF.
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
Approximation by Cylinder Surfaces
DEFF Research Database (Denmark)
Randrup, Thomas
1997-01-01
We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...
Casado-Riobó, Alfonso
2008-01-01
The calculus of the acid-base equilibria can be rationalized by applying the proton condition or the hydroxyl condition in every case, on solutions of strong bases, mixtures of bases, mixtures of acids and bases, and different salts. Furthermore, applying the proton condition or the hydroxyl condition in equilibrium, it is clearly pointed out that the hydroxyls in equilibrium are additive in solutions of strong bases as well as in those of weak bases.
Strong Coupling and Classicalization
Dvali, Gia
2016-01-01
Classicalization is a phenomenon in which a theory prevents itself from entering into a strong-coupling regime, by redistributing the energy among many weakly-interacting soft quanta. In this way, the scattering process of some initial hard quanta splits into a large number of soft elementary processes. In short, the theory trades the strong coupling for a high-multiplicity of quanta. At very high energies, the outcome of such a scattering experiment is a production of soft states of high occupation number that are approximately classical. It is evident that black hole creation in particle collision at super-Planckian energies is a result of classicalization, but there is no a priory reason why this phenomenon must be limited to gravity. If the hierarchy problem is solved by classicalization, the LHC has a chance of detecting a tower of new resonances. The lowest-lying resonances must appear right at the strong coupling scale in form of short-lived elementary particles. The heavier members of the tower must b...
Topology, calculus and approximation
Komornik, Vilmos
2017-01-01
Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2011-01-01
Most prestack traveltime relations we tend work with are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multi-focusing or double square-root (DSR) and the common reflection stack (CRS) equations. Using the DSR equation, I analyze the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I derive expansion based solutions of this eikonal based on polynomial expansions in terms of the reflection and dip angles in a generally inhomogenous background medium. These approximate solutions are free of singularities and can be used to estimate travetimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. A Marmousi example demonstrates the usefulness of the approach. © 2011 Society of Exploration Geophysicists.
Optimization and approximation
Pedregal, Pablo
2017-01-01
This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.
Ferraro, N. M.; Jardin, S. C.; Lao, L. L.; Shephard, M. S.; Zhang, F.
2016-05-01
Free-boundary 3D tokamak equilibria and resistive wall instabilities are calculated using a new resistive wall model in the two-fluid M3D-C1 code. In this model, the resistive wall and surrounding vacuum region are included within the computational domain. This implementation contrasts with the method typically used in fluid codes in which the resistive wall is treated as a boundary condition on the computational domain boundary and has the advantage of maintaining purely local coupling of mesh elements. This new capability is used to simulate perturbed, free-boundary non-axisymmetric equilibria; the linear evolution of resistive wall modes; and the linear and nonlinear evolution of axisymmetric vertical displacement events (VDEs). Calculated growth rates for a resistive wall mode with arbitrary wall thickness are shown to agree well with the analytic theory. Equilibrium and VDE calculations are performed in diverted tokamak geometry, at physically realistic values of dissipation, and with resistive walls of finite width. Simulations of a VDE disruption extend into the current-quench phase, in which the plasma becomes limited by the first wall, and strong currents are observed to flow in the wall, in the SOL, and from the plasma to the wall.
Energy Technology Data Exchange (ETDEWEB)
Ferraro, N. M., E-mail: nferraro@pppl.gov; Lao, L. L. [General Atomics, La Jolla, California 92186 (United States); Jardin, S. C. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); Shephard, M. S.; Zhang, F. [Rensselaer Polytechnic Institute, Troy, New York 12180 (United States)
2016-05-15
Free-boundary 3D tokamak equilibria and resistive wall instabilities are calculated using a new resistive wall model in the two-fluid M3D-C1 code. In this model, the resistive wall and surrounding vacuum region are included within the computational domain. This implementation contrasts with the method typically used in fluid codes in which the resistive wall is treated as a boundary condition on the computational domain boundary and has the advantage of maintaining purely local coupling of mesh elements. This new capability is used to simulate perturbed, free-boundary non-axisymmetric equilibria; the linear evolution of resistive wall modes; and the linear and nonlinear evolution of axisymmetric vertical displacement events (VDEs). Calculated growth rates for a resistive wall mode with arbitrary wall thickness are shown to agree well with the analytic theory. Equilibrium and VDE calculations are performed in diverted tokamak geometry, at physically realistic values of dissipation, and with resistive walls of finite width. Simulations of a VDE disruption extend into the current-quench phase, in which the plasma becomes limited by the first wall, and strong currents are observed to flow in the wall, in the SOL, and from the plasma to the wall.
Topics in Metric Approximation
Leeb, William Edward
This thesis develops effective approximations of certain metrics that occur frequently in pure and applied mathematics. We show that distances that often arise in applications, such as the Earth Mover's Distance between two probability measures, can be approximated by easily computed formulas for a wide variety of ground distances. We develop simple and easily computed characterizations both of norms measuring a function's regularity -- such as the Lipschitz norm -- and of their duals. We are particularly concerned with the tensor product of metric spaces, where the natural notion of regularity is not the Lipschitz condition but the mixed Lipschitz condition. A theme that runs throughout this thesis is that snowflake metrics (metrics raised to a power less than 1) are often better-behaved than ordinary metrics. For example, we show that snowflake metrics on finite spaces can be approximated by the average of tree metrics with a distortion bounded by intrinsic geometric characteristics of the space and not the number of points. Many of the metrics for which we characterize the Lipschitz space and its dual are snowflake metrics. We also present applications of the characterization of certain regularity norms to the problem of recovering a matrix that has been corrupted by noise. We are able to achieve an optimal rate of recovery for certain families of matrices by exploiting the relationship between mixed-variable regularity conditions and the decay of a function's coefficients in a certain orthonormal basis.
Numbers of Relative Equilibria in the Planar Four-Vortex Problem: Some Special Cases
Tsai, Ya-Lun
2016-11-01
Three planar four-vortex problems are considered in this paper. In the (3+1) -vortex problem, we study the relative equilibria of the four point vortices when one vortex has zero vorticity and the other three with nonzero vorticities form an equilateral triangle. In the (1+3) -vortex problem, we study the limiting cases of the relative equilibria when one of the four point vortices has fixed nonzero vorticity and other vorticities approach zero. The third problem is the case of vanishing total vorticity. All problems involve two real vorticity parameters. We consider all meaningful pairs of parameters and find there can only be 4, 8, 9 or 10 relative equilibria in the (3+1) -vortex problem, and 8, 10, 12 or 14 relative equilibria in the (1+3) -vortex problem. For the case of zero total vorticity, there are 0, 1 or 2 collinear relative equilibria and 2, 3 or 4 strictly planar relative equilibria. We completely classify parameters according to the different numbers of relative equilibria. For all cases, we reduce them to the problems of counting common zeros in an open region of {{{R}}}2 for polynomial systems with two equations, two variables, and two parameters. We propose a method to count zeros for such type of systems for all parameters in an open region of R2 through symbolic computations. Therefore, all of our results are proved rigorously.
Phase Equilibria and Transition in Mixtures of a Homopolymer and a Block Copolymer. II.
1983-01-26
AD-A124 929 PHASE EQUILIBRIA AND TRANSITION IN MIXTURES OF A In- NOMOPOLYMER AND’A BLOCK..(U) CINCINNATI UNJY ON DEPT OF MATERIALS SCIENCE AND...REPORT NO. 7 v2 L Phase Equilibria and Transition in Mixtures of a Homopolymer and a Block Copolymer II. The Phase Diagram by R. J. Roe and W. C. Zin...homopolymers as in our systems. The phase equilibria at temperatures above the "pseudo-triple point" BCD can be interpreted in terms of the free energy of
Energy Technology Data Exchange (ETDEWEB)
Chalasani, P.; Saias, I. [Los Alamos National Lab., NM (United States); Jha, S. [Carnegie Mellon Univ., Pittsburgh, PA (United States)
1996-04-08
As increasingly large volumes of sophisticated options (called derivative securities) are traded in world financial markets, determining a fair price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk. In this model, the value of an n-period option on a stock is the expected time-discounted value of the future cash flow on an n-period stock price path. Path-dependent options are particularly difficult to value since the future cash flow depends on the entire stock price path rather than on just the final stock price. Currently such options are approximately priced by Monte carlo methods with error bounds that hold only with high probability and which are reduced by increasing the number of simulation runs. In this paper the authors show that pricing an arbitrary path-dependent option is {number_sign}-P hard. They show that certain types f path-dependent options can be valued exactly in polynomial time. Asian options are path-dependent options that are particularly hard to price, and for these they design deterministic polynomial-time approximate algorithms. They show that the value of a perpetual American put option (which can be computed in constant time) is in many cases a good approximation to the value of an otherwise identical n-period American put option. In contrast to Monte Carlo methods, the algorithms have guaranteed error bounds that are polynormally small (and in some cases exponentially small) in the maturity n. For the error analysis they derive large-deviation results for random walks that may be of independent interest.
Finite elements and approximation
Zienkiewicz, O C
2006-01-01
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o
Study of ionic equilibria of indotricarbocyanines in aromatic hydrocarbons
Energy Technology Data Exchange (ETDEWEB)
Dyadyusha, G.G.; Ishchenko, A.A.; Derevyanko, N.A.; Tolmachev, A.I.
1982-05-01
Study of the equilibria in nonpolar solvents is very complicated by the poor solubility of the salt-like dyes. Indotricarbocyanines I and II were found to be fairly soluble in aromatic hydrocarbons for solving these problems by means of electronic spectra. In the present work, their absorption spectra were studied in benzene, toluene, and m-xylene (the absorption spectra were measured on the SF-8 spectrophotometer). It was shown that the dyes studied in these solvents have spectral bands of unusual form of polymethine dyes. At the long wave edge of the spectra of indotricarbocyanines, a distinct band appears, whose intensity is very dependent on the nature of the anion. In the case of perchlorate I, it has a lower intensity, and in the case of iodide II, the intensity is higher.
Tautomeric equilibria in solutions of 1-methyl-2-phenacylbenzimidazoles
Skotnicka, Agnieszka; Czeleń, Przemysław; Gawinecki, Ryszard
2017-04-01
Until now the susceptibility of 1-methyl-2-phenacylbenzimidazoles to the proton transfer has not been carefully examined. There only have been selective trials to recognize tautomeric equilibrium of substituted compounds. Unfortunately, conclusions of these studies are often conflicting. Therefore, the aim of this work was to analyze the influence of the factors affecting the tautomeric processes of substituted 1-methyl-2-phenacylbenzimidazoles in solutions of chloroform by spectroscopic technique of 1H and 13C NMR. Complex equilibria may only take place when molecules of tautomeric species contain multiple basic and/or acidic centres. Analysis of NMR spectra show unequivocally that 1-methyl-2-phenacylbenzimidazoles (ketimine tautomeric form) are in equilibrium with (Z)-2-(1-methyl-1H-benzo[d]imidazol-2yl)-1-phenylethenols (enolimine).
Multiple equilibria of cross-equatorial Inertial jets
Institute of Scientific and Technical Information of China (English)
CHAO JiPing; LIU Fei
2007-01-01
Based on the developed Anderson and Moore's theory about cross-equatorial inertial jets and a nonlinear equivalence shallow water model, new universal functions are determined by the characters of the vortical large-scale air flow (atmosphere) or ocean current (ocean) related to the jet, then the potential vorticity and energy conservation equations along the streamline in the cross-equatorial inertial jets can be obtained. Because the governing equations are nonlinear, some limited multiple equilibria of cross-equatorial inertial jets may exist. According to the character of large-scale air flow or ocean current outside the jets, the existent criterion for multiple eqnilibria in cross-equatorial inertial jets is discussed, and two examples for multiple equilibia of nonlinear governing equations are given.
Multiple equilibria of cross-equatorial Inertial jets
Institute of Scientific and Technical Information of China (English)
2007-01-01
Based on the developed Anderson and Moore’s theory about cross-equatorial inertial jets and a nonlinear equivalence shallow water model, new universal functions are determined by the characters of the vortical large-scale air flow (atmosphere) or ocean current (ocean) related to the jet, then the potential vorticity and energy conservation equations along the streamline in the cross-equatorial in-ertial jets can be obtained. Because the governing equations are nonlinear, some limited multiple equi-libria of cross-equatorial inertial jets may exist. According to the character of large-scale air flow or ocean current outside the jets, the existent criterion for multiple eqnilibria in cross-equatorial inertial jets is discussed, and two examples for multiple equilibia of nonlinear governing equations are given.
Analytical solutions for Tokamak equilibria with reversed toroidal current
Energy Technology Data Exchange (ETDEWEB)
Martins, Caroline G. L.; Roberto, M.; Braga, F. L. [Departamento de Fisica, Instituto Tecnologico de Aeronautica, Sao Jose dos Campos, Sao Paulo 12228-900 (Brazil); Caldas, I. L. [Instituto de Fisica, Universidade de Sao Paulo, 05315-970 Sao Paulo, SP (Brazil)
2011-08-15
In tokamaks, an advanced plasma confinement regime has been investigated with a central hollow electric current with negative density which gives rise to non-nested magnetic surfaces. We present analytical solutions for the magnetohydrodynamic equilibria of this regime in terms of non-orthogonal toroidal polar coordinates. These solutions are obtained for large aspect ratio tokamaks and they are valid for any kind of reversed hollow current density profiles. The zero order solution of the poloidal magnetic flux function describes nested toroidal magnetic surfaces with a magnetic axis displaced due to the toroidal geometry. The first order correction introduces a poloidal field asymmetry and, consequently, magnetic islands arise around the zero order surface with null poloidal magnetic flux gradient. An analytic expression for the magnetic island width is deduced in terms of the equilibrium parameters. We give examples of the equilibrium plasma profiles and islands obtained for a class of current density profile.
Complex Networks as Nash Equilibria of Navigation Games
Gulyás, András; Kőrösi, Attila; Rétvári, Gábor; Krioukov, Dmitri
2014-01-01
The common sense suggests that networks are not random mazes of purposeless connections, but that these connections are organised so that networks can perform their functions. One common function that many networks perform is targeted transport or navigation. Here with the help of game theory we show that minimalistic networks designed to maximise the navigation efficiency at minimal cost share basic structural properties of real networks. These idealistic networks are Nash equilibria of a network construction game whose purpose is to find an optimal trade-off between the network cost and navigability. They are navigation skeletons that we show are present in the Internet, {\\it E. coli} metabolic network, English word network, US airport network, and the Hungarian road network. The knowledge of these skeletons allows one to identify the minimal number of edges by altering which one can dramatically improve or paralyse the navigation in the network.
Navigable networks as Nash equilibria of navigation games
Gulyás, András; Bíró, József J.; Kőrösi, Attila; Rétvári, Gábor; Krioukov, Dmitri
2015-07-01
Common sense suggests that networks are not random mazes of purposeless connections, but that these connections are organized so that networks can perform their functions well. One function common to many networks is targeted transport or navigation. Here, using game theory, we show that minimalistic networks designed to maximize the navigation efficiency at minimal cost share basic structural properties with real networks. These idealistic networks are Nash equilibria of a network construction game whose purpose is to find an optimal trade-off between the network cost and navigability. We show that these skeletons are present in the Internet, metabolic, English word, US airport, Hungarian road networks, and in a structural network of the human brain. The knowledge of these skeletons allows one to identify the minimal number of edges, by altering which one can efficiently improve or paralyse navigation in the network.
Axisymmetric equilibria of a gravitating plasma with incompressible flows
Throumoulopoulos, G N
2001-01-01
It is found that the ideal magnetohydrodynamic equilibrium of an axisymmetric gravitating magnetically confined plasma with incompressible flows is governed by a second-order elliptic differential equation for the poloidal magnetic flux function containing five flux functions coupled with a Poisson equation for the gravitation potential, and an algebraic relation for the pressure. This set of equations is amenable to analytic solutions. As an application, the magnetic-dipole static axisymmetric equilibria with vanishing poloidal plasma currents derived recently by Krasheninnikov, Catto, and Hazeltine [Phys. Rev. Lett. {\\bf 82}, 2689 (1999)] are extended to plasmas with finite poloidal currents, subject to gravitating forces from a massive body (a star or black hole) and inertial forces due to incompressible sheared flows. Explicit solutions are obtained in two regimes: (a) in the low-energy regime $\\beta_0\\approx \\gamma_0\\approx \\delta_0 \\approx\\epsilon_0\\ll 1$, where $\\beta_0$, $\\gamma_0$, $\\delta_0$, and $\\...
High-pressure fluid phase equilibria phenomenology and computation
Deiters, Ulrich K
2012-01-01
The book begins with an overview of the phase diagrams of fluid mixtures (fluid = liquid, gas, or supercritical state), which can show an astonishing variety when elevated pressures are taken into account; phenomena like retrograde condensation (single and double) and azeotropy (normal and double) are discussed. It then gives an introduction into the relevant thermodynamic equations for fluid mixtures, including some that are rarely found in modern textbooks, and shows how they can they be used to compute phase diagrams and related properties. This chapter gives a consistent and axiomatic approach to fluid thermodynamics; it avoids using activity coefficients. Further chapters are dedicated to solid-fluid phase equilibria and global phase diagrams (systematic search for phase diagram classes). The appendix contains numerical algorithms needed for the computations. The book thus enables the reader to create or improve computer programs for the calculation of fluid phase diagrams. introduces phase diagram class...
Morrison, Philip J; Tronko, Natalia
2013-01-01
Stability analyses for equilibria of the compressible reduced magnetohydrodynamics (CRMHD) model are carried out by means of the Energy-Casimir (EC) method. Stability results are compared with those obtained for ideal magnetohydrodynamics (MHD) from the classical {\\delta}W criterion. An identification of the terms in the second variation of the free energy functional for CRMHD with those of {\\delta}W is made: two destabilizing effects present for CRMHD turn out to correspond to the kink and interchange instabilities in usual MHD, while the stabilizing roles of field line bending and compressibility are also identified in the reduced model. Also, using the EC method, stability conditions in the presence of toroidal flow are obtained. A formal analogy between CRMHD and a reduced incompressible model for magnetized rotating disks, due to Julien and Knobloch [EAS Pub. Series, 21, 81 (2006)], is discovered. In light of this analogy, energy stability analysis shows that the condition for magnetorotational instabili...
Phase equilibria in the Ni-Co-Ga alloy system
Energy Technology Data Exchange (ETDEWEB)
Ducher, R. [Department of Materials Science, Graduate School of Engineering, Tohoku University, 6-6-02 Aoba-yama, Sendai 980-8579 (Japan); Kainuma, R. [Institute of Multidisciplinary Research for Advanced Materials (IMRAM), Tohoku University, 2-1-1 Katahira, Sendai 980-8577 (Japan)], E-mail: kainuma@tagen.tohoku.ac.jp; Ishida, K. [Department of Materials Science, Graduate School of Engineering, Tohoku University, 6-6-02 Aoba-yama, Sendai 980-8579 (Japan)
2008-10-20
Phase equilibria among the {alpha} (A1), {alpha}' (L1{sub 2}), {beta} (B2), {delta} (Ni{sub 5}Ga{sub 3}) and {epsilon} (Ni{sub 13}Ga{sub 9}) phases at elevated temperatures and the existing composition region of the martensite phase at room temperature in the Ni-Co side of the Ni-Co-Ga system were examined by electron probe microanalysis (EPMA) using diffusion triples which were fabricated by two-step diffusion coupling. It was confirmed that single-phase regions of the {alpha}, {alpha}' and {beta} phases at 700 and 1000 deg. C exist in a wide composition range parallel to Ni-Co section and that the existing region of the martensite phase at room temperature is also located over a wide range in the {beta} phase along the {beta} + {alpha} (or {alpha}') two-phase region.
Yasutake, Nobutoshi; Fujisawa, Kotaro; Yamada, Shoichi
2016-12-01
We have developed a new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. The formulation is based on the Lagrangian variational principle with a triangulated mesh. It treats not only barotropic but also baroclinic equations of state. We compare the various stellar equilibria obtained by our new scheme with those by Hachisu's self-consistent field scheme for the barotropic case, and those by Fujisawa's self-consistent field scheme for the baroclinic case. Included in these rotational configurations are those with shellular-type rotations, which are commonly assumed in the evolution calculation of rotating stars. Although radiation processes, convections and meridional flows have not been taken into account in this study, we have in mind the application of this method to the two-dimensional evolution calculations of rotating stars, for which the Lagrangian formulation is best suited.
Dynamic data evaluation for solid-liquid equilibria
DEFF Research Database (Denmark)
Cunico, Larissa; Ceriani, Roberta; Kang, Jeong Won
The accuracy and reliability of the measured data sets to be used in regression of model parameters is an important issue related to modeling of phase equilibria. It is clear that good parameters for any model cannot be obtained from low quality data. A thermodynamic consistency test for solid-liquid...... systems using a relation between the solid and liquid activity coefficients for systems containing metals [1], where the data from the two phases are given were proposed. However, as consistency tests based on the Gibbs–Duhem equation are not feasible, new consistency tests have been developed [2]. Some...... of the developed tests were based in the quality tests proposed for VLE data by Kang et al. [3] and a methodology that combines solute activity coefficients in the liquid phase at infinite dilution and a theoretically based term to account for the non-ideality in dilute solutions are discussed. In this work, case...
Extended Group Contribution Model for Polyfunctional Phase Equilibria
DEFF Research Database (Denmark)
Abildskov, Jens
-liquid equilibria from data on binary mixtures, composed of structurally simple molecules with a single functional group. More complex is the situation with mixtures composed of structurally more complicated molecules or molecules with more than one functional group. The UNIFAC method is extended to handle...... polyfunctional group situations, based on additional information on molecular structure. The extension involves the addition of second-order correction terms to the existing equation. In this way the current first-order formulation is retained. The second-order concept is developed for mixture properties based....... In chapter 4 parameters are estimated for the first-order UNIFAC model, based on which parameters are estimated for one of the second-order models described in chapter 3. The parameter estimation is based on measured binary data on around 4000 systems, covering 11 C-, H- and O-containing functional groups...
