On oscillation of second-order linear ordinary differential equations
Lomtatidze, A.; Šremr, Jiří
2011-01-01
Roč. 54, - (2011), s. 69-81 ISSN 1512-0015 Institutional research plan: CEZ:AV0Z10190503 Keywords : linear second-order ordinary differential equation * Kamenev theorem * oscillation Subject RIV: BA - General Mathematics http://www.rmi.ge/jeomj/memoirs/vol54/abs54-4.htm
Martini, Ruud; Kersten, P.H.M.
1983-01-01
Using 1-1 mappings, the complete symmetry groups of contact transformations of general linear second-order ordinary differential equations are determined from two independent solutions of those equations, and applied to the harmonic oscillator with and without damping.
Boyko, Vyacheslav M; Popovych, Roman O; Shapoval, Nataliya M
2013-01-01
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal Lie invariance algebras possessed by such systems are obtained using an effective algebraic approach.
POSITIVE SOLUTIONS TO SEMI-LINEAR SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACE
无
2008-01-01
In this paper,we study the existence of positive periodic solution to some second- order semi-linear differential equation in Banach space.By the fixed point index theory, we prove that the semi-linear differential equation has two positive periodic solutions.
Remark on periodic boundary-value problem for second-order linear ordinary differential equations
Dosoudilová, M.; Lomtatidze, Alexander
2018-01-01
Roč. 2018, č. 13 (2018), s. 1-7 ISSN 1072-6691 Institutional support: RVO:67985840 Keywords : second-order linear equation * periodic boundary value problem * unique solvability Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.954, year: 2016 https://ejde.math.txstate.edu/Volumes/2018/13/abstr.html
Remark on zeros of solutions of second-order linear ordinary differential equations
Dosoudilová, M.; Lomtatidze, Alexander
2016-01-01
Roč. 23, č. 4 (2016), s. 571-577 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : second-order linear equation * zeros of solutions * periodic boundary value problem Subject RIV: BA - General Mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2016.23.issue-4/gmj-2016-0052/gmj-2016-0052. xml
Remark on zeros of solutions of second-order linear ordinary differential equations
Dosoudilová, M.; Lomtatidze, Alexander
2016-01-01
Roč. 23, č. 4 (2016), s. 571-577 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : second-order linear equation * zero s of solutions * periodic boundary value problem Subject RIV: BA - General Mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2016.23.issue-4/gmj-2016-0052/gmj-2016-0052.xml
Lima, M.L.; Mignaco, J.A.
1985-01-01
It is shown that the rational power law potentials in the two-body radial Schrodinger equations admit a systematic treatment available from the classical theory of ordinary linear differential equations of the second order. The resulting potentials come into families evolved from equations having a fixed number of elementary regular singularities. As a consequence, relations are found and discussed among the several potentials in a family. (Author) [pt
Lima, M.L.; Mignaco, J.A.
1985-01-01
It is shown that the rational power law potentials in the two-body radial Schoedinger equation admit a systematic treatment available from the classical theory of ordinary linear differential equations of the second order. The admissible potentials come into families evolved from equations having a fixed number of elementary singularities. As a consequence, relations are found and discussed among the several potentials in a family. (Author) [pt
Lima, M.L.; Mignaco, J.A.
1983-01-01
The power law potentials in the Schroedinger equation solved recently are shown to come from the classical treatment of the singularities of a linear, second order differential equation. This allows to enlarge the class of solvable power law potentials. (Author) [pt
Low Dimensional Vessiot-Guldberg-Lie Algebras of Second-Order Ordinary Differential Equations
Rutwig Campoamor-Stursberg
2016-03-01
Full Text Available A direct approach to non-linear second-order ordinary differential equations admitting a superposition principle is developed by means of Vessiot-Guldberg-Lie algebras of a dimension not exceeding three. This procedure allows us to describe generic types of second-order ordinary differential equations subjected to some constraints and admitting a given Lie algebra as Vessiot-Guldberg-Lie algebra. In particular, well-known types, such as the Milne-Pinney or Kummer-Schwarz equations, are recovered as special cases of this classification. The analogous problem for systems of second-order differential equations in the real plane is considered for a special case that enlarges the generalized Ermakov systems.
Antiperiodic Boundary Value Problems for Second-Order Impulsive Ordinary Differential Equations
2009-02-01
Full Text Available We consider a second-order ordinary differential equation with antiperiodic boundary conditions and impulses. By using Schaefer's fixed-point theorem, some existence results are obtained.
Convolution of second order linear recursive sequences II.
Szakács Tamás
2017-12-01
Full Text Available We continue the investigation of convolutions of second order linear recursive sequences (see the first part in [1]. In this paper, we focus on the case when the characteristic polynomials of the sequences have common root.
Solving Second-Order Ordinary Differential Equations without Using Complex Numbers
Kougias, Ioannis E.
2009-01-01
Ordinary differential equations (ODEs) is a subject with a wide range of applications and the need of introducing it to students often arises in the last year of high school, as well as in the early stages of tertiary education. The usual methods of solving second-order ODEs with constant coefficients, among others, rely upon the use of complex…
Focal decompositions for linear differential equations of the second order
L. Birbrair
2003-01-01
two-points problems to itself such that the image of the focal decomposition associated to the first equation is a focal decomposition associated to the second one. In this paper, we present a complete classification for linear second-order equations with respect to this equivalence relation.
On nonnegative solutions of second order linear functional differential equations
Lomtatidze, Alexander; Vodstrčil, Petr
2004-01-01
Roč. 32, č. 1 (2004), s. 59-88 ISSN 1512-0015 Institutional research plan: CEZ:AV0Z1019905 Keywords : second order linear functional differential equations * nonnegative solution * two-point boundary value problem Subject RIV: BA - General Mathematics
Non-linear second-order periodic systems with non-smooth potential
In this paper we study second order non-linear periodic systems driven by the ordinary vector -Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth critical point theory. We prove existence and multiplicity results under general growth conditions on ...
Non-linear second-order periodic systems with non-smooth potential
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Abstract. In this paper we study second order non-linear periodic systems driven by the ordinary vector p-Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth critical point theory. We prove existence and multiplicity results under general growth ...
无
2009-01-01
In this paper, we consider a two-point boundary value problem for a system of second order ordinary differential equations. Under some conditions, we show the existence of positive solution to the system of second order ordinary differential equa-tions.
Gainetdinova, A A; Gazizov, R K
2017-01-01
We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures.
Nonoscillation criteria for half-linear second order difference equations
Došlý, Ondřej; Řehák, Pavel
2001-01-01
Roč. 42, - (2001), s. 453-464 ISSN 0898-1221 R&D Projects: GA ČR GA201/98/0677; GA ČR GA201/99/0295 Keywords : half-linear difference equation%nonoscillation criteria%variational principle Subject RIV: BA - General Mathematics Impact factor: 0.383, year: 2001
Linear reversible second-order cellular automata and their first-order matrix equivalents
Macfarlane, A. J.
2004-11-01
Linear or one-dimensional reversible second-order cellular automata, exemplified by three cases named as RCA1-3, are introduced. Displays of their evolution in discrete time steps, &{\\in}Z_2;) as for RCA1-3. MCA1-3 are tractable because it has been possible to generalize to them the heavy duty methods already well-developed for ordinary first-order cellular automata like those of Wolfram's Rules 90 and 150. While the automata MCA1-3 are thought to be of genuine interest in their own right, with untapped further mathematical potential, their treatment has been applied here to expediting derivation of a large body of general and explicit results for N(t) for RCA1-3. Amongst explicit results obtained are formulas also for each of RCA1-3 for the total weight of the configurations of the first &2^M; times, M =0, 1, 2,\\ldots.
The mixed BVP for second order nonlinear ordinary differential equation at resonance
Mukhigulashvili, Sulkhan
2017-01-01
Roč. 290, 2-3 (2017), s. 393-400 ISSN 0025-584X Institutional support: RVO:67985840 Keywords : mixed problem at resonance * nonlinear ordinary differencial equation Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.742, year: 2016
Lomtatidze, Alexander
2017-01-01
Roč. 24, č. 2 (2017), s. 241-263 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : nonlinear ordinary differential equations * periodic boundary value problem * solvability Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2017-0009/gmj-2017-0009.xml
Lomtatidze, Alexander
2017-01-01
Roč. 24, č. 2 (2017), s. 241-263 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : nonlinear ordinary differential equations * periodic boundary value problem * solvability Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2017-0009/gmj-2017-0009. xml
Man, Yiu-Kwong
2010-01-01
In this communication, we present a method for computing the Liouvillian solution of second-order linear differential equations via algebraic invariant curves. The main idea is to integrate Kovacic's results on second-order linear differential equations with the Prelle-Singer method for computing first integrals of differential equations. Some examples on using this approach are provided. (fast track communication)
On Solvability Theorems of Second-Order Ordinary Differential Equations with Delay
Nai-Sher Yeh
2018-01-01
Full Text Available For each x0∈[0,2π and k∈N, we obtain some existence theorems of periodic solutions to the two-point boundary value problem u′′(x+k2u(x-x0+g(x,u(x-x0=h(x in (0,2π with u(0-u(2π=u′(0-u′(2π=0 when g:(0,2π×R→R is a Caratheodory function which grows linearly in u as u→∞, and h∈L1(0,2π may satisfy a generalized Landesman-Lazer condition (1+sign(β∫02πh(xv(xdx0gβ+(xvx1-βdx+∫v(x<0gβ-(xvx1-βdx for all v∈N(L\\{0}. Here N(L denotes the subspace of L1(0,2π spanned by sinkx and coskx, -1<β≤0, gβ+(x=lim infu→∞(gx,uu/u1-β, and gβ-(x=lim infu→-∞(gx,uu/u1-β.
Linear reversible second-order cellular automata and their first-order matrix equivalents
Macfarlane, A J
2004-01-01
Linear or one-dimensional reversible second-order cellular automata, exemplified by three cases named as RCA1-3, are introduced. Displays of their evolution in discrete time steps, t=0, 1, 2, ..., from their simplest initial states and on the basis of updating rules in modulo 2 arithmetic, are presented. In these, shaded and unshaded squares denote cells whose cell variables are equal to one and zero respectively. This paper is devoted to finding general formulas for, and explicit numerical evaluations of, the weights N(t) of the states or configurations of RCA1-3, i.e. the total number of shaded cells in tth line of their displays. This is achieved by means of the replacement of RCA1-3 by the equivalent linear first-order matrix automata MCA1-3, for which the cell variables are 2x2 matrices, instead of just numbers (element of Z 2 ) as for RCA1-3. MCA1-3 are tractable because it has been possible to generalize to them the heavy duty methods already well-developed for ordinary first-order cellular automata like those of Wolfram's Rules 90 and 150. While the automata MCA1-3 are thought to be of genuine interest in their own right, with untapped further mathematical potential, their treatment has been applied here to expediting derivation of a large body of general and explicit results for N(t) for RCA1-3. Amongst explicit results obtained are formulas also for each of RCA1-3 for the total weight of the configurations of the first 2 M times, M=0, 1, 2, ..
ADM For Solving Linear Second-Order Fredholm Integro-Differential Equations
Karim, Mohd F.; Mohamad, Mahathir; Saifullah Rusiman, Mohd; Che-Him, Norziha; Roslan, Rozaini; Khalid, Kamil
2018-04-01
In this paper, we apply Adomian Decomposition Method (ADM) as numerically analyse linear second-order Fredholm Integro-differential Equations. The approximate solutions of the problems are calculated by Maple package. Some numerical examples have been considered to illustrate the ADM for solving this equation. The results are compared with the existing exact solution. Thus, the Adomian decomposition method can be the best alternative method for solving linear second-order Fredholm Integro-Differential equation. It converges to the exact solution quickly and in the same time reduces computational work for solving the equation. The result obtained by ADM shows the ability and efficiency for solving these equations.
Factorization of a class of almost linear second-order differential equations
Estevez, P G; Kuru, S; Negro, J; Nieto, L M
2007-01-01
A general type of almost linear second-order differential equations, which are directly related to several interesting physical problems, is characterized. The solutions of these equations are obtained using the factorization technique, and their non-autonomous invariants are also found by means of scale transformations
Hyers-Ulam stability for second-order linear differential equations with boundary conditions
Pasc Gavruta
2011-06-01
Full Text Available We prove the Hyers-Ulam stability of linear differential equations of second-order with boundary conditions or with initial conditions. That is, if y is an approximate solution of the differential equation $y''+ eta (x y = 0$ with $y(a = y(b =0$, then there exists an exact solution of the differential equation, near y.
Myshkis type oscillation criteria for second-order linear delay differential equations
Opluštil, Z.; Šremr, Jiří
2015-01-01
Roč. 178, č. 1 (2015), s. 143-161 ISSN 0026-9255 Institutional support: RVO:67985840 Keywords : linear second-order delay differential equation * oscillation criteria Subject RIV: BA - General Mathematics Impact factor: 0.664, year: 2015 http://link.springer.com/article/10.1007%2Fs00605-014-0719-y
Some oscillation criteria for the second-order linear delay differential equation
Opluštil, Z.; Šremr, Jiří
2011-01-01
Roč. 136, č. 2 (2011), s. 195-204 ISSN 0862-7959 Institutional research plan: CEZ:AV0Z10190503 Keywords : second-order linear differential equation with a delay * oscillatory solution Subject RIV: BA - General Mathematics http://www.dml.cz/handle/10338.dmlcz/141582
Bounded solutions of self-adjoint second order linear difference equations with periodic coeffients
Encinas A.M.
2018-02-01
Full Text Available In this work we obtain easy characterizations for the boundedness of the solutions of the discrete, self–adjoint, second order and linear unidimensional equations with periodic coefficients, including the analysis of the so-called discrete Mathieu equations as particular cases.
Linear Matrix Inequalities for Analysis and Control of Linear Vector Second-Order Systems
Adegas, Fabiano Daher; Stoustrup, Jakob
2015-01-01
the Lyapunov matrix and the system matrices by introducing matrix multipliers, which potentially reduce conservativeness in hard control problems. Multipliers facilitate the usage of parameter-dependent Lyapunov functions as certificates of stability of uncertain and time-varying vector second-order systems......SUMMARY Many dynamical systems are modeled as vector second-order differential equations. This paper presents analysis and synthesis conditions in terms of LMI with explicit dependence in the coefficient matrices of vector second-order systems. These conditions benefit from the separation between....... The conditions introduced in this work have the potential to increase the practice of analyzing and controlling systems directly in vector second-order form. Copyright © 2014 John Wiley & Sons, Ltd....
Hyers-Ulam stability of linear second-order differential equations in complex Banach spaces
Yongjin Li
2013-08-01
Full Text Available We prove the Hyers-Ulam stability of linear second-order differential equations in complex Banach spaces. That is, if y is an approximate solution of the differential equation $y''+ alpha y'(t +eta y = 0$ or $y''+ alpha y'(t +eta y = f(t$, then there exists an exact solution of the differential equation near to y.
On oscillations of solutions to second-order linear delay differential equations
Opluštil, Z.; Šremr, Jiří
2013-01-01
Roč. 20, č. 1 (2013), s. 65-94 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : linear second-order delay differential equation * oscillatory solution Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-1/gmj-2013-0001/gmj-2013-0001.xml?format=INT
On oscillations of solutions to second-order linear delay differential equations
Opluštil, Z.; Šremr, Jiří
2013-01-01
Roč. 20, č. 1 (2013), s. 65-94 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : linear second-order delay differential equation * oscillatory solution Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-1/gmj-2013-0001/gmj-2013-0001. xml ?format=INT
Solution of second order linear fuzzy difference equation by Lagrange's multiplier method
Sankar Prasad Mondal
2016-06-01
Full Text Available In this paper we execute the solution procedure for second order linear fuzzy difference equation by Lagrange's multiplier method. In crisp sense the difference equation are easy to solve, but when we take in fuzzy sense it forms a system of difference equation which is not so easy to solve. By the help of Lagrange's multiplier we can solved it easily. The results are illustrated by two different numerical examples and followed by two applications.
Maximum principles for boundary-degenerate second-order linear elliptic differential operators
Feehan, Paul M. N.
2012-01-01
We prove weak and strong maximum principles, including a Hopf lemma, for smooth subsolutions to equations defined by linear, second-order, partial differential operators whose principal symbols vanish along a portion of the domain boundary. The boundary regularity property of the smooth subsolutions along this boundary vanishing locus ensures that these maximum principles hold irrespective of the sign of the Fichera function. Boundary conditions need only be prescribed on the complement in th...
Mervan Pašić
2016-10-01
Full Text Available We study non-monotone positive solutions of the second-order linear differential equations: $(p(tx'' + q(t x = e(t$, with positive $p(t$ and $q(t$. For the first time, some criteria as well as the existence and nonexistence of non-monotone positive solutions are proved in the framework of some properties of solutions $\\theta (t$ of the corresponding integrable linear equation: $(p(t\\theta''=e(t$. The main results are illustrated by many examples dealing with equations which allow exact non-monotone positive solutions not necessarily periodic. Finally, we pose some open questions.
LaChapelle, J.
2004-01-01
A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions. The general solution can be specialized to solve elliptic, parabolic, and hyperbolic partial differential equations with boundary conditions. This extends the well-known path integral solution of the Schroedinger/diffusion equation in unbounded space. The construction is based on a framework for functional integration introduced by Cartier/DeWitt-Morette
Internal crisis in a second-order non-linear non-autonomous electronic oscillator
Stavrinides, S.G.; Deliolanis, N.C.; Miliou, A.N.; Laopoulos, Th.; Anagnostopoulos, A.N.
2008-01-01
The internal crisis of a second-order non-linear non-autonomous chaotic electronic circuit is studied. The phase portraits consist of two interacting sub-attractors, a chaotic and a periodic one. Maximal Lyapunov exponents were calculated, for both the periodic and the chaotic waveforms, in order to confirm their nature. Transitions between the chaotic and the periodic sub-attractors become more frequent by increasing the circuit driving frequency. The frequency distribution of the corresponding laminar lengths and their average values indicate that an internal crisis takes place in this circuit, manifested in the intermittent behaviour of the corresponding orbits
Growth and Zeros of Meromorphic Solutions to Second-Order Linear Differential Equations
Maamar Andasmas
2016-04-01
Full Text Available The main purpose of this article is to investigate the growth of meromorphic solutions to homogeneous and non-homogeneous second order linear differential equations f00+Af0+Bf = F, where A(z, B (z and F (z are meromorphic functions with finite order having only finitely many poles. We show that, if there exist a positive constants σ > 0, α > 0 such that |A(z| ≥ eα|z|σ as |z| → +∞, z ∈ H, where dens{|z| : z ∈ H} > 0 and ρ = max{ρ(B, ρ(F} < σ, then every transcendental meromorphic solution f has an infinite order. Further, we give some estimates of their hyper-order, exponent and hyper-exponent of convergence of distinct zeros.
Zhu, Yongning; Wang, Yuting; Hellrung, Jeffrey; Cantarero, Alejandro; Sifakis, Eftychios; Teran, Joseph M.
2012-08-01
We present a cut cell method in R2 for enforcing Dirichlet and Neumann boundary conditions with nearly incompressible linear elastic materials in irregular domains. Virtual nodes on cut uniform grid cells are used to provide geometric flexibility in the domain boundary shape without sacrificing accuracy. We use a mixed formulation utilizing a MAC-type staggered grid with piecewise bilinear displacements centered at cell faces and piecewise constant pressures at cell centers. These discretization choices provide the necessary stability in the incompressible limit and the necessary accuracy in cut cells. Numerical experiments suggest second order accuracy in L∞. We target high-resolution problems and present a class of geometric multigrid methods for solving the discrete equations for displacements and pressures that achieves nearly optimal convergence rates independent of grid resolution.
Passive impedance-based second-order sliding mode control for non-linear teleoperators
Luis G García-Valdovinos
2017-02-01
Full Text Available Bilateral teleoperation systems have attracted significant attention in the last decade mainly because of technological advancements in both the communication channel and computers performance. In addition, non-linear multi-degree-of-freedom bilateral teleoperators along with state observers have become an open research area. In this article, a model-free exact differentiator is used to estimate the full state along with a chattering-free second-order sliding mode controller to guarantee a robust impedance tracking under both constant and an unknown time delay of non-linear multi-degree-of-freedom robots. The robustness of the proposed controller is improved by introducing a change of coordinates in terms of a new nominal reference similar to that used in adaptive control theory. Experimental results that validate the predicted behaviour are presented and discussed using a Phantom Premium 1.0 as the master robot and a Catalyst-5 virtual model as the slave robot. The dynamics of the Catalyst-5 system is solved online.
M. P. Markakis
2010-01-01
Full Text Available Certain nonlinear autonomous ordinary differential equations of the second order are reduced to Abel equations of the first kind ((Ab-1 equations. Based on the results of a previous work, concerning a closed-form solution of a general (Ab-1 equation, and introducing an arbitrary function, exact one-parameter families of solutions are derived for the original autonomous equations, for the most of which only first integrals (in closed or parametric form have been obtained so far. Two-dimensional autonomous systems of differential equations of the first order, equivalent to the considered herein autonomous forms, are constructed and solved by means of the developed analysis.
Ho, Yuh-Shan
2006-01-01
A comparison was made of the linear least-squares method and a trial-and-error non-linear method of the widely used pseudo-second-order kinetic model for the sorption of cadmium onto ground-up tree fern. Four pseudo-second-order kinetic linear equations are discussed. Kinetic parameters obtained from the four kinetic linear equations using the linear method differed but they were the same when using the non-linear method. A type 1 pseudo-second-order linear kinetic model has the highest coefficient of determination. Results show that the non-linear method may be a better way to obtain the desired parameters.
FORCED OSCILLATIONS OF SECOND ORDER SUPER-LINEAR DIFFERENTIAL EQUATION WITH IMPULSES
无
2012-01-01
At first,by means of Kartsatos technique,we reduce the impulsive differential equation to a second order nonlinear impulsive homogeneous equation.We find some suitable impulse functions such that all the solutions to the equation are oscillatory.Several criteria on the oscillations of solutions are given.At last,we give an example to demonstrate our results.
The solutions of second-order linear differential systems with constant delays
Diblík, Josef; Svoboda, Zdeněk
2017-07-01
The representations of solutions to initial problems for non-homogenous n-dimensional second-order differential equations with delays x″(t )-2 A x'(t -τ )+(A2+B2)x (t -2 τ )=f (t ) by means of special matrix delayed functions are derived. Square matrices A and B are commuting and τ > 0. Derived representations use what is called a delayed exponential of a matrix and results generalize some of known results previously derived for homogenous systems.
OSCILLATION OF A SECOND-ORDER HALF-LINEAR NEUTRAL DAMPED DIFFERENTIAL EQUATION WITH TIME-DELAY
无
2012-01-01
In this paper,the oscillation for a class of second-order half-linear neutral damped differential equation with time-delay is studied.By means of Yang-inequality,the generalized Riccati transformation and a certain function,some new sufficient conditions for the oscillation are given for all solutions to the equation.
Oscillation of two-dimensional linear second-order differential systems
Kwong, M.K.; Kaper, H.G.
1985-01-01
This article is concerned with the oscillatory behavior at infinity of the solution y: [a, ∞) → R 2 of a system of two second-order differential equations, y''(t) + Q(t) y(t) = 0, t epsilon[a, ∞); Q is a continuous matrix-valued function on [a, ∞) whose values are real symmetric matrices of order 2. It is shown that the solution is oscillatory at infinity if the largest eigenvalue of the matrix integral/sub a//sup t/ Q(s) ds tends to infinity as t → ∞. This proves a conjecture of D. Hinton and R.T. Lewis for the two-dimensional case. Furthermore, it is shown that considerably weaker forms of the condition still suffice for oscillatory behavior at infinity. 7 references
General solutions of second-order linear difference equations of Euler type
Akane Hongyo
2017-01-01
Full Text Available The purpose of this paper is to give general solutions of linear difference equations which are related to the Euler-Cauchy differential equation \\(y^{\\prime\\prime}+(\\lambda/t^2y=0\\ or more general linear differential equations. We also show that the asymptotic behavior of solutions of the linear difference equations are similar to solutions of the linear differential equations.
A Second-Order Conditionally Linear Mixed Effects Model with Observed and Latent Variable Covariates
Harring, Jeffrey R.; Kohli, Nidhi; Silverman, Rebecca D.; Speece, Deborah L.
2012-01-01
A conditionally linear mixed effects model is an appropriate framework for investigating nonlinear change in a continuous latent variable that is repeatedly measured over time. The efficacy of the model is that it allows parameters that enter the specified nonlinear time-response function to be stochastic, whereas those parameters that enter in a…
Tunç, Cemil; Tunç, Osman
2016-01-01
In this paper, certain system of linear homogeneous differential equations of second-order is considered. By using integral inequalities, some new criteria for bounded and [Formula: see text]-solutions, upper bounds for values of improper integrals of the solutions and their derivatives are established to the considered system. The obtained results in this paper are considered as extension to the results obtained by Kroopnick (2014) [1]. An example is given to illustrate the obtained results.
Schwarz maps of algebraic linear ordinary differential equations
Sanabria Malagón, Camilo
2017-12-01
A linear ordinary differential equation is called algebraic if all its solution are algebraic over its field of definition. In this paper we solve the problem of finding closed form solution to algebraic linear ordinary differential equations in terms of standard equations. Furthermore, we obtain a method to compute all algebraic linear ordinary differential equations with rational coefficients by studying their associated Schwarz map through the Picard-Vessiot Theory.
Memon, Sajid; Nataraj, Neela; Pani, Amiya Kumar
2012-01-01
In this article, a posteriori error estimates are derived for mixed finite element Galerkin approximations to second order linear parabolic initial and boundary value problems. Using mixed elliptic reconstructions, a posteriori error estimates in L∞(L2)- and L2(L2)-norms for the solution as well as its flux are proved for the semidiscrete scheme. Finally, based on a backward Euler method, a completely discrete scheme is analyzed and a posteriori error bounds are derived, which improves upon earlier results on a posteriori estimates of mixed finite element approximations to parabolic problems. Results of numerical experiments verifying the efficiency of the estimators have also been provided. © 2012 Society for Industrial and Applied Mathematics.
Sunyaev, Rashid A.; Khatri, Rishi
2013-01-01
y-type spectral distortions of the cosmic microwave background allow us to detect clusters and groups of galaxies, filaments of hot gas and the non-uniformities in the warm hot intergalactic medium. Several CMB experiments (on small areas of sky) and theoretical groups (for full sky) have recently published y-type distortion maps. We propose to search for two artificial hot spots in such y-type maps resulting from the incomplete subtraction of the effect of the motion induced dipole on the cosmic microwave background sky. This dipole introduces, at second order, additional temperature and y-distortion anisotropy on the sky of amplitude few μK which could potentially be measured by Planck HFI and Pixie experiments and can be used as a source of cross channel calibration by CMB experiments. This y-type distortion is present in every pixel and is not the result of averaging the whole sky. This distortion, calculated exactly from the known linear dipole, can be subtracted from the final y-type maps, if desired
Somer, L.; Křížek, Michal
2017-01-01
Roč. 55, č. 3 (2017), s. 209-228 ISSN 0015-0517 Institutional support: RVO:67985840 Keywords : Lucas sequence * second-order * Fibonacci sequence Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics
Yumura, Takashi; Yamamoto, Wataru
2017-09-20
We employed density functional theory (DFT) calculations with dispersion corrections to investigate energetically preferred alignments of certain p,p'-dimethylaminonitrostilbene (DANS) molecules inside an armchair (m,m) carbon nanotube (n × DANS@(m,m)), where the number of inner molecules (n) is no greater than 3. Here, three types of alignments of DANS are considered: a linear alignment in a parallel fashion and stacking alignments in parallel and antiparallel fashions. According to DFT calculations, a threshold tube diameter for containing DANS molecules in linear or stacking alignments was found to be approximately 1.0 nm. Nanotubes with diameters smaller than 1.0 nm result in the selective formation of linearly aligned DANS molecules due to strong confinement effects within the nanotubes. By contrast, larger diameter nanotubes allow DANS molecules to align in a stacking and linear fashion. The type of alignment adopted by the DANS molecules inside a nanotube is responsible for their second-order non-linear optical properties represented by their static hyperpolarizability (β 0 values). In fact, we computed β 0 values of DANS assemblies taken from optimized n × DANS@(m,m) structures, and their values were compared with those of a single DANS molecule. DFT calculations showed that β 0 values of DANS molecules depend on their alignment, which decrease in the following order: linear alignment > parallel stacking alignment > antiparallel stacking alignment. In particular, a linear alignment has a β 0 value more significant than that of the same number of isolated molecules. Therefore, the linear alignment of DANS molecules, which is only allowed inside smaller diameter nanotubes, can strongly enhance their second-order non-linear optical properties. Since the nanotube confinement determines the alignment of DANS molecules, a restricted nanospace can be utilized to control their second-order non-linear optical properties. These DFT findings can assist in the
Runge-Kutta Methods for Linear Ordinary Differential Equations
Zingg, David W.; Chisholm, Todd T.
1997-01-01
Three new Runge-Kutta methods are presented for numerical integration of systems of linear inhomogeneous ordinary differential equations (ODES) with constant coefficients. Such ODEs arise in the numerical solution of the partial differential equations governing linear wave phenomena. The restriction to linear ODEs with constant coefficients reduces the number of conditions which the coefficients of the Runge-Kutta method must satisfy. This freedom is used to develop methods which are more efficient than conventional Runge-Kutta methods. A fourth-order method is presented which uses only two memory locations per dependent variable, while the classical fourth-order Runge-Kutta method uses three. This method is an excellent choice for simulations of linear wave phenomena if memory is a primary concern. In addition, fifth- and sixth-order methods are presented which require five and six stages, respectively, one fewer than their conventional counterparts, and are therefore more efficient. These methods are an excellent option for use with high-order spatial discretizations.
Liang, Hui; Chen, Xiaobo
2017-10-01
A novel multi-domain method based on an analytical control surface is proposed by combining the use of free-surface Green function and Rankine source function. A cylindrical control surface is introduced to subdivide the fluid domain into external and internal domains. Unlike the traditional domain decomposition strategy or multi-block method, the control surface here is not panelized, on which the velocity potential and normal velocity components are analytically expressed as a series of base functions composed of Laguerre function in vertical coordinate and Fourier series in the circumference. Free-surface Green function is applied in the external domain, and the boundary integral equation is constructed on the control surface in the sense of Galerkin collocation via integrating test functions orthogonal to base functions over the control surface. The external solution gives rise to the so-called Dirichlet-to-Neumann [DN2] and Neumann-to-Dirichlet [ND2] relations on the control surface. Irregular frequencies, which are only dependent on the radius of the control surface, are present in the external solution, and they are removed by extending the boundary integral equation to the interior free surface (circular disc) on which the null normal derivative of potential is imposed, and the dipole distribution is expressed as Fourier-Bessel expansion on the disc. In the internal domain, where the Rankine source function is adopted, new boundary integral equations are formulated. The point collocation is imposed over the body surface and free surface, while the collocation of the Galerkin type is applied on the control surface. The present method is valid in the computation of both linear and second-order mean drift wave loads. Furthermore, the second-order mean drift force based on the middle-field formulation can be calculated analytically by using the coefficients of the Fourier-Laguerre expansion.
Blitz, M A; Green, N J B; Shannon, R J; Pilling, M J; Seakins, P W; Western, C M; Robertson, S H
2015-07-16
Rate coefficients for the CH3 + CH3 reaction, over the temperature range 300-900 K, have been corrected for errors in the absorption coefficients used in the original publication ( Slagle et al., J. Phys. Chem. 1988 , 92 , 2455 - 2462 ). These corrections necessitated the development of a detailed model of the B̃(2)A1' (3s)-X̃(2)A2″ transition in CH3 and its validation against both low temperature and high temperature experimental absorption cross sections. A master equation (ME) model was developed, using a local linearization of the second-order decay, which allows the use of standard matrix diagonalization methods for the determination of the rate coefficients for CH3 + CH3. The ME model utilized inverse Laplace transformation to link the microcanonical rate constants for dissociation of C2H6 to the limiting high pressure rate coefficient for association, k∞(T); it was used to fit the experimental rate coefficients using the Levenberg-Marquardt algorithm to minimize χ(2) calculated from the differences between experimental and calculated rate coefficients. Parameters for both k∞(T) and for energy transfer ⟨ΔE⟩down(T) were varied and optimized in the fitting procedure. A wide range of experimental data were fitted, covering the temperature range 300-2000 K. A high pressure limit of k∞(T) = 5.76 × 10(-11)(T/298 K)(-0.34) cm(3) molecule(-1) s(-1) was obtained, which agrees well with the best available theoretical expression.
Algebraic properties of first integrals for systems of second-order ...
Symmetries of the rst integrals for scalar linear or linearizable second- order ordinary differential equations (ODEs) have already been derived and shown to exhibit interesting properties. One of these is that the symmetry algebra sl(3; R ) is generated by the three triplets of symmetries of the functionally independent first ...
Binocular Combination of Second-Order Stimuli
Zhou, Jiawei; Liu, Rong; Zhou, Yifeng; Hess, Robert F.
2014-01-01
Phase information is a fundamental aspect of visual stimuli. However, the nature of the binocular combination of stimuli defined by modulations in contrast, so-called second-order stimuli, is presently not clear. To address this issue, we measured binocular combination for first- (luminance modulated) and second-order (contrast modulated) stimuli using a binocular phase combination paradigm in seven normal adults. We found that the binocular perceived phase of second-order gratings depends on the interocular signal ratio as has been previously shown for their first order counterparts; the interocular signal ratios when the two eyes were balanced was close to 1 in both first- and second-order phase combinations. However, second-order combination is more linear than previously found for first-order combination. Furthermore, binocular combination of second-order stimuli was similar regardless of whether the carriers in the two eyes were correlated, anti-correlated, or uncorrelated. This suggests that, in normal adults, the binocular phase combination of second-order stimuli occurs after the monocular extracting of the second-order modulations. The sensory balance associated with this second-order combination can be obtained from binocular phase combination measurements. PMID:24404180
DeTrano, Alexander; Karimi, Naghmeh; Karri, Ramesh; Guo, Xiaofei; Carlet, Claude; Guilley, Sylvain
2015-01-01
Masking countermeasures, used to thwart side-channel attacks, have been shown to be vulnerable to mask-extraction attacks. State-of-the-art mask-extraction attacks on the Advanced Encryption Standard (AES) algorithm target S-Box recomputation schemes but have not been applied to scenarios where S-Boxes are precomputed offline. We propose an attack targeting precomputed S-Boxes stored in nonvolatile memory. Our attack targets AES implemented in software protected by a low entropy masking scheme and recovers the masks with 91% success rate. Recovering the secret key requires fewer power traces (in fact, by at least two orders of magnitude) compared to a classical second-order attack. Moreover, we show that this attack remains viable in a noisy environment or with a reduced number of leakage points. Eventually, we specify a method to enhance the countermeasure by selecting a suitable coset of the masks set. PMID:26491717
First and second order vortex dynamics
Kim, Yoonbai; Lee, Kimyeong
2002-01-01
The low energy dynamics of vortices in self-dual Abelian Higgs theory in (2+1)-dimensional spacetime is of second order in vortex velocity and characterized by the moduli space metric. When the Chern-Simons term with a small coefficient is added to the theory, we show that a term linear in vortex velocity appears and can be consistently added to the second order expression. We provide an additional check of the first and second order terms by studying the angular momentum in field theory
First order linear ordinary differential equations in associative algebras
Gordon Erlebacher
2004-01-01
Full Text Available In this paper, we study the linear differential equation $$ frac{dx}{dt}=sum_{i=1}^n a_i(t x b_i(t + f(t $$ in an associative but non-commutative algebra $mathcal{A}$, where the $b_i(t$ form a set of commuting $mathcal{A}$-valued functions expressed in a time-independent spectral basis consisting of mutually annihilating idempotents and nilpotents. Explicit new closed solutions are derived, and examples are presented to illustrate the theory.
Mallet, D. G.; McCue, S. W.
2009-01-01
The solution of linear ordinary differential equations (ODEs) is commonly taught in first-year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognizing what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to…
Camporesi, Roberto
2011-01-01
We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of…
Camporesi, Roberto
2016-01-01
This book presents a method for solving linear ordinary differential equations based on the factorization of the differential operator. The approach for the case of constant coefficients is elementary, and only requires a basic knowledge of calculus and linear algebra. In particular, the book avoids the use of distribution theory, as well as the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The case of variable coefficients is addressed using Mammana’s result for the factorization of a real linear ordinary differential operator into a product of first-order (complex) factors, as well as a recent generalization of this result to the case of complex-valued coefficients.
Dorodnitsyn, Vladimir A.; Kozlov, Roman; Meleshko, Sergey V.; Winternitz, Pavel
2018-05-01
A recent article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs, which have infinite-dimensional Lie point symmetry groups due to the linear superposition principle. Their symmetry algebra always contains a two-dimensional subalgebra realized by linearly connected vector fields. We identify all classes of linear first-order DODSs that have additional symmetries, not due to linearity alone, and we present representatives of each class. These additional symmetries are then used to construct exact analytical particular solutions using symmetry reduction.
A block Krylov subspace time-exact solution method for linear ordinary differential equation systems
Bochev, Mikhail A.
2013-01-01
We propose a time-exact Krylov-subspace-based method for solving linear ordinary differential equation systems of the form $y'=-Ay+g(t)$ and $y"=-Ay+g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial approximation of
Yoshitsugu Takei
2015-01-01
Full Text Available Using two concrete examples, we discuss the multisummability of WKB solutions of singularly perturbed linear ordinary differential equations. Integral representations of solutions and a criterion for the multisummability based on the Cauchy-Heine transform play an important role in the proof.
Second-Order Footsteps Illusions
Akiyoshi Kitaoka
2015-12-01
Full Text Available In the “footsteps illusion”, light and dark squares travel at constant speed across black and white stripes. The squares appear to move faster and slower as their contrast against the stripes varies. We now demonstrate some second-order footsteps illusions, in which all edges are defined by colors or textures—even though luminance-based neural motion detectors are blind to such edges.
Second order pedagogy as an example of second order cybernetics
Anne B. Reinertsen
2012-07-01
Full Text Available This article is about seeing/creating/trying out an idea of pedagogy and pedagogical/ educational research in/as/with self-reflexive, circular and diffractive perspectives and about using second order cybernetics as thinking tool. It is a move away from traditional hypothesis driven activities and a move towards data driven pedagogies and research: Teachers, teacher researchers and researchers simultaneously producing and theorizing our practices and ourselves. Deleuzian becomings- eventually becomings with data - theory - theodata is pivotal. It is a move towards a Derridean bricolage. A different science of pedagogy operating as a circular science of self-reflexivity and diffraction in search of quality again and again and again: Theopractical becomings and inspiractionresearch.
On one two-point BVP for the fourth order linear ordinary differential equation
Mukhigulashvili, Sulkhan; Manjikashvili, M.
2017-01-01
Roč. 24, č. 2 (2017), s. 265-275 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : fourth order linear ordinary differential equations * two-point boundary value problems Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0077/gmj-2016-0077.xml
On one two-point BVP for the fourth order linear ordinary differential equation
Mukhigulashvili, Sulkhan; Manjikashvili, M.
2017-01-01
Roč. 24, č. 2 (2017), s. 265-275 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : fourth order linear ordinary differential equations * two-point boundary value problems Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0077/gmj-2016-0077. xml
Oscillation theory for second order dynamic equations
Agarwal, Ravi P; O''Regan, Donal
2003-01-01
The qualitative theory of dynamic equations is a rapidly developing area of research. In the last 50 years, the Oscillation Theory of ordinary, functional, neutral, partial and impulsive differential equations, and their discrete versions, has inspired many scholars. Hundreds of research papers have been published in every major mathematical journal. Many books deal exclusively with the oscillation of solutions of differential equations, but most of these books appeal only to researchers who already know the subject. In an effort to bring Oscillation Theory to a new and broader audience, the authors present a compact, but thorough, understanding of Oscillation Theory for second order differential equations. They include several examples throughout the text not only to illustrate the theory, but also to provide new direction.
New results for exponential synchronization of linearly coupled ordinary differential systems
Tong Ping; Chen Shi-Hua
2017-01-01
This paper investigates the exponential synchronization of linearly coupled ordinary differential systems. The intrinsic nonlinear dynamics may not satisfy the QUAD condition or weak-QUAD condition. First, it gives a new method to analyze the exponential synchronization of the systems. Second, two theorems and their corollaries are proposed for the local or global exponential synchronization of the coupled systems. Finally, an application to the linearly coupled Hopfield neural networks and several simulations are provided for verifying the effectiveness of the theoretical results. (paper)
Numerical solution of second-order stochastic differential equations with Gaussian random parameters
Rahman Farnoosh
2014-07-01
Full Text Available In this paper, we present the numerical solution of ordinary differential equations (or SDEs, from each orderespecially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysisfor second-order equations in specially case of scalar linear second-order equations (damped harmonicoscillators with additive or multiplicative noises. Making stochastic differential equations system from thisequation, it could be approximated or solved numerically by different numerical methods. In the case oflinear stochastic differential equations system by Computing fundamental matrix of this system, it could becalculated based on the exact solution of this system. Finally, this stochastic equation is solved by numericallymethod like E.M. and Milstein. Also its Asymptotic stability and statistical concepts like expectationand variance of solutions are discussed.
Symmetry Classification of First Integrals for Scalar Linearizable Second-Order ODEs
K. S. Mahomed
2012-01-01
Full Text Available Symmetries of the fundamental first integrals for scalar second-order ordinary differential equations (ODEs which are linear or linearizable by point transformations have already been obtained. Firstly we show how one can determine the relationship between the symmetries and the first integrals of linear or linearizable scalar ODEs of order two. Secondly, a complete classification of point symmetries of first integrals of such linear ODEs is studied. As a consequence, we provide a counting theorem for the point symmetries of first integrals of scalar linearizable second-order ODEs. We show that there exists the 0-, 1-, 2-, or 3-point symmetry cases. It is shown that the maximal algebra case is unique.
Second order oscillations of a Vlasov-Poisson plasma in the Fourier transformed space
Sedlacek, Z.; Nocera, L.
1991-05-01
The Vlasov-Poisson system of equations in the Fourier-transformed velocity space is studied. At first some results of the linear theory are reformulated: in the new representation the Van Kampen eigenmodes and their adjoint are found to be ordinary functions with convenient piece-wise continuity properties. A transparent derivation is given of the free-streaming temporal echo in terms of the kinematics of wave packets in the Fourier-transformed velocity space. This analysis is further extended to include Coulomb interactions which allows to establish a connection between the echo theory, the second order oscillations of Best and the phenomenon of linear sidebands. The calculation of the time evolution of the global second order electric field is performed in detail in the case of a Maxwellian equilibrium distribution function. It is concluded that the phenomenon of linear sidebands may be properly explained in terms of the intrinsic features of the equilibrium distribution function. (author) 5 figs., 32 refs
A New Factorisation of a General Second Order Differential Equation
Clegg, Janet
2006-01-01
A factorisation of a general second order ordinary differential equation is introduced from which the full solution to the equation can be obtained by performing two integrations. The method is compared with traditional methods for solving these type of equations. It is shown how the Green's function can be derived directly from the factorisation…
Datta, Dhurjati Prasad; Bose, Manoj Kumar
2004-01-01
We present a new one parameter family of second derivative discontinuous solutions to the simplest scale invariant linear ordinary differential equation. We also point out how the construction could be extended to generate families of higher derivative discontinuous solutions as well. The discontinuity can occur only for a subset of even order derivatives, viz., 2nd, 4th, 8th, 16th,.... The solutions are shown to break the discrete parity (reflection) symmetry of the underlying equation. These results are expected to gain significance in the contemporary search of a new dynamical principle for understanding complex phenomena in nature
Sloss, J. M.; Kranzler, S. K.
1972-01-01
The equivalence of a considered integral equation form with an infinite system of linear equations is proved, and the localization of the eigenvalues of the infinite system is expressed. Error estimates are derived, and the problems of finding upper bounds and lower bounds for the eigenvalues are solved simultaneously.
Nontrivial Periodic Solutions for Nonlinear Second-Order Difference Equations
Tieshan He
2011-01-01
Full Text Available This paper is concerned with the existence of nontrivial periodic solutions and positive periodic solutions to a nonlinear second-order difference equation. Under some conditions concerning the first positive eigenvalue of the linear equation corresponding to the nonlinear second-order equation, we establish the existence results by using the topological degree and fixed point index theories.
Patel, Dhananjay; Singh, Vinay Kumar; Dalal, U. D.
2017-01-01
Single mode fibers (SMF) are typically used in Wide Area Networks (WAN), Metropolitan Area Networks (MAN) and also find applications in Radio over Fiber (RoF) architectures supporting data transmission in Fiber to the Home (FTTH), Remote Antenna Units (RAUs), in-building networks etc. Multi-mode fibers (MMFs) with low cost, ease of installation and low maintenance are predominantly (85-90%) deployed in-building networks providing data access in local area networks (LANs). The transmission of millimeter wave signals through the SMF in WAN and MAN, along with the reuse of MMF in-building networks will not levy fiber reinstallation cost. The transmission of the millimeter waves experiences signal impairments due to the transmitter non-linearity and modal dispersion of the MMF. The MMF exhibiting large modal dispersion limits the bandwidth-length product of the fiber. The second and higher-order harmonics present in the optical signal fall within the system bandwidth. This causes degradation in the received signal and an unwanted radiation of power at the RAU. The power of these harmonics is proportional to the non-linearity of the transmitter and the modal dispersion of the MMF and should be maintained below the standard values as per the international norms. In this paper, a mathematical model is developed for Second-order Harmonic Distortion (HD2) generated due to non-linearity of the transmitter and chromatic-modal dispersion of the SMF-MMF optic link. This is also verified using a software simulation. The model consists of a Mach Zehnder Modulator (MZM) that generates two m-QAM OFDM Single Sideband (SSB) signals based on phase shift of the hybrid coupler (90° and 120°). Our results show that the SSB signal with 120° hybrid coupler has suppresses the higher-order harmonics and makes the system more robust against the HD2 in the SMF-MMF optic link.
ACCURATE ESTIMATES OF CHARACTERISTIC EXPONENTS FOR SECOND ORDER DIFFERENTIAL EQUATION
无
2009-01-01
In this paper, a second order linear differential equation is considered, and an accurate estimate method of characteristic exponent for it is presented. Finally, we give some examples to verify the feasibility of our result.
Time-course window estimator for ordinary differential equations linear in the parameters
Vujacic, Ivan; Dattner, Itai; Gonzalez, Javier; Wit, Ernst
In many applications obtaining ordinary differential equation descriptions of dynamic processes is scientifically important. In both, Bayesian and likelihood approaches for estimating parameters of ordinary differential equations, the speed and the convergence of the estimation procedure may
Camporesi, Roberto
2016-01-01
We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as…
Hasegawa, Chihiro; Duffull, Stephen B
2018-02-01
Pharmacokinetic-pharmacodynamic systems are often expressed with nonlinear ordinary differential equations (ODEs). While there are numerous methods to solve such ODEs these methods generally rely on time-stepping solutions (e.g. Runge-Kutta) which need to be matched to the characteristics of the problem at hand. The primary aim of this study was to explore the performance of an inductive approximation which iteratively converts nonlinear ODEs to linear time-varying systems which can then be solved algebraically or numerically. The inductive approximation is applied to three examples, a simple nonlinear pharmacokinetic model with Michaelis-Menten elimination (E1), an integrated glucose-insulin model and an HIV viral load model with recursive feedback systems (E2 and E3, respectively). The secondary aim of this study was to explore the potential advantages of analytically solving linearized ODEs with two examples, again E3 with stiff differential equations and a turnover model of luteinizing hormone with a surge function (E4). The inductive linearization coupled with a matrix exponential solution provided accurate predictions for all examples with comparable solution time to the matched time-stepping solutions for nonlinear ODEs. The time-stepping solutions however did not perform well for E4, particularly when the surge was approximated by a square wave. In circumstances when either a linear ODE is particularly desirable or the uncertainty in matching the integrator to the ODE system is of potential risk, then the inductive approximation method coupled with an analytical integration method would be an appropriate alternative.
Yolci Omeroglu, Perihan; Ambrus, Árpad; Boyacioglu, Dilek
2018-03-28
Determination of pesticide residues is based on calibration curves constructed for each batch of analysis. Calibration standard solutions are prepared from a known amount of reference material at different concentration levels covering the concentration range of the analyte in the analysed samples. In the scope of this study, the applicability of both ordinary linear and weighted linear regression (OLR and WLR) for pesticide residue analysis was investigated. We used 782 multipoint calibration curves obtained for 72 different analytical batches with high-pressure liquid chromatography equipped with an ultraviolet detector, and gas chromatography with electron capture, nitrogen phosphorus or mass spectrophotometer detectors. Quality criteria of the linear curves including regression coefficient, standard deviation of relative residuals and deviation of back calculated concentrations were calculated both for WLR and OLR methods. Moreover, the relative uncertainty of the predicted analyte concentration was estimated for both methods. It was concluded that calibration curve based on WLR complies with all the quality criteria set by international guidelines compared to those calculated with OLR. It means that all the data fit well with WLR for pesticide residue analysis. It was estimated that, regardless of the actual concentration range of the calibration, relative uncertainty at the lowest calibrated level ranged between 0.3% and 113.7% for OLR and between 0.2% and 22.1% for WLR. At or above 1/3 of the calibrated range, uncertainty of calibration curve ranged between 0.1% and 16.3% for OLR and 0% and 12.2% for WLR, and therefore, the two methods gave comparable results.
Second-order nonlinearity induced transparency.
Zhou, Y H; Zhang, S S; Shen, H Z; Yi, X X
2017-04-01
In analogy to electromagnetically induced transparency, optomechanically induced transparency was proposed recently in [Science330, 1520 (2010)SCIEAS0036-807510.1126/science.1195596]. In this Letter, we demonstrate another form of induced transparency enabled by second-order nonlinearity. A practical application of the second-order nonlinearity induced transparency is to measure the second-order nonlinear coefficient. Our scheme might find applications in quantum optics and quantum information processing.
Source of second order chromaticity in RHIC
Luo, Y.; Gu, X.; Fischer, W.; Trbojevic, D.
2011-01-01
In this note we will answer the following questions: (1) what is the source of second order chromaticities in RHIC? (2) what is the dependence of second order chromaticity on the on-momentum β-beat? (3) what is the dependence of second order chromaticity on β* at IP6 and IP8? To answer these questions, we use the perturbation theory to numerically calculate the contributions of each quadrupole and sextupole to the first, second, and third order chromaticities.
Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel
2016-01-01
Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.
An Analysis of Second-Order Autoshaping
Ward-Robinson, Jasper
2004-01-01
Three mechanisms can explain second-order conditioning: (1) The second-order conditioned stimulus (CS2) could activate a representation of the first-order conditioned stimulus (CS1), thereby provoking the conditioned response (CR); The CS2 could enter into an excitatory association with either (2) the representation governing the CR, or (3) with a…
Camporesi, Roberto
2016-01-01
We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The approach presented here can be used in a first course on differential equations for science and engineering majors.
Second-Order Science of Interdisciplinary Research
Alrøe, Hugo Fjelsted; Noe, Egon
2014-01-01
require and challenge interdisciplinarity. Problem: The conventional methods of interdisciplinary research fall short in the case of wicked problems because they remain first-order science. Our aim is to present workable methods and research designs for doing second-order science in domains where...... there are many different scientific knowledges on any complex problem. Method: We synthesize and elaborate a framework for second-order science in interdisciplinary research based on a number of earlier publications, experiences from large interdisciplinary research projects, and a perspectivist theory...... of science. Results: The second-order polyocular framework for interdisciplinary research is characterized by five principles. Second-order science of interdisciplinary research must: 1. draw on the observations of first-order perspectives, 2. address a shared dynamical object, 3. establish a shared problem...
Second-order processing of four-stroke apparent motion.
Mather, G; Murdoch, L
1999-05-01
In four-stroke apparent motion displays, pattern elements oscillate between two adjacent positions and synchronously reverse in contrast, but appear to move unidirectionally. For example, if rightward shifts preserve contrast but leftward shifts reverse contrast, consistent rightward motion is seen. In conventional first-order displays, elements reverse in luminance contrast (e.g. light elements become dark, and vice-versa). The resulting perception can be explained by responses in elementary motion detectors turned to spatio-temporal orientation. Second-order motion displays contain texture-defined elements, and there is some evidence that they excite second-order motion detectors that extract spatio-temporal orientation following the application of a non-linear 'texture-grabbing' transform by the visual system. We generated a variety of second-order four-stroke displays, containing texture-contrast reversals instead of luminance contrast reversals, and used their effectiveness as a diagnostic test for the presence of various forms of non-linear transform in the second-order motion system. Displays containing only forward or only reversed phi motion sequences were also tested. Displays defined by variation in luminance, contrast, orientation, and size were effective. Displays defined by variation in motion, dynamism, and stereo were partially or wholly ineffective. Results obtained with contrast-reversing and four-stroke displays indicate that only relatively simple non-linear transforms (involving spatial filtering and rectification) are available during second-order energy-based motion analysis.
Second Order Ideal-Ward Continuity
Bipan Hazarika
2014-01-01
Full Text Available The main aim of the paper is to introduce a concept of second order ideal-ward continuity in the sense that a function f is second order ideal-ward continuous if I-limn→∞Δ2f(xn=0 whenever I-limn→∞Δ2xn=0 and a concept of second order ideal-ward compactness in the sense that a subset E of R is second order ideal-ward compact if any sequence x=(xn of points in E has a subsequence z=(zk=(xnk of the sequence x such that I-limk→∞Δ2zk=0 where Δ2zk=zk+2-2zk+1+zk. We investigate the impact of changing the definition of convergence of sequences on the structure of ideal-ward continuity in the sense of second order ideal-ward continuity and compactness of sets in the sense of second order ideal-ward compactness and prove related theorems.
Remarks on second-order quadratic systems in algebras
Art Sagle
2017-10-01
Full Text Available This paper is an addendum to our earlier paper [8], where a systematic study of quadratic systems of second order ordinary differential equations defined in commutative algebras was presented. Here we concentrate on special solutions and energy considerations of some quadratic systems defined in algebras which need not be commutative, however, we shall throughout assume the algebra to be associative. We here also give a positive answer to an open question, concerning periodic motions of such systems, posed in our earlier paper.
Systemic Design for Second-Order Effects
Evan Barba
2017-04-01
Full Text Available Second-order effects refer to changes within a system that are the result of changes made somewhere else in the system (the first-order effects. Second-order effects can occur at different spatial, temporal, or organizational scales from the original interventions, and are difficult to control. Some organizational theorists suggest that careful management of feedback processes can facilitate controlled change from one organizational configuration to another. Recognizing that skill in managing feedback processes is a core competency of design suggests that design skills are potentially useful tools in achieving organizational change. This paper describes a case study in which a co-design methodology was used to control the second-order effects resulting from a classroom intervention to create organizational change. This approach is then theorized as the Instigator Systems approach.
Scintillation camera with second order resolution
Muehllehner, G.
1976-01-01
A scintillation camera for use in radioisotope imaging to determine the concentration of radionuclides in a two-dimensional area is described in which means is provided for second order positional resolution. The phototubes, which normally provide only a single order of resolution, are modified to provide second order positional resolution of radiation within an object positioned for viewing by the scintillation camera. The phototubes are modified in that multiple anodes are provided to receive signals from the photocathode in a manner such that each anode is particularly responsive to photoemissions from a limited portion of the photocathode. Resolution of radioactive events appearing as an output of this scintillation camera is thereby improved
Wetting transitions: First order or second order
Teletzke, G.F.; Scriven, L.E.; Davis, H.T.