Fusion burn equilibria sensitive to the ratio between energy and helium transport
Jakobs, Merlijn; Lopes Cardozo, Niek; Jaspers, Roger
2014-12-01
An analysis of the burn equilibria of fusion reactors of the tokamak family is presented. The global (zero-dimensional) analysis is self-consistent in that it takes into account the dependence of the energy confinement on the variables of the burning plasma, such as temperature and density. Universal burn contours are presented for a selection of commonly used scaling laws for energy confinement. It is shown that the output power of a fusion reactor is to good approximation inversely proportional to the particle confinement time, due to the choking effect of the accumulation of helium, the ash of the fusion reaction. It is further shown that, whereas a fusion reactor requires a minimum energy confinement time to ignite, the output power reaches a maximum for an energy confinement that lies about 30% above this minimum. Further improvement of confinement will lower the output, although in some cases the β limit will be the limiting factor. Given that for maximum performance density the confinement and fuel mix are best chosen to be optimal, the particle confinement is proposed as an attractive parameter for burn control.
Oyetibo, Ganiyu Oladunjoye; Miyauchi, Keisuke; Suzuki, Hitoshi; Ishikawa, Satoru; Endo, Ginro
2016-12-01
Exopolymeric substances (EPS) produced by highly mercury-resistant strains of the yeast Yarrowia spp. (Idd1 and Idd2) were isolated and studied for their mercury binding potential. Excellent yield (approximately 0.3 g EPS per gram biomass) of soluble EPS in medium with 3% glucose was observed in the Yarrowia cultures 7 day post-inoculation. A gram dry weight of the EPS consists mainly of carbohydrates (0.4 g), protein (0.3-0.4 g), uronic acid (0.02 g), and nucleic acids (0.002 g). Mercury interactions with the biopolymer were measured as uptake kinetics from a simulated aquatic system and modelled with thermodynamics and calculated mass action equilibria. The EPS forms a complex with Hg(2+) in water with small activation energy (≤2 kJ mol(-1)), achieving about 30 mg Hg(2+) adsorption per gram dry weight of EPS. The adsorption models confirmed complexation of Hg(2+) by the EPS via heterogeneous multilayer adsorption that obey second-order kinetics at constant rate of 4.0 and 8.1 mg g(-1) min(-1). The EPS used chemisorption as rate-limiting step that controls the uptake of Hg(2+) from aquatic systems during micro-precipitation as bio-removal strategy. The EPS are promising biotechnological tools to design bioreactors for treatment of mercury-rich industrial wastewater.
Collision Index and Stability of Elliptic Relative Equilibria in Planar {n} -body Problem
Hu, Xijun; Ou, Yuwei
2016-06-01
It is well known that a planar central configuration of the {n} -body problem gives rise to solutions where each particle moves on a specific Keplerian orbit while the totality of the particles move on a homographic motion. When the eccentricity {e} of the Keplerian orbit belongs in {[0,1)} , following Meyer and Schmidt, we call such solutions elliptic relative equilibria (shortly, ERE). In order to study the linear stability of ERE in the near-collision case, namely when {1-e} is small enough, we introduce the collision index for planar central configurations. The collision index is a Maslov-type index for heteroclinic orbits and orbits parametrised by half-lines that, according to the definition given by Hu and Portaluri (An index theory for unbounded motions of Hamiltonian systems, Hu and Portaluri (2015, preprint)), we shall refer to as half-clinic orbits and whose definition in this context, is essentially based on a blow up technique in the case {e=1} . We get the fundamental properties of collision index and approximation theorems. As applications, we give some new hyperbolic criteria and prove that, generically, the ERE of minimal central configurations are hyperbolic in the near-collision case, and we give a detailed analysis of Euler collinear orbits in the near-collision case.
Approximate Bayesian computation.
Directory of Open Access Journals (Sweden)
Mikael Sunnåker
Full Text Available Approximate Bayesian computation (ABC constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology.
Phase equilibria constraints on the chemical and physical evolution of the campanian ignimbrite
Fowler, S.J.; Spera, F.J.; Bohrson, W.A.; Belkin, H.E.; de Vivo, B.
2007-01-01
The Campanian Ignimbrite is a > 200 km3 trachyte-phonolite pyroclastic deposit that erupted at 39.3 ?? 0.1 ka within the Campi Flegrei west of Naples, Italy. Here we test the hypothesis that Campanian Ignimbrite magma was derived by isobaric crystal fractionation of a parental basaltic trachyandesitic melt that reacted and came into local equilibrium with small amounts (5-10 wt%) of crustal rock (skarns and foid-syenites) during crystallization. Comparison of observed crystal and magma compositions with results of phase equilibria assimilation-fractionation simulations (MELTS) is generally very good. Oxygen fugacity was approximately buffered along QFM+1 (where QFM is the quartz-fayalite-magnetite buffer) during isobaric fractionation at 0.15 GPa (???6 km depth). The parental melt, reconstructed from melt inclusion and host clinopyroxene compositions, is found to be basaltic trachyandesite liquid (51.1 wt% SiO2, 9.3 wt% MgO, 3 wt% H2O). A significant feature of phase equilibria simulations is the existence of a pseudo-invariant temperature, ???883??C, at which the fraction of melt remaining in the system decreases abruptly from ???0.5 to < 0.1. Crystallization at the pseudo-invariant point leads to abrupt changes in the composition, properties (density, dissolved water content), and physical state (viscosity, volume fraction fluid) of melt and magma. A dramatic decrease in melt viscosity (from 1700 Pa s to ???200 Pa s), coupled with a change in the volume fraction of water in magma (from ??? 0.1 to 0.8) and a dramatic decrease in melt and magma density acted as a destabilizing eruption trigger. Thermal models suggest a timescale of ??? 200 kyr from the beginning of fractionation until eruption, leading to an apparent rate of evolved magma generation of about 10-3 km3/year. In situ crystallization and crystal settling in density-stratified regions, as well as in convectively mixed, less evolved subjacent magma, operate rapidly enough to match this apparent
Institute of Scientific and Technical Information of China (English)
LIN Zhengyan
2004-01-01
We introduce a new class of dependent sequences of random variables, which is a subclass of near-epoch dependent sequences, but can also be approximated by mixing sequences. For this kind of sequences of random variables, we call them strong nearepoch dependent sequences, a p-order, p ＞ 2, (maximum) moment inequality is established under weaker dependence sizes.
Roy, Swapnoneel; Thakur, Ashok Kumar
2008-01-01
Genome rearrangements have been modelled by a variety of primitives such as reversals, transpositions, block moves and block interchanges. We consider such a genome rearrangement primitive Strip Exchanges. Given a permutation, the challenge is to sort it by using minimum number of strip exchanges. A strip exchanging move interchanges the positions of two chosen strips so that they merge with other strips. The strip exchange problem is to sort a permutation using minimum number of strip exchanges. We present here the first non-trivial 2-approximation algorithm to this problem. We also observe that sorting by strip-exchanges is fixed-parameter-tractable. Lastly we discuss the application of strip exchanges in a different area Optical Character Recognition (OCR) with an example.
Approximation by Cylinder Surfaces
DEFF Research Database (Denmark)
Randrup, Thomas
1997-01-01
We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...... projection of the surface onto this plane, a reference curve is determined by use of methods for thinning of binary images. Finally, the cylinder surface is constructed as follows: the directrix of the cylinder surface is determined by a least squares method minimizing the distance to the points...... in the projection within a tolerance given by the reference curve, and the rulings are lines perpendicular to the projection plane. Application of the method in ship design is given....
S-Approximation: A New Approach to Algebraic Approximation
Directory of Open Access Journals (Sweden)
M. R. Hooshmandasl
2014-01-01
Full Text Available We intend to study a new class of algebraic approximations, called S-approximations, and their properties. We have shown that S-approximations can be used for applied problems which cannot be modeled by inclusion based approximations. Also, in this work, we studied a subclass of S-approximations, called Sℳ-approximations, and showed that this subclass preserves most of the properties of inclusion based approximations but is not necessarily inclusionbased. The paper concludes by studying some basic operations on S-approximations and counting the number of S-min functions.
A Multistep Equilibria-Redox-Complexation Demonstration to Illustrate Le Chatelier's Principle.
Berger, Tomas G.; Mellon, Edward K.
1996-01-01
Describes a process that can be used to illustrate a number of chemical principles including Le Chatelier's principle, redox chemistry, equilibria versus steady state situations, and solubility of species. (JRH)
Mottez, F
2003-01-01
The tangential layers are characterized by a bulk plasma velocity and a magnetic field that are perpendicular to the gradient direction. They have been extensively described in the frame of the Magneto-Hydro-Dynamic (MHD) theory. But the MHD theory does not look inside the transition region if the transition has a size of a few ion gyroradii. A series of kinetic tangential equilibria, valid for a collisionless plasma is presented. These equilibria are exact analytical solutions of the Maxwell-Vlasov equations. The particle distribution functions are sums of an infinite number of elementary functions parametrized by a vector potential. Examples of equilibria relevant to space plasmas are shown. A model for the deep and sharp density depletions observed in the auroral zone of the Earth is proposed. Tangential equilibria are also relevant for the study of planetary environments and of remote astrophysical plasmas.
Modeling of Vapor-Liquid-Solid Equilibria in Acidic Aqueous Solutions
DEFF Research Database (Denmark)
Christensen, Søren Gregers; Thomsen, Kaj
2003-01-01
The phase behavior (vapor - liquid equilibria (VLE) and solid - liquid equilibria (SLE)) and thermal properties of aqueous solutions of ions like (K+, Na+, NH4+, Ca2+, Cl-) in the presence of phosphoric acid (H3PO4, H2PO4-, HPO42- ) and nitric acid (HNO3, NO3-) are described by means of the Exten......The phase behavior (vapor - liquid equilibria (VLE) and solid - liquid equilibria (SLE)) and thermal properties of aqueous solutions of ions like (K+, Na+, NH4+, Ca2+, Cl-) in the presence of phosphoric acid (H3PO4, H2PO4-, HPO42- ) and nitric acid (HNO3, NO3-) are described by means...
Direct molecular dynamics simulation of liquid-solid phase equilibria for a three-component plasma.
Hughto, J; Horowitz, C J; Schneider, A S; Medin, Zach; Cumming, Andrew; Berry, D K
2012-12-01
The neutron-rich isotope ²²Ne may be a significant impurity in carbon and oxygen white dwarfs and could impact how the stars freeze. We perform molecular dynamics simulations to determine the influence of ²²Ne in carbon-oxygen-neon systems on liquid-solid phase equilibria. Both liquid and solid phases are present simultaneously in our simulation volumes. We identify liquid, solid, and interface regions in our simulations using a bond angle metric. In general we find good agreement for the composition of liquid and solid phases between our MD simulations and the semianalytic model of Medin and Cumming. The trace presence of a third component, neon, does not appear to strongly impact the chemical separation found previously for two-component carbon and oxygen systems. This suggests that small amounts of ²²Ne may not qualitatively change how the material in white dwarf stars freezes. However, we do find systematically lower melting temperatures (higher Γ) in our MD simulations compared to the semianalytic model. This difference seems to grow with impurity parameter Q_{imp} and suggests a problem with simple corrections to the linear mixing rule for the free energy of multicomponent solid mixtures that is used in the semianalytic model.
Direct MD simulation of liquid-solid phase equilibria for three-component plasma
Hughto, J; Schneider, A S; Medin, Zach; Cumming, Andrew; Berry, D K
2012-01-01
The neutron rich isotope 22Ne may be a significant impurity in carbon and oxygen white dwarfs and could impact how the stars freeze. We perform molecular dynamics simulations to determine the influence of 22Ne in carbon-oxygen-neon systems on liquid-solid phase equilibria. Both liquid and solid phases are present simultaneously in our simulation volumes. We identify liquid, solid, and interface regions in our simulations using a bond angle metric. In general we find good agreement for the composition of liquid and solid phases between our MD simulations and the semi analytic model of Medin and Cumming. The trace presence of a third component, neon, does not appear to strongly impact the chemical separation found previously for two component carbon and oxygen systems. This suggests that small amounts of 22Ne may not qualitatively change how the material in white dwarf stars freezes. However, we do find systematically lower melting temperatures (higher Gamma) in our MD simulations compared to the semi analytic ...
Solid Phase Equilibria in the Pi-Ga-As and Pt-Ga-Sb Systems
1988-07-22
OFFICE OF NAVAL RESEARCH Research Contract N00014-87-K-0014 R&T Code 413E026---01 AD-A 198 654 TECHNICAL REPORT No. 9 SOLID PHASE EQUILIBRIA IN THE...Classtcation) UNCLASSLFIED: Tech.Rept.#9 SOLID PHASE EQUILIBRIA IN T11: Pt-Ga-As AND Pt-Ga-Sb SYST’IS 12 PERSONAL AuTiOR(S) C.T. Tsai and R.S. Williats 13a TYPE
Calculation of Phase Equilibria Based on the Levenberg-Marquardt Method
Institute of Scientific and Technical Information of China (English)
Ruijie ZHANG; Lei LI; Zhongwei CHEN; Zhi HE; Wanqi JIE
2005-01-01
The Levenberg-Marquardt method, the best algorithm to obtain the least-square solution of nonlinear equations, is applied to calculate the stable phase equilibria. It can get the best combination between robustness and speed of the calculations. Its application to ternary Al-Si-Mg system is executed in detail. The calculated phase equilibria agree well with the experimental results. Furthermore, the Levenberg-Marquardt method is not sensitive to the initial values.
Thermodynamic characteristics of protolytic equilibria in aqueous solutions of glycyl peptides
Gridchin, S. N.
2016-11-01
Protolytic equilibria in aqueous solutions of glycyl-DL-serine, glycyl-DL-threonine, and glycyl-DL-valine are investigated by means of potentiometry and calorimetry. Dissociation constants and heat effects of the above dipeptides are determined. Standard thermodynamic characteristics (p K°, Δdis G°, Δdis H°, Δdis S°) of the investigated equilibria are calculated. The obtained results are compared to corresponding data on relative compounds.
Calculation of Binary Adsorption Equilibria: Hydrocarbons and Carbon Dioxide on Activated Carbon
DEFF Research Database (Denmark)
Marcussen, Lis; Krøll, A.
1999-01-01
Binary adsorption equilibria are calculated by means of a mathematical model for multicomponent mixtures combined with the SPD (Spreading Pressure Dependent) model for calculation of activity coefficients in the adsorbed phase. The model has been applied successfully for the adsorption of binary ...... mixtures of hydrocarbons and carbon dioxide on activated carbons. The model parameters have been determined, and the model has proven to be suited for prediction of adsorption equilibria in the investigated systems....
Nie, Xiaobing; Zheng, Wei Xing
2016-03-01
This paper addresses the problem of coexistence and dynamical behaviors of multiple equilibria for competitive neural networks. First, a general class of discontinuous nonmonotonic piecewise linear activation functions is introduced for competitive neural networks. Then based on the fixed point theorem and theory of strict diagonal dominance matrix, it is shown that under some conditions, such n -neuron competitive neural networks can have 5(n) equilibria, among which 3(n) equilibria are locally stable and the others are unstable. More importantly, it is revealed that the neural networks with the discontinuous activation functions introduced in this paper can have both more total equilibria and locally stable equilibria than the ones with other activation functions, such as the continuous Mexican-hat-type activation function and discontinuous two-level activation function. Furthermore, the 3(n) locally stable equilibria given in this paper are located in not only saturated regions, but also unsaturated regions, which is different from the existing results on multistability of neural networks with multiple level activation functions. A simulation example is provided to illustrate and validate the theoretical findings.
Laugier, S.; Richon, D.
1986-03-01
A new apparatus to measure vapor-liquid equilibria of mixture has been designed to work up to 10 MPa and 423 K. This apparatus makes it possible to take reproducible and representative samples and inject them directly into a chromatographic circuit {the same requirements were already satisfied by another apparatus described in a previous paper [P. Figuiére, J. F. Hom, S. Laugier, H. Renon, D. Richon, and H. Szwarc, AIChE J. 26, 872 (1980)]}. The use of the new apparatus is very simple. Comparisons with data from Kay and Albert [Ind. Eng. Chem. 48, 422 (1956)] reveal a strong similarity in the whole pressure range. Measurements in the critical region do not involve significant experimental difficulty.
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2012-05-01
Many of the explicit prestack traveltime relations used in practice are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multifocusing, based on the double square-root (DSR) equation, and the common reflection stack (CRS) approaches. Using the DSR equation, I constructed the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I recasted the eikonal in terms of the reflection angle, and thus, derived expansion based solutions of this eikonal in terms of the difference between the source and receiver velocities in a generally inhomogenous background medium. The zero-order term solution, corresponding to ignoring the lateral velocity variation in estimating the prestack part, is free of singularities and can be used to estimate traveltimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. The higher-order terms include limitations for horizontally traveling waves, however, we can readily enforce stability constraints to avoid such singularities. In fact, another expansion over reflection angle can help us avoid these singularities by requiring the source and receiver velocities to be different. On the other hand, expansions in terms of reflection angles result in singularity free equations. For a homogenous background medium, as a test, the solutions are reasonably accurate to large reflection and dip angles. A Marmousi example demonstrated the usefulness and versatility of the formulation. © 2012 Society of Exploration Geophysicists.
Empirical progress and nomic truth approximation revisited
Kuipers, Theodorus
2014-01-01
In my From Instrumentalism to Constructive Realism (2000) I have shown how an instrumentalist account of empirical progress can be related to nomic truth approximation. However, it was assumed that a strong notion of nomic theories was needed for that analysis. In this paper it is shown, in terms of
IONIS: Approximate atomic photoionization intensities
Heinäsmäki, Sami
2012-02-01
A program to compute relative atomic photoionization cross sections is presented. The code applies the output of the multiconfiguration Dirac-Fock method for atoms in the single active electron scheme, by computing the overlap of the bound electron states in the initial and final states. The contribution from the single-particle ionization matrix elements is assumed to be the same for each final state. This method gives rather accurate relative ionization probabilities provided the single-electron ionization matrix elements do not depend strongly on energy in the region considered. The method is especially suited for open shell atoms where electronic correlation in the ionic states is large. Program summaryProgram title: IONIS Catalogue identifier: AEKK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1149 No. of bytes in distributed program, including test data, etc.: 12 877 Distribution format: tar.gz Programming language: Fortran 95 Computer: Workstations Operating system: GNU/Linux, Unix Classification: 2.2, 2.5 Nature of problem: Photoionization intensities for atoms. Solution method: The code applies the output of the multiconfiguration Dirac-Fock codes Grasp92 [1] or Grasp2K [2], to compute approximate photoionization intensities. The intensity is computed within the one-electron transition approximation and by assuming that the sum of the single-particle ionization probabilities is the same for all final ionic states. Restrictions: The program gives nonzero intensities for those transitions where only one electron is removed from the initial configuration(s). Shake-type many-electron transitions are not computed. The ionized shell must be closed in the initial state. Running time: Few seconds for a
Operators of Approximations and Approximate Power Set Spaces
Institute of Scientific and Technical Information of China (English)
ZHANG Xian-yong; MO Zhi-wen; SHU Lan
2004-01-01
Boundary inner and outer operators are introduced; and union, intersection, complement operators of approximations are redefined. The approximation operators have a good property of maintaining union, intersection, complement operators, so the rough set theory has been enriched from the operator-oriented and set-oriented views. Approximate power set spaces are defined, and it is proved that the approximation operators are epimorphisms from power set space to approximate power set spaces. Some basic properties of approximate power set space are got by epimorphisms in contrast to power set space.
Liquid-liquid equilibria for ternary polymer mixtures
Energy Technology Data Exchange (ETDEWEB)
Oh, Suk Yung [Division of Chemical Engineering and Molecular Thermodynamics Laboratory, Hanyang University, Seoul 133-791 (Korea, Republic of); Bae, Young Chan, E-mail: ycbae@hanyang.ac.kr [Division of Chemical Engineering and Molecular Thermodynamics Laboratory, Hanyang University, Seoul 133-791 (Korea, Republic of)
2011-01-24
Graphical abstract: We developed a molecular thermodynamic model for multicomponent systems and discribed the phase equilibrium for ternary polymer mixtures by using the model parameters obtained from the binary systems. Research highlights: {yields} Model parameters were obtained from the binary systems. {yields} The obtained parameters were directly used to predict the ternary data. {yields} The undetermined parameters were used to correlate the ternary data. {yields} The proposed model agreed well with the experimental data. - Abstract: A molecular thermodynamic model for multicomponent systems based on a closed-packed lattice model is presented based on two contributions; entropy and energy contribution. The calculated liquid-liquid equilibria of ternary chainlike mixtures agreed with Monte Carlo simulation results. The proposed model can satisfactorily predict Types 0, 1, 2 and 3 phase separations of the Treybal classification. The model parameters obtained from the binary systems were used to directly predict real ternary systems and the calculated results correlated well with experimental data using few adjustable parameters. Specific interactions in associated binary systems were considered using a secondary lattice.
A molecular-thermodynamic framework for asphaltene-oil equilibria
Energy Technology Data Exchange (ETDEWEB)
Wu, J.; Prausnitz, J.M. [Univ. of California, Berkeley, CA (United States). Dept. of Chemical Engineering]|[Lawrence Berkeley National Lab., CA (United States). Chemical Sciences Div.; Firoozabadi, A. [Reservoir Engineering Research Inst., Palo Alto, CA (United States)
1997-02-01
Asphaltene precipitation is a perennial problem in production and refinery of crude oils. To avoid precipitation, it is useful to predict the solubility of asphaltenes in petroleum liquids as a function of temperature, pressure and liquid-phase composition. In the molecular-thermodynamic model presented here, both asphaltenes and resins are represented by pseudo-pure components, and all other components in the solution are represented by a continuous medium which affects interactions among asphaltene and resin particles. The effect of the medium on asphaltene-asphaltene, resin-asphaltene, resin-resin pair interactions is taken into account through its density and molecular-dispersion properties. To obtain expressions for the chemical potential of asphaltene and for the osmotic pressure of an asphaltene-containing solution, the authors use the integral theory of fluids coupled with the SAFT model to allow for asphaltene aggregation and for adsorption of resin on asphaltene particles. With these expressions, a variety of experimental observations can be explained including the effects of temperature, pressure and composition on the phase behavior of asphaltene-containing fluids. For engineering application, the molecular parameters in this model must be correlated to some macroproperties of oil such as density and molecular weight. When such correlations are established, it will be possible to calculate asphaltene-precipitation equilibria at a variety of conditions for realistic systems.