1982-01-01
A generalization of Sullivan's recently proposed theory of the equilibrium contact angle, the angle at which a fluid interface meets a solid surface, is investigated. The generalized theory admits either a first-order or second-order transition from a nonzero contact angle to perfect wetting as a critical point is approached, in contrast to Sullivan's original theory, which predicts only a second-order transition. The predictions of this computationally convenient theory are in qualitative agreement with a more rigorous theory to be presented in a future publication
Second-Order Conditioning in "Drosophila"
Tabone, Christopher J.; de Belle, J. Steven
2011-01-01
Associative conditioning in "Drosophila melanogaster" has been well documented for several decades. However, most studies report only simple associations of conditioned stimuli (CS, e.g., odor) with unconditioned stimuli (US, e.g., electric shock) to measure learning or establish memory. Here we describe a straightforward second-order conditioning…
Sidik, S. M.
1975-01-01
Ridge, Marquardt's generalized inverse, shrunken, and principal components estimators are discussed in terms of the objectives of point estimation of parameters, estimation of the predictive regression function, and hypothesis testing. It is found that as the normal equations approach singularity, more consideration must be given to estimable functions of the parameters as opposed to estimation of the full parameter vector; that biased estimators all introduce constraints on the parameter space; that adoption of mean squared error as a criterion of goodness should be independent of the degree of singularity; and that ordinary least-squares subset regression is the best overall method.
Calculating Second-Order Effects in MOSFET's
Benumof, Reuben; Zoutendyk, John A.; Coss, James R.
1990-01-01
Collection of mathematical models includes second-order effects in n-channel, enhancement-mode, metal-oxide-semiconductor field-effect transistors (MOSFET's). When dimensions of circuit elements relatively large, effects neglected safely. However, as very-large-scale integration of microelectronic circuits leads to MOSFET's shorter or narrower than 2 micrometer, effects become significant in design and operation. Such computer programs as widely-used "Simulation Program With Integrated Circuit Emphasis, Version 2" (SPICE 2) include many of these effects. In second-order models of n-channel, enhancement-mode MOSFET, first-order gate-depletion region diminished by triangular-cross-section deletions on end and augmented by circular-wedge-cross-section bulges on sides.
Scintillation camera with second order resolution
1975-01-01
A scintillation camera is described for use in radioisotope imaging to determine the concentration of radionuclides in a two-dimensional area in which means is provided for second-order positional resolution. The phototubes which normally provide only a single order of resolution, are modified to provide second-order positional resolution of radiation within an object positioned for viewing by the scintillation camera. The phototubes are modified in that multiple anodes are provided to receive signals from the photocathode in a manner such that each anode is particularly responsive to photoemissions from a limited portion of the photocathode. Resolution of radioactive events appearing as an output of this scintillation camera is thereby improved
Second Order Optimality in Markov Decision Chains
Sladký, Karel
2017-01-01
Roč. 53, č. 6 (2017), s. 1086-1099 ISSN 0023-5954 R&D Projects: GA ČR GA15-10331S Institutional support: RVO:67985556 Keywords : Markov decision chains * second order optimality * optimalilty conditions for transient, discounted and average models * policy and value iterations Subject RIV: BB - Applied Statistics, Operational Research OBOR OECD: Statistics and probability Impact factor: 0.379, year: 2016 http://library.utia.cas.cz/separaty/2017/E/sladky-0485146.pdf
Frankowska, Hélène; Hoehener, Daniel
2017-06-01
This paper is devoted to pointwise second-order necessary optimality conditions for the Mayer problem arising in optimal control theory. We first show that with every optimal trajectory it is possible to associate a solution p (ṡ) of the adjoint system (as in the Pontryagin maximum principle) and a matrix solution W (ṡ) of an adjoint matrix differential equation that satisfy a second-order transversality condition and a second-order maximality condition. These conditions seem to be a natural second-order extension of the maximum principle. We then prove a Jacobson like necessary optimality condition for general control systems and measurable optimal controls that may be only ;partially singular; and may take values on the boundary of control constraints. Finally we investigate the second-order sensitivity relations along optimal trajectories involving both p (ṡ) and W (ṡ).
Moryakov, A. V., E-mail: sailor@orc.ru [National Research Centre Kurchatov Institute (Russian Federation)
2016-12-15
An algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations is presented. The algorithm for systems of first-order differential equations is implemented in the EDELWEISS code with the possibility of parallel computations on supercomputers employing the MPI (Message Passing Interface) standard for the data exchange between parallel processes. The solution is represented by a series of orthogonal polynomials on the interval [0, 1]. The algorithm is characterized by simplicity and the possibility to solve nonlinear problems with a correction of the operator in accordance with the solution obtained in the previous iterative process.
Solving Ordinary Differential Equations
Krogh, F. T.
1987-01-01
Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.
Synchronization from Second Order Network Connectivity Statistics
Zhao, Liqiong; Beverlin, Bryce; Netoff, Theoden; Nykamp, Duane Q.
2011-01-01
We investigate how network structure can influence the tendency for a neuronal network to synchronize, or its synchronizability, independent of the dynamical model for each neuron. The synchrony analysis takes advantage of the framework of second order networks, which defines four second order connectivity statistics based on the relative frequency of two-connection network motifs. The analysis identifies two of these statistics, convergent connections, and chain connections, as highly influencing the synchrony. Simulations verify that synchrony decreases with the frequency of convergent connections and increases with the frequency of chain connections. These trends persist with simulations of multiple models for the neuron dynamics and for different types of networks. Surprisingly, divergent connections, which determine the fraction of shared inputs, do not strongly influence the synchrony. The critical role of chains, rather than divergent connections, in influencing synchrony can be explained by their increasing the effective coupling strength. The decrease of synchrony with convergent connections is primarily due to the resulting heterogeneity in firing rates. PMID:21779239
Synchronization from second order network connectivity statistics
Liqiong eZhao
2011-07-01
Full Text Available We investigate how network structure can influence the tendency for a neuronal network to synchronize, or its synchronizability, independent of the dynamical model for each neuron. The synchrony analysis takes advantage of the framework of second order networks (SONETs, which defines four second order connectivity statistics based on the relative frequency of two-connection network motifs. The analysis identifies two of these statistics, convergent connections and chain connections, as highly influencing the synchrony. Simulations verify that synchrony decreases with the frequency of convergent connections and increases with the frequency of chain connections. These trends persist with simulations of multiple models for the neuron dynamics and for different types of networks. Surprisingly, divergent connections, which determine the fraction of shared inputs, do not strongly influence the synchrony. The critical role of chains, rather than divergent connections, in influencing synchrony can be explained by a pool and redistribute mechanism. The pooling of many inputs averages out independent fluctuations, amplifying weak correlations in the inputs. With increased chain connections, neurons with many inputs tend to have many outputs. Hence, chains ensure that the amplified correlations in the neurons with many inputs are redistributed throughout the network, enhancing the development of synchrony across the network.
Second-order impartiality and public sphere
Sládeček Michal
2016-01-01
Full Text Available In the first part of the text the distinction between first- and second-order impartiality, along with Brian Barry’s thorough elaboration of their characteristics and the differences between them, is examined. While the former impartiality is related to non-favoring fellow-persons in everyday occasions, the latter is manifested in the institutional structure of society and its political and public morality. In the second part of the article, the concept of public impartiality is introduced through analysis of two examples. In the first example, a Caledonian Club with its exclusive membership is considered as a form of association which is partial, but nevertheless morally acceptable. In the second example, the so-called Heinz dilemma has been reconsidered and the author points to some flaws in Barry’s interpretation, arguing that Heinz’s right of giving advantage to his wife’s life over property rights can be recognized through mitigating circum-stances, and this partiality can be appreciated in the public sphere. Thus, public impartiality imposes limits to the restrictiveness and rigidity of political impartiality implied in second-order morality. [Projekat Ministarstva nauke Republike Srbije, br. 179049
Mejlbro, Leif
1997-01-01
An alternative formula for the solution of linear differential equations of order n is suggested. When applicable, the suggested method requires fewer and simpler computations than the well-known method using Wronskians.......An alternative formula for the solution of linear differential equations of order n is suggested. When applicable, the suggested method requires fewer and simpler computations than the well-known method using Wronskians....
Jimenez, J.C.
2009-06-01
Local Linearization (LL) methods conform a class of one-step explicit integrators for ODEs derived from the following primary and common strategy: the vector field of the differential equation is locally (piecewise) approximated through a first-order Taylor expansion at each time step, thus obtaining successive linear equations that are explicitly integrated. Hereafter, the LL approach may include some additional strategies to improve that basic affine approximation. Theoretical and practical results have shown that the LL integrators have a number of convenient properties. These include arbitrary order of convergence, A-stability, linearization preserving, regularity under quite general conditions, preservation of the dynamics of the exact solution around hyperbolic equilibrium points and periodic orbits, integration of stiff and high-dimensional equations, low computational cost, and others. In this paper, a review of the LL methods and their properties is presented. (author)
Nonlinear elliptic equations of the second order
Han, Qing
2016-01-01
Nonlinear elliptic differential equations are a diverse subject with important applications to the physical and social sciences and engineering. They also arise naturally in geometry. In particular, much of the progress in the area in the twentieth century was driven by geometric applications, from the Bernstein problem to the existence of Kähler-Einstein metrics. This book, designed as a textbook, provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge-Ampère equations. It gives a user-friendly introduction to the theory of nonlinear elliptic equations with special attention given to basic results and the most important techniques. Rather than presenting the topics in their full generality, the book aims at providing self-contained, clear, and "elementary" proofs for results in important special cases. This book will serve as a valuable resource for graduate stu...
Asymptotic behavior and stability of second order neutral delay differential equations
Chen, G.L.; van Gaans, O.W.; Verduyn Lunel, Sjoerd
2014-01-01
We study the asymptotic behavior of a class of second order neutral delay differential equations by both a spectral projection method and an ordinary differential equation method approach. We discuss the relation of these two methods and illustrate some features using examples. Furthermore, a fixed
Relative boundedness and compactness theory for second-order differential operators
Don B. Hinton
1997-01-01
Full Text Available The problem considered is to give necessary and sufficient conditions for perturbations of a second-order ordinary differential operator to be either relatively bounded or relatively compact. Such conditions are found for three classes of operators. The conditions are expressed in terms of integral averages of the coefficients of the perturbing operator.
Existence of infinitely many periodic solutions for second-order nonautonomous Hamiltonian systems
Wen Guan
2015-04-01
Full Text Available By using minimax methods and critical point theory, we obtain infinitely many periodic solutions for a second-order nonautonomous Hamiltonian systems, when the gradient of potential energy does not exceed linear growth.
Investigation of second-order hyperpolarizability of some organic compounds
Tajalli, H.; Zirak, P.; Ahmadi, S.
2003-04-01
In this work, we have measured the second order hyperpolarizability of some organic materials with (EFISH) method and also calculated the second order hyperpolarizability of 13 organic compound with Mopac6 software and investigated the different factors that affect the amount of second order hyperpolarizability and ways to increase it.
Second order logic, set theory and foundations of mathematics
Väänänen, J.A.; Dybjer, P; Lindström, S; Palmgren, E; Sundholm, G
2012-01-01
The question, whether second order logic is a better foundation for mathematics than set theory, is addressed. The main difference between second order logic and set theory is that set theory builds up a transfinite cumulative hierarchy while second order logic stays within one application of the
Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em
2017-12-01
Starting with the asymptotic expansion of the error equation of the shifted Gr\\"{u}nwald--Letnikov formula, we derive a new modified weighted shifted Gr\\"{u}nwald--Letnikov (WSGL) formula by introducing appropriate correction terms. We then apply one special case of the modified WSGL formula to solve multi-term fractional ordinary and partial differential equations, and we prove the linear stability and second-order convergence for both smooth and non-smooth solutions. We show theoretically and numerically that numerical solutions up to certain accuracy can be obtained with only a few correction terms. Moreover, the correction terms can be tuned according to the fractional derivative orders without explicitly knowing the analytical solutions. Numerical simulations verify the theoretical results and demonstrate that the new formula leads to better performance compared to other known numerical approximations with similar resolution.
The invariance of second-order functionals revisited
Battezzati, M.
1984-01-01
In this paper some invariance properties of certain homogeneous functional forms of perturbative second-order energies with respect to transformations on the arguments are briefly considered. It has been shown that, if this energy is regarded as an Hamiltonian governing the time evolution of the arguments, which are the components of the first-order perturbed functions, the x and y couples play naturally the role of canonically conjugated co-ordinates and momenta. A search has been made for those linear transformations on these functions which preserve the above duality or reciprocity relations. It has been found that certain canonical transformations are of this type. In particular, the spinorial covariant-contravariant transformations for rotations in four-dimensional space-time
Second-order splitting schemes for a class of reactive systems
Ren Zhuyin; Pope, Stephen B.
2008-01-01
We consider the numerical time integration of a class of reaction-transport systems that are described by a set of ordinary differential equations for primary variables. In the governing equations, the terms involved may require the knowledge of secondary variables, which are functions of the primary variables. Specifically, we consider the case where, given the primary variables, the evaluation of the secondary variables is computationally expensive. To solve this class of reaction-transport equations, we develop and demonstrate several computationally efficient splitting schemes, wherein the portions of the governing equations containing chemical reaction terms are separated from those parts containing the transport terms. A computationally efficient solution to the transport sub-step is achieved through the use of linearization or predictor-corrector methods. The splitting schemes are applied to the reactive flow in a continuously stirred tank reactor (CSTR) with the Davis-Skodjie reaction model, to the CO+H 2 oxidation in a CSTR with detailed chemical kinetics, and to a reaction-diffusion system with an extension of the Oregonator model of the Belousov-Zhabotinsky reaction. As demonstrated in the test problems, the proposed splitting schemes, which yield efficient solutions to the transport sub-step, achieve second-order accuracy in time
Lomtatidze, Alexander
2016-01-01
Roč. 67, č. 1 (2016), s. 1-129 ISSN 1512-0015 Institutional support: RVO:67985840 Keywords : periodic boundary value problem * positive solution * singular equation Subject RIV: BA - General Mathematics http://rmi.tsu.ge/jeomj/memoirs/vol67/abs67-1.htm
Approximating second-order vector differential operators on distorted meshes in two space dimensions
Hermeline, F.
2008-01-01
A new finite volume method is presented for approximating second-order vector differential operators in two space dimensions. This method allows distorted triangle or quadrilateral meshes to be used without the numerical results being too much altered. The matrices that need to be inverted are symmetric positive definite therefore, the most powerful linear solvers can be applied. The method has been tested on a few second-order vector partial differential equations coming from elasticity and fluids mechanics areas. These numerical experiments show that it is second-order accurate and locking-free. (authors)
Ebaid, Abdelhalim; Wazwaz, Abdul-Majid; Alali, Elham; Masaedeh, Basem S.
2017-03-01
Very recently, it was observed that the temperature of nanofluids is finally governed by second-order ordinary differential equations with variable coefficients of exponential orders. Such coefficients were then transformed to polynomials type by using new independent variables. In this paper, a class of second-order ordinary differential equations with variable coefficients of polynomials type has been solved analytically. The analytical solution is expressed in terms of a hypergeometric function with generalized parameters. Moreover, applications of the present results have been applied on some selected nanofluids problems in the literature. The exact solutions in the literature were derived as special cases of our generalized analytical solution.
Ordinary differential equations principles and applications
Nandakumaran, A K; George, Raju K
2017-01-01
Written in a clear, logical and concise manner, this comprehensive resource allows students to quickly understand the key principles, techniques and applications of ordinary differential equations. Important topics including first and second order linear equations, initial value problems and qualitative theory are presented in separate chapters. The concepts of two point boundary value problems, physical models and first order partial differential equations are discussed in detail. The text uses tools of calculus and real analysis to get solutions in explicit form. While discussing first order linear systems, linear algebra techniques are used. The real-life applications are interspersed throughout the book to invoke reader's interest. The methods and tricks to solve numerous mathematical problems with sufficient derivations and explanation are provided. The proofs of theorems are explained for the benefit of the readers.
Park, K. C.; Belvin, W. Keith
1990-01-01
A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.
Probabilistic Sophistication, Second Order Stochastic Dominance, and Uncertainty Aversion
Simone Cerreia-Vioglio; Fabio Maccheroni; Massimo Marinacci; Luigi Montrucchio
2010-01-01
We study the interplay of probabilistic sophistication, second order stochastic dominance, and uncertainty aversion, three fundamental notions in choice under uncertainty. In particular, our main result, Theorem 2, characterizes uncertainty averse preferences that satisfy second order stochastic dominance, as well as uncertainty averse preferences that are probabilistically sophisticated.
Abnormal Waves Modelled as Second-order Conditional Waves
Jensen, Jørgen Juncher
2005-01-01
The paper presents results for the expected second order short-crested wave conditional of a given wave crest at a specific point in time and space. The analysis is based on the second order Sharma and Dean shallow water wave theory. Numerical results showing the importance of the spectral densit...
The second-order decomposition model of nonlinear irregular waves
Yang, Zhi Wen; Bingham, Harry B.; Li, Jin Xuan
2013-01-01
into the first- and the second-order super-harmonic as well as the second-order sub-harmonic components by transferring them into an identical Fourier frequency-space and using a Newton-Raphson iteration method. In order to evaluate the present model, a variety of monochromatic waves and the second...
Modulation masking produced by second-order modulators
Füllgrabe, Christian; Moore, Brian C.J.; Demany, Laurent
2005-01-01
Recent studies suggest that an auditory nonlinearity converts second-order sinusoidal amplitude modulation (SAM) (i.e., modulation of SAM depth) into a first-order SAM component, which contributes to the perception of second-order SAM. However, conversion may also occur in other ways such as coch...
Second-Order Learning Methods for a Multilayer Perceptron
Ivanov, V.V.; Purehvdorzh, B.; Puzynin, I.V.
1994-01-01
First- and second-order learning methods for feed-forward multilayer neural networks are studied. Newton-type and quasi-Newton algorithms are considered and compared with commonly used back-propagation algorithm. It is shown that, although second-order algorithms require enhanced computer facilities, they provide better convergence and simplicity in usage. 13 refs., 2 figs., 2 tabs
Mitchell, Jason
2002-01-01
A method is presented for the generation of exact numerical coefficients found in two families of implicit Chebyshev methods for the numerical integration of first- and second-order ordinary differential equations...
Second order sliding mode control for a quadrotor UAV.
Zheng, En-Hui; Xiong, Jing-Jing; Luo, Ji-Liang
2014-07-01
A method based on second order sliding mode control (2-SMC) is proposed to design controllers for a small quadrotor UAV. For the switching sliding manifold design, the selection of the coefficients of the switching sliding manifold is in general a sophisticated issue because the coefficients are nonlinear. In this work, in order to perform the position and attitude tracking control of the quadrotor perfectly, the dynamical model of the quadrotor is divided into two subsystems, i.e., a fully actuated subsystem and an underactuated subsystem. For the former, a sliding manifold is defined by combining the position and velocity tracking errors of one state variable, i.e., the sliding manifold has two coefficients. For the latter, a sliding manifold is constructed via a linear combination of position and velocity tracking errors of two state variables, i.e., the sliding manifold has four coefficients. In order to further obtain the nonlinear coefficients of the sliding manifold, Hurwitz stability analysis is used to the solving process. In addition, the flight controllers are derived by using Lyapunov theory, which guarantees that all system state trajectories reach and stay on the sliding surfaces. Extensive simulation results are given to illustrate the effectiveness of the proposed control method. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Ram Verma
2016-02-01
Full Text Available This paper deals with mainly establishing numerous sets of generalized second order paramertic sufficient optimality conditions for a semiinfinite discrete minmax fractional programming problem, while the results on semiinfinite discrete minmax fractional programming problem achieved based on some partitioning schemes under various types of generalized second order univexity assumptions.
Heydari, Somayeh; Siddiqui, Afzal
2010-01-01
Energy prices are often highly volatile with unexpected spikes. Capturing these sudden spikes may lead to more informed decision-making in energy investments, such as valuing gas-fired power plants, than ignoring them. In this paper, non-linear regime-switching models and models with mean-reverting stochastic volatility are compared with ordinary linear models. The study is performed using UK electricity and natural gas daily spot prices and suggests that with the aim of valuing a gas-fired power plant with and without operational flexibility, non-linear models with stochastic volatility, specifically for logarithms of electricity prices, provide better out-of-sample forecasts than both linear models and regime-switching models.
Weak value amplification via second-order correlated technique
Cui Ting; Huang Jing-Zheng; Zeng Gui-Hua; Liu Xiang
2016-01-01
We propose a new framework combining weak measurement and second-order correlated technique. The theoretical analysis shows that weak value amplification (WVA) experiment can also be implemented by a second-order correlated system. We then build two-dimensional second-order correlated function patterns for achieving higher amplification factor and discuss the signal-to-noise ratio influence. Several advantages can be obtained by our proposal. For instance, detectors with high resolution are not necessary. Moreover, detectors with low saturation intensity are available in WVA setup. Finally, type-one technical noise can be effectively suppressed. (paper)
Method to render second order beam optics programs symplectic
Douglas, D.; Servranckx, R.V.
1984-10-01
We present evidence that second order matrix-based beam optics programs violate the symplectic condition. A simple method to avoid this difficulty, based on a generating function approach to evaluating transfer maps, is described. A simple example illustrating the non-symplectricity of second order matrix methods, and the effectiveness of our solution to the problem, is provided. We conclude that it is in fact possible to bring second order matrix optics methods to a canonical form. The procedure for doing so has been implemented in the program DIMAT, and could be implemented in programs such as TRANSPORT and TURTLE, making them useful in multiturn applications. 15 refs
Recursive belief manipulation and second-order false-beliefs
Braüner, Torben; Blackburn, Patrick Rowan; Polyanskaya, Irina
2016-01-01
it indicate that a more fundamental *conceptual change* has taken place? In this paper we extend Braüner's hybrid-logical analysis of first-order false-belief tasks to the second-order case, and argue that our analysis supports a version of the conceptual change position.......The literature on first-order false-belief is extensive, but less is known about the second-order case. The ability to handle second-order false-beliefs correctly seems to mark a cognitively significant step, but what is its status? Is it an example of *complexity only* development, or does...
Second-order nonlinear optical metamaterials: ABC-type nanolaminates
Alloatti, L.; Kieninger, C.; Lauermann, M.; Köhnle, K.; Froelich, A.; Wegener, M.; Frenzel, T.; Freude, W.; Leuthold, J.; Koos, C.
2015-01-01
We demonstrate a concept for second-order nonlinear metamaterials that can be obtained from non-metallic centrosymmetric constituents with inherently low optical absorption. The concept is based on iterative atomic-layer deposition of three different materials, A = Al 2 O 3 , B = TiO 2 , and C = HfO 2 . The centrosymmetry of the resulting ABC stack is broken since the ABC and the inverted CBA sequences are not equivalent—a necessary condition for non-zero second-order nonlinearity. In our experiments, we find that the bulk second-order nonlinear susceptibility depends on the density of interfaces, leading to a nonlinear susceptibility of 0.26 pm/V at a wavelength of 800 nm. ABC-type nanolaminates can be deposited on virtually any substrate and offer a promising route towards engineering of second-order optical nonlinearities at both infrared and visible wavelengths
Improved system blind identification based on second-order ...
An improved system blind identification method based on second- order cyclostationary statistics and the properties of group delay, has been ... In the last decade, there has been considerable research on achieving blind identification.
Second Order Sliding Mode Controller Design for Pneumatic Artificial Muscle
Ammar Al-Jodah; Laith Khames
2018-01-01
In this paper, first and second order sliding mode controllers are designed for a single link robotic arm actuated by two Pneumatic Artificial Muscles (PAMs). A new mathematical model for the arm has been developed based on the model of large scale pneumatic muscle actuator model. Uncertainty in parameters has been presented and tested for the two controllers. The simulation results of the second-order sliding mode controller proves to have a low tracking error and chattering effect as compar...
Kubo Formulas for Second-Order Hydrodynamic Coefficients
Moore, Guy D.; Sohrabi, Kiyoumars A.
2011-01-01
At second order in gradients, conformal relativistic hydrodynamics depends on the viscosity η and on five additional ''second-order'' hydrodynamical coefficients τ Π , κ, λ 1 , λ 2 , and λ 3 . We derive Kubo relations for these coefficients, relating them to equilibrium, fully retarded three-point correlation functions of the stress tensor. We show that the coefficient λ 3 can be evaluated directly by Euclidean means and does not in general vanish.
Second-order gauge-invariant perturbations during inflation
Finelli, F.; Marozzi, G.; Vacca, G. P.; Venturi, G.
2006-01-01
The evolution of gauge invariant second-order scalar perturbations in a general single field inflationary scenario are presented. Different second-order gauge-invariant expressions for the curvature are considered. We evaluate perturbatively one of these second order curvature fluctuations and a second-order gauge-invariant scalar field fluctuation during the slow-roll stage of a massive chaotic inflationary scenario, taking into account the deviation from a pure de Sitter evolution and considering only the contribution of super-Hubble perturbations in mode-mode coupling. The spectra resulting from their contribution to the second order quantum correlation function are nearly scale-invariant, with additional logarithmic corrections with respect to the first order spectrum. For all scales of interest the amplitude of these spectra depends on the total number of e-folds. We find, on comparing first and second order perturbation results, an upper limit to the total number of e-folds beyond which the two orders are comparable
First- and second-order processing in transient stereopsis.
Edwards, M; Pope, D R; Schor, C M
2000-01-01
Large-field stimuli were used to investigate the interaction of first- and second-order pathways in transient-stereo processing. Stimuli consisted of sinewave modulations in either the mean luminance (first-order stimulus) or the contrast (second-order stimulus) of a dynamic-random-dot field. The main results of the present study are that: (1) Depth could be extracted with both the first-order and second-order stimuli; (2) Depth could be extracted from dichoptically mixed first- and second-order stimuli, however, the same stimuli, when presented as a motion sequence, did not result in a motion percept. Based upon these findings we conclude that the transient-stereo system processes both first- and second-order signals, and that these two signals are pooled prior to the extraction of transient depth. This finding of interaction between first- and second-order stereoscopic processing is different from the independence that has been found with the motion system.
On the Robustness of Hysteretic Second-Order Systems with PID : iISS approach
Ouyang, Ruiyue; Jayawardhana, Bayu; Andrieu, Vincent
2012-01-01
In this paper, we study the robustness property of a second-order linear plant controlled by a proportional, integral and derivative (PID) controller with a hysteretic actuator. The hysteretic actuator is modeled by a Duhem model that exhibits clockwise (CW) input-output (I/O) dynamics (such as the
Lomtatidze, Alexander; Vodstrčil, Petr
2005-01-01
Roč. 84, č. 2 (2005), s. 197-209 ISSN 0003-6811 Institutional research plan: CEZ:AV0Z10190503 Keywords : second order linear functional differential equations * nonnegative solution * two-point boundary value problem Subject RIV: BA - General Mathematics http://www.tandfonline.com/doi/full/10.1080/00036810410001724427
Decomposition of a symmetric second-order tensor
Heras, José A.
2018-05-01
In the three-dimensional space there are different definitions for the dot and cross products of a vector with a second-order tensor. In this paper we show how these products can uniquely be defined for the case of symmetric tensors. We then decompose a symmetric second-order tensor into its ‘dot’ part, which involves the dot product, and the ‘cross’ part, which involves the cross product. For some physical applications, this decomposition can be interpreted as one in which the dot part identifies with the ‘parallel’ part of the tensor and the cross part identifies with the ‘perpendicular’ part. This decomposition of a symmetric second-order tensor may be suitable for undergraduate courses of vector calculus, mechanics and electrodynamics.
On holographic entanglement entropy with second order excitations
He, Song; Sun, Jia-Rui; Zhang, Hai-Qing
2018-03-01
We study the low-energy corrections to the holographic entanglement entropy (HEE) in the boundary CFT by perturbing the bulk geometry up to second order excitations. Focusing on the case that the boundary subsystem is a strip, we show that the area of the bulk minimal surface can be expanded in terms of the conserved charges, such as mass, angular momentum and electric charge of the AdS black brane. We also calculate the variation of the energy in the subsystem and verify the validity of the first law-like relation of thermodynamics at second order. Moreover, the HEE is naturally bounded at second order perturbations if the cosmic censorship conjecture for the dual black hole still holds.
Second-Order Risk Constraints in Decision Analysis
Love Ekenberg
2014-01-01
Full Text Available Recently, representations and methods aimed at analysing decision problems where probabilities and values (utilities are associated with distributions over them (second-order representations have been suggested. In this paper we present an approach to how imprecise information can be modelled by means of second-order distributions and how a risk evaluation process can be elaborated by integrating procedures for numerically imprecise probabilities and utilities. We discuss some shortcomings of the use of the principle of maximising the expected utility and of utility theory in general, and offer remedies by the introduction of supplementary decision rules based on a concept of risk constraints taking advantage of second-order distributions.
On holographic entanglement entropy with second order excitations
Song He
2018-03-01
Full Text Available We study the low-energy corrections to the holographic entanglement entropy (HEE in the boundary CFT by perturbing the bulk geometry up to second order excitations. Focusing on the case that the boundary subsystem is a strip, we show that the area of the bulk minimal surface can be expanded in terms of the conserved charges, such as mass, angular momentum and electric charge of the AdS black brane. We also calculate the variation of the energy in the subsystem and verify the validity of the first law-like relation of thermodynamics at second order. Moreover, the HEE is naturally bounded at second order perturbations if the cosmic censorship conjecture for the dual black hole still holds.
Second Order Sliding Mode Controller Design for Pneumatic Artificial Muscle
Ammar Al-Jodah
2018-01-01
Full Text Available In this paper, first and second order sliding mode controllers are designed for a single link robotic arm actuated by two Pneumatic Artificial Muscles (PAMs. A new mathematical model for the arm has been developed based on the model of large scale pneumatic muscle actuator model. Uncertainty in parameters has been presented and tested for the two controllers. The simulation results of the second-order sliding mode controller proves to have a low tracking error and chattering effect as compared to the first order one. The verification has been done by using MATLAB and Simulink software.
A second-order class-D audio amplifier
Cox, Stephen M.; Tan, M.T.; Yu, J.
2011-01-01
Class-D audio amplifiers are particularly efficient, and this efficiency has led to their ubiquity in a wide range of modern electronic appliances. Their output takes the form of a high-frequency square wave whose duty cycle (ratio of on-time to off-time) is modulated at low frequency according to the audio signal. A mathematical model is developed here for a second-order class-D amplifier design (i.e., containing one second-order integrator) with negative feedback. We derive exact expression...
The Poisson equation at second order in relativistic cosmology
Hidalgo, J.C.; Christopherson, Adam J.; Malik, Karim A.
2013-01-01
We calculate the relativistic constraint equation which relates the curvature perturbation to the matter density contrast at second order in cosmological perturbation theory. This relativistic ''second order Poisson equation'' is presented in a gauge where the hydrodynamical inhomogeneities coincide with their Newtonian counterparts exactly for a perfect fluid with constant equation of state. We use this constraint to introduce primordial non-Gaussianity in the density contrast in the framework of General Relativity. We then derive expressions that can be used as the initial conditions of N-body codes for structure formation which probe the observable signature of primordial non-Gaussianity in the statistics of the evolved matter density field
Conformal conservation laws for second-order scalar fields
Blakeskee, J.S.; Logan, J.D.
1976-01-01
It is considered an action integral over space-time whose Lagrangian depends upon a scalar field an upon derivatives of the field function up to second order. From invariance identities obtained by the authors in an earlier work it is shown how a new proof of Noether's theorem for this second-order problem follows in the multiple integral case. Finally, conservation laws are written down in the case that the given action integral be invariant under the fifteen-parameter special conformal group
Solution of second order supersymmetrical intertwining relations in Minkowski plane
Ioffe, M. V., E-mail: m.ioffe@spbu.ru; Kolevatova, E. V., E-mail: e.v.kolev@yandex.ru [Saint Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg 199034 (Russian Federation); Nishnianidze, D. N., E-mail: cutaisi@yahoo.com [Saint Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg 199034 (Russian Federation); Akaki Tsereteli State University, 4600 Kutaisi, Georgia (United States)
2016-08-15
Supersymmetrical (SUSY) intertwining relations are generalized to the case of quantum Hamiltonians in Minkowski space. For intertwining operators (supercharges) of second order in derivatives, the intertwined Hamiltonians correspond to completely integrable systems with the symmetry operators of fourth order in momenta. In terms of components, the intertwining relations correspond to the system of nonlinear differential equations which are solvable with the simplest—constant—ansatzes for the “metric” matrix in second order part of the supercharges. The corresponding potentials are built explicitly both for diagonalizable and nondiagonalizable form of “metric” matrices, and their properties are discussed.
An integral for second-order multiple scattering perturbation theory
Hoffman, G.G.
1997-01-01
This paper presents the closed form evaluation of a six-dimensional integral. The integral arises in the application to many-electron systems of a multiple scattering perturbation expansion at second order when formulated in fourier space. The resulting function can be used for the calculation of both the electron density and the effective one-electron potential in an SCF calculations. The closed form expression derived here greatly facilitates these calculations. In addition, the evaluated integral can be used for the computation of second-order corrections to the open-quotes optimized Thomas-Fermi theory.close quotes 10 refs., 2 figs
Spectrum of Discrete Second-Order Difference Operator with Sign-Changing Weight and Its Applications
Ruyun Ma
2014-01-01
Full Text Available Let T>1 be an integer, and let=1,2,…,T. We discuss the spectrum of discrete linear second-order eigenvalue problems Δ2ut-1+λmtut=0, t∈, u0=uT+1=0, where λ≠0 is a parameter, m:→ℝ changes sign and mt≠0 on . At last, as an application of this spectrum result, we show the existence of sign-changing solutions of discrete nonlinear second-order problems by using bifurcate technique.
Guermond, Jean-Luc; Nazarov, Murtazo; Popov, Bojan; Yang, Yong
2014-01-01
© 2014 Society for Industrial and Applied Mathematics. This paper proposes an explicit, (at least) second-order, maximum principle satisfying, Lagrange finite element method for solving nonlinear scalar conservation equations. The technique is based on a new viscous bilinear form introduced in Guermond and Nazarov [Comput. Methods Appl. Mech. Engrg., 272 (2014), pp. 198-213], a high-order entropy viscosity method, and the Boris-Book-Zalesak flux correction technique. The algorithm works for arbitrary meshes in any space dimension and for all Lipschitz fluxes. The formal second-order accuracy of the method and its convergence properties are tested on a series of linear and nonlinear benchmark problems.
The effects of second-order hydrodynamics on a semisubmersible floating offshore wind turbine
Bayati, I; Jonkman, J; Robertson, A; Platt, A
2014-01-01
The objective of this paper is to assess the second-order hydrodynamic effects on a semisubmersible floating offshore wind turbine. Second-order hydrodynamics induce loads and motions at the sum- and difference-frequencies of the incident waves. These effects have often been ignored in offshore wind analysis, under the assumption that they are significantly smaller than first-order effects. The sum- and difference-frequency loads can, however, excite eigenfrequencies of a floating system, leading to large oscillations that strain the mooring system or vibrations that cause fatigue damage to the structure. Observations of supposed second-order responses in wave-tank tests performed by the DeepCwind consortium at the Maritime Research Institute Netherlands (MARIN) offshore basin suggest that these effects might be more important than originally expected. These observations inspired interest in investigating how second-order excitation affects floating offshore wind turbines and whether second-order hydrodynamics should be included in offshore wind simulation tools like FAST. In this work, the effects of second-order hydrodynamics on a floating semisubmersible offshore wind turbine are investigated. Because FAST is currently unable to account for second-order effects, a method to assess these effects was applied in which linearized properties of the floating wind system derived from FAST (including the 6x6 mass and stiffness matrices) are used by WAMIT to solve the first- and second-order hydrodynamics problems in the frequency domain. The method was applied to the Offshore Code Comparison Collaboration Continuation OC4-DeepCwind semisubmersible platform, supporting the National Renewable Energy Laboratory's 5-MW baseline wind turbine. In this paper, the loads and response of the system caused by the second-order hydrodynamics are analysed and compared to the first-order hydrodynamic loads and induced motions in the frequency domain. Further, the second-order
Nonlinear second order evolution inclusions with noncoercive viscosity term
Papageorgiou, Nikolaos S.; Rădulescu, Vicenţiu D.; Repovš, Dušan D.
2018-04-01
In this paper we deal with a second order nonlinear evolution inclusion, with a nonmonotone, noncoercive viscosity term. Using a parabolic regularization (approximation) of the problem and a priori bounds that permit passing to the limit, we prove that the problem has a solution.
Global weighted estimates for second-order nondivergence elliptic ...
Fengping Yao
2018-03-21
Mar 21, 2018 ... One of the key a priori estimates in the theory of second-order elliptic .... It is well known that the maximal functions satisfy strong p–p .... Here we prove the following auxiliary result, which will be a crucial ingredient in the proof.
A probabilistic approach to second order variational inequalities with ...
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
. TX 78712, USA. ‡CMI, Université de Provence, 39, Rue F. J. Curie, 13 453 Marseille, France. Email: mkg@math.iisc.ernet.in; mrinal@ece.utexas.edu. MS received 5 April 2002; revised 8 May 2003. Abstract. We study a class of second order ...
Validity of second order analysis of superdense matter
Bowers, R.L.; Gleeson, A.M.; Pedigo, R.D.
1975-01-01
The limitations of relativistic calculations of the properties of superdense matter obtained from strictly second order terms is discussed. Extension of the model to overcome these limitations leads to serious complications which can only be overcome by a fully self-consistent treatment. (U.S.)
Self-triggered rendezvous of gossiping second-order agents
De Persis, Claudio; Frasca, Paolo; Hendrickx, Julien M.
2013-01-01
A recent paper by some of the authors introduced several self-triggered coordination algorithms for first-order continuous-time systems. The extension of these algorithms to second-order agents is relevant in many practical applications but presents some challenges that are tackled in this
Generalized second-order Coulomb phase shift functions
Rosendorff, S.
1982-01-01
Some specific properties and the evaluation of the generalized second-order Coulomb phase shift functions (two-dimensional integrals of four spherical cylinder functions) are discussed. The dependence on the three momenta k 1 ,k-bar,k 2 , corresponding to the final, intermediate, and initial states is illustrated
Modeling Ability Differentiation in the Second-Order Factor Model
Molenaar, Dylan; Dolan, Conor V.; van der Maas, Han L. J.
2011-01-01
In this article we present factor models to test for ability differentiation. Ability differentiation predicts that the size of IQ subtest correlations decreases as a function of the general intelligence factor. In the Schmid-Leiman decomposition of the second-order factor model, we model differentiation by introducing heteroscedastic residuals,…
PID control of second-order systems with hysteresis
Jayawardhana, Bayu; Logemann, Hartmut; Ryan, Eugene P.
2008-01-01
The efficacy of proportional, integral and derivative (PID) control for set point regulation and disturbance rejection is investigated in a context of second-order systems with hysteretic components. Two basic structures are studied: in the first, the hysteretic component resides (internally) in the
Numerov iteration method for second order integral-differential equation
Zeng Fanan; Zhang Jiaju; Zhao Xuan
1987-01-01
In this paper, Numerov iterative method for second order integral-differential equation and system of equations are constructed. Numerical examples show that this method is better than direct method (Gauss elimination method) in CPU time and memoy requireing. Therefore, this method is an efficient method for solving integral-differential equation in nuclear physics
Oscillation of second order neutral dynamic equations with distributed delay
Qiaoshun Yang
2016-06-01
Full Text Available In this paper, we establish new oscillation criteria for second order neutral dynamic equations with distributed delay by employing the generalized Riccati transformation. The obtained theorems essentially improve the oscillation results in the literature. And two examples are provided to illustrate to the versatility of our main results.
Existence of solutions for second-order evolution inclusions
Nikolaos S. Papageorgiou
1994-01-01
Full Text Available In this paper we examine second-order nonlinear evolution inclusions and prove two existence theorems; one with a convex-valued orientor field and the other with a nonconvex-valued field. An example of a hyperbolic partial differential inclusion is also presented.
Second order guiding-center Vlasov–Maxwell equations
Madsen, Jens
2010-01-01
Second order gyrogauge invariant guiding-center coordinates with strong E×B-flow are derived using the Lie transformation method. The corresponding Poisson bracket structure and equations of motion are obtained. From a variational principle the explicit Vlasov–Maxwell equations are derived...
Discrete second order trajectory generator with nonlinear constraints
Morselli, R.; Zanasi, R.; Stramigioli, Stefano
2005-01-01
A discrete second order trajectory generator for motion control systems is presented. The considered generator is a nonlinear system which receives as input a raw reference signal and provides as output a smooth reference signal satisfying nonlinear constraints on the output derivatives as UM-(x) ≤
Skyrme interaction to second order in nuclear matter
Kaiser, N.
2015-09-01
Based on the phenomenological Skyrme interaction various density-dependent nuclear matter quantities are calculated up to second order in many-body perturbation theory. The spin-orbit term as well as two tensor terms contribute at second order to the energy per particle. The simultaneous calculation of the isotropic Fermi-liquid parameters provides a rigorous check through the validity of the Landau relations. It is found that published results for these second order contributions are incorrect in most cases. In particular, interference terms between s-wave and p-wave components of the interaction can contribute only to (isospin or spin) asymmetry energies. Even with nine adjustable parameters, one does not obtain a good description of the empirical nuclear matter saturation curve in the low density region 0\\lt ρ \\lt 2{ρ }0. The reason for this feature is the too strong density-dependence {ρ }8/3 of several second-order contributions. The inclusion of the density-dependent term \\frac{1}{6}{t}3{ρ }1/6 is therefore indispensable for a realistic description of nuclear matter in the Skyrme framework.
Deconvolution of the thermoluminescent emission curve. Second order kinetics
Moreno y M, A.; Moreno B, A.
1999-01-01
In this work it is described the Randall and Wilkins second order kinetics in Microsoft Excel language, which allows its expression as the sum of Gaussian and the correction factors corresponding. These factors are obtained of the differences between the real thermoluminescent curve and the Gaussian proposed. The results obtained justify the Gaussian expression added to the correction factor. (Author)
Second Order Impulsive Retarded Differential Inclusions with Nonlocal Conditions
Hernán R. Henríquez
2014-01-01
Full Text Available In this work we establish some existence results for abstract second order Cauchy problems modeled by a retarded differential inclusion involving nonlocal and impulsive conditions. Our results are obtained by using fixed point theory for the measure of noncompactness.
Modeling of second order space charge driven coherent sum and difference instabilities
Yao-Shuo Yuan
2017-10-01
Full Text Available Second order coherent oscillation modes in intense particle beams play an important role for beam stability in linear or circular accelerators. In addition to the well-known second order even envelope modes and their instability, coupled even envelope modes and odd (skew modes have recently been shown in [Phys. Plasmas 23, 090705 (2016PHPAEN1070-664X10.1063/1.4963851] to lead to parametric instabilities in periodic focusing lattices with sufficiently different tunes. While this work was partly using the usual envelope equations, partly also particle-in-cell (PIC simulation, we revisit these modes here and show that the complete set of second order even and odd mode phenomena can be obtained in a unifying approach by using a single set of linearized rms moment equations based on “Chernin’s equations.” This has the advantage that accurate information on growth rates can be obtained and gathered in a “tune diagram.” In periodic focusing we retrieve the parametric sum instabilities of coupled even and of odd modes. The stop bands obtained from these equations are compared with results from PIC simulations for waterbag beams and found to show very good agreement. The “tilting instability” obtained in constant focusing confirms the equivalence of this method with the linearized Vlasov-Poisson system evaluated in second order.
Dosoudilová, M.; Lomtatidze, Alexander; Šremr, Jiří
2015-01-01
Roč. 120, June (2015), s. 57-75 ISSN 0362-546X Institutional support: RVO:67985840 Keywords : half-linear system * Hartman -Wintner theorem * Kamenev theorem Subject RIV: BA - General Mathematics Impact factor: 1.125, year: 2015 http://www.sciencedirect.com/science/article/pii/S0362546X15000620
Second order optical nonlinearity in silicon by symmetry breaking
Cazzanelli, Massimo, E-mail: massimo.cazzanelli@unitn.it [Laboratorio IdEA, Dipartimento di Fisica, Università di Trento, via Sommarive, 14 Povo (Trento) (Italy); Schilling, Joerg, E-mail: joerg.schilling@physik.uni-halle.de [Centre for Innovation Competence SiLi-nano, Martin-Luther-University Halle-Wittenberg, Karl-Freiherr-von-Fritsch Str. 3, 06120 Halle (Germany)
2016-03-15
Although silicon does not possess a dipolar bulk second order nonlinear susceptibility due to its centro-symmetric crystal structure, in recent years several attempts were undertaken to create such a property in silicon. This review presents the different sources of a second order susceptibility (χ{sup (2)}) in silicon and the connected second order nonlinear effects which were investigated up to now. After an introduction, a theoretical overview discusses the second order nonlinearity in general and distinguishes between the dipolar contribution—which is usually dominating in non-centrosymmetric structures—and the quadrupolar contribution, which even exists in centro-symmetric materials. Afterwards, the classic work on second harmonic generation from silicon surfaces in reflection measurements is reviewed. Due to the abrupt symmetry breaking at surfaces and interfaces locally a dipolar second order susceptibility appears, resulting in, e.g., second harmonic generation. Since the bulk contribution is usually small, the study of this second harmonic signal allows a sensitive observation of the surface/interface conditions. The impact of covering films, strain, electric fields, and defect states at the interfaces was already investigated in this way. With the advent of silicon photonics and the search for ever faster electrooptic modulators, the interest turned to the creation of a dipolar bulk χ{sup (2)} in silicon. These efforts have been focussing on several experiments applying an inhomogeneous strain to the silicon lattice to break its centro-symmetry. Recent results suggesting the impact of electric fields which are exerted from fixed charges in adjacent covering layers are also included. After a subsequent summary on “competing” concepts using not Si but Si-related materials, the paper will end with some final conclusions, suggesting possible future research direction in this dynamically developing field.
First- and second-order charged particle optics
Brown, K.L.; Servranckx, R.V.
1984-07-01
Since the invention of the alternating gradient principle there has been a rapid evolution of the mathematics and physics techniques applicable to charged particle optics. In this publication we derive a differential equation and a matrix algebra formalism valid to second-order to present the basic principles governing the design of charged particle beam transport systems. A notation first introduced by John Streib is used to convey the essential principles dictating the design of such beam transport systems. For example the momentum dispersion, the momentum resolution, and all second-order aberrations are expressed as simple integrals of the first-order trajectories (matrix elements) and of the magnetic field parameters (multipole components) characterizing the system. 16 references, 30 figures
Second-Order Assortative Mixing in Social Networks
Zhou, Shi; Cox, Ingemar; Hansen, Lars Kai
2017-01-01
In a social network, the number of links of a node, or node degree, is often assumed as a proxy for the node’s importance or prominence within the network. It is known that social networks exhibit the (first-order) assortative mixing, i.e. if two nodes are connected, they tend to have similar node...... degrees, suggesting that people tend to mix with those of comparable prominence. In this paper, we report the second-order assortative mixing in social networks. If two nodes are connected, we measure the degree correlation between their most prominent neighbours, rather than between the two nodes...... themselves. We observe very strong second-order assortative mixing in social networks, often significantly stronger than the first-order assortative mixing. This suggests that if two people interact in a social network, then the importance of the most prominent person each knows is very likely to be the same...
Measuring of Second-order Stochastic Dominance Portfolio Efficiency
Kopa, Miloš
2010-01-01
Roč. 46, č. 3 (2010), s. 488-500 ISSN 0023-5954 R&D Projects: GA ČR GAP402/10/1610 Institutional research plan: CEZ:AV0Z10750506 Keywords : stochastic dominance * stability * SSD porfolio efficiency Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.461, year: 2010 http://library.utia.cas.cz/separaty/2010/E/kopa-measuring of second-order stochastic dominance portfolio efficiency.pdf
Discrete Weighted Pseudo Asymptotic Periodicity of Second Order Difference Equations
Zhinan Xia
2014-01-01
Full Text Available We define the concept of discrete weighted pseudo-S-asymptotically periodic function and prove some basic results including composition theorem. We investigate the existence, and uniqueness of discrete weighted pseudo-S-asymptotically periodic solution to nonautonomous semilinear difference equations. Furthermore, an application to scalar second order difference equations is given. The working tools are based on the exponential dichotomy theory and fixed point theorem.
Comparison of second-order impact line shifts
Griem, H.R.; Iglesias, C.A.; Boercker, D.B.
1991-01-01
The second-order impact shifts in hydrogen obtained from the Baranger formalism are compared with those from a kinetic theory approach. The resulting Δn=0 contributions to the shift from the two theories are shown to be identical, except for the neglect of electron-electron correlations in the Baranger formalism. It is also shown that some care is required in taking the classical limit for the perturbing electrons, or else the shift from Δn=0 interactions vanishes
Second order elastic metrics on the shape space of curves
Bauer, Martin; Bruveris, Martins; Harms, Philipp
2015-01-01
Second order Sobolev metrics on the space of regular unparametrized planar curves have several desirable completeness properties not present in lower order metrics, but numerics are still largely missing. In this paper, we present algorithms to numerically solve the initial and boundary value......, due to its generality, it could be applied to more general spaces of mapping. We demonstrate the effectiveness of our approach by analyzing a collection of shapes representing physical objects....
On the dynamics of second-order Lagrangian systems
Ronald Adams
2017-04-01
Full Text Available In this article we are concerned with improving the twist condition for second-order Lagrangian systems. We characterize a local Twist property and demonstrate how results on the existence of simple closed characteristics can be extended in the case of the Swift-Hohenberg / extended Fisher-Kolmogorov Lagrangian. Finally, we describe explicit evolution equations for broken geodesic curves that could be used to investigate more general systems or closed characteristics.
Gravitational waves from global second order phase transitions
Jr, John T. Giblin [Department of Physics, Kenyon College, 201 North College Rd, Gambier, OH 43022 (United States); Price, Larry R.; Siemens, Xavier; Vlcek, Brian, E-mail: giblinj@kenyon.edu, E-mail: larryp@caltech.edu, E-mail: siemens@gravity.phys.uwm.edu, E-mail: bvlcek@uwm.edu [Center for Gravitation and Cosmology, Department of Physics, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201 (United States)
2012-11-01
Global second-order phase transitions are expected to produce scale-invariant gravitational wave spectra. In this manuscript we explore the dynamics of a symmetry-breaking phase transition using lattice simulations. We explicitly calculate the stochastic gravitational wave background produced during the transition and subsequent self-ordering phase. We comment on this signal as it compares to the scale-invariant spectrum produced during inflation.
Pyrolytic Graphite as a Tunable Second order Neutron Filter
Adib, M.
2009-01-01
A study has been carried out on the neutron transmission through pyrolytic graphite (PG) crystals in order to check its applicability as an efficient tunable second order neutron filter. The neutron transmission have been calculated as a function of neutron wavelengths in the range from 0.01 nm up to 0.7 nm at various PG mosaic spread, thickness and orientation of its c-axis with respect to the beam direction The Computer package Graphite has been used to provide the required calculation. It was shown that highly aligned (10 FWHM on mosaic spread) PG crystal ∼2 cm thick, may be tuned for optimum scattering of 2 second order neutrons within some favorable wavelength intervals in the range between 0.112 and 0.425 nm by adjusting the crystal in an appropriate orientation. .However, a less quality and thinner PG was found to almost eliminate 2 second order neutrons at only tuned values of wavelength corresponding to the poison of the triple intersection points of the curves (hkl) ± and (00l)
Mixed hyperbolic-second-order-parabolic formulations of general relativity
Paschalidis, Vasileios
2008-01-01
Two new formulations of general relativity are introduced. The first one is a parabolization of the Arnowitt-Deser-Misner formulation and is derived by the addition of combinations of the constraints and their derivatives to the right-hand side of the Arnowitt-Deser-Misner evolution equations. The desirable property of this modification is that it turns the surface of constraints into a local attractor because the constraint propagation equations become second-order parabolic independently of the gauge conditions employed. This system may be classified as mixed hyperbolic--second-order parabolic. The second formulation is a parabolization of the Kidder-Scheel-Teukolsky formulation and is a manifestly mixed strongly hyperbolic--second-order-parabolic set of equations, bearing thus resemblance to the compressible Navier-Stokes equations. As a first test, a stability analysis of flat space is carried out and it is shown that the first modification exponentially damps and smoothes all constraint-violating modes. These systems provide a new basis for constructing schemes for long-term and stable numerical integration of the Einstein field equations.
Supriyono; Miyoshi, T.
1997-01-01
NECD Method and runge-Kutta method for large system of second order ordinary differential equations in comparing algorithm. The paper introduce a extrapolation method used for solving the large system of second order ordinary differential equation. We call this method the modified extrapolated central difference (MECD) method. for the accuracy and efficiency MECD method. we compare the method with 4-th order runge-Kutta method. The comparison results show that, this method has almost the same accuracy as the 4-th order runge-Kutta method, but the computation time is about half of runge-Kutta. The MECD was declare by the author and Tetsuhiko Miyoshi of the Dept. Applied Science Yamaguchi University Japan
Existence of positive solutions for systems of second order multi ...
Multi-point boundary value problems (BVPs) for ordinary differential or difference ... of a curved beam having a constant or varying cross section, three layer ..... Applying Theorem 2.5 to (3.1) and (3.2), we obtain that T has a fixed point (u, v).
The shooting method and multiple solutions of two/multi-point BVPs of second-order ODE
Man Kam Kwong
2006-06-01
Full Text Available Within the last decade, there has been growing interest in the study of multiple solutions of two- and multi-point boundary value problems of nonlinear ordinary differential equations as fixed points of a cone mapping. Undeniably many good results have emerged. The purpose of this paper is to point out that, in the special case of second-order equations, the shooting method can be an effective tool, sometimes yielding better results than those obtainable via fixed point techniques.
An implicit second order numerical method for two-fluid models
Toumi, I.
1995-01-01
We present an implicit upwind numerical method for a six equation two-fluid model based on a linearized Riemann solver. The construction of this approximate Riemann solver uses an extension of Roe's scheme. Extension to second order accurate method is achieved using a piecewise linear approximation of the solution and a slope limiter method. For advancing in time, a linearized implicit integrating step is used. In practice this new numerical method has proved to be stable and capable of generating accurate non-oscillating solutions for two-phase flow calculations. The scheme was applied both to shock tube problems and to standard tests for two-fluid codes. (author)
Class of unconditionally stable second-order implicit schemes for hyperbolic and parabolic equations
Lui, H.C.
The linearized Burgers equation is considered as a model u/sub t/ tau/sub x/ = bu/sub xx/, where the subscripts t and x denote the derivatives of the function u with respect to time t and space x; a and b are constants (b greater than or equal to 0). Numerical schemes for solving the equation are described that are second-order accurate, unconditionally stable, and dissipative of higher order. (U.S.)
Second order approximation for optical polaron in the strong coupling case
Bogolubov, N.N. Jr.
1993-11-01
Here we propose a method of construction second order approximation for ground state energy for class of model Hamiltonian with linear type interaction on Bose operators in strong coupling case. For the application of the above method we have considered polaron model and propose construction set of nonlinear differential equations for definition ground state energy in strong coupling case. We have considered also radial symmetry case. (author). 10 refs
Green's matrix for a second-order self-adjoint matrix differential operator
Sisman, Tahsin Cagri; Tekin, Bayram
2010-01-01
A systematic construction of the Green's matrix for a second-order self-adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out. We follow the general approach of extracting the Green's matrix from the Green's matrix of the corresponding first-order system. This construction is required in the cases where the differential equation set cannot be turned to an algebraic equation set via transform techniques.
On the second-order temperature jump coefficient of a dilute gas
Radtke, Gregg A.; Hadjiconstantinou, N. G.; Takata, S.; Aoki, K.
2012-09-01
We use LVDSMC simulations to calculate the second-order temperature jump coefficient for a dilute gas whose temperature is governed by the Poisson equation with a constant forcing term. Both the hard sphere gas and the BGK model of the Boltzmann equation are considered. Our results show that the temperature jump coefficient is different from the well known linear and steady case where the temperature is governed by the homogeneous heat conduction (Laplace) equation.