Transitions of Spherical Thermohaline Circulation to Multiple Equilibria
Özer, Saadet; Şengül, Taylan
2017-06-01
The main aim of the paper is to investigate the transitions of the thermohaline circulation in a spherical shell in a parameter regime which only allows transitions to multiple equilibria. We find that the first transition is either continuous (Type-I) or drastic (Type-II) depending on the sign of the transition number. The transition number depends on the system parameters and l_c , which is the common degree of spherical harmonics of the first critical eigenmodes, and it can be written as a sum of terms describing the nonlinear interactions of various modes with the critical modes. We obtain the exact formulas of this transition number for l_c=1 and l_c=2 cases. Numerically, we find that the main contribution to the transition number is due to nonlinear interactions with modes having zero wave number and the contribution from the nonlinear interactions with higher frequency modes is negligible. In our numerical experiments we encountered both types of transition for Le1 . In the continuous transition scenario, we rigorously prove that an attractor in the phase space bifurcates which is homeomorphic to the 2l_c dimensional sphere and consists entirely of degenerate steady state solutions.
Phase equilibria in the Ni-Fe-Ga alloy system
Energy Technology Data Exchange (ETDEWEB)
Ducher, R. [Department of Materials Science, Graduate School of Engineering, Tohoku University, 6-6-02 Aoba-yama, Sendai 980-8579 (Japan); Kainuma, R. [Institute of Multidisciplinary Research for Advanced Materials (IMRAM), Tohoku University, 2-1-1 Katahira, Sendai 980-8577 (Japan)], E-mail: kainuma@tagen.tohoku.ac.jp; Ishida, K. [Department of Materials Science, Graduate School of Engineering, Tohoku University, 6-6-02 Aoba-yama, Sendai 980-8579 (Japan)
2008-09-08
The phase equilibria, A2/B2 and B2/L2{sub 1} (or D0{sub 3}) order-disorder transitions and martensitic transformation on the Ni-Fe side of the Ni-Fe-Ga system were examined by electron probe microanalysis (EPMA) and differential scanning calorimetric (DSC) measurement. The equilibrium compositions of interrelations mainly among the {alpha} (A2), {beta} (B2), {beta}' (L2{sub 1} or D0{sub 3}), {gamma} (A1) and {gamma}' (L1{sub 2}) phases were determined using diffusion triples which were fabricated by two-step diffusion coupling. It was confirmed that a bcc single-phase region composed of {alpha}, {beta} and {beta}' at 850-1000 deg. C exists in a wide composition range and that the critical temperature of the B2/L2{sub 1} order-disorder transformation in the Fe{sub 3}Ga-Ni{sub 3}Ga pseudo-binary section gradually increases with increasing Ni content. The existing composition region of the martensite phase at room temperature was also determined by the diffusion triple method.
Molecular equilibria and condensation sequences in carbon rich gases
Sharp, C. M.; Wasserburg, G. J.
1993-01-01
Chemical equilibria in stellar atmospheres have been investigated by many authors. Lattimer, Schramm, and Grossman presented calculations in both O rich and C rich environments and predicted possible presolar condensates. A recent paper by Cherchneff and Barker considered a C rich composition with PAH's included in the calculations. However, the condensation sequences of C bearing species have not been investigated in detail. In a carbon rich gas surrounding an AGB star, it is often assumed that graphite (or diamond) condenses out before TiC and SiC. However, Lattimer et al. found some conditions under which TiC condenses before graphite. We have performed molecular equilibrium calculations to establish the stability fields of C(s), TiC(s), and SiC(s) and other high temperature phases under conditions of different pressures and C/O. The preserved presolar interstellar dust grains so far discovered in meteorites are graphite, diamond, SiC, TiC, and possibly Al2O3.
López, O. E.; Guazzotto, L.
2017-03-01
The Grad-Shafranov-Bernoulli system of equations is a single fluid magnetohydrodynamical description of axisymmetric equilibria with mass flows. Using a variational perturbative approach [E. Hameiri, Phys. Plasmas 20, 024504 (2013)], analytic approximations for high-beta equilibria in circular, elliptical, and D-shaped cross sections in the high aspect ratio approximation are found, which include finite toroidal and poloidal flows. Assuming a polynomial dependence of the free functions on the poloidal flux, the equilibrium problem is reduced to an inhomogeneous Helmholtz partial differential equation (PDE) subject to homogeneous Dirichlet conditions. An application of the Green's function method leads to a closed form for the circular solution and to a series solution in terms of Mathieu functions for the elliptical case, which is valid for arbitrary elongations. To extend the elliptical solution to a D-shaped domain, a boundary perturbation in terms of the triangularity is used. A comparison with the code FLOW [L. Guazzotto et al., Phys. Plasmas 11(2), 604-614 (2004)] is presented for relevant scenarios.
International Conference Approximation Theory XV
Schumaker, Larry
2017-01-01
These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, a...
Flavour Democracy in Strong Unification
Abel, S A; Abel, Steven; King, Steven
1998-01-01
We show that the fermion mass spectrum may naturally be understood in terms of flavour democratic fixed points in supersymmetric theories which have a large domain of attraction in the presence of "strong unification". Our approach provides an alternative to the approximate Yukawa texture zeroes of the Froggatt-Nielsen mechanism. We discuss a particular model based on a broken gauged $SU(3)_L\\times SU(3)_R$ family symmetry which illustrates our approach.
Strong Langmuir turbulence at Jupiter?
Cairns, Iver H.; Robinson, P. A.
1992-01-01
Langmuir wave packets with short scale lengths less than an approximately equal to 100 lambda e have been observed in Jupiter's foreshock. Theoretical constraints on the electric fields and scale sizes of collapsing wave packets are summarized, extended and placed in a form suitable for easy comparison with Voyager and Ulysses data. The published data are reviewed and possible instrumental underestimation of fields discussed. New upper limits for the fields of the published wave packets are estimated. Wave packets formed at the nucleation scale from the observed large-scale fields cannot collapse because they are disrupted before collapse occurs. The published wave packets are quantitatively inconsistent with strong turbulence collapse. Strict constraints exist for more intense wave packets to be able to collapse: E greater than or approximately equals to 1-8 mV/m for scales less than or approximately equal to 100 lambda e. Means for testing these conclusions using Voyager and Ulysses data are suggested.
ClassSTRONG: Classical simulations of Strong Field processes
Ciappina, M F; Lewenstein, M
2013-01-01
A set of Mathematica functions is presented to model classically two of the most important processes in strong field physics, namely high-order harmonic generation (HHG) and above-threshold ionization (ATI). Our approach is based on the numerical solution of the Newton-Lorentz equation of an electron moving on an electric field and takes advantage of the symbolic languages features and graphical power of Mathematica. Similarly as in the Strong Field Approximation (SFA), the effects of atomic potential on the motion of electron in the laser field are neglected. The SFA has proven to be an essential tool in strong field physics in the sense that it is able to predict with great precision the harmonic (in the HHG) and energy (in the ATI) limits. We have extended substantially the conventional classical simulations, where the electric field is only dependent on time, including spatial nonhomogeneous fields and spatial and temporal synthesized fields. Spatial nonhomogeneous fields appear when metal nanosystems int...
Hierarchical low-rank approximation for high dimensional approximation
Nouy, Anthony
2016-01-07
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.
Bifurcations and selection of equilibria in a simple cosymmetric model of filtrational convection.
Govorukhin, V. N.; Yudovich, V. I.
1999-06-01
A three-dimensional set of ordinary differential equations that constitutes a simple abstract model of Darcy convection is investigated. The model reproduces a number of effects that are typical for dynamic systems with nontrivial cosymmetry. Nontrivial cosymmetry can give rise to a continuous family of equilibria where, in this case, the equilibrium stability spectrum varies along the family. The family of equilibria and its stability are examined analytically, and special bifurcations that occur in the system are investigated. It is shown that discrete and continual symmetries, called "flash symmetries," can be present in the system for certain parameter values. Computer experiments on the selection of equilibria in the symmetric and cosymmetric cases have been carried out. They showed that, for initial points that are far enough from a cycle of equilibria, the neighborhood of a single equilibrium is established in the case of cosymmetry, but all the equilibria are equivalent in the case of symmetry. The authors hope that these results, as well as the formulation of the problems and the approach to their solution, will serve as a sample in the investigation of more complex systems in mathematical physics. (c) 1999 American Institute of Physics.
Nonlinear Approximation Using Gaussian Kernels
Hangelbroek, Thomas
2009-01-01
It is well-known that non-linear approximation has an advantage over linear schemes in the sense that it provides comparable approximation rates to those of the linear schemes, but to a larger class of approximands. This was established for spline approximations and for wavelet approximations, and more recently for homogeneous radial basis function (surface spline) approximations. However, no such results are known for the Gaussian function. The crux of the difficulty lies in the necessity to vary the tension parameter in the Gaussian function spatially according to local information about the approximand: error analysis of Gaussian approximation schemes with varying tension are, by and large, an elusive target for approximators. We introduce and analyze in this paper a new algorithm for approximating functions using translates of Gaussian functions with varying tension parameters. Our scheme is sophisticated to a degree that it employs even locally Gaussians with varying tensions, and that it resolves local ...
Forms of Approximate Radiation Transport
Brunner, G
2002-01-01
Photon radiation transport is described by the Boltzmann equation. Because this equation is difficult to solve, many different approximate forms have been implemented in computer codes. Several of the most common approximations are reviewed, and test problems illustrate the characteristics of each of the approximations. This document is designed as a tutorial so that code users can make an educated choice about which form of approximate radiation transport to use for their particular simulation.
Approximation by Multivariate Singular Integrals
Anastassiou, George A
2011-01-01
Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator. The basic approximation properties of the general multivariate singular integral operators is presented quantitatively, particularly special cases such as the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators are examined thoroughly. This book studies the rate of convergence of these operators to the unit operator as well as the related simultaneous approximation. The last cha
Approximations of fractional Brownian motion
Li, Yuqiang; 10.3150/10-BEJ319
2012-01-01
Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the one-parameter fractional Brownian motion is constructed using a two-parameter Poisson process. The proof involves the tightness and identification of finite-dimensional distributions.
Approximation by planar elastic curves
DEFF Research Database (Denmark)
Brander, David; Gravesen, Jens; Nørbjerg, Toke Bjerge
2016-01-01
We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient......-driven optimization is then used to find the approximating elastic curve....
Correlation of three-liquid-phase equilibria involving ionic liquids.
Rodríguez-Escontrela, I; Arce, A; Soto, A; Marcilla, A; Olaya, M M; Reyes-Labarta, J A
2016-08-03
The difficulty in achieving a good thermodynamic description of phase equilibria is finding a model that can be extended to a large variety of chemical families and conditions. This problem worsens in the case of systems containing more than two phases or involving complex compounds such as ionic liquids. However, there are interesting applications that involve multiphasic systems, and the promising features of ionic liquids suggest that they will play an important role in many future processes. In this work, for the first time, the simultaneous correlation of liquid-liquid and liquid-liquid-liquid equilibrium data for ternary systems involving ionic liquids has been carried out. To that end, the phase diagram of the water + [P6 6 6 14][DCA] + hexane system has been determined at 298.15 K and 323.15 K and atmospheric pressure. The importance of this system lies in the possibility of using the surface active ionic liquid to improve surfactant enhanced oil recovery methods. With those and previous measurements, thirteen sets of equilibrium data for water + ionic liquid + oil ternary systems have been correlated. The isoactivity equilibrium condition, using the NRTL model, and some pivotal strategies are proposed to correlate these complex systems. Good agreement has been found between experimental and calculated data in all the regions (one triphasic and two biphasic) of the diagrams. The geometric aspects related to the Gibbs energy of mixing function obtained using the model, together with the minor common tangent plane equilibrium condition, are valuable tools to check the consistency of the obtained correlation results.
International Conference Approximation Theory XIV
Schumaker, Larry
2014-01-01
This volume developed from papers presented at the international conference Approximation Theory XIV, held April 7–10, 2013 in San Antonio, Texas. The proceedings contains surveys by invited speakers, covering topics such as splines on non-tensor-product meshes, Wachspress and mean value coordinates, curvelets and shearlets, barycentric interpolation, and polynomial approximation on spheres and balls. Other contributed papers address a variety of current topics in approximation theory, including eigenvalue sequences of positive integral operators, image registration, and support vector machines. This book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.
Exact constants in approximation theory
Korneichuk, N
1991-01-01
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base
The thermodynamic fundamentals relating phase equilibria in binary and ternary systems to the thermodynamic properties of the phases are reviewed and...system demonstrate the application of the equations for extracting thermodynamic data from phase diagrams and also for the prediction of phase equilibria .
DEFF Research Database (Denmark)
Fonseca, José M.S.; von Solms, Nicolas
2012-01-01
A new apparatus for the study of high-pressure phase equilibria at low temperatures using an analytical method was designed, assembled and tested. The apparatus was specially developed for the study of multi-phase equilibria in systems containing hydrocarbons, water and hydrate inhibitors...
Isotropic-nematic phase equilibria of hard-sphere chain fluids—Pure components and binary mixtures
Oyarzun, B.; Van Westen, T.; Vlugt, T.J.H.
2015-01-01
The isotropic-nematic phase equilibria of linear hard-sphere chains and binary mixtures of them are obtained from Monte Carlo simulations. In addition, the infinite dilution solubility of hard spheres in the coexisting isotropic and nematic phases is determined. Phase equilibria calculations are
A Continuous Family of Equilibria in Ferromagnetic Media are Ground States
Su, Xifeng; de la Llave, Rafael
2017-09-01
We show that a foliation of equilibria (a continuous family of equilibria whose graph covers all the configuration space) in ferromagnetic transitive models are ground states. The result we prove is very general, and it applies to models with long range and many-body interactions. As an application, we consider several models of networks of interacting particles including models of Frenkel-Kontorova type on Z^d and one-dimensional quasi-periodic media. The result above is an analogue of several results in the calculus of variations (fields of extremals) and in PDE's. Since the models we consider are discrete and long range, new proofs need to be given. We also note that the main hypothesis of our result (the existence of foliations of equilibria) is the conclusion (using KAM theory) of several recent papers. Hence, we obtain that the KAM solutions recently established are minimizers when the interaction is ferromagnetic and transitive (these concepts are defined later).
A note on relative equilibria in a rotating shallow water layer
Ait Abderrahmane, Hamid
2013-05-08
Relative equilibria of two and three satellite vortices in a rotating shallow water layer have been recorded via particle image velocimetry (PIV) and their autorotation speed was estimated. This study shows that these equilibria retain the fundamental characteristics of Kelvin\\'s equilibria, and could be adequately described by the classical idealized point vortex theory. The same conclusion can also be inferred using the experimental dataset of Bergmann etÂ al.Â (J.Â FluidÂ Mech., vol. 679, 2011, pp. 415-431; J. Fluid Mech., vol. 691, 2012, pp. 605-606) if the assigned field\\'s contribution to pattern rotation is included. © 2013 Cambridge University Press.
Effect of temperature on acid-base equilibria in separation techniques. A review.
Gagliardi, Leonardo G; Tascon, Marcos; Castells, Cecilia B
2015-08-19
Studies on the theoretical principles of acid-base equilibria are reviewed and the influence of temperature on secondary chemical equilibria within the context of separation techniques, in water and also in aqueous-organic solvent mixtures, is discussed. In order to define the relationships between the retention in liquid chromatography or the migration velocity in capillary electrophoresis and temperature, the main properties of acid-base equilibria have to be taken into account for both, the analytes and the conjugate pairs chosen to control the solution pH. The focus of this review is based on liquid-liquid extraction (LLE), liquid chromatography (LC) and capillary electrophoresis (CE), with emphasis on the use of temperature as a useful variable to modify selectivity on a predictable basis. Simpliﬁed models were evaluated to achieve practical optimizations involving pH and temperature (in LLE and CE) as well as solvent composition in reversed-phase LC.
Variational principles in chemical equilibria: Complex chemical systems with interacting subsystems
Zilbergleyt, B
2010-01-01
The goal of the paper is to derive a revised condition of global equilibrium in complex chemical systems as variational principle in formalism of recently developed discrete thermodynamics (DTD) of chemical equilibria. In classical approach the problem of complex equilibrium is solved by minimization of the system Gibbsâ free energy subject to logistic constraints. DTD demands any isolated system to comprise smaller subentities, which individual equilibria are based on the balance of internal and external thermodynamic forces, acting against them. The internal forces are equal to the subsystems thermodynamic affinities, while external forces originate from subsystems mutual interactions. Those interactions impose additional constraints on the mother system Gibbsâ free energy minimum. Basic expression of discrete thermodynamics, being multiplied by subsystems deviations from their âtrueâ thermodynamic equilibria, is naturally identical to dâAlembertâs principle. A thermodynamic ve...
Horizontal mergers and weak and strong competition commissions
Directory of Open Access Journals (Sweden)
Ristić Bojan
2014-01-01
Full Text Available In this paper we analyse the horizontal merger of companies in an already concentrated industry. The participants in mergers are obliged to submit notification to the Competition Commission but they also have the option of rejecting the merger. At the time of the notification submission the participants do not know whether the Commission is strong or weak, and they can complain to the Court if the Commission prohibits the merger. We model the strategic interaction between Participants and Commission in a dynamic game of incomplete information and determine weak perfect Bayesian equilibria. The main finding of our paper is that Participants will base their decision to submit notification on their belief in a weak Commission decision and will almost completely ignore the possibility of a strong Commission decision. We also provide a detailed examination of one case from Serbian regulatory practice, which coincides with the results of our game theoretical model.
Approximate gauge symemtry of composite vector bosons
Energy Technology Data Exchange (ETDEWEB)
Suzuki, Mahiko
2010-06-01
It can be shown in a solvable field theory model that the couplings of the composite vector mesons made of a fermion pair approach the gauge couplings in the limit of strong binding. Although this phenomenon may appear accidental and special to the vector bosons made of a fermion pair, we extend it to the case of bosons being constituents and find that the same phenomenon occurs in more an intriguing way. The functional formalism not only facilitates computation but also provides us with a better insight into the generating mechanism of approximate gauge symmetry, in particular, how the strong binding and global current conservation conspire to generate such an approximate symmetry. Remarks are made on its possible relevance or irrelevance to electroweak and higher symmetries.
Sasidevan, V
2015-01-01
The study of games and their equilibria is central to developing insights for understanding many socio-economic phenomena. Here we present a dynamical systems view of the equilibria of two-person, payoff-symmetric games. In particular, using this perspective, we discuss the differences between two solution concepts for such games - namely, those of Nash equilibrium and co-action equilibrium. For the Nash equilibrium, we show that the dynamical view can provide an equilibrium refinement, selecting one equilibrium among several possibilities, thereby solving the issue of multiple equilibria that appear in some games. We illustrate in detail this dynamical perspective by considering three well known 2-person games namely the Prisoner's Dilemma, game of Chicken and the Stag-Hunt. We find that in all of these cases, co-action equilibria tends to correspond to `nicer' strategies than those corresponding to Nash equilibria.
Approximation Limits of Linear Programs (Beyond Hierarchies)
Braun, Gábor; Pokutta, Sebastian; Steurer, David
2012-01-01
We develop a framework for approximation limits of polynomial-size linear programs from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any linear program as opposed to only programs generated by hierarchies. Using our framework, we prove that O(n^{1/2-eps})-approximations for CLIQUE require linear programs of size 2^{n^\\Omega(eps)}. (This lower bound applies to linear programs using a certain encoding of CLIQUE as a linear optimization problem.) Moreover, we establish a similar result for approximations of semidefinite programs by linear programs. Our main ingredient is a quantitative improvement of Razborov's rectangle corruption lemma for the high error regime, which gives strong lower bounds on the nonnegative rank of certain perturbations of the unique disjointness matrix.
Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization
Canale, Eduardo A.
2015-02-01
© 2015 AIP Publishing LLC. This work is concerned with stability of equilibria in the homogeneous (equal frequencies) Kuramoto model of weakly coupled oscillators. In 2012 [R. Taylor, J. Phys. A: Math. Theor. 45, 1-15 (2012)], a sufficient condition for almost global synchronization was found in terms of the minimum degree-order ratio of the graph. In this work, a new lower bound for this ratio is given. The improvement is achieved by a concrete infinite sequence of regular graphs. Besides, non standard unstable equilibria of the graphs studied in Wiley et al. [Chaos 16, 015103 (2006)] are shown to exist as conjectured in that work.
Existence of three-dimensional ideal-magnetohydrodynamic equilibria with current sheets
Energy Technology Data Exchange (ETDEWEB)
Loizu, J. [Max-Planck-Institut für Plasmaphysik, D-17491 Greifswald (Germany); Princeton Plasma Physics Laboratory, PO Box 451, Princeton, New Jersey 08543 (United States); Hudson, S. R.; Bhattacharjee, A.; Lazerson, S. [Princeton Plasma Physics Laboratory, PO Box 451, Princeton, New Jersey 08543 (United States); Helander, P. [Max-Planck-Institut für Plasmaphysik, D-17491 Greifswald (Germany)
2015-09-15
We consider the linear and nonlinear ideal plasma response to a boundary perturbation in a screw pinch. We demonstrate that three-dimensional, ideal-MHD equilibria with continuously nested flux-surfaces and with discontinuous rotational-transform across the resonant rational-surfaces are well defined and can be computed both perturbatively and using fully nonlinear equilibrium calculations. This rescues the possibility of constructing MHD equilibria with current sheets and continuous, smooth pressure profiles. The results predict that, even if the plasma acts as a perfectly conducting fluid, a resonant magnetic perturbation can penetrate all the way into the center of a tokamak without being shielded at the resonant surface.
Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization
Energy Technology Data Exchange (ETDEWEB)
Canale, Eduardo A., E-mail: ecanale@pol.una.py [Facultad Politénica, UNA, Asunción (Paraguay); Monzón, Pablo, E-mail: monzon@fing.edu.uy [School of Engineering, UDELAR, Montevideo 11300 (Uruguay)
2015-02-15
This work is concerned with stability of equilibria in the homogeneous (equal frequencies) Kuramoto model of weakly coupled oscillators. In 2012 [R. Taylor, J. Phys. A: Math. Theor. 45, 1–15 (2012)], a sufficient condition for almost global synchronization was found in terms of the minimum degree–order ratio of the graph. In this work, a new lower bound for this ratio is given. The improvement is achieved by a concrete infinite sequence of regular graphs. Besides, non standard unstable equilibria of the graphs studied in Wiley et al. [Chaos 16, 015103 (2006)] are shown to exist as conjectured in that work.
A comparison of Nash equilibria analysis and agent-based modelling for power markets
Energy Technology Data Exchange (ETDEWEB)
Krause, T.; Andersson, G. [EEH Power Systems Laboratory, ETH Zuerich, (Switzerland); Beck, E.V.; Cherkaoui, R.; Germond, A. [LRE Laboratoire de Reseaux Electriques, EPFL-STI-LRE, Lausanne (Switzerland); Ernst, D. [Universitede Liege, Institut Montefiore Batiment B28, Liege (Belgium)
2006-11-15
In this paper we compare Nash equilibria analysis and agent-based modelling for assessing the market dynamics of network-constrained pool markets. Power suppliers submit their bids to the market place in order to maximize their payoffs, where we apply reinforcement learning as a behavioral agent model. The market clearing mechanism is based on the locational marginal pricing scheme. Simulations are carried out on a benchmark power system. We show how the evolution of the agent-based approach relates to the existence of a unique Nash equilibrium or multiple equilibria in the system. Additionally, the parameter sensitivity of the results is discussed. (author)
High temperature phase equilibria studies in the Bi-Sr-Ca-Cu-O-Ag system
Energy Technology Data Exchange (ETDEWEB)
Margulies, Lawrence
1999-11-08
A variety of experimental techniques were utilized to examine the high temperature phase equilibria in the Bi-Sr-Ca-Cu-O-Ag system. Quenching studies were used to determine the liquid solubility of Ag in the Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8} (Bi2212) melt and the details of the peritectic decomposition pathway of Bi2212 as a function on Ag content and oxygen partial pressure (PO{sub 2}). A liquid immiscibility region between oxide and Ag liquids in the 8--98 at% range was found above 900 C. Two eutectics were found in the Bi2212-Ag pseudobinary. On the oxide rich side, a eutectic exists at approximately 4 at% Ag. On the Ag rich side, a eutectic exists at approximately 98 at% Ag at a temperature of 15 C below the melting point of pure Ag. Six distinct solid phases were found to be in equilibrium with the partial melt within the Ag content and PO{sub 2} range studied. The stability of these solid phases were found to be highly sensitive to PO{sub 2}, and to a much lesser extent Ag content. High temperature x-ray diffraction (HTXRD) studies of this system are in conflict with these results. It is suggested that these discrepancies are due to experimental artifacts caused by the significant thermal gradients and lack of full bulk sampling which is inherent in conventional HTXRD designs. In part 2, a new furnace design compatible with synchrotron radiation sources is introduced to address these problems. This design allows for full bulk sampling in a low thermal gradient environment using Debye-Scherrer transmission geometry. Sample spinning is also introduced in the design to eliminate preferred orientation and incomplete powder averaging and allow for quantitative phase analysis and structural refinement. Studies on model systems are presented to demonstrate the capabilities for high resolution structural studies (Al{sub 2}O{sub 3}) and time resolved phase transformation studies (SrCO{sub 3}). Finally, the Bi2212 system is examined to confirm the quenching results
DYNAMICS OF STRONGLY TWISTED RELATIVISTIC MAGNETOSPHERES
Energy Technology Data Exchange (ETDEWEB)
Parfrey, Kyle [Astronomy Department, Columbia University, 550 West 120th Street, New York, NY 10027 (United States); Beloborodov, Andrei M.; Hui, Lam, E-mail: parfrey@astro.princeton.edu [Physics Department and Columbia Astrophysics Laboratory, Columbia University, 538 West 120th Street, New York, NY 10027 (United States)
2013-09-10
Magnetar magnetospheres are believed to be strongly twisted due to shearing of the stellar crust by internal magnetic stresses. We present time-dependent axisymmetric simulations showing in detail the evolution of relativistic force-free magnetospheres subjected to slow twisting through large angles. When the twist amplitude is small, the magnetosphere moves quasi-statically through a sequence of equilibria of increasing free energy. At some twist amplitude the magnetosphere becomes tearing-mode unstable to forming a resistive current sheet, initiating large-scale magnetic reconnection in which a significant fraction of the magnetic free energy can be dissipated. This ''critical'' twist angle is insensitive to the resistive length scale. Rapid shearing temporarily stabilizes the magnetosphere beyond the critical angle, allowing the magnetosphere of a rapidly differentially rotating star to store and dissipate more free energy. In addition to these effects, shearing the surface of a rotating star increases the spindown torque applied to the star. If shearing is much slower than rotation, the resulting spikes in spindown rate can occur on timescales anywhere from the long twisting timescale to the stellar spin period or shorter, depending both on the stellar shear distribution and the existing distribution of magnetospheric twists. A model in which energy is stored in the magnetosphere and released by a magnetospheric instability therefore predicts large changes in the measured spindown rate before soft gamma repeater giant flares.
Strong vector valued integrals
Beckmann, Ralf
2011-01-01
Strong Bochner type integrals with values in locally convex spaces are introduced. It is shown that the strong integral exists in the same cases as the weak (Gelfand-Pettis) integral is known to exist. The strong integral has better continuity properties that the weak integral.
BDD Minimization for Approximate Computing
Soeken, Mathias; Grosse, Daniel; Chandrasekharan, Arun; Drechsler, Rolf
2016-01-01
We present Approximate BDD Minimization (ABM) as a problem that has application in approximate computing. Given a BDD representation of a multi-output Boolean function, ABM asks whether there exists another function that has a smaller BDD representation but meets a threshold w.r.t. an error metric. We present operators to derive approximated functions and present algorithms to exactly compute the error metrics directly on the BDD representation. An experimental evaluation demonstrates the app...
Tree wavelet approximations with applications
Institute of Scientific and Technical Information of China (English)
XU Yuesheng; ZOU Qingsong
2005-01-01
We construct a tree wavelet approximation by using a constructive greedy scheme(CGS). We define a function class which contains the functions whose piecewise polynomial approximations generated by the CGS have a prescribed global convergence rate and establish embedding properties of this class. We provide sufficient conditions on a tree index set and on bi-orthogonal wavelet bases which ensure optimal order of convergence for the wavelet approximations encoded on the tree index set using the bi-orthogonal wavelet bases. We then show that if we use the tree index set associated with the partition generated by the CGS to encode a wavelet approximation, it gives optimal order of convergence.
Diophantine approximation and automorphic spectrum
Ghosh, Anish; Nevo, Amos
2010-01-01
The present paper establishes qunatitative estimates on the rate of diophantine approximation in homogeneous varieties of semisimple algebraic groups. The estimates established generalize and improve previous ones, and are sharp in a number of cases. We show that the rate of diophantine approximation is controlled by the spectrum of the automorphic representation, and is thus subject to the generalised Ramanujan conjectures.
Some results in Diophantine approximation
DEFF Research Database (Denmark)
the basic concepts on which the papers build. Among other it introduces metric Diophantine approximation, Mahler’s approach on algebraic approximation, the Hausdorff measure, and properties of the formal Laurent series over Fq. The introduction ends with a discussion on Mahler’s problem when considered...
Beyond the random phase approximation
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian S.
2013-01-01
We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for ab initio calculations of electronic correlation energies in solids and molecules. The method is an extension of the random phase approximation (RPA) derived from time-dependent density...
Uniform approximation by (quantum) polynomials
Drucker, A.; de Wolf, R.
2011-01-01
We show that quantum algorithms can be used to re-prove a classical theorem in approximation theory, Jackson's Theorem, which gives a nearly-optimal quantitative version of Weierstrass's Theorem on uniform approximation of continuous functions by polynomials. We provide two proofs, based respectivel
Energy Technology Data Exchange (ETDEWEB)
Egorysheva, A.V., E-mail: anna_egorysheva@rambler.ru [Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences, Leninskii pr. 31, Moscow 119991 (Russian Federation); Ellert, O.G. [Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences, Leninskii pr. 31, Moscow 119991 (Russian Federation); Maksimov, Yu.V. [Semenov Institute of Chemical Physics, Russian Academy of Sciences, Kosygina 4, Moscow 119991 (Russian Federation); Volodin, V.D.; Efimov, N.N.; Novotortsev, V.M. [Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences, Leninskii pr. 31, Moscow 119991 (Russian Federation)
2013-12-05
Highlights: •We have constructed the isothermal section of the system Bi{sub 2}O{sub 3}–Fe{sub 2}O{sub 3}–Sb{sub 2}O{sub x}. •Ternary compound formation is limited to pyrochlore, which forms a solid solution region. •The phase diagram points out that 7–25% of Bi-positions are occupied with Fe{sup 3+}. •The Mossbauer data confirmed that Fe{sup 3+} ions enter the Bi-positions. •Magnetic measurements revealed spin-glass magnetic transition at 9 K. -- Abstract: The subsolidus phase equilibria of the Bi{sub 2}O{sub 3}–Fe{sub 2}O{sub 3}–Sb{sub 2}O{sub x} system have been investigated by X-ray powder diffraction. The isothermal section of the system at 775–800 °C has been constructed. It can be represented by 9 phase assemblage triangles. Ternary compound formation is limited to pyrochlore which forms a substantial solid solution region of Bi-deficient compositions relative to Bi{sub 2}FeSbO{sub 7}. As follows from the phase diagram, approximately 7–25% of Bi positions in pyrochlore may be occupied with Fe{sup 3+} ions that was confirmed by Mossbauer data. Magnetic measurements were carried out on the pyrochlore specimen of quasi-chemical formula (Bi{sub 1.8}Fe{sub 0.2})(FeSb)O{sub 7}. The existence of the strong short-range antiferromagnetic superexchange interactions and spin-glass magnetic transition at around 9 K were revealed.
Strongly interacting light dark matter
Energy Technology Data Exchange (ETDEWEB)
Bruggisser, Sebastian [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Riva, Francesco; Urbano, Alfredo [CERN, Geneva (Switzerland). Theoretical Physics Dept.
2016-07-15
In the presence of approximate global symmetries that forbid relevant interactions, strongly coupled light Dark Matter (DM) can appear weakly coupled at small-energy and generate a sizable relic abundance. Fundamental principles like unitarity restrict these symmetries to a small class, where the leading interactions are captured by effective operators up to dimension-8. Chiral symmetry, spontaneously broken global symmetries and non-linearly realized supersymmetry are examples of this. Their DM candidates (composite fermions, pseudo-Nambu-Goldstone Bosons and Goldstini) are interesting targets for LHC missing-energy searches.
Strongly Interacting Light Dark Matter
Bruggisser, Sebastian; Urbano, Alfredo
2016-01-01
In the presence of approximate global symmetries that forbid relevant interactions, strongly coupled light Dark Matter (DM) can appear weakly coupled at small energy and generate a sizable relic abundance. Fundamental principles like unitarity restrict these symmetries to a small class, where the leading interactions are captured by effective operators up to dimension-8. Chiral symmetry, spontaneously broken global symmetries and non-linearly realized supersymmetry are examples of this. Their DM candidates (composite fermions, pseudo Nambu-Goldstone Bosons and Goldstini) are interesting targets for LHC missing-energy searches.
Approximate circuits for increased reliability
Energy Technology Data Exchange (ETDEWEB)
Hamlet, Jason R.; Mayo, Jackson R.
2015-08-18
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
Approximate circuits for increased reliability
Energy Technology Data Exchange (ETDEWEB)
Hamlet, Jason R.; Mayo, Jackson R.
2015-12-22
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
Strongly nonlinear oscillators analytical solutions
Cveticanin, Livija
2014-01-01
This book provides the presentation of the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. The book presents the original author’s method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter is considered. Special attention is given to the one and two mass oscillatory systems with two-degrees-of-freedom. The criteria for the deterministic chaos in ideal and non-ideal pure nonlinear oscillators are derived analytically. The method for suppressing chaos is developed. Important problems are discussed in didactic exercises. The book is self-consistent and suitable as a textbook for students and also for profess...
Kinetic mixing at strong coupling
Del Zotto, Michele; Heckman, Jonathan J.; Kumar, Piyush; Malekian, Arada; Wecht, Brian
2017-01-01
A common feature of many string-motivated particle physics models is additional strongly coupled U (1 )'s. In such sectors, electric and magnetic states have comparable mass, and integrating out modes also charged under U (1 ) hypercharge generically yields C P preserving electric kinetic mixing and C P violating magnetic kinetic mixing terms. Even though these extra sectors are strongly coupled, we show that in the limit where the extra sector has approximate N =2 supersymmetry, we can use formal methods from Seiberg-Witten theory to compute these couplings. We also calculate various quantities of phenomenological interest such as the cross section for scattering between visible sector states and heavy extra sector states as well as the effects of supersymmetry breaking induced from coupling to the minimal supersymmetric Standard Model.
Vegh, Laszlo A.
2011-01-01
A well-studied nonlinear extension of the minimum-cost flow problem is to minimize the objective $\\sum_{ij\\in E} C_{ij}(f_{ij})$ over feasible flows $f$, where on every arc $ij$ of the network, $C_{ij}$ is a convex function. We give a strongly polynomial algorithm for the case when all $C_{ij}$'s are convex quadratic functions, settling an open problem raised e.g. by Hochbaum [1994]. We also give strongly polynomial algorithms for computing market equilibria in Fisher markets with linear util...
Approximate Augmented Lagrangian Functions and Nonlinear Semidefinite Programs
Institute of Scientific and Technical Information of China (English)
X. X. HUANG; K. L. TEO; X. Q. YANG
2006-01-01
In this paper, an approximate augmented Lagrangian function for nonlinear semidefinite programs is introduced. Some basic properties of the approximate augmented Lagrange function such as monotonicity and convexity are discussed. Necessary and sufficient conditions for approximate strong duality results are derived. Conditions for an approximate exact penalty representation in the framework of augmented Lagrangian are given. Under certain conditions, it is shown that any limit point of a sequence of stationary points of approximate augmented Lagrangian problems is a KKT point of the original semidefinite program and that a sequence of optimal solutions to augmented Lagrangian problems converges to a solution of the original semidefinite program.
Phase equilibria in the Ag-Au-In system at 500°C
Ptashkina, E. A.; Romanova, A. G.; Pavlenko, A. S.; Kabanova, E. G.; Kuznetsov, V. N.
2017-02-01
Phase equilibria in Ag-Au-In system at 500°C are investigated by means of electron microscopy, electron probe microanalysis, and X-ray powder diffraction. The part of the system's isothermal cross section with an indium content of up to 50 at % is constructed.
New investigation of phase equilibria in the system Al-Cu-Si.
Ponweiser, Norbert; Richter, Klaus W
2012-01-25
The phase equilibria and invariant reactions in the system Al-Cu-Si were investigated by a combination of optical microscopy, powder X-ray diffraction (XRD), differential thermal analysis (DTA) and electron probe micro analysis (EPMA). Isothermal phase equilibria were investigated within two isothermal sections. The isothermal section at 500 °C covers the whole ternary composition range and largely confirms the findings of previous phase diagram investigations. The isothermal section at 700 °C describes phase equilibria only in the complex Cu-rich part of the phase diagram. A new ternary compound τ was found in the region between (Al,Cu)-γ(1) and (Cu,Si)-γ and its solubility range was determined. The solubility of Al in κ-CuSi was found to be extremely high at 700 °C. In contrast, no ternary solubility in the β-phase of Cu-Al was found, although this phase is supposed to form a complete solid solution according to previous phase diagram assessments. Two isopleths, at 10 and 40 at.% Si, were investigated by means of DTA and a partial ternary reaction scheme (Scheil diagram) was constructed, based on the current work and the latest findings in the binary systems Al-Cu and Cu-Si. The current study shows that the high temperature equilibria in the Cu-rich corner are still poorly understood and additional studies in this area would be favorable.
Modelling of phase equilibria of glycol ethers mixtures using an association model
DEFF Research Database (Denmark)
Garrido, Nuno M.; Folas, Georgios; Kontogeorgis, Georgios
2008-01-01
Vapor-liquid and liquid-liquid equilibria of glycol ethers (surfactant) mixtures with hydrocarbons, polar compounds and water are calculated using an association model, the Cubic-Plus-Association Equation of State. Parameters are estimated for several non-ionic surfactants of the polyoxyethylene ...
Simulation of the high-pressure phase equilibria of hydrocarbon-water/brine systems
DEFF Research Database (Denmark)
Zuo, You-Xiang; Stenby, Erling Halfdan; Guo, Tian-Min
1996-01-01
The major objectives of this work are: (1) extend the modified Patel-Teja (MPT) equation of state proposed for aqueous electrolyte systems (Zuo and Guo, 1991) to describe the liquid-liquid and vapor-liquid-liquid equilibria of hydrocarbon-water/brine systems through introducing an unconventional ...
A numerical approach to investigate the stability of equilibria for structured population models
Breda, D.; Diekmann, O.; Maset, S.; Vermiglio, R.
2013-01-01
We are interested in the asymptotic stability of equilibria of structured populations modelled in terms of systems ofVolterra functional equations coupled with delay differential equations. The standard approach based on studying the characteristic equation of the linearized system is often involved
Hommes, C.
2013-01-01
We discuss recent work on bounded rationality and learning in relation to Soros’ principle of reflexivity and stress the empirical importance of non-rational, almost selffulfilling equilibria in positive feedback systems. As an empirical example, we discuss a behavioral asset pricing model with hete
Rexwinkel, G.; Heesink, A.B.M.; Swaaij, van W.P.M.
1999-01-01
Single-solute adsorption equilibria have been measured for the adsorption of the gaseous solutes chloroform, chlorobenzene, and 1,1,1-trichloroethane onto Amberlite XAD-4 resin. For 1,1,1-trichloroethane the adsorption equilibrium has also been measured with activated carbon Norit ROW 0.8 SUPRA as a
Engwerda, Jacob
2015-01-01
This note deals with solving scalar coupled algebraic Riccati equations. These equations arise in finding linear feedback Nash equilibria of the scalar N-player affine quadratic differential game. A numerical procedure is provided to compute all the stabilizing solutions. The main idea is to reformu
Transport and Phase Equilibria Properties for Steam Flooding of Heavy Oils
Energy Technology Data Exchange (ETDEWEB)
Gabitto, Jorge; Barrufet, Maria
2001-12-18
The objectives of this research included experimental determination and rigorous modeling and computation of phase equilibria, volumetric, and transport properties of hydrocarbon/CO2/water mixtures at pressures and temperatures typical of steam injection processes for thermal recovery of heavy oils.
Liquid-liquid equilibria for binary and ternary polymer solutions with PC-SAFT
DEFF Research Database (Denmark)
Lindvig, Thomas; Michelsen, Michael Locht; Kontogeorgis, Georgios
2004-01-01
Two algorithms for evaluating liquid-liquid equilibria (LLE) for binary and ternary polymer solutions are presented. The binary algorithm provides the temperature versus concentration cloud-point curve at fixed pressure, whereas the ternary algorithm provides component 1 versus component 2...
The Representation of Highly Non-Ideal Phase Equilibria Using Computer Graphics.
Charos, Georgios N.; And Others
1986-01-01
Previous work focused on use of computer graphics in teaching thermodynamic phase equilibria for classes I and II. Extends this work to include the considerably more non-ideal phase behavior shown by classes III, IV, and V. Student and instructor response has been overwhelmingly positive about the approach. (JN)
van Bennekom, Joost G.; Winkelman, Jozef G. M.; Venderbosch, Robertus H.; Nieland, Sebastiaan D. G. B.; Heeres, Hero J.
2012-01-01
A solution method was developed to calculate the simultaneous phase and chemical equilibria in high-pressure methanol synthesis (P = 20 MPa, 463
Vapor-Liquid Equilibria Using the Gibbs Energy and the Common Tangent Plane Criterion
Olaya, Maria del Mar; Reyes-Labarta, Juan A.; Serrano, Maria Dolores; Marcilla, Antonio
2010-01-01
Phase thermodynamics is often perceived as a difficult subject with which many students never become fully comfortable. The Gibbsian geometrical framework can help students to gain a better understanding of phase equilibria. An exercise to interpret the vapor-liquid equilibrium of a binary azeotropic mixture, using the equilibrium condition based…
New investigation of phase equilibria in the system Al–Cu–Si
Ponweiser, Norbert; Richter, Klaus W.
2012-01-01
The phase equilibria and invariant reactions in the system Al–Cu–Si were investigated by a combination of optical microscopy, powder X-ray diffraction (XRD), differential thermal analysis (DTA) and electron probe micro analysis (EPMA). Isothermal phase equilibria were investigated within two isothermal sections. The isothermal section at 500 °C covers the whole ternary composition range and largely confirms the findings of previous phase diagram investigations. The isothermal section at 700 °C describes phase equilibria only in the complex Cu-rich part of the phase diagram. A new ternary compound τ was found in the region between (Al,Cu)-γ1 and (Cu,Si)-γ and its solubility range was determined. The solubility of Al in κ-CuSi was found to be extremely high at 700 °C. In contrast, no ternary solubility in the β-phase of Cu–Al was found, although this phase is supposed to form a complete solid solution according to previous phase diagram assessments. Two isopleths, at 10 and 40 at.% Si, were investigated by means of DTA and a partial ternary reaction scheme (Scheil diagram) was constructed, based on the current work and the latest findings in the binary systems Al–Cu and Cu–Si. The current study shows that the high temperature equilibria in the Cu-rich corner are still poorly understood and additional studies in this area would be favorable. PMID:22287828
A Computer Algebra Approach to Solving Chemical Equilibria in General Chemistry
Kalainoff, Melinda; Lachance, Russ; Riegner, Dawn; Biaglow, Andrew
2012-01-01
In this article, we report on a semester-long study of the incorporation into our general chemistry course, of advanced algebraic and computer algebra techniques for solving chemical equilibrium problems. The method presented here is an alternative to the commonly used concentration table method for describing chemical equilibria in general…
Anisimov, M. P.
2016-12-01
One can find in scientific literature a pretty fresh idea of the nucleation rate surfaces design over the diagrams of phase equilibria. That idea looks like profitable for the nucleation theory development and for various practical applications where predictions of theory have no high enough accuracy for today. The common thermodynamics has no real ability to predict parameters of the first order phase transition. Nucleation experiment can be provided in very local nucleation conditions even the nucleation takes place from the critical line (in two-component case) down to the absolute zero temperature limit and from zero nucleation rates at phase equilibria up to the spinodal conditions. Theory predictions have low reliability as a rule. The computational chemistry has chance to make solution of that problem easier when a set of the used axiomatic statements will adapt enough progressive assumptions [1]. Semiempirical design of the nucleation rate surfaces over diagrams of phase equilibria have a potential ability to provide a reasonable quality information on nucleation rate for each channel of nucleation. Consideration and using of the nucleation rate surface topologies to optimize synthesis of a given phase of the target material can be available when data base on nucleation rates over diagrams of phase equilibria will be created.
Synthetic methods in phase equilibria: A new apparatus and error analysis of the method
DEFF Research Database (Denmark)
Fonseca, José; von Solms, Nicolas
2014-01-01
A new apparatus for the study of high-pressure phase equilibria using a synthetic method is described. The apparatus was especially developed for the study of solubilities of gases in condensed phases, at temperatures ranging from 243 K to 353 K and pressures up to 20 MPa. The quality of the equi...
Study of Phase Equilibria of Petrochemical Fluids using Gibbs Ensemble Monte Carlo Methods
Nath, Shyamal
2001-03-01
Knowledge of phase behavior of hydrocarbons and related compounds are highly of interest to chemical and petrochemical industries. For example, design of processes such as supercritical fluid extraction, petroleum refining, enhanced oil recovery, gas treatment, and fractionation of wax products. A precise knowledge of the phase equilibria of alkanes, alkenes and related compounds and their mixtures are required for efficient design of these processes. Experimental studies to understand the related phase equilibria often become unsuitable for various reasons. With the advancement of simulation technology, molecular simulations could provide a useful complement and alternative in the study and description of phase behavior of these systems. In this work we study vapor-liquid phase equilibria of pure hydrocarbons and their mixtures using Gibbs ensemble simulation. Insertion of long and articulated chain molecules are facilitated in our simulations by means of configurational bias and expanded ensemble methods. We use the newly developed NERD force field in our simulation. In this work NERD force field is extended to provide coverage for hydrocarbons with any arbitrary architecture. Our simulation results provide excellent quantitative agreement with available experimental phase equilibria data for both the pure components and mixtures.
Effect of temperature on acid–base equilibria in separation techniques. A review
Energy Technology Data Exchange (ETDEWEB)
Gagliardi, Leonardo G.; Tascon, Marcos; Castells, Cecilia B., E-mail: castells@isis.unlp.edu.ar
2015-08-19
Studies on the theoretical principles of acid–base equilibria are reviewed and the influence of temperature on secondary chemical equilibria within the context of separation techniques, in water and also in aqueous-organic solvent mixtures, is discussed. In order to define the relationships between the retention in liquid chromatography or the migration velocity in capillary electrophoresis and temperature, the main properties of acid–base equilibria have to be taken into account for both, the analytes and the conjugate pairs chosen to control the solution pH. The focus of this review is based on liquid–liquid extraction (LLE), liquid chromatography (LC) and capillary electrophoresis (CE), with emphasis on the use of temperature as a useful variable to modify selectivity on a predictable basis. Simplified models were evaluated to achieve practical optimizations involving pH and temperature (in LLE and CE) as well as solvent composition in reversed-phase LC. - Highlights: • The study of theoretical principles of acid–base equilibrium has been reviewed. • The proton transfer process is often present in the analytical separation practice. • The influence of temperature on secondary chemical equilibria is examined. • The focus is laid on liquid chromatography and capillary electrophoresis. • Temperature can be a useful variable to modify selectivity under predictable basis.
Structures and Chemical Equilibria of Some N-Heterocycles Containing Amide Linkages
Directory of Open Access Journals (Sweden)
N. H. Abd El Moneim
2003-05-01
Full Text Available Structures and chemical equilibria of 5-carboxy-2-thiouracil (1, 5,6-diphenyl-3-hydroxy-1,2,4-triazine (2, 1-phenyl-3-methyl-5-pyrazolone (3 and 2-mercapto-4,6-dimethylpyrimidine hydrochloride (4 are reported. Their electronic transitions are assigned and pK values are evaluated and discussed.
DEFF Research Database (Denmark)
Marcussen, Lis; Aasberg-Petersen, K.; Krøll, Annette Elisabeth
2000-01-01
An adsorption isotherm equation for nonideal pure component adsorption based on vacancy solution theory and the Non-Random-Two-Liquid (NRTL) equation is found to be useful for predicting pure component adsorption equilibria at a variety of conditions. The isotherm equation is evaluated successfully...... adsorption systems, spreading pressure and isosteric heat of adsorption are also calculated....
Vapor-Liquid-Solid Equilibria of Sulfur Dioxide in Aqueous Electrolyte Solutions
DEFF Research Database (Denmark)
Pereda, Selva; Thomsen, Kaj; Rasmussen, Peter
2000-01-01
The Extended UNIQUAC model for electrolyte systems, combined with the Soave-Redlich-Kwong equation of state is used to describe the complex vapor-liquid-solid equilibria of sulfur dioxide in electrolyte solutions. Model parameters based on 1500 experimental data points are presented. The paramete...
Ternary liquid–liquid equilibria for mixtures of toluene + n-heptane + an ionic liquid
Meindersma, G. Wytze; Podt, Anita J.G.; Haan, de André B.
2006-01-01
This research has been focused on a study of sulfolane and four ionic liquids as solvents in liquid–liquid extraction. Liquid–liquid equilibria data were obtained for mixtures of (sulfolane or 4-methyl-N-butylpyridinium tetrafluoroborate ([mebupy]BF4) or 1-ethyl-3-methylimidazolium ethylsulfate ([em
A Computer Algebra Approach to Solving Chemical Equilibria in General Chemistry
Kalainoff, Melinda; Lachance, Russ; Riegner, Dawn; Biaglow, Andrew
2012-01-01
In this article, we report on a semester-long study of the incorporation into our general chemistry course, of advanced algebraic and computer algebra techniques for solving chemical equilibrium problems. The method presented here is an alternative to the commonly used concentration table method for describing chemical equilibria in general…
Equilibria of ternary system acetic acid-water-CO2 under subcritical conditions
DEFF Research Database (Denmark)
Gutierrez, Jose M. Jimenez; Mussatto, Solange I.; Tsou, Joana
, such as acetic acid in fermentations [2, 3]. Thus, from a biotechnological perspective, it is highly interesting to research on the system CO2—H2O with different concentrations of acetic acid (HAc). Based on previous studies [4, 5], this project aims to investigate the vapour/liquid equilibria (VLE...
Dynamics of parabolic equations via the finite element method I. Continuity of the set of equilibria
Figueroa-López, R. N.; Lozada-Cruz, G.
2016-11-01
In this paper we study the dynamics of parabolic semilinear differential equations with homogeneous Dirichlet boundary conditions via the discretization of finite element method. We provide an appropriate functional setting to treat this problem and, as a first step, we show the continuity of the set of equilibria and of its linear unstable manifolds.
Control Algorithms Along Relative Equilibria of Underactuated Lagrangian Systems on Lie Groups
DEFF Research Database (Denmark)
Nordkvist, Nikolaj; Bullo, F.
2008-01-01
We present novel algorithms to control underactuated mechanical systems. For a class of invariant systems on Lie groups, we design iterative small-amplitude control forces to accelerate along, decelerate along, and stabilize relative equilibria. The technical approach is based upon a perturbation...
Institute of Scientific and Technical Information of China (English)
ZHOU Xiaopeng; SU Xueli; SUN Yan
2007-01-01
A study of nonlinear competitive adsorption equilibria of proteins is of fundamental importance in understanding the behavior of preparative chromatographic separation.This work describes the nonlinear binary protein adsorption equilibria on ion exchangers by the statistical thermodynamic (ST) model.The single-component and binary protein adsorption isotherms of bovine hemoglobin (Hb) and bovine serum albumin(BSA)on SP Sepharose FF were determined by batch adsorption experiments in 0.05 mol/L sodium acetate buffer at three pH values(4.5,5.0 and 5.5)and three NaCl concentrations(0.05,0.10 and 0.15 mol/L)at pH 5.0.The ST model was found to depict the effects of pH and ionic strength on the single-component equilibria well,with model parameters depending on the pH and ionic strength.Moreover,the ST model gave acceptable fitting to the binary adsorption data with the fltted singlecomponent model parameters,leading to the estimation of the binary ST model parameter.The effects of pH and ionic strength on the model parameters are reasonably interpreted by the electrostatic and thermodynamic theories.Results demonstrate the availability of the ST model for describing nonlinear competitive protein adsorption equilibria in the presence of two proteins.
Strongly Gorenstein Flat Dimensions
Institute of Scientific and Technical Information of China (English)
Chun Xia ZHANG; Li Min WANG
2011-01-01
This article is concerned with the strongly Gorenstein flat dimensions of modules and rings.We show this dimension has nice properties when the ring is coherent,and extend the well-known Hilbert's syzygy theorem to the strongly Gorenstein flat dimensions of rings.Also,we investigate the strongly Gorenstein flat dimensions of direct products of rings and (almost)excellent extensions of rings.
Directory of Open Access Journals (Sweden)
ALEKSANDAR ORLOVIC
2007-01-01
Full Text Available The non-catalytic synthesis of biodiesel (fatty acids methyl esters from triglycerides and methanol proceeds at elevated pressures above 100 bar and temperatures above 523 K. Kinetic investigations of the system revealed an unusual behavior of the reaction rate constant with increasing temperature and pressure. In order to explain this phenomenon, the phase behavior of the triglycerides–methanol mixture was investigated. The phase equilibria of the binary system sunflower oil–methanol were measured at different temperatures between 473 and 503 K, and a range of pressures between 10 and 56 bar. The experimental data were correlated using the Peng–Robinson, Soave–Redlich–Kwong and Redlich–Kwong–Aspen equations of state and different mixing rules. The best results were obtained with the RK–ASPEN equation of state and the Van derWaals mixing rule (VdW, which were then used to calculate the distribution of the phases at pressures and temperatures usual for the non-catalytic synthesis of biodiesel under high pressures. The obtained data indicated a strong influence of the phase equilibria on the reaction kinetics.
Odic, Darko; Lisboa, Juan Valle; Eisinger, Robert; Olivera, Magdalena Gonzalez; Maiche, Alejandro; Halberda, Justin
2016-01-01
What is the relationship between our intuitive sense of number (e.g., when estimating how many marbles are in a jar), and our intuitive sense of other quantities, including time (e.g., when estimating how long it has been since we last ate breakfast)? Recent work in cognitive, developmental, comparative psychology, and computational neuroscience has suggested that our representations of approximate number, time, and spatial extent are fundamentally linked and constitute a "generalized magnitude system". But, the shared behavioral and neural signatures between number, time, and space may alternatively be due to similar encoding and decision-making processes, rather than due to shared domain-general representations. In this study, we investigate the relationship between approximate number and time in a large sample of 6-8 year-old children in Uruguay by examining how individual differences in the precision of number and time estimation correlate with school mathematics performance. Over four testing days, each child completed an approximate number discrimination task, an approximate time discrimination task, a digit span task, and a large battery of symbolic math tests. We replicate previous reports showing that symbolic math abilities correlate with approximate number precision and extend those findings by showing that math abilities also correlate with approximate time precision. But, contrary to approximate number and time sharing common representations, we find that each of these dimensions uniquely correlates with formal math: approximate number correlates more strongly with formal math compared to time and continues to correlate with math even when precision in time and individual differences in working memory are controlled for. These results suggest that there are important differences in the mental representations of approximate number and approximate time and further clarify the relationship between quantity representations and mathematics.
Dorville, Nicolas; Belmont, Gérard; Aunai, Nicolas; Dargent, Jérémy; Rezeau, Laurence
2015-09-01
Finding kinetic equilibria for non-collisional/collisionless tangential current layers is a key issue as well for their theoretical modeling as for our understanding of the processes that disturb them, such as tearing or Kelvin Helmholtz instabilities. The famous Harris equilibrium [E. Harris, Il Nuovo Cimento Ser. 10 23, 115-121 (1962)] assumes drifting Maxwellian distributions for ions and electrons, with constant temperatures and flow velocities; these assumptions lead to symmetric layers surrounded by vacuum. This strongly particular kind of layer is not suited for the general case: asymmetric boundaries between two media with different plasmas and different magnetic fields. The standard method for constructing more general kinetic equilibria consists in using Jeans theorem, which says that any function depending only on the Hamiltonian constants of motion is a solution to the steady Vlasov equation [P. J. Channell, Phys. Fluids (1958-1988) 19, 1541 (1976); M. Roth et al., Space Sci. Rev. 76, 251-317 (1996); and F. Mottez, Phys. Plasmas 10, 1541-1545 (2003)]. The inverse implication is however not true: when using the motion invariants as variables instead of the velocity components, the general stationary particle distributions keep on depending explicitly of the position, in addition to the implicit dependence introduced by these invariants. The standard approach therefore strongly restricts the class of solutions to the problem and probably does not select the most physically reasonable. The BAS (Belmont-Aunai-Smets) model [G. Belmont et al., Phys. Plasmas 19, 022108 (2012)] used for the first time the concept of particle accessibility to find new solutions: considering the case of a coplanar-antiparallel magnetic field configuration without electric field, asymmetric solutions could be found while the standard method can only lead to symmetric ones. These solutions were validated in a hybrid simulation [N. Aunai et al., Phys. Plasmas (1994-present) 20
Energy Technology Data Exchange (ETDEWEB)
Dorville, Nicolas, E-mail: nicolas.dorville@lpp.polytechnique.fr; Belmont, Gérard; Aunai, Nicolas; Dargent, Jérémy; Rezeau, Laurence [LPP, Ecole Polytechnique, CNRS, UPMC, Université Paris Sud, Palaiseau (France)
2015-09-15
Finding kinetic equilibria for non-collisional/collisionless tangential current layers is a key issue as well for their theoretical modeling as for our understanding of the processes that disturb them, such as tearing or Kelvin Helmholtz instabilities. The famous Harris equilibrium [E. Harris, Il Nuovo Cimento Ser. 10 23, 115–121 (1962)] assumes drifting Maxwellian distributions for ions and electrons, with constant temperatures and flow velocities; these assumptions lead to symmetric layers surrounded by vacuum. This strongly particular kind of layer is not suited for the general case: asymmetric boundaries between two media with different plasmas and different magnetic fields. The standard method for constructing more general kinetic equilibria consists in using Jeans theorem, which says that any function depending only on the Hamiltonian constants of motion is a solution to the steady Vlasov equation [P. J. Channell, Phys. Fluids (1958–1988) 19, 1541 (1976); M. Roth et al., Space Sci. Rev. 76, 251–317 (1996); and F. Mottez, Phys. Plasmas 10, 1541–1545 (2003)]. The inverse implication is however not true: when using the motion invariants as variables instead of the velocity components, the general stationary particle distributions keep on depending explicitly of the position, in addition to the implicit dependence introduced by these invariants. The standard approach therefore strongly restricts the class of solutions to the problem and probably does not select the most physically reasonable. The BAS (Belmont-Aunai-Smets) model [G. Belmont et al., Phys. Plasmas 19, 022108 (2012)] used for the first time the concept of particle accessibility to find new solutions: considering the case of a coplanar-antiparallel magnetic field configuration without electric field, asymmetric solutions could be found while the standard method can only lead to symmetric ones. These solutions were validated in a hybrid simulation [N. Aunai et al., Phys. Plasmas (1994-present
Approximation of Jump Diffusions in Finance and Economics
Nicola Bruti-Liberati; Eckhard Platen
2006-01-01
In finance and economics the key dynamics are often specified via stochastic differential equations (SDEs) of jump-diffusion type. The class of jump-diffusion SDEs that admits explicit solutions is rather limited. Consequently, discrete time approximations are required. In this paper we give a survey of strong and weak numerical schemes for SDEs with jumps. Strong schemes provide pathwise approximations and therefore can be employed in scenario analysis, filtering or hedge simulation. Weak sc...
Institute of Scientific and Technical Information of China (English)
向雪萍; 孟京华; 李红
2011-01-01
对具数列的渐近非扩张型映像T给出了修正的Ishikawa Reich-Takahashi迭代序列,讨论其对T的不动点的强收敛性.同时,给出了T有不动点且序列Sm(y)=(1-αm)x+αm Tm y强收敛到T的不动点的充分条件,其中x∈D,y∈D,D是Banach空间E中闭凸子集,αm∈[0.1],αm→1.改进和推广了近期一些文献的相关结果.%The modified lshikawa Reich-Takahashi Iterative sequances for asymptotically nonexpansive type mapping T with sequence of number were discussed, which had a strong convergence for the fixed point of T. The sufficient conditions of the existence of fixed point of T and some sequences Sm (y) = ( 1 - am ) x + am,Tmy converging to a fLxed point of T were derived, with D being an nonempty closed convex subset of a Banach space E,x,y ∈ D, am, ∈[ 0,1 ] and am→l. The outcome improved and extended some recent results.
Energy Technology Data Exchange (ETDEWEB)
Bernard, O., E-mail: olivier.bernard@upmc.fr; Simonin, J.-P. [Laboratoire Physicochimie des Electrolytes, Colloïdes et Sciences Analytiques, PECSA (UMR CNRS 7195), Université P. M. Curie, Case 51, 4 Place Jussieu, 75252 Paris Cedex 05 (France); Torres-Arenas, J. [División de Ciencias e Ingenierías, Universidad de Guanajuato, Loma del Bosque 103, Colonia Lomas del Campestre, León, Guanajuato, CP 37150 (Mexico)
2014-01-21
Ionic solutions exhibiting multiple association are described within the binding mean spherical approximation (BiMSA). This model is based on the Wertheim formalism, in the framework of the primitive model at the McMillan-Mayer level. The cation and the anion form the various complexes according to stepwise complexation-equilibria. Analytic expressions for the Helmholtz energy, the internal energy, the speciation, and for the osmotic and activity coefficients are given considering a binary solution with an arbitrary number of association sites on one type of ion (polyion) and one site on the ions of opposite sign (counterions). As an alternative, mean field expressions, as developed in SAFT-type theories, are also presented. The result obtained from the latter approximate method exhibits a reasonable agreement with those from BiMSA for the speciation, and a remarkable one for the osmotic coefficient.
Bernard, O.; Torres-Arenas, J.; Simonin, J.-P.
2014-01-01
Ionic solutions exhibiting multiple association are described within the binding mean spherical approximation (BiMSA). This model is based on the Wertheim formalism, in the framework of the primitive model at the McMillan-Mayer level. The cation and the anion form the various complexes according to stepwise complexation-equilibria. Analytic expressions for the Helmholtz energy, the internal energy, the speciation, and for the osmotic and activity coefficients are given considering a binary solution with an arbitrary number of association sites on one type of ion (polyion) and one site on the ions of opposite sign (counterions). As an alternative, mean field expressions, as developed in SAFT-type theories, are also presented. The result obtained from the latter approximate method exhibits a reasonable agreement with those from BiMSA for the speciation, and a remarkable one for the osmotic coefficient.
Bernard, O; Torres-Arenas, J; Simonin, J-P
2014-01-21
Ionic solutions exhibiting multiple association are described within the binding mean spherical approximation (BiMSA). This model is based on the Wertheim formalism, in the framework of the primitive model at the McMillan-Mayer level. The cation and the anion form the various complexes according to stepwise complexation-equilibria. Analytic expressions for the Helmholtz energy, the internal energy, the speciation, and for the osmotic and activity coefficients are given considering a binary solution with an arbitrary number of association sites on one type of ion (polyion) and one site on the ions of opposite sign (counterions). As an alternative, mean field expressions, as developed in SAFT-type theories, are also presented. The result obtained from the latter approximate method exhibits a reasonable agreement with those from BiMSA for the speciation, and a remarkable one for the osmotic coefficient.
Rollout sampling approximate policy iteration
Dimitrakakis, C.; Lagoudakis, M.G.
2008-01-01
Several researchers have recently investigated the connection between reinforcement learning and classification. We are motivated by proposals of approximate policy iteration schemes without value functions, which focus on policy representation using classifiers and address policy learning as a
Approximate common divisors via lattices
Cohn, Henry
2011-01-01
We analyze the multivariate generalization of Howgrave-Graham's algorithm for the approximate common divisor problem. In the m-variable case with modulus N and approximate common divisor of size N^beta, this improves the size of the error tolerated from N^(beta^2) to N^(beta^((m+1)/m)), under a commonly used heuristic assumption. This gives a more detailed analysis of the hardness assumption underlying the recent fully homomorphic cryptosystem of van Dijk, Gentry, Halevi, and Vaikuntanathan. While these results do not challenge the suggested parameters, a 2^sqrt(n) approximation algorithm for lattice basis reduction in n dimensions could be used to break these parameters. We have implemented our algorithm, and it performs better in practice than the theoretical analysis suggests. Our results fit into a broader context of analogies between cryptanalysis and coding theory. The multivariate approximate common divisor problem is the number-theoretic analogue of noisy multivariate polynomial interpolation, and we ...