Method of construction of the Riemann function for a second-order hyperbolic equation
Aksenov, A. V.
2017-12-01
A linear hyperbolic equation of the second order in two independent variables is considered. The Riemann function of the adjoint equation is shown to be invariant with respect to the fundamental solutions transformation group. Symmetries and symmetries of fundamental solutions of the Euler-Poisson-Darboux equation are found. The Riemann function is constructed with the aid of fundamental solutions symmetries. Examples of the application of the algorithm for constructing Riemann function are given.
Estimates of solutions of certain classes of second-order differential equations in a Hilbert space
Artamonov, N V
2003-01-01
Linear second-order differential equations of the form u''(t)+(B+iD)u'(t)+(T+iS)u(t)=0 in a Hilbert space are studied. Under certain conditions on the (generally speaking, unbounded) operators T, S, B and D the correct solubility of the equation in the 'energy' space is proved and best possible (in the general case) estimates of the solutions on the half-axis are obtained
Finite difference schemes for second order systems describing black holes
Motamed, Mohammad; Kreiss, H-O.; Babiuc, M.; Winicour, J.; Szilagyi, B.
2006-01-01
In the harmonic description of general relativity, the principal part of Einstein's equations reduces to 10 curved space wave equations for the components of the space-time metric. We present theorems regarding the stability of several evolution-boundary algorithms for such equations when treated in second order differential form. The theorems apply to a model black hole space-time consisting of a spacelike inner boundary excising the singularity, a timelike outer boundary and a horizon in between. These algorithms are implemented as stable, convergent numerical codes and their performance is compared in a 2-dimensional excision problem
Constrained generalized mechanics. The second-order case
Tapia, V.
1985-01-01
The Dirac formalism for constrained systems is developed for systems described by a Lagrangian depending on up to a second-order time derivatives of the generalized co-ordinates (accelerations). It turns out that for a Lagrangian of this kind differing by a total time derivative from a Lagrangian depending on only up to first-order time-derivatives of the generalized co-ordinates (velocities), both classical mechanics at the Lagrangian level are the same; at the Hamiltonian level the two classical mechanics differ conceptually even when the solutions to both sets of Hamiltonian equations of motion are the same
Second Order Sliding Mode Control of the Coupled Tanks System
Fayiz Abu Khadra
2015-01-01
Full Text Available Four classes of second order sliding mode controllers (2-SMC have been successfully applied to regulate the liquid level in the second tank of a coupled tanks system. The robustness of these classes of 2-SMC is investigated and their performances are compared with a first order controller to show the merits of these controllers. The effectiveness of these controllers is verified through computer simulations. Comparison between the controllers is based on the time domain performance measures such as rise time, settling time, and the integral absolute error. Results showed that controllers are able to regulate the liquid level with small differences in their performance.
Dynamic Uncertainty for Compensated Second-Order Systems
Clemens Elster
2010-08-01
Full Text Available The compensation of LTI systems and the evaluation of the according uncertainty is of growing interest in metrology. Uncertainty evaluation in metrology ought to follow specific guidelines, and recently two corresponding uncertainty evaluation schemes have been proposed for FIR and IIR filtering. We employ these schemes to compare an FIR and an IIR approach for compensating a second-order LTI system which has relevance in metrology. Our results suggest that the FIR approach is superior in the sense that it yields significantly smaller uncertainties when real-time evaluation of uncertainties is desired.
Hwang, Jai-chan; Noh, Hyerim
2007-01-01
We present general relativistic correction terms appearing in Newton's gravity to the second-order perturbations of cosmological fluids. In our previous work we have shown that to the second-order perturbations, the density and velocity perturbation equations of general relativistic zero-pressure, irrotational, single-component fluid in a spatially flat background coincide exactly with the ones known in Newton's theory without using the gravitational potential. We also have shown the effect of gravitational waves to the second order, and pure general relativistic correction terms appearing in the third-order perturbations. Here, we present results of second-order perturbations relaxing all the assumptions made in our previous works. We derive the general relativistic correction terms arising due to (i) pressure, (ii) multicomponent, (iii) background spatial curvature, and (iv) rotation. In the case of multicomponent zero-pressure, irrotational fluids under the flat background, we effectively do not have relativistic correction terms, thus the relativistic equations expressed in terms of density and velocity perturbations again coincide with the Newtonian ones. In the other three cases we generally have pure general relativistic correction terms. In the case of pressure, the relativistic corrections appear even in the level of background and linear perturbation equations. In the presence of background spatial curvature, or rotation, pure relativistic correction terms directly appear in the Newtonian equations of motion of density and velocity perturbations to the second order; to the linear order, without using the gravitational potential (or metric perturbations), we have relativistic/Newtonian correspondences for density and velocity perturbations of a single-component fluid including the rotation even in the presence of background spatial curvature. In the small-scale limit (far inside the horizon), to the second-order, relativistic equations of density and
Ismagilov, Timur Z., E-mail: ismagilov@academ.org
2015-02-01
This paper presents a second order finite volume scheme for numerical solution of Maxwell's equations with discontinuous dielectric permittivity and magnetic permeability on unstructured meshes. The scheme is based on Godunov scheme and employs approaches of Van Leer and Lax–Wendroff to increase the order of approximation. To keep the second order of approximation near dielectric permittivity and magnetic permeability discontinuities a novel technique for gradient calculation and limitation is applied near discontinuities. Results of test computations for problems with linear and curvilinear discontinuities confirm second order of approximation. The scheme was applied to modelling propagation of electromagnetic waves inside photonic crystal waveguides with a bend.
Adaptive suboptimal second-order sliding mode control for microgrids
Incremona, Gian Paolo; Cucuzzella, Michele; Ferrara, Antonella
2016-09-01
This paper deals with the design of adaptive suboptimal second-order sliding mode (ASSOSM) control laws for grid-connected microgrids. Due to the presence of the inverter, of unpredicted load changes, of switching among different renewable energy sources, and of electrical parameters variations, the microgrid model is usually affected by uncertain terms which are bounded, but with unknown upper bounds. To theoretically frame the control problem, the class of second-order systems in Brunovsky canonical form, characterised by the presence of matched uncertain terms with unknown bounds, is first considered. Four adaptive strategies are designed, analysed and compared to select the most effective ones to be applied to the microgrid case study. In the first two strategies, the control amplitude is continuously adjusted, so as to arrive at dominating the effect of the uncertainty on the controlled system. When a suitable control amplitude is attained, the origin of the state space of the auxiliary system becomes attractive. In the other two strategies, a suitable blend between two components, one mainly working during the reaching phase, the other being the predominant one in a vicinity of the sliding manifold, is generated, so as to reduce the control amplitude in steady state. The microgrid system in a grid-connected operation mode, controlled via the selected ASSOSM control strategies, exhibits appreciable stability properties, as proved theoretically and shown in simulation.
Paridaens, Richard [DynFluid, Arts et Metiers, 151 boulevard de l' Hopital, Paris (France); Kouidri, Smaine [LIMSI-CNRS, Orsay Cedex (France)
2016-11-15
Nonlinear phenomena in oscillating flow devices cause the appearance of a relatively minor secondary flow known as acoustic streaming, which is superimposed on the primary oscillating flow. Knowledge of control parameters, such as the time-averaged second-order velocity and pressure, would elucidate the non-linear phenomena responsible for this part of the decrease in the system's energetic efficiency. This paper focuses on the characterization of a travelling wave oscillating flow engine by measuring the time-averaged second order pressure and velocity. Laser Doppler velocimetry technique was used to measure the time-averaged second-order velocity. As streaming is a second-order phenomenon, its measurement requires specific settings especially in a pressurized device. Difficulties in obtaining the proper settings are highlighted in this study. The experiments were performed for mean pressures varying from 10 bars to 22 bars. Non-linear effect does not constantly increase with pressure.
Imran Talib
2015-12-01
Full Text Available In this article, study the existence of solutions for the second-order nonlinear coupled system of ordinary differential equations $$\\displaylines{ u''(t=f(t,v(t,\\quad t\\in [0,1],\\cr v''(t=g(t,u(t,\\quad t\\in [0,1], }$$ with nonlinear coupled boundary conditions $$\\displaylines{ \\phi(u(0,v(0,u(1,v(1,u'(0,v'(0=(0,0, \\cr \\psi(u(0,v(0,u(1,v(1,u'(1,v'(1=(0,0, }$$ where $f,g:[0,1]\\times \\mathbb{R}\\to \\mathbb{R}$ and $\\phi,\\psi:\\mathbb{R}^6\\to \\mathbb{R}^2$ are continuous functions. Our main tools are coupled lower and upper solutions, Arzela-Ascoli theorem, and Schauder's fixed point theorem.
SECOND-ORDER CYBERNETICS, SEMIOTICS AND THE ART
Niculae V. Mihaita
2011-04-01
Full Text Available We take into consideration the concept of second order cybernetics and Pierce‘s approach of semiotics fundamentals. I am also an observer, experimenter and mental interpreter of metasigns given to the audience by Eugene Ionesco‘s absurd theatre. The interpreting of signs meaning is determinate by the context. From Semiotics ‗point of view, the objects I‘m studying (The Love Poem Lucifer or Evening Star, the short play Foursome and the most known, The Chairs gives me a lot of information about differences or NOT between actors, positive and negative interactions and become knowledge when I see them as signs. Second order cybernetics brings to the semiotics the idea of closure of structural coupling, interpretation and language [Soren, Cybersemiotics, 2008]. Them, the objects chosen are, for EXPERIMENTER, the YOYO in figure 1, and signifies the OBJECT of recursion. Boje [Boje, David, 2005] redefines antenarrative communication more holistically as an enactive phenomenon, and makes connections between varieties of disciplines in order to find out how antenarratives help us understand communication in the world. Instead of the finite event of producing an artifact, betting is a process and an end in itself, through which the practitioners might gain self-awareness. By synthesizing enactive-thinking in virtual space and the practice of communicating we appeal for valuable insights into the creative mind, challenging scholars and practitioners alike. Drawing contributions as above ideograms are useful for practicing cyberneticians, statisticians, researchers and academics, Informational Statistics applications [Mihaita, 2010] explores the ways in which liberal arts writers seek to involve, create and engage with new and diverse audiences from beginners encountering and participating in the work unexpectedly, to professionals from other disciplines and members of particular communities. Taking into consideration the Second-order Cybernetics
A new implementation of the second-order polarization propagator approximation (SOPPA)
Packer, Martin J.; Dalskov, Erik K.; Enevoldsen, Thomas
1996-01-01
We present a new implementation of the second-order polarization propagator approximation (SOPPA) using a direct linear transformation approach, in which the SOPPA equations are solved iteratively. This approach has two important advantages over its predecessors. First, the direct linear...... and triplet transitions for benzene and naphthalene. The results compare well with experiment and CASPT2 values, calculated with identical basis sets and molecular geometries. This indicates that SOPPA can provide reliable values for excitation energies and response properties for relatively large molecular...
Second-order differential-delay equation to describe a hybrid bistable device
Vallee, R.; Dubois, P.; Cote, M.; Delisle, C.
1987-08-01
The problem of a dynamical system with delayed feedback, a hybrid bistable device, characterized by n response times and described by an nth-order differential-delay equation (DDE) is discussed. Starting from a linear-stability analysis of the DDE, the effects of the second-order differential terms on the position of the first bifurcation and on the frequency of the resulting self-oscillation are shown. The effects of the third-order differential terms on the first bifurcation are also considered. Experimental results are shown to support the linear analysis.
Second-order analysis of semiparametric recurrent event processes.
Guan, Yongtao
2011-09-01
A typical recurrent event dataset consists of an often large number of recurrent event processes, each of which contains multiple event times observed from an individual during a follow-up period. Such data have become increasingly available in medical and epidemiological studies. In this article, we introduce novel procedures to conduct second-order analysis for a flexible class of semiparametric recurrent event processes. Such an analysis can provide useful information regarding the dependence structure within each recurrent event process. Specifically, we will use the proposed procedures to test whether the individual recurrent event processes are all Poisson processes and to suggest sensible alternative models for them if they are not. We apply these procedures to a well-known recurrent event dataset on chronic granulomatous disease and an epidemiological dataset on meningococcal disease cases in Merseyside, United Kingdom to illustrate their practical value. © 2011, The International Biometric Society.
Second order chromaticity of the interaction regions in the collider
Sen, T.; Syphers, M.J.
1993-01-01
The collider in the SSC has large second order chromaticity (ξ 2 ) with the interaction regions (IRs) contributing substantially to it. The authors calculate the general expression for ξ 2 in a storage ring and find that it is driven by the first order chromatic beta wave. Specializing to the interaction regions, they show that ξ 2 is a minimum when the phase advance (Δμ IP -IP) between adjacent interaction points is an odd multiple of π/2 and both IRs are identical. In this case the first order chromatic beta wave is confined within the IRs. Conversely, ξ 2 is large either if δμ IP -IP = (2n + 1)π/2 and the two IRs are very far from equality or if the two IRs are equal but Δμ IP -IP = nπ
Feature Scaling via Second-Order Cone Programming
Zhizheng Liang
2016-01-01
Full Text Available Feature scaling has attracted considerable attention during the past several decades because of its important role in feature selection. In this paper, a novel algorithm for learning scaling factors of features is proposed. It first assigns a nonnegative scaling factor to each feature of data and then adopts a generalized performance measure to learn the optimal scaling factors. It is of interest to note that the proposed model can be transformed into a convex optimization problem: second-order cone programming (SOCP. Thus the scaling factors of features in our method are globally optimal in some sense. Several experiments on simulated data, UCI data sets, and the gene data set are conducted to demonstrate that the proposed method is more effective than previous methods.
Riccati-parameter solutions of nonlinear second-order ODEs
Reyes, M A; Rosu, H C
2008-01-01
It has been proven by Rosu and Cornejo-Perez (Rosu and Cornejo-Perez 2005 Phys. Rev. E 71 046607, Cornejo-Perez and Rosu 2005 Prog. Theor. Phys. 114 533) that for some nonlinear second-order ODEs it is a very simple task to find one particular solution once the nonlinear equation is factorized with the use of two first-order differential operators. Here, it is shown that an interesting class of parametric solutions is easy to obtain if the proposed factorization has a particular form, which happily turns out to be the case in many problems of physical interest. The method that we exemplify with a few explicitly solved cases consists in using the general solution of the Riccati equation, which contributes with one parameter to this class of parametric solutions. For these nonlinear cases, the Riccati parameter serves as a 'growth' parameter from the trivial null solution up to the particular solution found through the factorization procedure
A unified model for transfer alignment at random misalignment angles based on second-order EKF
Cui, Xiao; Qin, Yongyuan; Yan, Gongmin; Liu, Zhenbo; Mei, Chunbo
2017-01-01
In the transfer alignment process of inertial navigation systems (INSs), the conventional linear error model based on the small misalignment angle assumption cannot be applied to large misalignment situations. Furthermore, the nonlinear model based on the large misalignment angle suffers from redundant computation with nonlinear filters. This paper presents a unified model for transfer alignment suitable for arbitrary misalignment angles. The alignment problem is transformed into an estimation of the relative attitude between the master INS (MINS) and the slave INS (SINS), by decomposing the attitude matrix of the latter. Based on the Rodriguez parameters, a unified alignment model in the inertial frame with the linear state-space equation and a second order nonlinear measurement equation are established, without making any assumptions about the misalignment angles. Furthermore, we employ the Taylor series expansions on the second-order nonlinear measurement equation to implement the second-order extended Kalman filter (EKF2). Monte-Carlo simulations demonstrate that the initial alignment can be fulfilled within 10 s, with higher accuracy and much smaller computational cost compared with the traditional unscented Kalman filter (UKF) at large misalignment angles. (paper)
A unified model for transfer alignment at random misalignment angles based on second-order EKF
Cui, Xiao; Mei, Chunbo; Qin, Yongyuan; Yan, Gongmin; Liu, Zhenbo
2017-04-01
In the transfer alignment process of inertial navigation systems (INSs), the conventional linear error model based on the small misalignment angle assumption cannot be applied to large misalignment situations. Furthermore, the nonlinear model based on the large misalignment angle suffers from redundant computation with nonlinear filters. This paper presents a unified model for transfer alignment suitable for arbitrary misalignment angles. The alignment problem is transformed into an estimation of the relative attitude between the master INS (MINS) and the slave INS (SINS), by decomposing the attitude matrix of the latter. Based on the Rodriguez parameters, a unified alignment model in the inertial frame with the linear state-space equation and a second order nonlinear measurement equation are established, without making any assumptions about the misalignment angles. Furthermore, we employ the Taylor series expansions on the second-order nonlinear measurement equation to implement the second-order extended Kalman filter (EKF2). Monte-Carlo simulations demonstrate that the initial alignment can be fulfilled within 10 s, with higher accuracy and much smaller computational cost compared with the traditional unscented Kalman filter (UKF) at large misalignment angles.
Second order time evolution of the multigroup diffusion and P1 equations for radiation transport
Olson, Gordon L.
2011-01-01
Highlights: → An existing multigroup transport algorithm is extended to be second-order in time. → A new algorithm is presented that does not require a grey acceleration solution. → The two algorithms are tested with 2D, multi-material problems. → The two algorithms have comparable computational requirements. - Abstract: An existing solution method for solving the multigroup radiation equations, linear multifrequency-grey acceleration, is here extended to be second order in time. This method works for simple diffusion and for flux-limited diffusion, with or without material conduction. A new method is developed that does not require the solution of an averaged grey transport equation. It is effective solving both the diffusion and P 1 forms of the transport equation. Two dimensional, multi-material test problems are used to compare the solution methods.
Pap-smear Classification Using Efficient Second Order Neural Network Training Algorithms
Ampazis, Nikolaos; Dounias, George; Jantzen, Jan
2004-01-01
In this paper we make use of two highly efficient second order neural network training algorithms, namely the LMAM (Levenberg-Marquardt with Adaptive Momentum) and OLMAM (Optimized Levenberg-Marquardt with Adaptive Momentum), for the construction of an efficient pap-smear test classifier. The alg......In this paper we make use of two highly efficient second order neural network training algorithms, namely the LMAM (Levenberg-Marquardt with Adaptive Momentum) and OLMAM (Optimized Levenberg-Marquardt with Adaptive Momentum), for the construction of an efficient pap-smear test classifier....... The algorithms are methodologically similar, and are based on iterations of the form employed in the Levenberg-Marquardt (LM) method for non-linear least squares problems with the inclusion of an additional adaptive momentum term arising from the formulation of the training task as a constrained optimization...
A second order discontinuous Galerkin fast sweeping method for Eikonal equations
Li, Fengyan; Shu, Chi-Wang; Zhang, Yong-Tao; Zhao, Hongkai
2008-09-01
In this paper, we construct a second order fast sweeping method with a discontinuous Galerkin (DG) local solver for computing viscosity solutions of a class of static Hamilton-Jacobi equations, namely the Eikonal equations. Our piecewise linear DG local solver is built on a DG method developed recently [Y. Cheng, C.-W. Shu, A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations, Journal of Computational Physics 223 (2007) 398-415] for the time-dependent Hamilton-Jacobi equations. The causality property of Eikonal equations is incorporated into the design of this solver. The resulting local nonlinear system in the Gauss-Seidel iterations is a simple quadratic system and can be solved explicitly. The compactness of the DG method and the fast sweeping strategy lead to fast convergence of the new scheme for Eikonal equations. Extensive numerical examples verify efficiency, convergence and second order accuracy of the proposed method.
Understanding operational risk capital approximations: First and second orders
Gareth W. Peters
2013-07-01
Full Text Available We set the context for capital approximation within the framework of the Basel II / III regulatory capital accords. This is particularly topical as the Basel III accord is shortly due to take effect. In this regard, we provide a summary of the role of capital adequacy in the new accord, highlighting along the way the significant loss events that have been attributed to the Operational Risk class that was introduced in the Basel II and III accords. Then we provide a semi-tutorial discussion on the modelling aspects of capital estimation under a Loss Distributional Approach (LDA. Our emphasis is to focuss on the important loss processes with regard to those that contribute most to capital, the so called “high consequence, low frequency" loss processes. This leads us to provide a tutorial overview of heavy tailed loss process modelling in OpRisk under Basel III, with discussion on the implications of such tail assumptions for the severity model in an LDA structure. This provides practitioners with a clear understanding of the features that they may wish to consider when developing OpRisk severity models in practice. From this discussion on heavy tailed severity models, we then develop an understanding of the impact such models have on the right tail asymptotics of the compound loss process and we provide detailed presentation of what are known as first and second order tail approximations for the resulting heavy tailed loss process. From this we develop a tutorial on three key families of risk measures and their equivalent second order asymptotic approximations: Value-at-Risk (Basel III industry standard; Expected Shortfall (ES and the Spectral Risk Measure. These then form the capital approximations. We then provide a few example case studies to illustrate the accuracy of these asymptotic captial approximations, the rate of the convergence of the assymptotic result as a function of the LDA frequency and severity model parameters, the sensitivity
Asteroid proper elements from an analytical second order theory
Knezevic, Z.; Milani, A.
1989-01-01
The authors have computed by a fully analytical method a new set of proper elements for 3322 numbered main-belt asteroids. They are presented in the following format: asteroid number, proper semimajor axis (AU), proper eccentricity, sine of proper inclination and quality code (see below). This new set is significantly more accurate than all the previous ones at low to moderate eccentricities and inclinations, and especially near the main mean-motion resonances (e.g., the Themis region). This is because the short periodic perturbations are rigorously removed, and the main effects of the second-order (containing the square of the ratio [the mass of Jupiter/mass of the Sun]) are accounted for. Effects arising from the terms in the Hamiltonian of degree up to four in the eccentricity and inclination of both the asteroid and Jupiter are taken into account, and the fundamental frequencies g (for the perihelion) and s(for the node) of the asteroid are computed with a interative algorithm consistent with the basic results of modern dynamics (e.g., Kolmogorov-Arnold-Moser theory)
Fuzzy Random Walkers with Second Order Bounds: An Asymmetric Analysis
Georgios Drakopoulos
2017-03-01
Full Text Available Edge-fuzzy graphs constitute an essential modeling paradigm across a broad spectrum of domains ranging from artificial intelligence to computational neuroscience and social network analysis. Under this model, fundamental graph properties such as edge length and graph diameter become stochastic and as such they are consequently expressed in probabilistic terms. Thus, algorithms for fuzzy graph analysis must rely on non-deterministic design principles. One such principle is Random Walker, which is based on a virtual entity and selects either edges or, like in this case, vertices of a fuzzy graph to visit. This allows the estimation of global graph properties through a long sequence of local decisions, making it a viable strategy candidate for graph processing software relying on native graph databases such as Neo4j. As a concrete example, Chebyshev Walktrap, a heuristic fuzzy community discovery algorithm relying on second order statistics and on the teleportation of the Random Walker, is proposed and its performance, expressed in terms of community coherence and number of vertex visits, is compared to the previously proposed algorithms of Markov Walktrap, Fuzzy Walktrap, and Fuzzy Newman–Girvan. In order to facilitate this comparison, a metric based on the asymmetric metrics of Tversky index and Kullback–Leibler divergence is used.
Spherically symmetric solutions of general second-order gravity
Whitt, B.
1988-01-01
The general second-order gravity theory, whose Lagrangian includes higher powers of the curvature, is considered in arbitrary dimensions. It is shown that spherically symmetric solutions are static, except in certain, special, unphysical cases. Spherically symmetric solutions are found and classified. Each theory's solutions fall into a number of distinct branches, which may represent finite space with two singular boundaries, or an asymptotically either flat or (anti--)de Sitter space with one singular boundary. A theory may contain at most one branch of solutions in which all singularities are hidden by event horizons. Such horizons generally emit Hawking radiation, though in certain cases the horizon may have zero temperature. Black holes do not necessarily radiate away all their mass: they may terminate in a zero-temperature black hole, a naked singularity, or a hot black hole in equilibrium with a ''cosmological'' event horizon. The thermodynamics of black-hole solutions is discussed; entropy is found to be an increasing function of horizon area, and the first law is shown to hold
Second-Order Nonlinear Optical Dendrimers and Dendronized Hyperbranched Polymers.
Tang, Runli; Li, Zhen
2017-01-01
Second-order nonlinear optical (NLO) dendrimers with a special topological structure were regarded as the most promising candidates for practical applications in the field of optoelectronic materials. Dendronized hyperbranched polymers (DHPs), a new type of polymers with dendritic structures, proposed and named by us recently, demonstrated interesting properties and some advantages over other polymers. Some of our work concerning these two types of polymers are presented herein, especially focusing on the design idea and structure-property relationship. To enhance their comprehensive NLO performance, dendrimers were designed and synthesized by adjusting their isolation mode, increasing the number of the dendritic generation, modifying their topological structure, introducing isolation chromophores, and utilizing the Ar-Ar F self-assembly effect. To make full use of the advantages of both the structural integrity of dendrimers and the convenient one-pot synthesis of hyperbranched polymers, DHPs were explored by utilizing low-generation dendrons as big monomers to construct hyperbranched polymers. These selected works could provide valuable information to deeply understand the relationship between the structure and properties of functional polymers with dendritic structures, but not only limited to the NLO ones, and might contribute much to the further development of functional polymers with rational design. © 2017 The Chemical Society of Japan & Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
SOME PROPERTIES OF HORN TYPE SECOND ORDER DOUBLE HYPERGEOMETRIC SERIES
Anvar Hasanov
2018-04-01
Full Text Available Horn [1931, Hypergeometrische Funktionen zweier Veranderlichen, Math. Ann.,105(1, 381-407], (corrections in Borngasser [1933, Uber hypergeometrische funkionen zweier Veranderlichen, Dissertation, Darmstadt], defined and investigated ten second order hypergeometric series of two variables. In the course of further investigation of Horn’s series, we noticed the existence of hypergeometric double series H*2 analogous to Horn’s double series H*2. The principal object of this paper is to present a natural further step toward the mathematical properties and presentations concerning the analogous hypergeometric double series H*2 Indeed, motivated by the important role of the Horn’s functions in several diverse fields of physics and the contributions toward the unification and generalization of the hyper-geometric functions, we establish a system of partial differential equations, integral representations, expansions, analytic continuation, transformation formulas and generating relations. Also, we discuss the links for the various results, which are presented in this paper, with known results.
Correction of the second-order degree of coherence measurement
Congcong Li; Xiangdong Chen; Shen Li; Fangwen Sun
2016-01-01
The measurement of the second-order degree of coherence [g(2)(τ)] is one of the important methods used to study the dynamical evolution of photon-matter interaction systems.Here,we use a nitrogen-vacancy center in a diamond to compare the measurement of g(2)(τ) with two methods.One is the prototype measurement process with a tunable delay.The other is a start-stop process based on the time-to-amplitude conversion (TAC) and multichannel analyzer (MCA) system,which is usually applied to achieve efficient measurements.The divergence in the measurement results is observed when the delay time is comparable with the mean interval time between two neighboring detected photons.Moreover,a correction function is presented to correct the results from the TAC-MCA system to the genuine g(2)(τ).Such a correction method will provide a way to study the dynamics in photonic systems for quantum information techniques.
Lagrangian generic second order traffic flow models for node
Asma Khelifi
2018-02-01
Full Text Available This study sheds light on higher order macroscopic traffic flow modeling on road networks, thanks to the generic second order models (GSOM family which embeds a myriad of traffic models. It has been demonstrated that such higher order models are easily solved in Lagrangian coordinates which are compatible with both microscopic and macroscopic descriptions. The generalized GSOM model is reformulated in the Lagrangian coordinate system to develop a more efficient numerical method. The difficulty in applying this approach on networks basically resides in dealing with node dynamics. Traffic flow characteristics at node are different from that on homogeneous links. Different geometry features can lead to different critical research issues. For instance, discontinuity in traffic stream can be an important issue for traffic signal operations, while capacity drop may be crucial for lane-merges. The current paper aims to establish and analyze a new adapted node model for macroscopic traffic flow models by applying upstream and downstream boundary conditions on the Lagrangian coordinates in order to perform simulations on networks of roads, and accompanying numerical method. The internal node dynamics between upstream and downstream links are taken into account of the node model. Therefore, a numerical example is provided to underscore the efficiency of this approach. Simulations show that the discretized node model yields accurate results. Additional kinematic waves and contact discontinuities are induced by the variation of the driver attribute.