Approximate Implicitization Using Linear Algebra
Directory of Open Access Journals (Sweden)
Oliver J. D. Barrowclough
2012-01-01
Full Text Available We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD systems. We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms. We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.
Binary nucleation beyond capillarity approximation
Kalikmanov, V.I.
2010-01-01
Large discrepancies between binary classical nucleation theory (BCNT) and experiments result from adsorption effects and inability of BCNT, based on the phenomenological capillarity approximation, to treat small clusters. We propose a model aimed at eliminating both of these deficiencies. Adsorption
Nonlinear approximation with redundant dictionaries
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, M.; Gribonval, R.
2005-01-01
In this paper we study nonlinear approximation and data representation with redundant function dictionaries. In particular, approximation with redundant wavelet bi-frame systems is studied in detail. Several results for orthonormal wavelets are generalized to the redundant case. In general......, for a wavelet bi-frame system the approximation properties are limited by the number of vanishing moments of the system. In some cases this can be overcome by oversampling, but at a price of replacing the canonical expansion by another linear expansion. Moreover, for special non-oversampled wavelet bi-frames we...... can obtain good approximation properties not restricted by the number of vanishing moments, but again without using the canonical expansion....
Mathematical algorithms for approximate reasoning
Murphy, John H.; Chay, Seung C.; Downs, Mary M.
1988-01-01
Most state of the art expert system environments contain a single and often ad hoc strategy for approximate reasoning. Some environments provide facilities to program the approximate reasoning algorithms. However, the next generation of expert systems should have an environment which contain a choice of several mathematical algorithms for approximate reasoning. To meet the need for validatable and verifiable coding, the expert system environment must no longer depend upon ad hoc reasoning techniques but instead must include mathematically rigorous techniques for approximate reasoning. Popular approximate reasoning techniques are reviewed, including: certainty factors, belief measures, Bayesian probabilities, fuzzy logic, and Shafer-Dempster techniques for reasoning. A group of mathematically rigorous algorithms for approximate reasoning are focused on that could form the basis of a next generation expert system environment. These algorithms are based upon the axioms of set theory and probability theory. To separate these algorithms for approximate reasoning various conditions of mutual exclusivity and independence are imposed upon the assertions. Approximate reasoning algorithms presented include: reasoning with statistically independent assertions, reasoning with mutually exclusive assertions, reasoning with assertions that exhibit minimum overlay within the state space, reasoning with assertions that exhibit maximum overlay within the state space (i.e. fuzzy logic), pessimistic reasoning (i.e. worst case analysis), optimistic reasoning (i.e. best case analysis), and reasoning with assertions with absolutely no knowledge of the possible dependency among the assertions. A robust environment for expert system construction should include the two modes of inference: modus ponens and modus tollens. Modus ponens inference is based upon reasoning towards the conclusion in a statement of logical implication, whereas modus tollens inference is based upon reasoning away
Twisted inhomogeneous Diophantine approximation and badly approximable sets
Harrap, Stephen
2010-01-01
For any real pair i, j geq 0 with i+j=1 let Bad(i, j) denote the set of (i, j)-badly approximable pairs. That is, Bad(i, j) consists of irrational vectors x:=(x_1, x_2) in R^2 for which there exists a positive constant c(x) such that max {||qx_1||^(-i), ||qx_2||^(-j)} > c(x)/q for all q in N. Building on a result of Kurzweil, a new characterization of the set Bad(i, j) in terms of `well-approximable' vectors in the area of `twisted' inhomogeneous Diophantine approximation is established. In addition, it is shown that Bad^x(i, j), the `twisted' inhomogeneous analogue of Bad(i, j), has full Hausdorff dimension 2 when x is chosen from the set Bad(i, j).
On Cournot-Nash equilibria with exogenous uncertainty
Aaftink, J.; Ireland, N.; Sertel, M.
1986-01-01
A large body of literature has accumulated which examines how the optimal solution of an agent maximizing the expectation of a real-valued function, depending on a random parameterp and the agent's behaviorx, reacts to perturbations in the first and second moments ofp. Here, by an approximation vali
Institute of Scientific and Technical Information of China (English)
FU Dong; YAN Shu-Mei; WANG Xue-Min
2008-01-01
The excess Helmholtz free energy functional for four-site associating Lennard-Jones(LJ)fluid was formulated in terms of a modified fundamental measure theory for short-ranged interactions and a first-order mean-spherical approximation theory for long-ranged attraction.Within the framework of density functional theory,the thermodynamic properties including the average density isotherms,density profiles and fractions of not bonded monomers characterizing the coexistences between gas-like and liquid-like phases for capillary condensation,phase equilibria and equilibrium plate-fluid interfacial tensions were investigated.The influences of association energy,fluid-solid interaction and pore width on the inhomogeneous behavior of four-site associating LJ fluids confined in slit pores were discussed.
Strong Field, Noncommutative QED
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Anton Ilderton
2010-05-01
Full Text Available We review the effects of strong background fields in noncommutative QED. Beginning with the noncommutative Maxwell and Dirac equations, we describe how combined noncommutative and strong field effects modify the propagation of fermions and photons. We extend these studies beyond the case of constant backgrounds by giving a new and revealing interpretation of the photon dispersion relation. Considering scattering in background fields, we then show that the noncommutative photon is primarily responsible for generating deviations from strong field QED results. Finally, we propose a new method for constructing gauge invariant variables in noncommutative QED, and use it to analyse the physics of our null background fields.
Directory of Open Access Journals (Sweden)
Lu-Chuan Ceng
2014-01-01
Full Text Available We present a hybrid iterative algorithm for finding a common element of the set of solutions of a finite family of generalized mixed equilibrium problems, the set of solutions of a finite family of variational inequalities for inverse strong monotone mappings, the set of fixed points of an infinite family of nonexpansive mappings, and the set of solutions of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed hybrid iterative algorithm has strong convergence under some mild conditions imposed on algorithm parameters. Here, our hybrid algorithm is based on Korpelevič’s extragradient method, hybrid steepest-descent method, and viscosity approximation method.
How strong is the strong interaction?
Energy Technology Data Exchange (ETDEWEB)
Blomgren, J.; Bergenwall, B.; Hildebrand, A.; Johansson, C.; Klug, J.; Mermod, P.; Nilsson, L.; Pomp, S.; Oesterlund, M. [Dept. of Neutron Research, Uppsala Univ., Uppsala (Sweden); Tippawan, U. [Dept. of Neutron Research, Uppsala Univ., Uppsala (Sweden)]|[Fast Neutron Research Facility, Dept. of Physics, Chiang Mai Univ. (Thailand); Jonsson, O.; Prokofiev, A.V. [The Svedberg Lab., Uppsala Univ., Uppsala (Sweden); Nadel-Turonski, P. [Dept. of Radiation Sciences, Uppsala Univ., Uppsala (Sweden); Olsson, N. [Dept. of Neutron Research, Uppsala Univ., Uppsala (Sweden)]|[Swedish Defence Research Agency, Stockholm (Sweden); Dangtip, S. [Fast Neutron Research Facility, Dept. of Physics, Chiang Mai Univ. (Thailand)
2003-07-01
Elastic neutron scattering plays a key role in establishing the neutron-nucleus potential, i.e., the interaction strength between a neutron and a nucleus. In ADS applications, this information is useful in many different ways. Elastic scattering data are needed when determining the neutron intensity profile in and ADS system. In addition, the optical potentials derived from elastic neutron scattering data are used as input in every model calculation with a neutron in the incident or exit channel. Recently, there has been intense international debate on the neutron-proton scattering cross section. In the global data base, the backward cross section differs by 10% or even more at energies above 100 MeV. It is difficult to overemphasize the importance of this issue. The np scattering cross section is used as cross section reference in essentially all measurements of neutron-induced cross sections. Thus, for many applied cross sections the absolute scale is uncertain by the same amount. Moreover, the np scattering cross section has been used to derive the pion-nucleon coupling constant, i.e., the absolute strength of the strong interaction. It is annoying to have such a large uncertainty for such a fundamental parameter. We are presenting new data on elastic neutron scattering at 96 MeV from {sup 12}C and {sup 208}Pb, where the latter is part of the HINDAS project. In addition, new data on np scattering at 190 MeV will be presented. The impact on ADS and fundamental physics will be discussed. (orig.)
The solid state phase equilibria of the metal-rich regions of the Titanium-Molybdenum-Carbon and Titanium-Niobium-Carbon systems with up to 12 At...Rhenium and 10 At.% Aluminum additions, respectively, have been determined on hot pressed, heat treated, and in part arc melted alloys. The phase ... equilibria in the metal-rich regions, with these additions, is practically unchanged over that of the ternary Titanium-Molybdenum-Carbon and Titanium
Methods of Approximation Theory in Complex Analysis and Mathematical Physics
Saff, Edward
1993-01-01
The book incorporates research papers and surveys written by participants ofan International Scientific Programme on Approximation Theory jointly supervised by Institute for Constructive Mathematics of University of South Florida at Tampa, USA and the Euler International Mathematical Instituteat St. Petersburg, Russia. The aim of the Programme was to present new developments in Constructive Approximation Theory. The topics of the papers are: asymptotic behaviour of orthogonal polynomials, rational approximation of classical functions, quadrature formulas, theory of n-widths, nonlinear approximation in Hardy algebras,numerical results on best polynomial approximations, wavelet analysis. FROM THE CONTENTS: E.A. Rakhmanov: Strong asymptotics for orthogonal polynomials associated with exponential weights on R.- A.L. Levin, E.B. Saff: Exact Convergence Rates for Best Lp Rational Approximation to the Signum Function and for Optimal Quadrature in Hp.- H. Stahl: Uniform Rational Approximation of x .- M. Rahman, S.K. ...
Isenberg, James
2017-01-01
The Hawking-Penrose theorems tell us that solutions of Einstein's equations are generally singular, in the sense of the incompleteness of causal geodesics (the paths of physical observers). These singularities might be marked by the blowup of curvature and therefore crushing tidal forces, or by the breakdown of physical determinism. Penrose has conjectured (in his `Strong Cosmic Censorship Conjecture`) that it is generically unbounded curvature that causes singularities, rather than causal breakdown. The verification that ``AVTD behavior'' (marked by the domination of time derivatives over space derivatives) is generically present in a family of solutions has proven to be a useful tool for studying model versions of Strong Cosmic Censorship in that family. I discuss some of the history of Strong Cosmic Censorship, and then discuss what is known about AVTD behavior and Strong Cosmic Censorship in families of solutions defined by varying degrees of isometry, and discuss recent results which we believe will extend this knowledge and provide new support for Strong Cosmic Censorship. I also comment on some of the recent work on ``Weak Null Singularities'', and how this relates to Strong Cosmic Censorship.
Reinforcement Learning via AIXI Approximation
Veness, Joel; Hutter, Marcus; Silver, David
2010-01-01
This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. This approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement learning agents. Previously, it has been unclear whether the theory of AIXI could motivate the design of practical algorithms. We answer this hitherto open question in the affirmative, by providing the first computationally feasible approximation to the AIXI agent. To develop our approximation, we introduce a Monte Carlo Tree Search algorithm along with an agent-specific extension of the Context Tree Weighting algorithm. Empirically, we present a set of encouraging results on a number of stochastic, unknown, and partially observable domains.
Approximate Matching of Hierarchial Data
DEFF Research Database (Denmark)
Augsten, Nikolaus
The goal of this thesis is to design, develop, and evaluate new methods for the approximate matching of hierarchical data represented as labeled trees. In approximate matching scenarios two items should be matched if they are similar. Computing the similarity between labeled trees is hard...... as in addition to the data values also the structure must be considered. A well-known measure for comparing trees is the tree edit distance. It is computationally expensive and leads to a prohibitively high run time. Our solution for the approximate matching of hierarchical data are pq-grams. The pq...... formally proof that the pq-gram index can be incrementally updated based on the log of edit operations without reconstructing intermediate tree versions. The incremental update is independent of the data size and scales to a large number of changes in the data. We introduce windowed pq...
Concept Approximation between Fuzzy Ontologies
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Fuzzy ontologies are efficient tools to handle fuzzy and uncertain knowledge on the semantic web; but there are heterogeneity problems when gaining interoperability among different fuzzy ontologies. This paper uses concept approximation between fuzzy ontologies based on instances to solve the heterogeneity problems. It firstly proposes an instance selection technology based on instance clustering and weighting to unify the fuzzy interpretation of different ontologies and reduce the number of instances to increase the efficiency. Then the paper resolves the problem of computing the approximations of concepts into the problem of computing the least upper approximations of atom concepts. It optimizes the search strategies by extending atom concept sets and defining the least upper bounds of concepts to reduce the searching space of the problem. An efficient algorithm for searching the least upper bounds of concept is given.
Approximating Graphic TSP by Matchings
Mömke, Tobias
2011-01-01
We present a framework for approximating the metric TSP based on a novel use of matchings. Traditionally, matchings have been used to add edges in order to make a given graph Eulerian, whereas our approach also allows for the removal of certain edges leading to a decreased cost. For the TSP on graphic metrics (graph-TSP), the approach yields a 1.461-approximation algorithm with respect to the Held-Karp lower bound. For graph-TSP restricted to a class of graphs that contains degree three bounded and claw-free graphs, we show that the integrality gap of the Held-Karp relaxation matches the conjectured ratio 4/3. The framework allows for generalizations in a natural way and also leads to a 1.586-approximation algorithm for the traveling salesman path problem on graphic metrics where the start and end vertices are prespecified.
Diophantine approximation and Dirichlet series
Queffélec, Hervé
2013-01-01
This self-contained book will benefit beginners as well as researchers. It is devoted to Diophantine approximation, the analytic theory of Dirichlet series, and some connections between these two domains, which often occur through the Kronecker approximation theorem. Accordingly, the book is divided into seven chapters, the first three of which present tools from commutative harmonic analysis, including a sharp form of the uncertainty principle, ergodic theory and Diophantine approximation to be used in the sequel. A presentation of continued fraction expansions, including the mixing property of the Gauss map, is given. Chapters four and five present the general theory of Dirichlet series, with classes of examples connected to continued fractions, the famous Bohr point of view, and then the use of random Dirichlet series to produce non-trivial extremal examples, including sharp forms of the Bohnenblust-Hille theorem. Chapter six deals with Hardy-Dirichlet spaces, which are new and useful Banach spaces of anal...
Approximation methods in probability theory
Čekanavičius, Vydas
2016-01-01
This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.
Approximate Sparse Regularized Hyperspectral Unmixing
Directory of Open Access Journals (Sweden)
Chengzhi Deng
2014-01-01
Full Text Available Sparse regression based unmixing has been recently proposed to estimate the abundance of materials present in hyperspectral image pixel. In this paper, a novel sparse unmixing optimization model based on approximate sparsity, namely, approximate sparse unmixing (ASU, is firstly proposed to perform the unmixing task for hyperspectral remote sensing imagery. And then, a variable splitting and augmented Lagrangian algorithm is introduced to tackle the optimization problem. In ASU, approximate sparsity is used as a regularizer for sparse unmixing, which is sparser than l1 regularizer and much easier to be solved than l0 regularizer. Three simulated and one real hyperspectral images were used to evaluate the performance of the proposed algorithm in comparison to l1 regularizer. Experimental results demonstrate that the proposed algorithm is more effective and accurate for hyperspectral unmixing than state-of-the-art l1 regularizer.
A periodic point-based method for the analysis of Nash equilibria in 2 x 2 symmetric quantum games
Energy Technology Data Exchange (ETDEWEB)
Schneider, David, E-mail: schneide@tandar.cnea.gov.ar [Departamento de Fisica, Comision Nacional de EnergIa Atomica. Av. del Libertador 8250, 1429 Buenos Aires (Argentina)
2011-03-04
We present a novel method of looking at Nash equilibria in 2 x 2 quantum games. Our method is based on a mathematical connection between the problem of identifying Nash equilibria in game theory, and the topological problem of the periodic points in nonlinear maps. To adapt our method to the original protocol designed by Eisert et al (1999 Phys. Rev. Lett. 83 3077-80) to study quantum games, we are forced to extend the space of strategies from the initial proposal. We apply our method to the extended strategy space version of the quantum Prisoner's dilemma and find that a new set of Nash equilibria emerge in a natural way. Nash equilibria in this set are optimal as Eisert's solution of the quantum Prisoner's dilemma and include this solution as a limit case.
Generalized Mixed Equilibria, Variational Inclusions, and Fixed Point Problems
Directory of Open Access Journals (Sweden)
A. E. Al-Mazrooei
2014-01-01
Full Text Available We propose two iterative algorithms for finding a common element of the set of solutions of finite generalized mixed equilibrium problems, the set of solutions of finite variational inclusions for maximal monotone and inverse strong monotone mappings, and the set of common fixed points of infinite nonexpansive mappings and an asymptotically κ-strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove some strong and weak convergence theorems for the proposed iterative algorithms under suitable conditions.
Transfinite Approximation of Hindman's Theorem
Beiglböck, Mathias
2010-01-01
Hindman's Theorem states that in any finite coloring of the integers, there is an infinite set all of whose finite sums belong to the same color. This is much stronger than the corresponding finite form, stating that in any finite coloring of the integers there are arbitrarily long finite sets with the same property. We extend the finite form of Hindman's Theorem to a "transfinite" version for each countable ordinal, and show that Hindman's Theorem is equivalent to the appropriate transfinite approximation holding for every countable ordinal. We then give a proof of Hindman's Theorem by directly proving these transfinite approximations.
Tree wavelet approximations with applications
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
[1]Baraniuk, R. G., DeVore, R. A., Kyriazis, G., Yu, X. M., Near best tree approximation, Adv. Comput. Math.,2002, 16: 357-373.[2]Cohen, A., Dahmen, W., Daubechies, I., DeVore, R., Tree approximation and optimal encoding, Appl. Comput.Harmonic Anal., 2001, 11: 192-226.[3]Dahmen, W., Schneider, R., Xu, Y., Nonlinear functionals of wavelet expansions-adaptive reconstruction and fast evaluation, Numer. Math., 2000, 86: 49-101.[4]DeVore, R. A., Nonlinear approximation, Acta Numer., 1998, 7: 51-150.[5]Davis, G., Mallat, S., Avellaneda, M., Adaptive greedy approximations, Const. Approx., 1997, 13: 57-98.[6]DeVore, R. A., Temlyakov, V. N., Some remarks on greedy algorithms, Adv. Comput. Math., 1996, 5: 173-187.[7]Kashin, B. S., Temlyakov, V. N., Best m-term approximations and the entropy of sets in the space L1, Mat.Zametki (in Russian), 1994, 56: 57-86.[8]Temlyakov, V. N., The best m-term approximation and greedy algorithms, Adv. Comput. Math., 1998, 8:249-265.[9]Temlyakov, V. N., Greedy algorithm and m-term trigonometric approximation, Constr. Approx., 1998, 14:569-587.[10]Hutchinson, J. E., Fractals and self similarity, Indiana. Univ. Math. J., 1981, 30: 713-747.[11]Binev, P., Dahmen, W., DeVore, R. A., Petruchev, P., Approximation classes for adaptive methods, Serdica Math.J., 2002, 28: 1001-1026.[12]Gilbarg, D., Trudinger, N. S., Elliptic Partial Differential Equations of Second Order, Berlin: Springer-Verlag,1983.[13]Ciarlet, P. G., The Finite Element Method for Elliptic Problems, New York: North Holland, 1978.[14]Birman, M. S., Solomiak, M. Z., Piecewise polynomial approximation of functions of the class Wαp, Math. Sb.,1967, 73: 295-317.[15]DeVore, R. A., Lorentz, G. G., Constructive Approximation, New York: Springer-Verlag, 1993.[16]DeVore, R. A., Popov, V., Interpolation of Besov spaces, Trans. Amer. Math. Soc., 1988, 305: 397-414.[17]Devore, R., Jawerth, B., Popov, V., Compression of wavelet decompositions, Amer. J. Math., 1992, 114: 737-785.[18]Storozhenko, E
Phase Equilibria of H2SO4, HNO3, and HCl Hydrates and the Composition of Polar Stratospheric Clouds
Wooldridge, Paul J.; Zhang, Renyi; Molina, Mario J.
1995-01-01
Thermodynamic properties and phase equilibria behavior for the hydrates and coexisting pairs of hydrates of common acids which exist in the stratosphere are assembled from new laboratory measurements and standard literature data. The analysis focuses upon solid-vapor and solid-solid-vapor equilibria at temperatures around 200 K and includes new calorimetric and vapor pressure data. Calculated partial pressures versus 1/T slopes for the hydrates and coexisting hydrates agree well with experimental data where available.
Institute of Scientific and Technical Information of China (English)
FU,Dong(付东); LU,Jiu-Fang(陆九芳); WU,Wei(吴畏); Li,Yi-Gui(李以圭)
2004-01-01
An equation of state (EOS) was established to study the osmotic pressure and liquid-liquid equilibria for micelle,colloid and microemulsion systems. The Carnahan-Starling equation was used for the hard sphere repulsion. The Yukawa potential was used to describe both the attractive dispersion and the double-layer repulsion. By using the established EOS, the osmotic pressures for charged colloid, uncharged micelle, uncharged and weakly charged microemuslion, the phase equilibria for uncharged micelle and charged colloid systems were studied.
Nash Equilibria in Symmetric Games with Partial Observation
DEFF Research Database (Denmark)
Bouyer, Patricia; Markey, Nicolas; Vester, Steen
2014-01-01
We investigate a model for representing large multiplayer games, which satisfy strong symmetry properties. This model is made of multiple copies of an arena; each player plays in his own arena, and can partially observe what the other players do. Therefore, this game has partial information and s...
Kim, SungKun; Lee, Hunpyo
2017-06-01
Via a dynamical cluster approximation with N c = 4 in combination with a semiclassical approximation (DCA+SCA), we study the doped two-dimensional Hubbard model. We obtain a plaquette antiferromagnetic (AF) Mott insulator, a plaquette AF ordered metal, a pseudogap (or d-wave superconductor) and a paramagnetic metal by tuning the doping concentration. These features are similar to the behaviors observed in copper-oxide superconductors and are in qualitative agreement with the results calculated by the cluster dynamical mean field theory with the continuous-time quantum Monte Carlo (CDMFT+CTQMC) approach. The results of our DCA+SCA differ from those of the CDMFT+CTQMC approach in that the d-wave superconducting order parameters are shown even in the high doped region, unlike the results of the CDMFT+CTQMC approach. We think that the strong plaquette AF orderings in the dynamical cluster approximation (DCA) with N c = 4 suppress superconducting states with increasing doping up to strongly doped region, because frozen dynamical fluctuations in a semiclassical approximation (SCA) approach are unable to destroy those orderings. Our calculation with short-range spatial fluctuations is initial research, because the SCA can manage long-range spatial fluctuations in feasible computational times beyond the CDMFT+CTQMC tool. We believe that our future DCA+SCA calculations should supply information on the fully momentum-resolved physical properties, which could be compared with the results measured by angle-resolved photoemission spectroscopy experiments.
WKB Approximation in Noncommutative Gravity
Directory of Open Access Journals (Sweden)
Maja Buric
2007-12-01
Full Text Available We consider the quasi-commutative approximation to a noncommutative geometry defined as a generalization of the moving frame formalism. The relation which exists between noncommutativity and geometry is used to study the properties of the high-frequency waves on the flat background.
Approximation properties of haplotype tagging
Directory of Open Access Journals (Sweden)
Dreiseitl Stephan
2006-01-01
Full Text Available Abstract Background Single nucleotide polymorphisms (SNPs are locations at which the genomic sequences of population members differ. Since these differences are known to follow patterns, disease association studies are facilitated by identifying SNPs that allow the unique identification of such patterns. This process, known as haplotype tagging, is formulated as a combinatorial optimization problem and analyzed in terms of complexity and approximation properties. Results It is shown that the tagging problem is NP-hard but approximable within 1 + ln((n2 - n/2 for n haplotypes but not approximable within (1 - ε ln(n/2 for any ε > 0 unless NP ⊂ DTIME(nlog log n. A simple, very easily implementable algorithm that exhibits the above upper bound on solution quality is presented. This algorithm has running time O((2m - p + 1 ≤ O(m(n2 - n/2 where p ≤ min(n, m for n haplotypes of size m. As we show that the approximation bound is asymptotically tight, the algorithm presented is optimal with respect to this asymptotic bound. Conclusion The haplotype tagging problem is hard, but approachable with a fast, practical, and surprisingly simple algorithm that cannot be significantly improved upon on a single processor machine. Hence, significant improvement in computatational efforts expended can only be expected if the computational effort is distributed and done in parallel.
Truthful approximations to range voting
DEFF Research Database (Denmark)
Filos-Ratsika, Aris; Miltersen, Peter Bro
We consider the fundamental mechanism design problem of approximate social welfare maximization under general cardinal preferences on a finite number of alternatives and without money. The well-known range voting scheme can be thought of as a non-truthful mechanism for exact social welfare...
Approximate Reasoning with Fuzzy Booleans
Broek, van den P.M.; Noppen, J.A.R.
2004-01-01
This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp ante
Ultrafast Approximation for Phylogenetic Bootstrap
Bui Quang Minh, [No Value; Nguyen, Thi; von Haeseler, Arndt
2013-01-01
Nonparametric bootstrap has been a widely used tool in phylogenetic analysis to assess the clade support of phylogenetic trees. However, with the rapidly growing amount of data, this task remains a computational bottleneck. Recently, approximation methods such as the RAxML rapid bootstrap (RBS) and
On badly approximable complex numbers
DEFF Research Database (Denmark)
Esdahl-Schou, Rune; Kristensen, S.
We show that the set of complex numbers which are badly approximable by ratios of elements of , where has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably...
Rational approximation of vertical segments
Salazar Celis, Oliver; Cuyt, Annie; Verdonk, Brigitte
2007-08-01
In many applications, observations are prone to imprecise measurements. When constructing a model based on such data, an approximation rather than an interpolation approach is needed. Very often a least squares approximation is used. Here we follow a different approach. A natural way for dealing with uncertainty in the data is by means of an uncertainty interval. We assume that the uncertainty in the independent variables is negligible and that for each observation an uncertainty interval can be given which contains the (unknown) exact value. To approximate such data we look for functions which intersect all uncertainty intervals. In the past this problem has been studied for polynomials, or more generally for functions which are linear in the unknown coefficients. Here we study the problem for a particular class of functions which are nonlinear in the unknown coefficients, namely rational functions. We show how to reduce the problem to a quadratic programming problem with a strictly convex objective function, yielding a unique rational function which intersects all uncertainty intervals and satisfies some additional properties. Compared to rational least squares approximation which reduces to a nonlinear optimization problem where the objective function may have many local minima, this makes the new approach attractive.
Approximation on the complex sphere
Alsaud, Huda; Kushpel, Alexander; Levesley, Jeremy
2012-01-01
We develop new elements of harmonic analysis on the complex sphere on the basis of which Bernstein's, Jackson's and Kolmogorov's inequalities are established. We apply these results to get order sharp estimates of $m$-term approximations. The results obtained is a synthesis of new results on classical orthogonal polynomials, harmonic analysis on manifolds and geometric properties of Euclidean spaces.
On badly approximable complex numbers
DEFF Research Database (Denmark)
Esdahl-Schou, Rune; Kristensen, S.
We show that the set of complex numbers which are badly approximable by ratios of elements of , where has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably...
Pythagorean Approximations and Continued Fractions
Peralta, Javier
2008-01-01
In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers…
Approximation of Surfaces by Cylinders
DEFF Research Database (Denmark)
Randrup, Thomas
1998-01-01
We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...
Approximate Reanalysis in Topology Optimization
DEFF Research Database (Denmark)
Amir, Oded; Bendsøe, Martin P.; Sigmund, Ole
2009-01-01
In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, the integration of an approximate reanalysis procedure into the framework of topology optimization of continuum structures...
Low Rank Approximation in $G_0W_0$ Approximation
Shao, Meiyue; Yang, Chao; Liu, Fang; da Jornada, Felipe H; Deslippe, Jack; Louie, Steven G
2016-01-01
The single particle energies obtained in a Kohn--Sham density functional theory (DFT) calculation are generally known to be poor approximations to electron excitation energies that are measured in transport, tunneling and spectroscopic experiments such as photo-emission spectroscopy. The correction to these energies can be obtained from the poles of a single particle Green's function derived from a many-body perturbation theory. From a computational perspective, the accuracy and efficiency of such an approach depends on how a self energy term that properly accounts for dynamic screening of electrons is approximated. The $G_0W_0$ approximation is a widely used technique in which the self energy is expressed as the convolution of a non-interacting Green's function ($G_0$) and a screened Coulomb interaction ($W_0$) in the frequency domain. The computational cost associated with such a convolution is high due to the high complexity of evaluating $W_0$ at multiple frequencies. In this paper, we discuss how the cos...
Indian Academy of Sciences (India)
Vaddeboina Sridhar; S Satyanarayana
2000-12-01
Kinetics and equilibria of the axial ligation of alkyl(aquo)cobaloximes by imidazole and cyanide have been measured spectrophotometrically in aqueous solutions of ionic strength 1.0 M at 25°C as a function of H. Comparison of IMD and CN- of CH3, C2H5 and BrCH2 cobaloximes indicates that their stability is in the order BrCH2 > CH3 > C2H5. As the electron-withdrawing capacity of the alkyl group trans to water increases, the electron density of the cobalt(III) decreases and thus it becomes a stronger Lewis acid and binds more strongly to imidazole and cyanide. The association and dissociation rate constants are better correlated to the relative softness of the ligand showing that cyanide binds 30 times faster than imidazole. These complexes are isolated and are characterized by IR and 1H NMR spectra.
Strongly correlated Bose gases
Chevy, F.; Salomon, C.
2016-10-01
The strongly interacting Bose gas is one of the most fundamental paradigms of quantum many-body physics and the subject of many experimental and theoretical investigations. We review recent progress on strongly correlated Bose gases, starting with a description of beyond mean-field corrections. We show that the Efimov effect leads to non universal phenomena and to a metastability of the low temperature Bose gas through three-body recombination to deeply bound molecular states. We outline differences and similarities with ultracold Fermi gases, discuss recent experiments on the unitary Bose gas, and finally present a few perspectives for future research.
Abortion: Strong's counterexamples fail
DEFF Research Database (Denmark)
Di Nucci, Ezio
2009-01-01
This paper shows that the counterexamples proposed by Strong in 2008 in the Journal of Medical Ethics to Marquis's argument against abortion fail. Strong's basic idea is that there are cases--for example, terminally ill patients--where killing an adult human being is prima facie seriously morally......'s scenarios have some valuable future or admitted that killing them is not seriously morally wrong. Finally, if "valuable future" is interpreted as referring to objective standards, one ends up with implausible and unpalatable moral claims....
Protonation Equilibria of L-Aspartic, Citric and Succinic Acids in Anionic Micellar Media
Directory of Open Access Journals (Sweden)
P. Srinivasa Rao
2009-01-01
Full Text Available The impact of sodium lauryl sulphate (SLS on the protonation equilibria of L-aspartic acid, citric acid and succinic acid has been studied in various concentrations (0.5-2.5% w/v of SLS solution maintaining an ionic strength of 0.16 mol dm-3 at 303 K. The protonation constants have been calculated with the computer program MINIQUAD75 and the best fit models have been calculated based on statistical parameters. The trend of log values of step-wise protonation constants with mole fraction of the medium has been explained based on electrostatic and non-electrostatic forces operating on the protonation equilibria. The effects of errors on the protonation constants have also been presented.
GLOBAL ANALYSIS OF SIS EPIDEMIC MODEL WITH A SIMPLE VACCINATION AND MULTIPLE ENDEMIC EQUILIBRIA
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
An SIS epidemic model with a simple vaccination is investigated in this article.The efficiency of vaccine, the disease-related death rate and population dynamics are also considered in this model. The authors find two threshold R0 and Rc (Rc may not exist).There is a unique endemic equilibrium for R0 ＞ 1 or Rc = R0; there are two endemic equilibria for Rc ＜ R0 ＜ 1; and there is no endemic equilibrium for R0 ＜ Rc ＜ 1. When Rc exists, there is a backward bifurcation from the disease-free equilibrium for R0 = 1.They analyze the stability of equilibria and obtain the globally dynamic behaviors of the model. The results acquired in this article show that an accurate estimation of the efficiency of vaccine is necessary to prevent and controll the spread of disease.
Schur, W. W.
2004-01-01
Excess in skin material of a pneumatic envelope beyond what is required for minimum enclosure of a gas bubble is a necessary but by no means sufficient condition for the existence of multiple equilibrium configurations for that pneumatic envelope. The very design of structurally efficient super-pressure balloons of the pumpkin shape type requires such excess. Undesired stable equilibria in pumpkin shape balloons have been observed on experimental pumpkin shape balloons. These configurations contain regions with stress levels far higher than those predicted for the cyclically symmetric design configuration under maximum pressurization. Successful designs of pumpkin shape super-pressure balloons do not allow such undesired stable equilibria under full pressurization. This work documents efforts made so far and describes efforts still underway by the National Aeronautics and Space Administration's Balloon Program Office to arrive on guidance on the design of pumpkin shape super-pressure balloons that guarantee full and proper deployment.
Microbial control of mineral–groundwater equilibria:Macroscale to microscale
Bennett, Philip C.; Hiebert, Franz K.; Roger, Jennifer Roberts
2000-01-01
macroscaleprocesses that perturb general groundwater chemistry and therefore mineral–water equilibria; and microscale interactions, where attached organisms locally perturb mineral–water equilibria, potentially releasing limiting trace nutrients from the dissolving mineral.In the contaminated unconfined glacio-fluvial aquifer near Bemidji, Minnesota, USA, carbonate chemistry is influenced primarily at the macroscale. Under oxic conditions, respiration by native aerobic heterotrophs produces excess carbon dioxide that promotes calcite and dolomite dissolution. Aerobic microorganisms do not colonize dolomite surfaces and few occur on calcite. Within the anoxic groundwater, calcite overgrowths form on uncolonized calcite cleavage surfaces, possibly due to the consumption of acidity by dissimilatory iron-reducing bacteria. As molecular oxygen concentration increases downgradient of the oil pool, aerobes again dominate and residual hydrocarbons and ferrous iron are oxidized, resulting in macroscale carbonate-mineral dissolution and iron precipitation.
Thermodynamic calculations in the system CH4-H2O and methane hydrate phase equilibria
Circone, S.; Kirby, S.H.; Stern, L.A.
2006-01-01
Using the Gibbs function of reaction, equilibrium pressure, temperature conditions for the formation of methane clathrate hydrate have been calculated from the thermodynamic properties of phases in the system CH4-H 2O. The thermodynamic model accurately reproduces the published phase-equilibria data to within ??2 K of the observed equilibrium boundaries in the range 0.08-117 MPa and 190-307 K. The model also provides an estimate of the third-law entropy of methane hydrate at 273.15 K, 0.1 MPa of 56.2 J mol-1 K-1 for 1/n CH4??H 2O, where n is the hydrate number. Agreement between the calculated and published phase-equilibria data is optimized when the hydrate composition is fixed and independent of the pressure and temperature for the conditions modeled. ?? 2006 American Chemical Society.
Calculation of phase equilibria of the Ag-In-Sb system by the calphad method
Directory of Open Access Journals (Sweden)
Borisov Ivana I.
2007-01-01
Full Text Available The ternary Ag-In-Sb system is a promising candidate for use as a Pb-free solder. The results of phase equilibria calculation by the CALPHAD method are presented in this study. The isothermal section at 400°C was calculated using optimized thermodynamic parameters of the constitutive binary systems. Calculated vertical sections from the indium and antimony corners were compared with the DTA results from this study and from the literature.
Equation-of-State Modeling of Phase Equilibria in Petroleum Fluids
DEFF Research Database (Denmark)
Jørgensen, Marianne
1996-01-01
The Soave-Redlich-Kwong (SRK) equation of state was used to investigate and develop several aspects of the modeling of natural petroleum fluids.A new method was presented for numerical evaluation of PVT experiments. This method was used in the estimation of binary interaction parameters. A comphr...... that exists for mixtures of CO2 and crude oils. Good results are obtained, and a tuning procedure is proposed for improved representation of the three phase equilibria....
Thermal analysis and prediction of phase equilibria in ternary Pb-Zn-Ag system
2011-01-01
Ternary Pb-Zn-Ag system is typical for some physicochemical processes going on in refining phase in the extractive metallurgy of lead. Therefore, investigation of mentioned system is important from both theoretical and practical research of the phenomena occurring during the lead desilverizing process. The results of experimental investigation using differential thermal analysis (DTA) and thermodynamic calculation of phase equilibria in Pb-Zn-Ag system according to CALPHAD method, in th...
Control algorithms along relative equilibria of underactuated Lagrangian systems on Lie groups
DEFF Research Database (Denmark)
Nordkvist, Nikolaj; Bullo, Francesco
2007-01-01
We present novel algorithms to control underactuated mechanical systems. For a class of invariant systems on Lie groups, we design iterative small-amplitude control forces to accelerate along, decelerate along, and stabilize relative equilibria. The technical approach is based upon a perturbation...... analysis and the design of inversion primitives and composition methods. We illustrate the algorithms on an underactuated planar rigid body and on a satellite with two thrusters....
Further work on experimental plagioclase equilibria and the Skaergaard liquidus temperature
DEFF Research Database (Denmark)
Thy, Peter; Lesher, Charles E.; Tegner, Christian
2013-01-01
Equilibria between plagioclase and ferrobasaltic melt in low-pressure, dry melting experiments can be demonstrated near the liquidus. Further analyses of melting experiments using optimized beam conditions reveals that previous data for understanding the Skaergaard intrusion potentially suffered...... data set provides tighter bounds on experimental plagioclase composition and documents composition-dependent partitioning of Na and Ca between plagioclase and melt. Application of the results to modeling the Skaergaard requires only minor adjustments to the previously proposed liquidus temperatures...
Phase equilibria in stratified thin liquid films stabilized by colloidal particles
Blawzdziewicz, J.; Wajnryb, E.
2005-01-01
Phase equilibria between regions of different thickness in thin liquid films stabilized by colloidal particles are investigated using a quasi-two-dimensional thermodynamic formalism. Appropriate equilibrium conditions for the film tension, normal pressure, and chemical potential of the particles in the film are formulated, and it is shown that the relaxation of these parameters occurs consecutively on three distinct time scales. Film stratification is described quantitatively for a hard-spher...
A combined theory for magnetohydrodynamic equilibria with anisotropic pressure and magnetic shear
Hodgson, J. D. B.; Neukirch, T.
2017-03-01
We present a new approach to the theory of magnetohydrodynamic equilibria with anisotropic pressure, magnetic shear and translational/rotational invariance. This approach involves combining two existing formalisms in order to eliminate their individual weaknesses. The theoretical aspects of the method are explored in detail along with numerical solutions which make use of the method. Eventually, this method could be applied to model various plasma systems, such as planetary magnetospheres.
Strongly interacting Fermi gases
Directory of Open Access Journals (Sweden)
Bakr W.
2013-08-01
Full Text Available Strongly interacting gases of ultracold fermions have become an amazingly rich test-bed for many-body theories of fermionic matter. Here we present our recent experiments on these systems. Firstly, we discuss high-precision measurements on the thermodynamics of a strongly interacting Fermi gas across the superfluid transition. The onset of superfluidity is directly observed in the compressibility, the chemical potential, the entropy, and the heat capacity. Our measurements provide benchmarks for current many-body theories on strongly interacting fermions. Secondly, we have studied the evolution of fermion pairing from three to two dimensions in these gases, relating to the physics of layered superconductors. In the presence of p-wave interactions, Fermi gases are predicted to display toplogical superfluidity carrying Majorana edge states. Two possible avenues in this direction are discussed, our creation and direct observation of spin-orbit coupling in Fermi gases and the creation of fermionic molecules of 23Na 40K that will feature strong dipolar interactions in their absolute ground state.
Moloney, Michael J.
2007-01-01
Did you know that some strong little cylindrical magnets available in local hardware stores can have an effective circumferential current of 2500 A? This intriguing information can be obtained by hanging a pair of magnets at the center of a coil, as shown in Fig. 1, and measuring the oscillation frequency as a function of coil current.
Phase equilibria in carbon dioxide expanded solvents: Experiments and molecular simulations.
Houndonougbo, Yao; Jin, Hong; Rajagopalan, Bhuma; Wong, Kean; Kuczera, Krzysztof; Subramaniam, Bala; Laird, Brian
2006-07-06
We present complementary molecular simulations and experimental results of phase equilibria for carbon dioxide expanded acetonitrile, methanol, ethanol, acetone, acetic acid, toluene, and 1-octene. The volume expansion measurements were done using a high-pressure Jerguson view cell. Molecular simulations were performed using the Gibbs ensemble Monte Carlo method. Calculations in the canonical ensemble (NVT) were performed to determine the coexistence curve of the pure solvent systems. Binary mixtures were simulated in the isobaric-isothermal distribution (NPT). Predictions of vapor-liquid equilibria of the pure components agree well with experimental data. The simulations accurately reproduced experimental data on saturated liquid and vapor densities for carbon dioxide, methanol, ethanol, acetone, acetic acid, toluene, and 1-octene. In all carbon dioxide expanded liquids (CXL's) studied, the molecular simulation results for the volume expansion of these binary mixtures were found to be as good as, and in many cases superior to, predictions based on the Peng-Robinson equation of state, demonstrating the utility of molecular simulation in the prediction of CXL phase equilibria.
Qin, Sanbo; Zhou, Huan-Xiang
2016-08-25
Chemical potential is a fundamental property for determining thermodynamic equilibria involving exchange of molecules, such as between two phases of molecular systems. Previously, we developed the fast Fourier transform (FFT)-based method for Modeling Atomistic Protein-crowder interactions (FMAP) to calculate excess chemical potentials according to the Widom insertion. Intermolecular interaction energies were expressed as correlation functions and evaluated via FFT. Here, we extend this method to calculate liquid-liquid phase equilibria of macromolecular solutions. Chemical potentials are calculated by FMAP over a wide range of molecular densities, and the condition for coexistence of low- and high-density phases is determined by the Maxwell equal-area rule. When benchmarked on Lennard-Jones fluids, our method produces an accurate phase diagram at 18% of the computational cost of the current best method. Importantly, the gain in computational speed increases dramatically as the molecules become more complex, leading to many orders of magnitude in speed up for atomistically represented proteins. We demonstrate the power of FMAP by reporting the first results for the liquid-liquid coexistence curve of γII-crystallin represented at the all-atom level. Our method may thus open the door to accurate determination of phase equilibria for macromolecular mixtures such as protein-protein mixtures and protein-RNA mixtures, that are known to undergo liquid-liquid phase separation, both in vitro and in vivo.
3D low-beta magnetized plasma equilibria from external shaping
Hassam, A.; Tenbarge, J.; Landreman, M.; Dorland, W.; Sengupta, W.