Pradeep, R Gladwin; Chandrasekar, V K; Senthilvelan, M; Lakshmanan, M
2011-01-01
In this paper, we devise a systematic procedure to obtain nonlocal symmetries of a class of scalar nonlinear ordinary differential equations (ODEs) of arbitrary order related to linear ODEs through nonlocal relations. The procedure makes use of the Lie point symmetries of the linear ODEs and the nonlocal connection to deduce the nonlocal symmetries of the corresponding nonlinear ODEs. Using these nonlocal symmetries, we obtain reduction transformations and reduced equations to specific examples. We find that the reduced equations can be explicitly integrated to deduce the general solutions for these cases. We also extend this procedure to coupled higher order nonlinear ODEs with specific reference to second-order nonlinear ODEs. (paper)
Nonparametric Second-Order Theory of Error Propagation on Motion Groups.
Wang, Yunfeng; Chirikjian, Gregory S
2008-01-01
Error propagation on the Euclidean motion group arises in a number of areas such as in dead reckoning errors in mobile robot navigation and joint errors that accumulate from the base to the distal end of kinematic chains such as manipulators and biological macromolecules. We address error propagation in rigid-body poses in a coordinate-free way. In this paper we show how errors propagated by convolution on the Euclidean motion group, SE(3), can be approximated to second order using the theory of Lie algebras and Lie groups. We then show how errors that are small (but not so small that linearization is valid) can be propagated by a recursive formula derived here. This formula takes into account errors to second-order, whereas prior efforts only considered the first-order case. Our formulation is nonparametric in the sense that it will work for probability density functions of any form (not only Gaussians). Numerical tests demonstrate the accuracy of this second-order theory in the context of a manipulator arm and a flexible needle with bevel tip.
Second-Order Systems of ODEs Admitting Three-Dimensional Lie Algebras and Integrability
Muhammad Ayub
2013-01-01
the case of k≥3. We discuss the singular invariant representations of canonical forms for systems of two second-order ODEs admitting three-dimensional Lie algebras. Furthermore, we give an integration procedure for canonical forms for systems of two second-order ODEs admitting three-dimensional Lie algebras which comprises of two approaches, namely, division into four types I, II, III, and IV and that of integrability of the invariant representations. We prove that if a system of two second-order ODEs has a three-dimensional solvable Lie algebra, then, its general solution can be obtained from a partially linear, partially coupled or reduced invariantly represented system of equations. A natural extension of this result is provided for a system of two kth-order (k≥3 ODEs. We present illustrative examples of familiar integrable physical systems which admit three-dimensional Lie algebras such as the classical Kepler problem and the generalized Ermakov systems that give rise to closed trajectories.
Hunt, L. R.; Villarreal, Ramiro
1987-01-01
System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differentail equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralleled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation.
Normal-mode-based analysis of electron plasma waves with second-order Hermitian formalism
Ramos, J. J.; White, R. L.
2018-03-01
The classic problem of the dynamic evolution and Landau damping of linear Langmuir electron waves in a collisionless plasma with Maxwellian background is cast as a second-order, self-adjoint problem with a continuum spectrum of real and positive squared frequencies. The corresponding complete basis of singular normal modes is obtained, along with their orthogonality relation. This yields easily the general expression of the time-reversal-invariant solution for any initial-value problem. Examples are given for specific initial conditions that illustrate different behaviors of the Landau-damped macroscopic moments of the perturbations.
Iterative oscillation results for second-order differential equations with advanced argument
Irena Jadlovska
2017-07-01
Full Text Available This article concerns the oscillation of solutions to a linear second-order differential equation with advanced argument. Sufficient oscillation conditions involving limit inferior are given which essentially improve known results. We base our technique on the iterative construction of solution estimates and some of the recent ideas developed for first-order advanced differential equations. We demonstrate the advantage of our results on Euler-type advanced equation. Using MATLAB software, a comparison of the effectiveness of newly obtained criteria as well as the necessary iteration length in particular cases are discussed.
Introduction to ordinary differential equations
Rabenstein, Albert L
1966-01-01
Introduction to Ordinary Differential Equations is a 12-chapter text that describes useful elementary methods of finding solutions using ordinary differential equations. This book starts with an introduction to the properties and complex variable of linear differential equations. Considerable chapters covered topics that are of particular interest in applications, including Laplace transforms, eigenvalue problems, special functions, Fourier series, and boundary-value problems of mathematical physics. Other chapters are devoted to some topics that are not directly concerned with finding solutio
Wubshet Ibrahim
Full Text Available This article presents the effect of thermal radiation on magnetohydrodynamic flow of tangent hyperbolic fluid with nanoparticle past an enlarging sheet with second order slip and convective boundary condition. Condition of zero normal flux of nanoparticles at the wall is used for the concentration boundary condition, which is the current topic that have yet to be studied extensively. The solution for the velocity, temperature and nanoparticle concentration is governed by parameters viz. power-law index (n, Weissenberg number We, Biot number Bi, Prandtl number Pr, velocity slip parameters δ and γ, Lewis number Le, Brownian motion parameter Nb and the thermophoresis parameter Nt. Similarity transformation is used to metamorphosed the governing non-linear boundary-value problem into coupled higher order non-linear ordinary differential equation. The succeeding equations were numerically solved using the function bvp4c from the matlab for different values of emerging parameters. Numerical results are deliberated through graphs and tables for velocity, temperature, concentration, the skin friction coefficient and local Nusselt number. The results designate that the skin friction coefficient Cf deplete as the values of Weissenberg number We, slip parameters γ and δ upturn and it rises as the values of power-law index n increase. The local Nusselt number -θ′(0 decreases as slip parameters γ and δ, radiation parameter Nr, Weissenberg number We, thermophoresis parameter Nt and power-law index n increase. However, the local Nusselt number increases as the Biot number Bi increase. Keywords: Tangent hyperbolic fluid, Second order slip flow, MHD, Convective boundary condition, Radiation effect, Passive control of nanoparticles
Roof planes detection via a second-order variational model
Benciolini, Battista; Ruggiero, Valeria; Vitti, Alfonso; Zanetti, Massimo
2018-04-01
The paper describes a unified automatic procedure for the detection of roof planes in gridded height data. The procedure exploits the Blake-Zisserman (BZ) model for segmentation in both 2D and 1D, and aims to detect, to model and to label roof planes. The BZ model relies on the minimization of a functional that depends on first- and second-order derivatives, free discontinuities and free gradient discontinuities. During the minimization, the relative strength of each competitor is controlled by a set of weight parameters. By finding the minimum of the approximated BZ functional, one obtains: (1) an approximation of the data that is smoothed solely within regions of homogeneous gradient, and (2) an explicit detection of the discontinuities and gradient discontinuities of the approximation. Firstly, input data is segmented using the 2D BZ. The maps of data and gradient discontinuities are used to isolate building candidates and planar patches (i.e. regions with homogeneous gradient) that correspond to roof planes. Connected regions that can not be considered as buildings are filtered according to both patch dimension and distribution of the directions of the normals to the boundary. The 1D BZ model is applied to the curvilinear coordinates of boundary points of building candidates in order to reduce the effect of data granularity when the normals are evaluated. In particular, corners are preserved and can be detected by means of gradient discontinuity. Lastly, a total least squares model is applied to estimate the parameters of the plane that best fits the points of each planar patch (orthogonal regression with planar model). Refinement of planar patches is performed by assigning those points that are close to the boundaries to the planar patch for which a given proximity measure assumes the smallest value. The proximity measure is defined to account for the variance of a fitting plane and a weighted distance of a point from the plane. The effectiveness of the
Second order effects in adjustment processes of cross sections
Silva, F.C. da; D'Angelo, A.; Gandini, A.; Rado, V.
1982-01-01
An iterative processe, that take in account the non linear effects of some integral quantities in relation to cross sections, is used to execute an adjustment of cross sections of some elements that constitute the fast reactors shielding. (E.G.) [pt
Individual differences in first- and second-order temporal judgment.
Corcoran, Andrew W; Groot, Christopher; Bruno, Aurelio; Johnston, Alan; Cropper, Simon J
2018-01-01
The ability of subjects to identify and reproduce brief temporal intervals is influenced by many factors whether they be stimulus-based, task-based or subject-based. The current study examines the role individual differences play in subsecond and suprasecond timing judgments, using the schizoptypy personality scale as a test-case approach for quantifying a broad range of individual differences. In two experiments, 129 (Experiment 1) and 141 (Experiment 2) subjects completed the O-LIFE personality questionnaire prior to performing a modified temporal-bisection task. In the bisection task, subjects responded to two identical instantiations of a luminance grating presented in a 4deg window, 4deg above fixation for 1.5 s (Experiment 1) or 3 s (Experiment 2). Subjects initiated presentation with a button-press, and released the button when they considered the stimulus to be half-way through (750/1500 ms). Subjects were then asked to indicate their 'most accurate estimate' of the two intervals. In this way we measure both performance on the task (a first-order measure) and the subjects' knowledge of their performance (a second-order measure). In Experiment 1 the effect of grating-drift and feedback on performance was also examined. Experiment 2 focused on the static/no-feedback condition. For the group data, Experiment 1 showed a significant effect of presentation order in the baseline condition (no feedback), which disappeared when feedback was provided. Moving the stimulus had no effect on perceived duration. Experiment 2 showed no effect of stimulus presentation order. This elimination of the subsecond order-effect was at the expense of accuracy, as the mid-point of the suprasecond interval was generally underestimated. Response precision increased as a proportion of total duration, reducing the variance below that predicted by Weber's law. This result is consistent with a breakdown of the scalar properties of time perception in the early suprasecond range. All
Efficient education policy: A second-order elasticity rule
Richter, Wolfram F.
2010-01-01
Assuming a two-period model with endogenous choices of labour, education, and saving, efficient education policy is characterized for a Ramsey-like scenario in which the government is constrained to use linear instruments. It is shown that education should be effectively subsidized if, and only if, the elasticity of the earnings function is increasing in education. The strength of second-best subsidization increases in the elasticity of the elasticity of the earnings function. This second-ord...
Second-order wave diffraction by a circular cylinder using scaled boundary finite element method
Song, H; Tao, L
2010-01-01
The scaled boundary finite element method (SBFEM) has achieved remarkable success in structural mechanics and fluid mechanics, combing the advantage of both FEM and BEM. Most of the previous works focus on linear problems, in which superposition principle is applicable. However, many physical problems in the real world are nonlinear and are described by nonlinear equations, challenging the application of the existing SBFEM model. A popular idea to solve a nonlinear problem is decomposing the nonlinear equation to a number of linear equations, and then solves them individually. In this paper, second-order wave diffraction by a circular cylinder is solved by SBFEM. By splitting the forcing term into two parts, the physical problem is described as two second-order boundary-value problems with different asymptotic behaviour at infinity. Expressing the velocity potentials as a series of depth-eigenfunctions, both of the 3D boundary-value problems are decomposed to a number of 2D boundary-value sub-problems, which are solved semi-analytically by SBFEM. Only the cylinder boundary is discretised with 1D curved finite-elements on the circumference of the cylinder, while the radial differential equation is solved completely analytically. The method can be extended to solve more complex wave-structure interaction problems resulting in direct engineering applications.
First and second order operator splitting methods for the phase field crystal equation
Lee, Hyun Geun; Shin, Jaemin; Lee, June-Yub
2015-01-01
In this paper, we present operator splitting methods for solving the phase field crystal equation which is a model for the microstructural evolution of two-phase systems on atomic length and diffusive time scales. A core idea of the methods is to decompose the original equation into linear and nonlinear subequations, in which the linear subequation has a closed-form solution in the Fourier space. We apply a nonlinear Newton-type iterative method to solve the nonlinear subequation at the implicit time level and thus a considerably large time step can be used. By combining these subequations, we achieve the first- and second-order accuracy in time. We present numerical experiments to show the accuracy and efficiency of the proposed methods
Construction of a Smooth Lyapunov Function for the Robust and Exact Second-Order Differentiator
Tonametl Sanchez
2016-01-01
Full Text Available Differentiators play an important role in (continuous feedback control systems. In particular, the robust and exact second-order differentiator has shown some very interesting properties and it has been used successfully in sliding mode control, in spite of the lack of a Lyapunov based procedure to design its gains. As contribution of this paper, we provide a constructive method to determine a differentiable Lyapunov function for such a differentiator. Moreover, the Lyapunov function is used to provide a procedure to design the differentiator’s parameters. Also, some sets of such parameters are provided. The determination of the positive definiteness of the Lyapunov function and negative definiteness of its derivative is converted to the problem of solving a system of inequalities linear in the parameters of the Lyapunov function candidate and also linear in the gains of the differentiator, but bilinear in both.
Relaxation approximations to second-order traffic flow models by high-resolution schemes
Nikolos, I.K.; Delis, A.I.; Papageorgiou, M.
2015-01-01
A relaxation-type approximation of second-order non-equilibrium traffic models, written in conservation or balance law form, is considered. Using the relaxation approximation, the nonlinear equations are transformed to a semi-linear diagonilizable problem with linear characteristic variables and stiff source terms with the attractive feature that neither Riemann solvers nor characteristic decompositions are in need. In particular, it is only necessary to provide the flux and source term functions and an estimate of the characteristic speeds. To discretize the resulting relaxation system, high-resolution reconstructions in space are considered. Emphasis is given on a fifth-order WENO scheme and its performance. The computations reported demonstrate the simplicity and versatility of relaxation schemes as numerical solvers
Diem Dang Huan
2015-12-01
Full Text Available The current paper is concerned with the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a new set of sufficient conditions for the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps. Finally, an application to the stochastic nonlinear wave equation with infinite delay and Poisson jumps is given.
Theory of second order tide forces and gravitational wave experiment
Tammelo, R.R.
1989-01-01
Theory of tide forces square by vector radius is presented. The mechanism of 10 18 time gravitational wave pressure increase in case of radiation from pulsars and 10 15 time one in case of standard burst of radiation from astrophysical catastrophe is proposed. This leads to secular shifts of longitudinally free receivers by 10 -16 cm during 10 5 s in the first case and by 10 -19 cm during 10 s in the second one. A possibility of increase effect modulation is available. It is indicated that it is possible to construct a device which produces more energy at the expense of square tide forces than at the expense of linear ones. 21 refs
RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems
Farrell, Patricio
2013-01-01
In this paper, we discuss multiscale radial basis function collocation methods for solving elliptic partial differential equations on bounded domains. The approximate solution is constructed in a multilevel fashion, each level using compactly supported radial basis functions of smaller scale on an increasingly fine mesh. On each level, standard symmetric collocation is employed. A convergence theory is given, which builds on recent theoretical advances for multiscale approximation using compactly supported radial basis functions. We are able to show that the convergence is linear in the number of levels. We also discuss the condition numbers of the arising systems and the effect of simple, diagonal preconditioners, now proving rigorously previous numerical observations. © 2013 Society for Industrial and Applied Mathematics.
Pereyra, Brandon; Wendt, Fabian; Robertson, Amy; Jonkman, Jason
2017-03-09
The hydrodynamic loads on an offshore wind turbine's support structure present unique engineering challenges for offshore wind. Two typical approaches used for modeling these hydrodynamic loads are potential flow (PF) and strip theory (ST), the latter via Morison's equation. This study examines the first- and second-order wave-excitation surge forces on a fixed cylinder in regular waves computed by the PF and ST approaches to (1) verify their numerical implementations in HydroDyn and (2) understand when the ST approach breaks down. The numerical implementation of PF and ST in HydroDyn, a hydrodynamic time-domain solver implemented as a module in the FAST wind turbine engineering tool, was verified by showing the consistency in the first- and second-order force output between the two methods across a range of wave frequencies. ST is known to be invalid at high frequencies, and this study investigates where the ST solution diverges from the PF solution. Regular waves across a range of frequencies were run in HydroDyn for a monopile substructure. As expected, the solutions for the first-order (linear) wave-excitation loads resulting from these regular waves are similar for PF and ST when the diameter of the cylinder is small compared to the length of the waves (generally when the diameter-to-wavelength ratio is less than 0.2). The same finding applies to the solutions for second-order wave-excitation loads, but for much smaller diameter-to-wavelength ratios (based on wavelengths of first-order waves).
A second order anti-diffusive Lagrange-remap scheme for two-component flows
Lagoutière Frédéric
2011-11-01
Full Text Available We build a non-dissipative second order algorithm for the approximate resolution of the one-dimensional Euler system of compressible gas dynamics with two components. The considered model was proposed in [1]. The algorithm is based on [8] which deals with a non-dissipative first order resolution in Lagrange-remap formalism. In the present paper we describe, in the same framework, an algorithm that is second order accurate in time and space, and that preserves sharp interfaces. Numerical results reported at the end of the paper are very encouraging, showing the interest of the second order accuracy for genuinely non-linear waves. Nous construisons un algorithme d’ordre deux et non dissipatif pour la résolution approchée des équations d’Euler de la dynamique des gaz compressibles à deux constituants en dimension un. Le modèle que nous considérons est celui à cinq équations proposé et analysé dans [1]. L’algorithme est basé sur [8] qui proposait une résolution approchée à l’ordre un et non dissipative au moyen d’un splitting de type Lagrange-projection. Dans le présent article, nous décrivons, dans le même formalisme, un algorithme d’ordre deux en temps et en espace, qui préserve des interfaces « parfaites » entre les constituants. Les résultats numériques rapportés à la fin de l’article sont très encourageants ; ils montrent clairement les avantages d’un schéma d’ordre deux pour les ondes vraiment non linéaires.
A porous flow model of flank eruptions on Mt. Etna: second-order perturbation theory
N. Cenni
1997-06-01
Full Text Available A porous flow model for magma migration from a deep source within a volcanic edifice is developed. The model is based on the assumption that an isotropic and homogeneous system of fractures allows magma migration from one localized feeding dyke up to the surface of the volcano. The maximum level that magma can reach within the volcano (i.e., the «free surface» of magma, where fluid pressure equals the atmospheric pressure is reproduced through a second-order perturbation approach to the non-linear equations governing the migration of incompressible fluids through a porous medium. The perturbation parameter is found to depend on the ratio of the volumic discharge rate at the source (m3/s divided by the product of the hydraulic conductivity of the medium (m1/s times the square of the source depth. The second-order corrections for the free surface of Mt. Etna are found to be small but not negligible; from the comparison between first-order and second-order free surfaces it appears that the former is higher near the summit, slightly lower at intermediate altitudes and slightly higher far away from the axis of the volcano. Flank eruptions in the southern sector are found to be located in regions where the topography is actually lower than the theoretical free surface of magma. In this sector, modulations in the eruption site density correlate well with even minor differences between free surface and topography. In the northern and western sectors similar good fits are found, while the NE rift and the eastern sector seem to require mechanisms or structures respectively favouring and inhibiting magma migration.
Steinmann, Paul
2015-01-01
This book illustrates the deep roots of the geometrically nonlinear kinematics of generalized continuum mechanics in differential geometry. Besides applications to first- order elasticity and elasto-plasticity an appreciation thereof is particularly illuminating for generalized models of continuum mechanics such as second-order (gradient-type) elasticity and elasto-plasticity. After a motivation that arises from considering geometrically linear first- and second- order crystal plasticity in Part I several concepts from differential geometry, relevant for what follows, such as connection, parallel transport, torsion, curvature, and metric for holonomic and anholonomic coordinate transformations are reiterated in Part II. Then, in Part III, the kinematics of geometrically nonlinear continuum mechanics are considered. There various concepts of differential geometry, in particular aspects related to compatibility, are generically applied to the kinematics of first- and second- order geometrically nonlinear con...
Larciprete, M.C.; Passeri, D.; Michelotti, F.; Paoloni, S.; Sibilia, C.; Bertolotti, M.; Belardini, A.; Sarto, F.; Somma, F.; Lo Mastro, S.
2005-01-01
We investigated second order optical nonlinearity of zinc oxide thin films, grown on glass substrates by the dual ion beam sputtering technique under different deposition conditions. Linear optical characterization of the films was carried out by spectrophotometric optical transmittance and reflectance measurements, giving the complex refractive index dispersion. Resistivity of the films was determined using the four-point probe sheet resistance method. Second harmonic generation measurements were performed by means of the Maker fringes technique where the fundamental beam was originated by nanosecond laser at λ=1064 nm. We found a relatively high nonlinear optical response, and evidence of a dependence of the nonlinear coefficient on the deposition parameters for each sample. Moreover, the crystalline properties of the films were investigated by x-ray diffraction measurements and correlation with second order nonlinearity were analyzed. Finally, we investigated the influence of the oxygen flow rate during the deposition process on both the second order nonlinearity and the structural properties of the samples
Second-order sliding mode controller with model reference adaptation for automatic train operation
Ganesan, M.; Ezhilarasi, D.; Benni, Jijo
2017-11-01
In this paper, a new approach to model reference based adaptive second-order sliding mode control together with adaptive state feedback is presented to control the longitudinal dynamic motion of a high speed train for automatic train operation with the objective of minimal jerk travel by the passengers. The nonlinear dynamic model for the longitudinal motion of the train comprises of a locomotive and coach subsystems is constructed using multiple point-mass model by considering the forces acting on the vehicle. An adaptation scheme using Lyapunov criterion is derived to tune the controller gains by considering a linear, stable reference model that ensures the stability of the system in closed loop. The effectiveness of the controller tracking performance is tested under uncertain passenger load, coupler-draft gear parameters, propulsion resistance coefficients variations and environmental disturbances due to side wind and wet rail conditions. The results demonstrate improved tracking performance of the proposed control scheme with a least jerk under maximum parameter uncertainties when compared to constant gain second-order sliding mode control.
A second order penalized direct forcing for hybrid Cartesian/immersed boundary flow simulations
Introini, C.; Belliard, M.; Fournier, C.
2014-01-01
In this paper, we propose a second order penalized direct forcing method to deal with fluid-structure interaction problems involving complex static or time-varying geometries. As this work constitutes a first step toward more complicated problems, our developments are restricted to Dirichlet boundary condition in purely hydraulic context. The proposed method belongs to the class of immersed boundary techniques and consists in immersing the physical domain in a Cartesian fictitious one of simpler geometry on fixed grids. A penalized forcing term is added to the momentum equation to take the boundary conditions around/inside the obstacles into account. This approach avoids the tedious task of re-meshing and allows us to use fast and accurate numerical schemes. In contrary, as the immersed boundary is described by a set of Lagrangian points that does not generally coincide with those of the Eulerian grid, numerical procedures are required to reconstruct the velocity field near the immersed boundary. Here, we develop a second order linear interpolation scheme and we compare it to a simpler model of order one. As far as the governing equations are concerned, we use a particular fractional-step method in which the penalized forcing term is distributed both in prediction and correction equations. The accuracy of the proposed method is assessed through 2-D numerical experiments involving static and rotating solids. We show in particular that the numerical rate of convergence of our method is quasi-quadratic. (authors)
Linearization: Geometric, Complex, and Conditional
Asghar Qadir
2012-01-01
Full Text Available Lie symmetry analysis provides a systematic method of obtaining exact solutions of nonlinear (systems of differential equations, whether partial or ordinary. Of special interest is the procedure that Lie developed to transform scalar nonlinear second-order ordinary differential equations to linear form. Not much work was done in this direction to start with, but recently there have been various developments. Here, first the original work of Lie (and the early developments on it, and then more recent developments based on geometry and complex analysis, apart from Lie’s own method of algebra (namely, Lie group theory, are reviewed. It is relevant to mention that much of the work is not linearization but uses the base of linearization.
Xuewen Mu
2015-01-01
quadratic programming over second-order cones and a bounded set. At each iteration, we only need to compute the metric projection onto the second-order cones and the projection onto the bound set. The result of convergence is given. Numerical results demonstrate that our method is efficient for the convex quadratic second-order cone programming problems with bounded constraints.
Second-Order Conformally Equivariant Quantization in Dimension 1|2
Najla Mellouli
2009-12-01
Full Text Available This paper is the next step of an ambitious program to develop conformally equivariant quantization on supermanifolds. This problem was considered so far in (superdimensions 1 and 1|1. We will show that the case of several odd variables is much more difficult. We consider the supercircle S^{1|2} equipped with the standard contact structure. The conformal Lie superalgebra K(2 of contact vector fields on S^{1|2} contains the Lie superalgebra osp(2|2. We study the spaces of linear differential operators on the spaces of weighted densities as modules over osp(2|2. We prove that, in the non-resonant case, the spaces of second order differential operators are isomorphic to the corresponding spaces of symbols as osp(2|2-modules. We also prove that the conformal equivariant quantization map is unique and calculate its explicit formula.
A Separation Algorithm for Sources with Temporal Structure Only Using Second-order Statistics
J.G. Wang
2013-09-01
Full Text Available Unlike conventional blind source separation (BSS deals with independent identically distributed (i.i.d. sources, this paper addresses the separation from mixtures of sources with temporal structure, such as linear autocorrelations. Many sequential extraction algorithms have been reported, resulting in inevitable cumulated errors introduced by the deflation scheme. We propose a robust separation algorithm to recover original sources simultaneously, through a joint diagonalizer of several average delayed covariance matrices at positions of the optimal time delay and its integers. The proposed algorithm is computationally simple and efficient, since it is based on the second-order statistics only. Extensive simulation results confirm the validity and high performance of the algorithm. Compared with related extraction algorithms, its separation signal-to-noise rate for a desired source can reach 20dB higher, and it seems rather insensitive to the estimation error of the time delay.
An optimal PID controller via LQR for standard second order plus time delay systems.
Srivastava, Saurabh; Misra, Anuraag; Thakur, S K; Pandit, V S
2016-01-01
An improved tuning methodology of PID controller for standard second order plus time delay systems (SOPTD) is developed using the approach of Linear Quadratic Regulator (LQR) and pole placement technique to obtain the desired performance measures. The pole placement method together with LQR is ingeniously used for SOPTD systems where the time delay part is handled in the controller output equation instead of characteristic equation. The effectiveness of the proposed methodology has been demonstrated via simulation of stable open loop oscillatory, over damped, critical damped and unstable open loop systems. Results show improved closed loop time response over the existing LQR based PI/PID tuning methods with less control effort. The effect of non-dominant pole on the stability and robustness of the controller has also been discussed. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.
Sound dispersion in a spin-1 Ising system near the second-order phase transition point
Erdem, Ryza; Keskin, Mustafa
2003-01-01
Sound dispersion relation is derived for a spin-1 Ising system and its behaviour near the second-order phase transition point or the critical point is analyzed. The method used is a combination of molecular field approximation and Onsager theory of irreversible thermodynamics. If we assume a linear coupling of sound wave with the order parameter fluctuations in the system, we find that the dispersion which is the relative sound velocity change with frequency behaves as ω 0 ε 0 , where ω is the sound frequency and ε the temperature distance from the critical point. In the ordered region, one also observes a frequency-dependent velocity or dispersion minimum which is shifted from the corresponding attenuation maxima. These phenomena are in good agreement with the calculations of sound velocity in other magnetic systems such as magnetic metals, magnetic insulators, and magnetic semiconductors
Dimal A. Shah
2017-02-01
Full Text Available A simple and accurate method for the analysis of ibuprofen (IBU and famotidine (FAM in their combined dosage form was developed using second order derivative spectrophotometery. IBU and FAM were quantified using second derivative responses at 272.8 nm and 290 nm in the spectra of their solutions in methanol. The calibration curves were linear in the concentration range of 100–600 μg/mL for IBU and 5–25 μg/mL for FAM. The method was validated and found to be accurate and precise. Developed method was successfully applied for the estimation of IBU and FAM in their combined dosage form.