2016-10-01
A 3D nonlinear dissipative MHD code is in development to allow relaxation to low-beta MHD equilibrium inside a shaped 3D conducting boundary with prescribed conserved axial magnetic flux and no external current. Formation of magnetic islands is expected. Heat sources would be eventually introduced to allow the possibility of non-stationary convection depending on the stability properties of the accessible MHD equilibria. The initial development will be done using the code UMHD. The initial emphasis will be on recovering expected physics in simpler 3D geometries. A primary objective is to minimize numerical boundary noise. In particular, codes which specify the normal magnetic field B.n on bounding surfaces are prone to noise generation. We plan to shape the boundary to conform to the desired field shape so that B.n is zero on the boundary. Non-orthogonal coordinates will be chosen to effect this. We will test noise reduction within the tangential field approach. Results obtained to date support this conjecture. Initial results from simple 2D code equilibria have been verified against analytic solution of equilibria in weak shaping. Initial results also recover the expected features of the Hahm- Kulsrud island formation solution. Work supported by US DOE.
Prediction of vapour-liquid equilibria for the kinetic study of processes based on synthesis gas
Energy Technology Data Exchange (ETDEWEB)
Di Serio, M.; Tesser, R.; Cozzolino, M.; Santacesaria, E. [Naples Univ., Napoli (Italy). Dept. of Chemistry
2006-07-01
Syngas is normally used in the production of a broad range of chemicals and fuels. In many of these processes multiphase reactors, gas-liquid or gas-liquid-solid are used. Kinetic studies in multiphase systems are often complicated by the non-ideal behaviour of reagents and/or products that are consistently partitioned between the liquid and the vapour phase. Moreover, as often kinetic data are collected in batch conditions for the liquid phase, activity coefficients of the partitioned components can consistently change during the time as a consequence of changing the composition of the reaction mixture. Therefore, it is necessary, in these cases, to known the vapor-liquid equilibria (VLE) in order to collect and to interpret correctly the kinetic data. The description of phase equilibria, at high pressures, is usually performed by means of an EOS (Equation of State) allowing the calculation of fugacity coefficients, for each component, in both phases and determining the partition coefficients but the EOS approach involves the experimental determination of the interaction parameters for all the possible binary system of the mixture. For multicomponent mixtures a complete experimental determination of vapourliquid equilibria is very hard, also considering the high pressure and temperatures used. Some predictive group contribution methods have been recently developed. In this paper, we will describe in detail the application of these methods to the methanol homologation, as an example, with the scope of determining more reliable kinetic parameters for this reaction. (orig.)
Ruthenium redox equilibria: 1. Thermodynamic stability of Ru(III and Ru(IV hydroxides
Directory of Open Access Journals (Sweden)
Igor Povar
2016-04-01
Full Text Available On the basis of the selected thermodynamic data for Ru(III and Ru(IV compounds in addition to original thermodynamic and graphical approach used in this paper, the thermodynamic stability areas of sparingly soluble hydroxides as well as the repartition of their soluble and insoluble chemical species towards the solution pH and initial concentrations of ruthenium in heterogeneous mixture solid phase–saturated solution have been investigated. By means of the ΔG–pH diagrams, the areas of thermodynamic stability of Ru(III and Ru(IV hydroxides have been established for a number of analytical concentrations in heterogeneous mixtures. The diagrams of heterogeneous and homogeneous chemical equilibria have been used for graphical representation of complex equilibria in aqueous solutions containing Ru(III and Ru(IV. The obtained results, based on the thermodynamic analysis and graphic design of the calculated data in the form of the diagrams of heterogeneous chemical equilibria, are in good agreement with the available experimental data.
Stability of the relative equilibria of a rigid body in a J2 gravity field
Wang, Yue; Xu, Shijie
2014-01-01
The motion of a point mass in the J2 problem is generalized to that of a rigid body in a J2 gravity field. Different with the original J2 problem, the gravitational orbit-rotation coupling of the rigid body is considered in this generalized problem. The linear stability of the classical type of relative equilibria of the rigid body, which have been obtained in our previous paper, is studied in the framework of geometric mechanics with the second-order gravitational potential. Non-canonical Hamiltonian structure of the problem, i.e., Poisson tensor, Casimir functions and equations of motion, are obtained through a Poisson reduction process by means of the symmetry of the problem. The linear system matrix at the relative equilibria is given through the multiplication of the Poisson tensor and Hessian matrix of the variational Lagrangian. Based on the characteristic equation of the linear system matrix, the conditions of linear stability of the relative equilibria are obtained. With the stability conditions obta...
Density-functional study on the equilibria in the ThDP activation.
Delgado, Eduardo J; Alderete, Joel B; Jaña, Gonzalo A
2011-11-01
The equilibria among the various ionization and tautomeric states involved in the activation of ThDP is addressed using high level density functional theory calculations, X3LYP/6-311++G(d,p)//X3LYP(PB)/6-31++G(d,p). This study provides the first theoretically derived thermodynamic data for the internal equilibria in the activation of ThDP. The role of the medium polarity on the geometry and thermodynamics of the diverse equilibria of ThDP is addressed. The media chosen are cyclohexane and water, as paradigms of apolar and polar media. The results suggest that all ionization and tautomeric states are accessible during the catalytic cycle, even in the absence of substrate, being APH(+) the form required to interconvert the AP and IP tautomers; and the generation of the ylide proceeds via the formation of the IP form. Additionally, the calculated ΔG° values allow to calculate all the equilibrium constants, including the pK(C2) for the thiazolium C2 atom whose ionization is believed to initiate the catalytic cycle.
Theoretical models of non-Maxwellian equilibria for one-dimensional collisionless plasmas
Allanson, O.; Neukirch, T.; Wilson, F.; Troscheit, S.
2016-12-01
It is ideal to use exact equilibrium solutions of the steady state Vlasov-Maxwell system to intialise collsionless simulations. However, exact equilibrium distribution functions (DFs) for a given macroscopic configuration are typically unknown, and it is common to resort to using `flow-shifted' Maxwellian DFs in their stead. These DFs may be consistent with a macrosopic system with the target number density and current density, but could well have inaccurate higher order moments. We present recent theoretical work on the `inverse problem in Vlasov-Maxwell equilibria', namely calculating an exact solution of the Vlasov equation for a specific given magnetic field. In particular, we focus on one-dimensional geometries in Cartesian (current sheets) coordinates.1. From 1D fields to Vlasov equilibria: Theory and application of Hermite Polynomials: (O. Allanson, T. Neukirch, S. Troscheit and F. Wilson, Journal of Plasma Physics, 82, 905820306 (2016) [28 pages, Open Access] )2. An exact collisionless equilibrium for the Force-Free Harris Sheet with low plasma beta: (O. Allanson, T. Neukirch, F. Wilson and S. Troscheit, Physics of Plasmas, 22, 102116 (2015) [11 pages, Open Access])3. Neutral and non-neutral collisionless plasma equilibria for twisted flux tubes: The Gold-Hoyle model in a background field (O. Allanson, F. Wilson and T. Neukirch, (2016)) (accepted, Physics of Plasmas)
Strong convergence results for hemivariational inequalities
Institute of Scientific and Technical Information of China (English)
LIU Zhenhai; ZOU Jiezhong
2006-01-01
The purpose of this paper is to study a regularization method of solutions of ill-posed problems involving hemivariational inequalities in Banach spaces. Under the assumption that the hemivariational inequality is solvable, a strongly convergent approximation procedure is designed by means of the so-called Browder-Tikhonov regularization method. Our results generalize and extend the previously known theorems.
Quantum transport velocity in strongly scattering media
Malfliet, R
1998-01-01
Based on the Kadanoff-Baym equations of quantum transport: theory, an approach is proposed which goes beyond the usual quasiparticle approximation. It allows one to deduct the correct transport velocity for propagation in strongly scattering media, a quantity of great importance for localization phe
Approximate Inference for Wireless Communications
DEFF Research Database (Denmark)
Hansen, Morten
This thesis investigates signal processing techniques for wireless communication receivers. The aim is to improve the performance or reduce the computationally complexity of these, where the primary focus area is cellular systems such as Global System for Mobile communications (GSM) (and extensions...... complexity can potentially lead to limited power consumption, which translates into longer battery life-time in the handsets. The scope of the thesis is more specifically to investigate approximate (nearoptimal) detection methods that can reduce the computationally complexity significantly compared...... to the optimal one, which usually requires an unacceptable high complexity. Some of the treated approximate methods are based on QL-factorization of the channel matrix. In the work presented in this thesis it is proven how the QL-factorization of frequency-selective channels asymptotically provides the minimum...
Hydrogen Beyond the Classic Approximation
Scivetti, I
2003-01-01
The classical nucleus approximation is the most frequently used approach for the resolution of problems in condensed matter physics.However, there are systems in nature where it is necessary to introduce the nuclear degrees of freedom to obtain a correct description of the properties.Examples of this, are the systems with containing hydrogen.In this work, we have studied the resolution of the quantum nuclear problem for the particular case of the water molecule.The Hartree approximation has been used, i.e. we have considered that the nuclei are distinguishable particles.In addition, we have proposed a model to solve the tunneling process, which involves the resolution of the nuclear problem for configurations of the system away from its equilibrium position
Validity of the eikonal approximation
Kabat, D
1992-01-01
We summarize results on the reliability of the eikonal approximation in obtaining the high energy behavior of a two particle forward scattering amplitude. Reliability depends on the spin of the exchanged field. For scalar fields the eikonal fails at eighth order in perturbation theory, when it misses the leading behavior of the exchange-type diagrams. In a vector theory the eikonal gets the exchange diagrams correctly, but fails by ignoring certain non-exchange graphs which dominate the asymptotic behavior of the full amplitude. For spin--2 tensor fields the eikonal captures the leading behavior of each order in perturbation theory, but the sum of eikonal terms is subdominant to graphs neglected by the approximation. We also comment on the eikonal for Yang-Mills vector exchange, where the additional complexities of the non-abelian theory may be absorbed into Regge-type modifications of the gauge boson propagators.
Approximate Privacy: Foundations and Quantification
Feigenbaum, Joan; Schapira, Michael
2009-01-01
Increasing use of computers and networks in business, government, recreation, and almost all aspects of daily life has led to a proliferation of online sensitive data about individuals and organizations. Consequently, concern about the privacy of these data has become a top priority, particularly those data that are created and used in electronic commerce. There have been many formulations of privacy and, unfortunately, many negative results about the feasibility of maintaining privacy of sensitive data in realistic networked environments. We formulate communication-complexity-based definitions, both worst-case and average-case, of a problem's privacy-approximation ratio. We use our definitions to investigate the extent to which approximate privacy is achievable in two standard problems: the second-price Vickrey auction and the millionaires problem of Yao. For both the second-price Vickrey auction and the millionaires problem, we show that not only is perfect privacy impossible or infeasibly costly to achieve...
Validity of the Eikonal Approximation
Kabat, Daniel
1992-01-01
We summarize results on the reliability of the eikonal approximation in obtaining the high energy behavior of a two particle forward scattering amplitude. Reliability depends on the spin of the exchanged field. For scalar fields the eikonal fails at eighth order in perturbation theory, when it misses the leading behavior of the exchange-type diagrams. In a vector theory the eikonal gets the exchange diagrams correctly, but fails by ignoring certain non-exchange graphs which dominate the asymp...
Approximate Counting of Graphical Realizations.
Erdős, Péter L; Kiss, Sándor Z; Miklós, István; Soukup, Lajos
2015-01-01
In 1999 Kannan, Tetali and Vempala proposed a MCMC method to uniformly sample all possible realizations of a given graphical degree sequence and conjectured its rapidly mixing nature. Recently their conjecture was proved affirmative for regular graphs (by Cooper, Dyer and Greenhill, 2007), for regular directed graphs (by Greenhill, 2011) and for half-regular bipartite graphs (by Miklós, Erdős and Soukup, 2013). Several heuristics on counting the number of possible realizations exist (via sampling processes), and while they work well in practice, so far no approximation guarantees exist for such an approach. This paper is the first to develop a method for counting realizations with provable approximation guarantee. In fact, we solve a slightly more general problem; besides the graphical degree sequence a small set of forbidden edges is also given. We show that for the general problem (which contains the Greenhill problem and the Miklós, Erdős and Soukup problem as special cases) the derived MCMC process is rapidly mixing. Further, we show that this new problem is self-reducible therefore it provides a fully polynomial randomized approximation scheme (a.k.a. FPRAS) for counting of all realizations.
Approximate Counting of Graphical Realizations.
Directory of Open Access Journals (Sweden)
Péter L Erdős
Full Text Available In 1999 Kannan, Tetali and Vempala proposed a MCMC method to uniformly sample all possible realizations of a given graphical degree sequence and conjectured its rapidly mixing nature. Recently their conjecture was proved affirmative for regular graphs (by Cooper, Dyer and Greenhill, 2007, for regular directed graphs (by Greenhill, 2011 and for half-regular bipartite graphs (by Miklós, Erdős and Soukup, 2013. Several heuristics on counting the number of possible realizations exist (via sampling processes, and while they work well in practice, so far no approximation guarantees exist for such an approach. This paper is the first to develop a method for counting realizations with provable approximation guarantee. In fact, we solve a slightly more general problem; besides the graphical degree sequence a small set of forbidden edges is also given. We show that for the general problem (which contains the Greenhill problem and the Miklós, Erdős and Soukup problem as special cases the derived MCMC process is rapidly mixing. Further, we show that this new problem is self-reducible therefore it provides a fully polynomial randomized approximation scheme (a.k.a. FPRAS for counting of all realizations.
Many Faces of Boussinesq Approximations
Vladimirov, Vladimir A
2016-01-01
The \\emph{equations of Boussinesq approximation} (EBA) for an incompressible and inhomogeneous in density fluid are analyzed from a viewpoint of the asymptotic theory. A systematic scaling shows that there is an infinite number of related asymptotic models. We have divided them into three classes: `poor', `reasonable' and `good' Boussinesq approximations. Each model can be characterized by two parameters $q$ and $k$, where $q =1, 2, 3, \\dots$ and $k=0, \\pm 1, \\pm 2,\\dots$. Parameter $q$ is related to the `quality' of approximation, while $k$ gives us an infinite set of possible scales of velocity, time, viscosity, \\emph{etc.} Increasing $q$ improves the quality of a model, but narrows the limits of its applicability. Parameter $k$ allows us to vary the scales of time, velocity and viscosity and gives us the possibility to consider any initial and boundary conditions. In general, we discover and classify a rich variety of possibilities and restrictions, which are hidden behind the routine use of the Boussinesq...
The general conditional equations which govern the phase equilibria in three-component systems are presented. Using the general conditional equations...a general method has been developed to precalculate the phase equilibria in three-component systems from first principle using computer technique...The method developed has been applied to several model examples and the system Ta-Hf-C. The phase equilibria in three-component systems calculated
Phase equilibria in the ternary system vanadium-niobium-carbon from 800C through the melting ranges of the cubic monocarbide solid solutions were...established on the basis of X-ray, melting point and metallographic studies. The phase equilibria above 1400C are presented in a three-dimensional...temperature-composition constitutional diagram, since the phase equilibria below 1400C were not thoroughly investigated due to kinetic problems. Vanadium
A perturbative analysis of the time-envelope approximation in strong Langmuir turbulence
DEFF Research Database (Denmark)
Bergé, L.; Bidegaray, B.; Colin, T.
1996-01-01
) -->, +infinity is detailed for a fixed value of c(2). Under some specific initial data, the solution E is proved to blow up at least in an infinite time provided that omega lies below a threshold value. When this condition is not fulfilled, the global existence of the solution set (E, n) is finally restored...
Phase equilibria in polymer blend thin films: a Hamiltonian approach.
Souche, M; Clarke, N
2009-12-28
We propose a Hamiltonian formulation of the Flory-Huggins-de Gennes theory describing a polymer blend thin film. We then focus on the case of 50:50 polymer blends confined between antisymmetric walls. The different phases of the system and the transitions between them, including finite-size effects, are systematically studied through their relation with the geometry of the Hamiltonian flow in phase space. This method provides an easy and efficient way, with strong graphical insight, to infer the qualitative physical behavior of polymer blend thin films.
Stability of Hall equilibria in neutron star crusts
Marchant P.; Reisenegger A.; Valdivia J.A.; Hoyos J.H.
2014-01-01
In the solid crusts of neutron stars, the advection of the magnetic field by the current-carrying electrons, an effect known as Hall drift, should play a very important role as the ions remain essentially fixed (as long as the solid does not break). Although Hall drift preserves the magnetic field energy, it has been argued that it may drive a turbulent cascade to scales at which Ohmic dissipation becomes effective, allowing a much faster decay in objects with very strong fields. On the other...
Strong Field Spherical Dynamos
Dormy, Emmanuel
2014-01-01
Numerical models of the geodynamo are usually classified in two categories: those denominated dipolar modes, observed when the inertial term is small enough, and multipolar fluctuating dynamos, for stronger forcing. I show that a third dynamo branch corresponding to a dominant force balance between the Coriolis force and the Lorentz force can be produced numerically. This force balance is usually referred to as the strong field limit. This solution co-exists with the often described viscous branch. Direct numerical simulations exhibit a transition from a weak-field dynamo branch, in which viscous effects set the dominant length scale, and the strong field branch in which viscous and inertial effects are largely negligible. These results indicate that a distinguished limit needs to be sought to produce numerical models relevant to the geodynamo and that the usual approach of minimizing the magnetic Prandtl number (ratio of the fluid kinematic viscosity to its magnetic diffusivity) at a given Ekman number is mi...
Morosan, Emilia; Natelson, Douglas; Nevidomskyy, Andriy H.; Si, Qimiao
2013-01-01
Strongly correlated materials are profoundly affected by the repulsive electron-electron interaction. This stands in contrast to many commonly used materials such as silicon and aluminum, whose properties are comparatively unaffected by the Coulomb repulsion. Correlated materials often have remarkable properties and transitions between distinct, competing phases with dramatically different electronic and magnetic orders. These rich phenomena are fascinating from the basic science perspective ...
García-Tecocoatzi, H.; Bijker, R.; Ferretti, J.; Galatà, G.; Santopinto, E.
2016-10-01
In this contribution, we discuss the results of a QM calculation of the open-flavor strong decays of **** light nucleon resonances. These are the results of a recent calculation, where we used a modified ^3P_0 model for the amplitudes and the U(7) algebraic model and the hypercentral quark model to predict the baryon spectrum. The decay amplitudes are compared with the existing experimental data.
Strongly Correlated Topological Insulators
2016-02-03
Research Triangle Park , NC 27709-2211 Condensed Matter, Topological Phases of Matter REPORT DOCUMENTATION PAGE 11. SPONSOR/MONITOR’S REPORT NUMBER(S...Strongly Correlated Topological Insulators In the past year, the grant was used for work in the field of topological phases, with emphasis on finding...surface of topological insulators. In the past 3 years, we have started a new direction, that of fractional topological insulators. These are materials
Concave Generalized Flows with Applications to Market Equilibria
Vegh, Laszlo A
2011-01-01
We consider a nonlinear extension of the generalized network flow model, with the flow leaving an arc being an increasing concave function of the flow entering it, as proposed by Truemper and Shigeno. We give the first polynomial time combinatorial algorithm for solving corresponding optimization problems, finding a epsilon-approximate solution in O(m(m+\\log n)\\log(MUm/epsilon)) arithmetic operations and value oracle queries, where M and U are upper bounds on simple parameters. For (linear) generalized flows, our algorithm can be seen as a variant of the highest-gain augmenting path algorithm by Goldfarb, Jin and Orlin. We show that this general convex programming model serves as a common framework for several market equilibrium problems, including the linear Fisher market model and its various extensions. Our result immediately enables us to extend these market models to more general settings and to solve some open problems in the literature.
Rollout Sampling Approximate Policy Iteration
Dimitrakakis, Christos
2008-01-01
Several researchers have recently investigated the connection between reinforcement learning and classification. We are motivated by proposals of approximate policy iteration schemes without value functions which focus on policy representation using classifiers and address policy learning as a supervised learning problem. This paper proposes variants of an improved policy iteration scheme which addresses the core sampling problem in evaluating a policy through simulation as a multi-armed bandit machine. The resulting algorithm offers comparable performance to the previous algorithm achieved, however, with significantly less computational effort. An order of magnitude improvement is demonstrated experimentally in two standard reinforcement learning domains: inverted pendulum and mountain-car.
Approximate Deconvolution Reduced Order Modeling
Xie, Xuping; Wang, Zhu; Iliescu, Traian
2015-01-01
This paper proposes a large eddy simulation reduced order model(LES-ROM) framework for the numerical simulation of realistic flows. In this LES-ROM framework, the proper orthogonal decomposition(POD) is used to define the ROM basis and a POD differential filter is used to define the large ROM structures. An approximate deconvolution(AD) approach is used to solve the ROM closure problem and develop a new AD-ROM. This AD-ROM is tested in the numerical simulation of the one-dimensional Burgers equation with a small diffusion coefficient(10^{-3})
Approximation for Bayesian Ability Estimation.
1987-02-18
posterior pdfs of ande are given by p(-[Y) p(F) F P((y lei’ j)P )d. SiiJ i (4) a r~d p(e Iy) - p(t0) 1 J i P(Yij ei, (5) As shown in Tsutakawa and Lin...inverse A Hessian of the log of (27) with respect to , evaulatedat a Then, under regularity conditions, the marginal posterior pdf of O is...two-way contingency tables. Journal of Educational Statistics, 11, 33-56. Lindley, D.V. (1980). Approximate Bayesian methods. Trabajos Estadistica , 31
MOLECULAR SIMULATION OF PHASE EQUILIBRIA FOR COMPLEX FLUIDS
Energy Technology Data Exchange (ETDEWEB)
Athanassios Z. Panagiotopoulos
2009-09-09
The general area of this project was the development and application of novel molecular simulation methods for prediction of thermodynamic and structural properties of complex polymeric, surfactant and ionic fluids. Over this project period, we have made considerable progress in developing novel algorithms to meet the computational challenges presented by the strong or long-range interactions in these systems and have generated data for well-defined mod-els that can be used to test theories and compare to experimental data. Overall, 42 archival papers and many invited and contributed presentations and lectures have been based on work supported by this project. 6 PhD, 1 M.S. and 2 postdoctoral students have been associated with this work, as listed in the body of the report.