Second-order optical effects in several pyrazolo-quinoline derivatives
Makowska-Janusik, M. [Solid State Department, Institute of Physics, WSP Czestochowa, Al. Armii Krajowej 13/15, Czestochowa PL42201 (Poland); Gondek, E. [Institute of Physics, Cracow University of Technology, ul. Podchorazych 1, 30-084 (Poland); Kityk, I.V. [Department of Biology and Biophysics, Technical University of Czestochowa, Al. Armii Krajowej 36, Czestochowa PL-42210 (Poland)]. E-mail: i.kityk@wsp.czest.pl; WisIa, J. [Departament of Chemistry, Hugon Kollataj Agricultural University, Al. Mickiewicza 24/28, 30-059 Cracow (Poland); Sanetra, J. [Institute of Physics, Cracow University of Technology, ul. Podchorazych 1, 30-084 (Poland); Danel, A. [Department of Chemistry, Hugon Kollataj Agricultural University, Al. Mickiewicza 24/28, 30-059 Cracow (Poland)
2004-11-15
Using optical poling of several pyazolo-quinoline (PAQ) derivatives we have found an existence of sufficiently high second order optical susceptibility at wavelength 1.76 {mu}m varying in the range 0.9-2.8 pm/V. The performed quantum chemical simulations of the UV-absorption for isolated, solvated and incorporated into the polymethacrylate (PMMA) polymer films have shown that the PM3 method is the best among the semi-empirical ones to simulate the optical properties. The calculations of the hyperpolarizabilites have shown a good correlation with experimentally measured susceptibilities obtained from the optical poling. We have found that experimental susceptibility depends on linear molecular polarizability and photoinducing changes of the molecular dipole moment. It is clearly seen for the PAQ4-PAQ6 molecules possessing halogen atoms with relatively large polarizabilities.
Second-order optical effects in several pyrazolo-quinoline derivatives
Makowska-Janusik, M.; Gondek, E.; Kityk, I. V.; Wisła, J.; Sanetra, J.; Danel, A.
2004-11-01
Using optical poling of several pyazolo-quinoline (PAQ) derivatives we have found an existence of sufficiently high second order optical susceptibility at wavelength 1.76 μm varying in the range 0.9-2.8 pm/V. The performed quantum chemical simulations of the UV-absorption for isolated, solvated and incorporated into the polymethacrylate (PMMA) polymer films have shown that the PM3 method is the best among the semi-empirical ones to simulate the optical properties. The calculations of the hyperpolarizabilites have shown a good correlation with experimentally measured susceptibilities obtained from the optical poling. We have found that experimental susceptibility depends on linear molecular polarizability and photoinducing changes of the molecular dipole moment. It is clearly seen for the PAQ4-PAQ6 molecules possessing halogen atoms with relatively large polarizabilities.
Second-order optical effects in several pyrazolo-quinoline derivatives
Makowska-Janusik, M.; Gondek, E.; Kityk, I.V.; WisIa, J.; Sanetra, J.; Danel, A.
2004-01-01
Using optical poling of several pyazolo-quinoline (PAQ) derivatives we have found an existence of sufficiently high second order optical susceptibility at wavelength 1.76 μm varying in the range 0.9-2.8 pm/V. The performed quantum chemical simulations of the UV-absorption for isolated, solvated and incorporated into the polymethacrylate (PMMA) polymer films have shown that the PM3 method is the best among the semi-empirical ones to simulate the optical properties. The calculations of the hyperpolarizabilites have shown a good correlation with experimentally measured susceptibilities obtained from the optical poling. We have found that experimental susceptibility depends on linear molecular polarizability and photoinducing changes of the molecular dipole moment. It is clearly seen for the PAQ4-PAQ6 molecules possessing halogen atoms with relatively large polarizabilities
Methods of Oscillation Theory of Half-Linear Second order Differential Equations
Došlý, Ondřej
2000-01-01
Roč. 125, č. 3 (2000), s. 657-671 ISSN 0011-4642 R&D Projects: GA ČR GA201/96/0410; GA ČR GA201/98/0677 Institutional research plan: CEZ:AV0Z1019905; CEZ:A05/98:Z1-019-9ii Subject RIV: BA - General Mathematics Impact factor: 0.103, year: 2000
Well-posedness of the second-order linear singular Dirichlet problem
Lomtatidze, Alexander; Opluštil, Z.
2015-01-01
Roč. 22, č. 3 (2015), s. 409-419 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : singular Dirichlet problem * well-posedness Subject RIV: BA - General Mathematics Impact factor: 0.417, year: 2015 http://www.degruyter.com/view/j/gmj.2015.22.issue-3/gmj-2015-0023/gmj-2015-0023. xml
Bruschetta, M.; Saccon, A.; Picci, G.
2014-01-01
The theory of variational integration provides a systematic procedure to discretize the equations of motion of a mechanical system, preserving key properties of the continuous time flow. The discrete-time model obtained by variational integration theory inherits structural conditions which in
SECOND-ORDER SOLUTIONS OF COSMOLOGICAL PERTURBATION IN THE MATTER-DOMINATED ERA
Hwang, Jai-chan; Noh, Hyerim; Gong, Jinn-Ouk
2012-01-01
We present the growing mode solutions of cosmological perturbations to the second order in the matter-dominated era. We also present several gauge-invariant combinations of perturbation variables to the second order in the most general fluid context. Based on these solutions, we study the Newtonian correspondence of relativistic perturbations to the second order. In addition to the previously known exact relativistic/Newtonian correspondence of density and velocity perturbations to the second order in the comoving gauge, here we show that in the sub-horizon limit we have the correspondences for density, velocity, and potential perturbations in the zero-shear gauge and in the uniform-expansion gauge to the second order. Density perturbation in the uniform-curvature gauge also shows the correspondence to the second order in the sub-horizon scale. We also identify the relativistic gravitational potential that shows exact correspondence to the Newtonian one to the second order.
M. Mallika Arjunan
2014-01-01
Full Text Available In this paper, we investigate the existence and controllability of mild solutions for a damped second order impulsive functional differential equation with state-dependent delay in Banach spaces. The results are obtained by using Sadovskii's fixed point theorem combined with the theories of a strongly continuous cosine family of bounded linear operators. Finally, an example is provided to illustrate the main results.
Structural changes of small amplitude kinetic Alfvén solitary waves due to second-order corrections
Choi, Cheong R.
2015-01-01
The structural changes of kinetic Alfvén solitary waves (KASWs) due to higher-order terms are investigated. While the first-order differential equation for KASWs provides the dispersion relation for kinetic Alfvén waves, the second-order differential equation describes the structural changes of the solitary waves due to higher-order nonlinearity. The reductive perturbation method is used to obtain the second-order and third-order partial differential equations; then, Kodama and Taniuti's technique [J. Phys. Soc. Jpn. 45, 298 (1978)] is applied in order to remove the secularities in the third-order differential equations and derive a linear second-order inhomogeneous differential equation. The solution to this new second-order equation indicates that, as the amplitude increases, the hump-type Korteweg-de Vries solution is concentrated more around the center position of the soliton and that dip-type structures form near the two edges of the soliton. This result has a close relationship with the interpretation of the complex KASW structures observed in space with satellites
Second-order Born effect in coplanar doubly symmetric (e,2e) collisions for sodium
Wang, Yang; Jiao, Liguang [Center for Theoretical Atomic and Molecular Physics, Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute of Technology, Harbin 150080 (China); Zhou, Yajun, E-mail: yajunzhou2003@yahoo.com.cn [Center for Theoretical Atomic and Molecular Physics, Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute of Technology, Harbin 150080 (China)
2012-06-18
The second-order distorted wave Born approximation (DWBA) method is employed to investigate the triple differential cross sections (TDCS) of coplanar doubly symmetric (e,2e) collisions for alkali target sodium at excess energies of 6–60 eV. Comparing with the first-order DWBA calculations, the inclusion of second-order Born term in the scattering amplitude improves the degree of agreement with experiments, especially for backward scattering region of TDCS. This indicates the present second-order Born term is capable to give a reasonable correction to DWBA model in studying coplanar symmetric (e,2e) problems in low and intermediate energy range. -- Highlights: ► We consider second-order Born effect in (e,2e) collisions for sodium. ► Our second-order term gives a correct description on the multi scattering process. ► Our second-order DWBA model improves the agreement between theory and experiment.
The contribution of second-order processes to (3He, n) calculations
Brissaud, I.
1978-01-01
The reactions 90 Zr, 116 Cd( 3 He, n) have been analysed by adding two second-order processes to the usual one-step DWBA calculations: sequential stripping or inelastic transition followed by double stripping. These second-order contributions increase the cross sections, especially for 90 Zr, and improve the shape of the angular distribution for 116 Cd. It shows that such second-order processes cannot be omitted in the analysis of two-particle stripping reactions. (author)
Barbot, Antoine; Landy, Michael S.; Carrasco, Marisa
2012-01-01
The visual system can use a rich variety of contours to segment visual scenes into distinct perceptually coherent regions. However, successfully segmenting an image is a computationally expensive process. Previously we have shown that exogenous attention—the more automatic, stimulus-driven component of spatial attention—helps extract contours by enhancing contrast sensitivity for second-order, texture-defined patterns at the attended location, while reducing sensitivity at unattended locations, relative to a neutral condition. Interestingly, the effects of exogenous attention depended on the second-order spatial frequency of the stimulus. At parafoveal locations, attention enhanced second-order contrast sensitivity to relatively high, but not to low second-order spatial frequencies. In the present study we investigated whether endogenous attention—the more voluntary, conceptually-driven component of spatial attention—affects second-order contrast sensitivity, and if so, whether its effects are similar to those of exogenous attention. To that end, we compared the effects of exogenous and endogenous attention on the sensitivity to second-order, orientation-defined, texture patterns of either high or low second-order spatial frequencies. The results show that, like exogenous attention, endogenous attention enhances second-order contrast sensitivity at the attended location and reduces it at unattended locations. However, whereas the effects of exogenous attention are a function of the second-order spatial frequency content, endogenous attention affected second-order contrast sensitivity independent of the second-order spatial frequency content. This finding supports the notion that both exogenous and endogenous attention can affect second-order contrast sensitivity, but that endogenous attention is more flexible, benefitting performance under different conditions. PMID:22895879
Barbot, Antoine; Landy, Michael S; Carrasco, Marisa
2012-08-15
The visual system can use a rich variety of contours to segment visual scenes into distinct perceptually coherent regions. However, successfully segmenting an image is a computationally expensive process. Previously we have shown that exogenous attention--the more automatic, stimulus-driven component of spatial attention--helps extract contours by enhancing contrast sensitivity for second-order, texture-defined patterns at the attended location, while reducing sensitivity at unattended locations, relative to a neutral condition. Interestingly, the effects of exogenous attention depended on the second-order spatial frequency of the stimulus. At parafoveal locations, attention enhanced second-order contrast sensitivity to relatively high, but not to low second-order spatial frequencies. In the present study we investigated whether endogenous attention-the more voluntary, conceptually-driven component of spatial attention--affects second-order contrast sensitivity, and if so, whether its effects are similar to those of exogenous attention. To that end, we compared the effects of exogenous and endogenous attention on the sensitivity to second-order, orientation-defined, texture patterns of either high or low second-order spatial frequencies. The results show that, like exogenous attention, endogenous attention enhances second-order contrast sensitivity at the attended location and reduces it at unattended locations. However, whereas the effects of exogenous attention are a function of the second-order spatial frequency content, endogenous attention affected second-order contrast sensitivity independent of the second-order spatial frequency content. This finding supports the notion that both exogenous and endogenous attention can affect second-order contrast sensitivity, but that endogenous attention is more flexible, benefitting performance under different conditions.
Snodgrass, Michael; Kalaida, Natasha; Winer, E Samuel
2009-06-01
Access can either be first-order or second-order. First order access concerns whether contents achieve representation in phenomenal consciousness at all; second-order access concerns whether phenomenally conscious contents are selected for metacognitive, higher order processing by reflective consciousness. When the optional and flexible nature of second-order access is kept in mind, there remain strong reasons to believe that exclusion failure can indeed isolate phenomenally conscious stimuli that are not so accessed. Irvine's [Irvine, E. (2009). Signal detection theory, the exclusion failure paradigm and weak consciousness-Evidence for the access/phenomenal distinction? Consciousness and Cognition.] partial access argument fails because exclusion failure is indeed due to lack of second-order access, not insufficient phenomenally conscious information. Further, the enable account conforms with both qualitative differences and subjective report, and is simpler than the endow account. Finally, although first-order access may be a distinct and important process, second-order access arguably reflects the core meaning of access generally.
The known unknowns: neural representation of second-order uncertainty, and ambiguity
Bach, Dominik R.; Hulme, Oliver; Penny, William D.; Dolan, Raymond J.
2011-01-01
Predictions provided by action-outcome probabilities entail a degree of (first-order) uncertainty. However, these probabilities themselves can be imprecise and embody second-order uncertainty. Tracking second-order uncertainty is important for optimal decision making and reinforcement learning. Previous functional magnetic resonance imaging investigations of second-order uncertainty in humans have drawn on an economic concept of ambiguity, where action-outcome associations in a gamble are either known (unambiguous) or completely unknown (ambiguous). Here, we relaxed the constraints associated with a purely categorical concept of ambiguity and varied the second-order uncertainty of gambles continuously, quantified as entropy over second-order probabilities. We show that second-order uncertainty influences decisions in a pessimistic way by biasing second-order probabilities, and that second-order uncertainty is negatively correlated with posterior cingulate cortex activity. The category of ambiguous (compared to non-ambiguous) gambles also biased choice in a similar direction, but was associated with distinct activation of a posterior parietal cortical area; an activation that we show reflects a different computational mechanism. Our findings indicate that behavioural and neural responses to second-order uncertainty are distinct from those associated with ambiguity and may call for a reappraisal of previous data. PMID:21451019
Munoz Aguirre, E. [Universidad Autonoma de Puebla, Oaxaca (Mexico); Alexandrov, V. V. [Benemerita Universidad Autonoma de Puebla, Puebla (Mexico)
2001-02-01
This paper will describe the generalized principal resonance of systems as described by the second order of ordinary differential equations and proved by the Pontriaguin maximal principle to coincide with the lengthened solution of an external problem of the same system. The results are verified in special cases of general resonance and parametric resonance for the Mathieu equation. [Spanish] En el presente articulo se estudia la resonancia principal generalizada para sistemas descritos por ecuaciones diferenciales ordinarias de segundo orden y se demuestra con ayuda del principio del maximo de Pontriaguin, la coincidencia de esta con la solucion prolongada de un problema extremal para el mismo sistema. Ademas se verifican estos resultados en los casos particulares de resonancia general y resonancia parametrica para la ecuacion de Mathieu.
Elbakry, M.Y.; El-Helly, M.; Elbakry, M.Y.
2010-01-01
Neural networks are widely for solving many scientific linear and non-linear problems. In this work ,we used the artificial neural network (ANN) to simulate and predict the torque and force acting on the outer stationary sphere due to steady state motion of the second order fluid between two eccentric spheres by a rotating inner sphere with an angular velocity Ω. the (ANN) model has been trained based on the experimental data to produce the torque and force at different eccentricities. The experimental and trained torque and force are compared. The designed ANN shows a good match to the experimental data.
Datta, D P
2003-01-01
A new class of finitely differentiable scale free solutions to the simplest class of ordinary differential equations is presented. Consequently, the real number set gets replaced by an extended physical set, each element of which is endowed with an equivalence class of infinitesimally separated neighbours in the form of random fluctuations. We show how a sense of time and evolution is intrinsically defined by the infinite continued fraction of the golden mean irrational number (Radical radicand 5 -1)/2, which plays a key role in this extended SL(2,R) formalism of calculus analogous to El Naschie's theory of E sup ( supinfinity sup ) spacetime manifold. Time may thereby undergo random inversions generating well defined random scales, thus allowing a dynamical system to evolve self similarly over the set of multiple scales. The late time stochastic fluctuations of a dynamical system enjoys the generic 1/f spectrum. A universal form of the related probability density is also derived. We prove that the golden mea...
Datta, Dhurjati Prasad
2003-01-01
A new class of finitely differentiable scale free solutions to the simplest class of ordinary differential equations is presented. Consequently, the real number set gets replaced by an extended physical set, each element of which is endowed with an equivalence class of infinitesimally separated neighbours in the form of random fluctuations. We show how a sense of time and evolution is intrinsically defined by the infinite continued fraction of the golden mean irrational number (Radical radicand 5 -1)/2, which plays a key role in this extended SL(2,R) formalism of calculus analogous to El Naschie's theory of E (∞) spacetime manifold. Time may thereby undergo random inversions generating well defined random scales, thus allowing a dynamical system to evolve self similarly over the set of multiple scales. The late time stochastic fluctuations of a dynamical system enjoys the generic 1/f spectrum. A universal form of the related probability density is also derived. We prove that the golden mean number is intrinsically random, letting all measurements in the physical universe fundamentally uncertain. The present analysis offers an explanation of the universal occurrence of the golden mean in diverse natural and biological processes as well as the mass spectrum of high energy particle physics
A Second Look at Second-Order Belief Attribution in Autism.
Tager-Flusberg, Helen; Sullivan, Kate
1994-01-01
Twelve students with autism and 12 with mental retardation, who had passed a first-order test of false belief, were given a second-order reasoning task. No intergroup performance differences were seen. Findings suggest that the difficulty for both groups with the second-order task lies in information processing demands rather than conceptual…
Optimization of an intracavity Q-switched solid-state second order Raman laser
Chen, Zhiqiong; Fu, Xihong; Peng, Hangyu; Zhang, Jun; Qin, Li; Ning, Yongqiang
2017-01-01
In this paper, the model of an intracavity Q-switched second order Raman laser is established, the characteristics of the output 2nd Stokes are simulated. The dynamic balance mechanism among intracavity conversion rates of stimulated emission, first order Raman and second order Raman is obtained. Finally, optimization solutions for increasing output 2nd Stokes pulse energy are proposed.
Investigating local network interactions underlying first- and second-order processing.
Ellemberg, Dave; Allen, Harriet A; Hess, Robert F
2004-01-01
We compared the spatial lateral interactions for first-order cues to those for second-order cues, and investigated spatial interactions between these two types of cues. We measured the apparent modulation depth of a target Gabor at fixation, in the presence and the absence of horizontally flanking Gabors. The Gabors' gratings were either added to (first-order) or multiplied with (second-order) binary 2-D noise. Apparent "contrast" or modulation depth (i.e., the perceived difference between the high and low luminance regions for the first-order stimulus, or between the high and low contrast regions for the second-order stimulus) was measured with a modulation depth-matching paradigm. For each observer, the first- and second-order Gabors were equated for apparent modulation depth without the flankers. Our results indicate that at the smallest inter-element spacing, the perceived reduction in modulation depth is significantly smaller for the second-order than for the first-order stimuli. Further, lateral interactions operate over shorter distances and the spatial frequency and orientation tuning of the suppression effect are broader for second- than first-order stimuli. Finally, first- and second-order information interact in an asymmetrical fashion; second-order flankers do not reduce the apparent modulation depth of the first-order target, whilst first-order flankers reduce the apparent modulation depth of the second-order target.
Combined First and Second Order Total Variation Inpainting using Split Bregman
Papafitsoros, Konstantinos
2013-07-12
In this article we discuss the implementation of the combined first and second order total variation inpainting that was introduced by Papafitsoros and Schdönlieb. We describe the algorithm we use (split Bregman) in detail, and we give some examples that indicate the difference between pure first and pure second order total variation inpainting.
Combined First and Second Order Total Variation Inpainting using Split Bregman
Papafitsoros, Konstantinos; Schoenlieb, Carola Bibiane; Sengul, Bati
2013-01-01
In this article we discuss the implementation of the combined first and second order total variation inpainting that was introduced by Papafitsoros and Schdönlieb. We describe the algorithm we use (split Bregman) in detail, and we give some examples that indicate the difference between pure first and pure second order total variation inpainting.
Second-order polarization-mode dispersion in photonic crystal fibers
Larsen, T; Bjarklev, Anders Overgaard; Peterson, A
2003-01-01
We report the first experimental measurements of second-order polarization-mode dispersion in two successive 900 meter pulls of a silica photonic crystal fiber.......We report the first experimental measurements of second-order polarization-mode dispersion in two successive 900 meter pulls of a silica photonic crystal fiber....
On Application of Second Order Sliding Mode Control to Electro-Hydraulic Systems
Schmidt, Lasse; Andersen, Torben Ole; Pedersen, Henrik C.
2014-01-01
This paper discusses the application of second order mode controls to hydraulic valve-cylinder drives with a special focus on the limitations resulting from nonlinear dynamic effects in flow control valves. Second order sliding mode algorithms appear highly attractive in the successive...
Optimality Conditions in Differentiable Vector Optimization via Second-Order Tangent Sets
Jimenez, Bienvenido; Novo, Vicente
2004-01-01
We provide second-order necessary and sufficient conditions for a point to be an efficient element of a set with respect to a cone in a normed space, so that there is only a small gap between necessary and sufficient conditions. To this aim, we use the common second-order tangent set and the asymptotic second-order cone utilized by Penot. As an application we establish second-order necessary conditions for a point to be a solution of a vector optimization problem with an arbitrary feasible set and a twice Frechet differentiable objective function between two normed spaces. We also establish second-order sufficient conditions when the initial space is finite-dimensional so that there is no gap with necessary conditions. Lagrange multiplier rules are also given
Electro-osmosis of nematic liquid crystals under weak anchoring and second-order surface effects
Poddar, Antarip; Dhar, Jayabrata; Chakraborty, Suman
2017-07-01
Advent of nematic liquid crystal flows has attracted renewed attention in view of microfluidic transport phenomena. Among various transport processes, electro-osmosis stands as one of the efficient flow actuation mechanisms through narrow confinements. In the present study, we explore the electrically actuated flow of an ordered nematic fluid with ionic inclusions, taking into account the influences from surface-induced elasticity and electrical double layer (EDL) phenomena. Toward this, we devise the coupled flow governing equations from fundamental free-energy analysis, considering the contributions from first- and second-order elastic, dielectric, flexoelectric, charged surface polarization, ionic and entropic energies. The present study focuses on the influence of surface charge and elasticity effects in the resulting linear electro-osmosis through a slit-type microchannel whose surfaces are chemically treated to display a homeotropic-type weak anchoring state. An optical periodic stripe configuration of the nematic director has been observed, especially for higher electric fields, wherein the Ericksen number for the dynamic study is restricted to the order of unity. Contrary to the isotropic electrolytes, the EDL potential in this case was found to be dependent on the external field strength. Through a systematic investigation, we brought out the fact that the wavelength of the oscillating patterns is dictated mainly by the external field, while the amplitude depends on most of the physical variables ranging from the anchoring strength and the flexoelectric coefficients to the surface charge density and electrical double layer thickness.
Optimal design of PID controller for second order plus time delay systems
Srivastava, S.; Misra, A.; Kumar, Y.; Thakur, S.K.
2015-01-01
It is well known that the effect of time delay in the forward path of control loop deteriorates the system performance and at the same time makes it difficult to compute the optimum PID controller parameters of the feedback control systems. PI/PID controller is most popular and used more than 80% in industries as well as in accelerators lab due to its simple structure and appropriate robustness. At VECC we have planned to use a PID controller for the speed control of DC motor which will be used to adjust the solenoid coil position of the 2.45 GHz microwave ion source for optimum performance during the online operation. In this paper we present a comparison of the two methods which have been used to design the optimum PID controller parameters: one by optimizing different time domain performance indices such as lAE, ITSE etc. and other using analytical formulation based on Linear Quadratic Regulator (LQR). We have performed numerical simulations using MATLAB and compare the closed loop time response performance measures using the PID parameters obtained from above mentioned two methods on a second order transfer function of a DC motor with time delay. (author)
Health Parameter Estimation with Second-Order Sliding Mode Observer for a Turbofan Engine
Xiaodong Chang
2017-07-01
Full Text Available In this paper the problem of health parameter estimation in an aero-engine is investigated by using an unknown input observer-based methodology, implemented by a second-order sliding mode observer (SOSMO. Unlike the conventional state estimator-based schemes, such as Kalman filters (KF and sliding mode observers (SMO, the proposed scheme uses a “reconstruction signal” to estimate health parameters modeled as artificial inputs, and is not only applicable to long-time health degradation, but reacts much quicker in handling abrupt fault cases. In view of the inevitable uncertainties in engine dynamics and modeling, a weighting matrix is created to minimize such effect on estimation by using the linear matrix inequalities (LMI. A big step toward uncertainty modeling is taken compared with our previous SMO-based work, in that uncertainties are considered in a more practical form. Moreover, to avoid chattering in sliding modes, the super-twisting algorithm (STA is employed in observer design. Various simulations are carried out, based on the comparisons between the KF-based scheme, the SMO-based scheme in our earlier research, and the proposed method. The results consistently demonstrate the capabilities and advantages of the proposed approach in health parameter estimation.
Nonadiabatic Dynamics for Electrons at Second-Order: Real-Time TDDFT and OSCF2.
Nguyen, Triet S; Parkhill, John
2015-07-14
We develop a new model to simulate nonradiative relaxation and dephasing by combining real-time Hartree-Fock and density functional theory (DFT) with our recent open-systems theory of electronic dynamics. The approach has some key advantages: it has been systematically derived and properly relaxes noninteracting electrons to a Fermi-Dirac distribution. This paper combines the new dissipation theory with an atomistic, all-electron quantum chemistry code and an atom-centered model of the thermal environment. The environment is represented nonempirically and is dependent on molecular structure in a nonlocal way. A production quality, O(N(3)) closed-shell implementation of our theory applicable to realistic molecular systems is presented, including timing information. This scaling implies that the added cost of our nonadiabatic relaxation model, time-dependent open self-consistent field at second order (OSCF2), is computationally inexpensive, relative to adiabatic propagation of real-time time-dependent Hartree-Fock (TDHF) or time-dependent density functional theory (TDDFT). Details of the implementation and numerical algorithm, including factorization and efficiency, are discussed. We demonstrate that OSCF2 approaches the stationary self-consistent field (SCF) ground state when the gap is large relative to k(b)T. The code is used to calculate linear-response spectra including the effects of bath dynamics. Finally, we show how our theory of finite-temperature relaxation can be used to correct ground-state DFT calculations.
P. A. Ermolaev
2014-03-01
Full Text Available Data processing in the interferometer systems requires high-resolution and high-speed algorithms. Recurrence algorithms based on parametric representation of signals execute consequent processing of signal samples. In some cases recurrence algorithms make it possible to increase speed and quality of data processing as compared with classic processing methods. Dependence of the measured interferometer signal on parameters of its model and stochastic nature of noise formation in the system is, in general, nonlinear. The usage of nonlinear stochastic filtering algorithms is expedient for such signals processing. Extended Kalman filter with linearization of state and output equations by the first vector parameters derivatives is an example of these algorithms. To decrease approximation error of this method the second order extended Kalman filtering is suggested with additionally usage of the second vector parameters derivatives of model equations. Examples of algorithm implementation with the different sets of estimated parameters are described. The proposed algorithm gives the possibility to increase the quality of data processing in interferometer systems in which signals are forming according to considered models. Obtained standard deviation of estimated amplitude envelope does not exceed 4% of the maximum. It is shown that signal-to-noise ratio of reconstructed signal is increased by 60%.
Prediction of stably stratified homogeneous shear flows with second-order turbulence models
Pereira, J C F; Rocha, J M P
2010-01-01
The present study investigated the role of pressure-correlation second-order turbulence modelling schemes on the predicted behaviour of stably stratified homogeneous vertical-sheared turbulence. The pressure-correlation terms were modelled with a nonlinear formulation (Craft 1991), which was compared with a linear pressure-strain model and the 'isotropization of production' model for the pressure-scalar correlation. Two additional modelling issues were investigated: the influence of the buoyancy term in the kinetic energy dissipation rate equation and the time scale in the thermal production term in the scalar variance dissipation equation. The predicted effects of increasing the Richardson number on turbulence characteristics were compared against a comprehensive set of direct numerical simulation databases. The linear models provide a broadly satisfactory description of the major effects of the Richardson number on stratified shear flow. The buoyancy term in the dissipation equation of the turbulent kinetic energy generates excessively low levels of dissipation. For moderate and large Richardson numbers, the term yields unrealistic linear oscillations in the shear and buoyancy production terms, and therefore should be dropped in this flow (or at least their coefficient c ε3 should be substantially reduced from its standard value). The mechanical dissipation time scale provides marginal improvements in comparison to the scalar time scale in the production. The observed inaccuracy of the linear model in predicting the magnitude of the effects on the velocity anisotropy was demonstrated to be attributed mainly to the defective behaviour of the pressure-correlation model, especially for stronger stratification. The turbulence closure embodying a nonlinear formulation for the pressure-correlations and specific versions of the dissipation equations failed to predict the tendency of the flow to anisotropy with increasing stratification. By isolating the effects of the
Second order bounce back boundary condition for the lattice Boltzmann fluid simulation
Kim, In Chan
2000-01-01
A new bounce back boundary method of the second order in error is proposed for the lattice Boltzmann fluid simulation. This new method can be used for the arbitrarily irregular lattice geometry of a non-slip boundary. The traditional bounce back boundary condition for the lattice Boltzmann simulation is of the first order in error. Since the lattice Boltzmann method is the second order scheme by itself, a boundary technique of the second order has been desired to replace the first order bounce back method. This study shows that, contrary to the common belief that the bounce back boundary condition is unilaterally of the first order, the second order bounce back boundary condition can be realized. This study also shows that there exists a generalized bounce back technique that can be characterized by a single interpolation parameter. The second order bounce back method can be obtained by proper selection of this parameter in accordance with the detailed lattice geometry of the boundary. For an illustrative purpose, the transient Couette and the plane Poiseuille flows are solved by the lattice Boltzmann simulation with various boundary conditions. The results show that the generalized bounce back method yields the second order behavior in the error of the solution, provided that the interpolation parameter is properly selected. Coupled with its intuitive nature and the ease of implementation, the bounce back method can be as good as any second order boundary method
Zheng, Guo; Wang, Jue; Wang, Lin; Zhou, Muchun; Xin, Yu; Song, Minmin
2017-11-15
The general formulae for second-order moments of Schell-model beams with various correlation functions in atmospheric turbulence are derived and validated by the Bessel-Gaussian Schell-model beams and cosine-Gaussian-correlated Schell-model beams. Our finding shows that the second-order moments of partially coherent Schell-model beams are related to the second-order partial derivatives of source spectral degree of coherence at the origin. The formulae we provide are much more convenient to analyze and research propagation problems in turbulence.
Consensus of second-order multi-agent dynamic systems with quantized data
Guan, Zhi-Hong, E-mail: zhguan@mail.hust.edu.cn [Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074 (China); Meng, Cheng [Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074 (China); Liao, Rui-Quan [Petroleum Engineering College,Yangtze University, Jingzhou, 420400 (China); Zhang, Ding-Xue, E-mail: zdx7773@163.com [Petroleum Engineering College,Yangtze University, Jingzhou, 420400 (China)
2012-01-09
The consensus problem of second-order multi-agent systems with quantized link is investigated in this Letter. Some conditions are derived for the quantized consensus of the second-order multi-agent systems by the stability theory. Moreover, a result characterizing the relationship between the eigenvalues of the Laplacians matrix and the quantized consensus is obtained. Examples are given to illustrate the theoretical analysis. -- Highlights: ► A second-order multi-agent model with quantized data is proposed. ► Two sufficient and necessary conditions are obtained. ► The relationship between the eigenvalues of the Laplacians matrix and the quantized consensus is discovered.
The second-order interference of two independent single-mode He-Ne lasers
Liu, Jianbin; Le, Mingnan; Bai, Bin; Wang, Wentao; Chen, Hui; Zhou, Yu; Li, Fu-li; Xu, Zhuo
2015-09-01
The second-order spatial and temporal interference patterns with two independent single-mode continuous-wave He-Ne lasers are observed when these two lasers are incident to two adjacent input ports of a 1:1 non-polarizing beam splitter, respectively. Two-photon interference based on the superposition principle in Feynman's path integral theory is employed to interpret the experimental results. The conditions to observe the second-order interference pattern with two independent single-mode continuous-wave lasers are discussed. It is concluded that frequency stability is important to observe the second-order interference pattern with two independent light beams.
Dong, B; Ding, G H; Lei, X L
2015-01-01
A general theoretical formulation for the effect of a strong on-site Coulomb interaction on the time-dependent electron transport through a quantum dot under the influence of arbitrary time-varying bias voltages and/or external fields is presented, based on slave bosons and the Keldysh nonequilibrium Green's function (GF) techniques. To avoid the difficulties of computing double-time GFs, we generalize the propagation scheme recently developed by Croy and Saalmann to combine the auxiliary-mode expansion with the celebrated Lacroix's decoupling approximation in dealing with the second-order correlated GFs and then establish a closed set of coupled equations of motion, called second-order quantum rate equations (SOQREs), for an exact description of transient dynamics of electron correlated tunneling. We verify that the stationary solution of our SOQREs is able to correctly describe the Kondo effect on a qualitative level. Moreover, a comparison with other methods, such as the second-order von Neumann approach and Hubbard-I approximation, is performed. As illustrations, we investigate the transient current behaviors in response to a step voltage pulse and a harmonic driving voltage, and linear admittance as well, in the cotunneling regime. (paper)
Closed form solution to a second order boundary value problem and its application in fluid mechanics
Eldabe, N.T.; Elghazy, E.M.; Ebaid, A.
2007-01-01
The Adomian decomposition method is used by many researchers to investigate several scientific models. In this Letter, the modified Adomian decomposition method is applied to construct a closed form solution for a second order boundary value problem with singularity
Estimates on the minimal period for periodic solutions of nonlinear second order Hamiltonian systems
Yiming Long.
1994-11-01
In this paper, we prove a sharper estimate on the minimal period for periodic solutions of autonomous second order Hamiltonian systems under precisely Rabinowitz' superquadratic condition. (author). 20 refs, 1 fig
Second-order domain derivative of normal-dependent boundary integrals
Balzer, Jonathan
2010-01-01
Numerous reconstruction tasks in (optical) surface metrology allow for a variational formulation. The occurring boundary integrals may be interpreted as shape functions. The paper is concerned with the second-order analysis of such functions. Shape
EXISTENCE OF SOLUTION TO NONLINEAR SECOND ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH DELAY
无
2010-01-01
This paper is concerned with nonlinear second order neutral stochastic differential equations with delay in a Hilbert space. Sufficient conditions for the existence of solution to the system are obtained by Picard iterations.
Accelerating distributed average consensus by exploring the information of second-order neighbors
Yuan Deming [School of Automation, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu (China); Xu Shengyuan, E-mail: syxu02@yahoo.com.c [School of Automation, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu (China); Zhao Huanyu [School of Automation, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu (China); Chu Yuming [Department of Mathematics, Huzhou Teacher' s College, Huzhou 313000, Zhejiang (China)
2010-05-17
The problem of accelerating distributed average consensus by using the information of second-order neighbors in both the discrete- and continuous-time cases is addressed in this Letter. In both two cases, when the information of second-order neighbors is used in each iteration, the network will converge with a speed faster than the algorithm only using the information of first-order neighbors. Moreover, the problem of using partial information of second-order neighbors is considered, and the edges are not chosen randomly from second-order neighbors. In the continuous-time case, the edges are chosen by solving a convex optimization problem which is formed by using the convex relaxation method. In the discrete-time case, for small network the edges are chosen optimally via the brute force method. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed algorithm.
Second order limit laws for occupation times of the fractional Brownian motion
Xu, Fangjun
2013-01-01
We prove second order limit laws for (additive) functionals of the $d$-dimensional fractional Brownian motion with Hurst index $H=\\frac{1}{d}$, using the method of moments, extending the Kallianpur-Robbins law.
A stochastic collocation method for the second order wave equation with a discontinuous random speed
Motamed, Mohammad; Nobile, Fabio; Tempone, Raul
2012-01-01
In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical
Comparison of Second-Order Loads on a Tension-Leg Platform for Wind Turbines: Preprint
Gueydon, S.; Wuillaume, P.; Jonkman, J.; Robertson, A.; Platt, A.
2015-03-01
The first objective of this work is to compare the two floating offshore wind turbine simulation packages {DIFFRAC+aNySIM} and {WAMIT+FAST}. The focus is on second-order wave loads, and so first- and second-order wave loads are applied to a structure sequentially for a detailed comparison and a more precise analysis of the effects of the second-order loads. aNySIM does not have the capability to model flexible bodies, and so the simulations performed in this tool are done assuming a rigid body. FAST also assumes that the platform is rigid, but can account for the flexibility of the tower. The second objective is to study the effects of the second-order loads on the response of a TLP floating wind turbine. The flexibility of the tower must be considered for this investigation, and therefore only FAST is used.
Dynamics of massless higher spins in the second order in curvatures
Vasiliev, M.A.
1989-08-01
The consistent equations of motion of interacting fields of all spins s=0,1/2,1...∞ are constructed explicitly to the second order of the expansion in powers of the higher spin strengths. (author). 14 refs
Dynamics of massless higher spins in the second order in curvatures
Vasiliev, M A [International Centre for Theoretical Physics, Trieste (Italy)
1990-04-05
The consistent equations of motion of interacting massless fields of all spins s=0, 1/2, 1, ..., {infinity} are constructed explicitly to the second order of the expansion in powers of the higher spin strengths. (orig.).
Second-order temporal interference of two independent light beams at an asymmetrical beam splitter
Liu Jianbin; Wang Jingjing; Xu Zhuo
2017-01-01
The second-order temporal interference of classical and nonclassical light at an asymmetrical beam splitter is discussed based on two-photon interference in Feynman’s path integral theory. The visibility of the second-order interference pattern is determined by the properties of the superposed light beams, the ratio between the intensities of these two light beams, and the reflectivity of the asymmetrical beam splitter. Some requirements about the asymmetrical beam splitter have to be satisfied in order to ensure that the visibility of the second-order interference pattern of nonclassical light beams exceeds the classical limit. The visibility of the second-order interference pattern of photons emitted by two independent single-photon sources is independent of the ratio between the intensities. These conclusions are important for the researches and applications in quantum optics and quantum information when an asymmetrical beam splitter is employed. (paper)
Aspects of second-order analysis of structured inhomogeneous spatio-temporal processes
Møller, Jesper; Ghorbani, Mohammad
2012-01-01
Statistical methodology for spatio-temporal point processes is in its infancy. We consider second-order analysis based on pair correlation functions and K-functions for general inhomogeneous spatio-temporal point processes and for inhomogeneous spatio-temporal Cox processes. Assuming spatio......-temporal separability of the intensity function, we clarify different meanings of second-order spatio-temporal separability. One is second-order spatio-temporal independence and relates to log-Gaussian Cox processes with an additive covariance structure of the underlying spatio-temporal Gaussian process. Another...... concerns shot-noise Cox processes with a separable spatio-temporal covariance density. We propose diagnostic procedures for checking hypotheses of second-order spatio-temporal separability, which we apply on simulated and real data....
Second-order analysis of structured inhomogeneous spatio-temporal point processes
Møller, Jesper; Ghorbani, Mohammad
Statistical methodology for spatio-temporal point processes is in its infancy. We consider second-order analysis based on pair correlation functions and K-functions for first general inhomogeneous spatio-temporal point processes and second inhomogeneous spatio-temporal Cox processes. Assuming...... spatio-temporal separability of the intensity function, we clarify different meanings of second-order spatio-temporal separability. One is second-order spatio-temporal independence and relates e.g. to log-Gaussian Cox processes with an additive covariance structure of the underlying spatio......-temporal Gaussian process. Another concerns shot-noise Cox processes with a separable spatio-temporal covariance density. We propose diagnostic procedures for checking hypotheses of second-order spatio-temporal separability, which we apply on simulated and real data (the UK 2001 epidemic foot and mouth disease data)....
The effect of variations in first- and second-order derivatives on airfoil aerodynamic performance
Penghui Yi
2017-01-01
Full Text Available The geometric factors which influence airfoil aerodynamic performance are attributed to variations in local first- and second-order curvature derivatives. Based on a self-developed computational fluid dynamics (CFD program called UCFD, the influence of local profile variations on airfoil aerodynamic performance in different pressure areas is investigated. The results show that variations in first- and second-order derivatives of the airfoil profiles can cause fluctuations in airfoil aerodynamic performance. The greater the variation in local first- and second-order derivatives, the greater the fluctuation amplitude of the airfoil aerodynamic coefficients. Moreover, at the area near the leading edge and the shock-wave position, the surface pressure is more sensitive to changes in first- and second-order derivatives. These results provide a reference for airfoil aerodynamic shape design.
Concordance measures and second order stochastic dominance-portfolio efficiency analysis
Kopa, Miloš; Tichý, T.
2012-01-01
Roč. 15, č. 4 (2012), s. 110-120 ISSN 1212-3609 R&D Projects: GA ČR(CZ) GBP402/12/G097 Institutional support: RVO:67985556 Keywords : dependency * concordance * portfolio selection * second order stochastic dominance Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.633, year: 2012 http://library.utia.cas.cz/separaty/2013/E/kopa-concordance measures and second order stochastic dominance- portfolio efficiency analysis.pdf
A comparative study of the second-order Born and Faddeev-Watson approximations: Pt. 3
Roberts, M.J.
1988-01-01
Singularities which arise in the second-order Born and Faddeev-Watson approximations for ionisation processes are examined. A regularisation procedure for the latter is suggested. Comparison with He(e,2e)He + experimental data in symmetric coplanar energy-sharing kinematics shows that the second-order Faddeev-Watson approximation is inferior to the second Born results of Byron et al. (1985. J. Phys. B: At. Mol. Phys. 18, 3203). (author)
Lagrange-Noether method for solving second-order differential equations
Wu Hui-Bin; Wu Run-Heng
2009-01-01
The purpose of this paper is to provide a new method called the Lagrange-Noether method for solving second-order differential equations. The method is,firstly,to write the second-order differential equations completely or partially in the form of Lagrange equations,and secondly,to obtain the integrals of the equations by using the Noether theory of the Lagrange system. An example is given to illustrate the application of the result.
Chadha, Alka; Bora, Swaroop Nandan
2017-11-01
This paper studies the existence, uniqueness, and exponential stability in mean square for the mild solution of neutral second order stochastic partial differential equations with infinite delay and Poisson jumps. By utilizing the Banach fixed point theorem, first the existence and uniqueness of the mild solution of neutral second order stochastic differential equations is established. Then, the mean square exponential stability for the mild solution of the stochastic system with Poisson jumps is obtained with the help of an established integral inequality.
Applications of the second-order achromat concept to the design of particle accelerators
Brown, K.L.; Servranckx, R.V.
1985-05-01
A property of the second-order achromat, whereby dipole and sextupole families may be inserted into a lattice for chromatic corrections without introducing second-order geometrical (on momentum) optical distortions, has been incorporated in several new particle accelerator designs. These include the SLC at SLAC, LEP at CERN, the EROS pulse stretcher ring at Saskatoon, the CEBAF ring at SURA, and the MIT ring
Second-order contributions to relativistic time delay in the parametrized post-Newtonian formalism
Richter, G.W.; Matzner, R.A.
1983-01-01
Using a parametrized expansion of the solar metric to second order in the Newtonian potential, we calculate the relativistic delay in the round-trip travel time of a radar signal reflected from a nearby planet. We find that one second-order contribution to the delay is on the order of ten nanoseconds, which is comparable to the uncertainties in present-day experiments involving the Viking spacecraft
Second-order accurate volume-of-fluid algorithms for tracking material interfaces
Pilliod, James Edward; Puckett, Elbridge Gerry
2004-01-01
We introduce two new volume-of-fluid interface reconstruction algorithms and compare the accuracy of these algorithms to four other widely used volume-of-fluid interface reconstruction algorithms. We find that when the interface is smooth (e.g., continuous with two continuous derivatives) the new methods are second-order accurate and the other algorithms are first-order accurate. We propose a design criteria for a volume-of-fluid interface reconstruction algorithm to be second-order accurate. Namely, that it reproduce lines in two space dimensions or planes in three space dimensions exactly. We also introduce a second-order, unsplit, volume-of-fluid advection algorithm that is based on a second-order, finite difference method for scalar conservation laws due to Bell, Dawson and Shubin. We test this advection algorithm by modeling several different interface shapes propagating in two simple incompressible flows and compare the results with the standard second-order, operator-split advection algorithm. Although both methods are second-order accurate when the interface is smooth, we find that the unsplit algorithm exhibits noticeably better resolution in regions where the interface has discontinuous derivatives, such as at corners
Ding Xiaohua; Su Huan; Liu Mingzhu
2008-01-01
The paper analyzes a discrete second-order, nonlinear delay differential equation with negative feedback. The characteristic equation of linear stability is solved, as a function of two parameters describing the strength of the feedback and the damping in the autonomous system. The existence of local Hopf bifurcations is investigated, and the direction and stability of periodic solutions bifurcating from the Hopf bifurcation of the discrete model are determined by the Hopf bifurcation theory of discrete system. Finally, some numerical simulations are performed to illustrate the analytical results found
Creation of second order magnetic barrier inside chaos created by NTMs in the ASDEX UG
Ali, Halima; Punjabi, Alkesh
2012-10-01
Understanding and stabilization of neoclassical tearing modes (NTM) in tokamaks is an important problem. For low temperature plasmas, tearing modes are believed to be mainly driven by current density gradient. For collisionless plasmas, even when plasma is stable to classical tearing modes, helical reduction in bootstrap current in O-point of an island can destabilize NTMs when an initial island is seeded by other global MHD instabilities or when microturbulence triggers the transition from a linear to nonlinear instability. The onset of NTMs leads to the most serious beta limit in ASDEX UG tokamak [O. Gubner et al 2005 NF 39 1321]. The important NTMs in the ASDDEX UG are (m,n)=(3,2)+(4,3)+(1,1). Realistic parameterization of these NTMs and the safety factor in ASDEX UG are given in [O. Dumbrajs et al 2005 POP 12 1107004]. We use a symplectic map in magnetic coordinates for the ASDEX UG to integrate field lines in presence of the NTMs. We add a second order control term [H. Ali and A. Punjabi 2007 PPCF 49 1565] to this ASDEX UG field line Hamiltonian to create an invariant magnetic surface inside the chaos generated by the NTMs. The relative strength, robustness, and resilience of this barrier are studied to ascertain the most desirable noble barrier in the ASDEX UG with NTMs. We present preliminary results of this work, and discuss its implications with regard to magnetic transport barriers for increasing strength of magnetic perturbations. This work is supported by the grants DE-FG02-01ER54624 and DE-FG02-04ER54793.
Sufia Zulfa Ahmad
2016-01-01
Full Text Available We derived a two-step, four-stage, and fifth-order semi-implicit hybrid method which can be used for solving special second-order ordinary differential equations. The method is then trigonometrically fitted so that it is suitable for solving problems which are oscillatory in nature. The methods are then used for solving oscillatory delay differential equations. Numerical results clearly show the efficiency of the new method when compared to the existing explicit and implicit methods in the scientific literature.
First order and second order fermi acceleration of energetic charged particles by shock waves
Webb, G.M.
1983-01-01
Steady state solutions of the cosmic ray transport equation describing first order Fermi acceleration of energetic charged particles at a plane shock (without losses) and second order Fermi acceleration in the downstream region of the shock are derived. The solutions for the isotropic part of the phase space distribution function are expressible as eigenfunction expansions, being superpositions of series of power law momentum spectra, with the power law indices being the roots of an eigenvalue equation. The above exact analytic solutions are for the case where the spatial diffusion coefficient kappa is independent of momentum. The solutions in general depend on the shock compression ratio, the modulation parameters V 1 L/kappa 1 , V 2 L/kappa 2 (V is the plasma velocity, kappa is the energetic particle diffusion coefficient, and L a characteristic length over which second order Fermi acceleration is effective) in the upstream and downstream regions of the shock, respectively, and also on a further dimensionless parameter, zeta, characterizing second order Fermi acceleration. In the limit as zeta→0 (no second order Fermi acceleration) the power law momentum spectrum characteristic of first order Fermi acceleration (depending only on the shock compression ratio) obtained previously is recovered. Perturbation solutions for the case where second order Fermi effects are small, and for realistic diffusion coefficients (kappainfinityp/sup a/, a>0, p = particle momentum), applicable at high momenta, are also obtained
Tajti, Attila; Szalay, Péter G
2016-11-08
Describing electronically excited states of molecules accurately poses a challenging problem for theoretical methods. Popular second order techniques like Linear Response CC2 (CC2-LR), Partitioned Equation-of-Motion MBPT(2) (P-EOM-MBPT(2)), or Equation-of-Motion CCSD(2) (EOM-CCSD(2)) often produce results that are controversial and are ill-balanced with their accuracy on valence and Rydberg type states. In this study, we connect the theory of these methods and, to investigate the origin of their different behavior, establish a series of intermediate variants. The accuracy of these on excitation energies of singlet valence and Rydberg electronic states is benchmarked on a large sample against high-accuracy Linear Response CC3 references. The results reveal the role of individual terms of the second order similarity transformed Hamiltonian, and the reason for the bad performance of CC2-LR in the description of Rydberg states. We also clarify the importance of the T̂ 1 transformation employed in the CC2 procedure, which is found to be very small for vertical excitation energies.
A Damped Gauss-Newton Method for the Second-Order Cone Complementarity Problem
Pan Shaohua; Chen, J.-S.
2009-01-01
We investigate some properties related to the generalized Newton method for the Fischer-Burmeister (FB) function over second-order cones, which allows us to reformulate the second-order cone complementarity problem (SOCCP) as a semismooth system of equations. Specifically, we characterize the B-subdifferential of the FB function at a general point and study the condition for every element of the B-subdifferential at a solution being nonsingular. In addition, for the induced FB merit function, we establish its coerciveness and provide a weaker condition than Chen and Tseng (Math. Program. 104:293-327, 2005) for each stationary point to be a solution, under suitable Cartesian P-properties of the involved mapping. By this, a damped Gauss-Newton method is proposed, and the global and superlinear convergence results are obtained. Numerical results are reported for the second-order cone programs from the DIMACS library, which verify the good theoretical properties of the method
New second order Mumford-Shah model based on Γ-convergence approximation for image processing
Duan, Jinming; Lu, Wenqi; Pan, Zhenkuan; Bai, Li
2016-05-01
In this paper, a second order variational model named the Mumford-Shah total generalized variation (MSTGV) is proposed for simultaneously image denoising and segmentation, which combines the original Γ-convergence approximated Mumford-Shah model with the second order total generalized variation (TGV). For image denoising, the proposed MSTGV can eliminate both the staircase artefact associated with the first order total variation and the edge blurring effect associated with the quadratic H1 regularization or the second order bounded Hessian regularization. For image segmentation, the MSTGV can obtain clear and continuous boundaries of objects in the image. To improve computational efficiency, the implementation of the MSTGV does not directly solve its high order nonlinear partial differential equations and instead exploits the efficient split Bregman algorithm. The algorithm benefits from the fast Fourier transform, analytical generalized soft thresholding equation, and Gauss-Seidel iteration. Extensive experiments are conducted to demonstrate the effectiveness and efficiency of the proposed model.
Constructing set-valued fundamental diagrams from jamiton solutions in second order traffic models
Seibold, Benjamin; Flynn, Morris R.; Kasimov, Aslan R.; Rosales, Rodolfo Rubé n
2013-01-01
Fundamental diagrams of vehicular traiic ow are generally multivalued in the congested ow regime. We show that such set-valued fundamental diagrams can be constructed systematically from simple second order macroscopic traiic models, such as the classical Payne-Whitham model or the inhomogeneous Aw-Rascle-Zhang model. These second order models possess nonlinear traveling wave solutions, called jamitons, and the multi-valued parts in the fundamental diagram correspond precisely to jamiton-dominated solutions. This study shows that transitions from function-valued to set-valued parts in a fundamental diagram arise naturally in well-known second order models. As a particular consequence, these models intrinsically reproduce traiic phases. © American Institute of Mathematical Sciences.
Second order gauge invariant measure of a tidally deformed black hole
Ahmadi, Nahid, E-mail: nahmadi@ut.ac.ir [Department of Physics, University of Tehran, Kargar Avenue North, Tehran 14395-547 (Iran, Islamic Republic of)
2012-08-01
In this paper, a Lagrangian perturbation theory for the second order treatment of small disturbances of the event horizon in Schwarzchild black holes is introduced. The issue of gauge invariance in the context of general relativistic theory is also discussed. The developments of this paper is a logical continuation of the calculations presented in [1], in which the first order coordinate dependance of the intrinsic and exterinsic geometry of the horizon is examined and the first order gauge invariance of the intrinsic geometry of the horizon is shown. In context of second order perturbation theory, It is shown that the rate of the expansion of the congruence of the horizon generators is invariant under a second order reparametrization; so it can be considered as a measure of tidal perturbation. A generally non-vanishing expression for this observable, which accomodates tidal perturbations and implies nonlinear response of the horizon, is also presented.
Constructing set-valued fundamental diagrams from jamiton solutions in second order traffic models
Seibold, Benjamin
2013-09-01
Fundamental diagrams of vehicular traiic ow are generally multivalued in the congested ow regime. We show that such set-valued fundamental diagrams can be constructed systematically from simple second order macroscopic traiic models, such as the classical Payne-Whitham model or the inhomogeneous Aw-Rascle-Zhang model. These second order models possess nonlinear traveling wave solutions, called jamitons, and the multi-valued parts in the fundamental diagram correspond precisely to jamiton-dominated solutions. This study shows that transitions from function-valued to set-valued parts in a fundamental diagram arise naturally in well-known second order models. As a particular consequence, these models intrinsically reproduce traiic phases. © American Institute of Mathematical Sciences.
Exact calculation of three-body contact interaction to second order
Kaiser, N.
2012-01-01
For a system of fermions with a three-body contact interaction the second-order contributions to the energy per particle anti E(k f ) are calculated exactly. The three-particle scattering amplitude in the medium is derived in closed analytical form from the corresponding two-loop rescattering diagram. We compare the (genuine) second-order three-body contribution to anti E(k f )∝k f 10 with the second-order term due to the density-dependent effective two-body interaction, and find that the latter term dominates. The results of the present study are of interest for nuclear many-body calculations where chiral three-nucleon forces are treated beyond leading order via a density-dependent effective two-body interaction. (orig.)
Time-dependent Second Order Scattering Theory for Weather Radar with a Finite Beam Width
Kobayashi, Satoru; Tanelli, Simone; Im, Eastwood; Ito, Shigeo; Oguchi, Tomohiro
2006-01-01
Multiple scattering effects from spherical water particles of uniform diameter are studied for a W-band pulsed radar. The Gaussian transverse beam-profile and the rectangular pulse-duration are used for calculation. An second-order analytical solution is derived for a single layer structure, based on a time-dependent radiative transfer theory as described in the authors' companion paper. When the range resolution is fixed, increase in footprint radius leads to increase in the second order reflectivity that is defined as the ratio of the second order return to the first order one. This feature becomes more serious as the range increases. Since the spaceborne millimeter-wavelength radar has a large footprint radius that is competitive to the mean free path, the multiple scattering effect must be taken into account for analysis.
Second-order generalized perturbation theory for source-driven systems
Greenspan, E.; Gilai, D.; Oblow, E.M.
1978-01-01
A second-order generalized perturbation theory (GPT) for the effect of multiple system variations on a general flux functional in source-driven systems is derived. The derivation is based on a functional Taylor series in which second-order derivatives are retained. The resulting formulation accounts for the nonlinear effect of a given variation accurate to third order in the flux and adjoint perturbations. It also accounts for the effect of interaction between any number of variations. The new formulation is compared with exact perturbation theory as well as with perturbation theory for altered systems. The usefulnes of the second-order GPT formulation is illustrated by applying it to optimization problems. Its applicability to areas of cross-section sensitivity analysis and system design and evaluation is also discussed
Cascading second-order nonlinear processes in a lithium niobate-on-insulator microdisk.
Liu, Shijie; Zheng, Yuanlin; Chen, Xianfeng
2017-09-15
Whispering-gallery-mode (WGM) microcavities are very important in both fundamental science and practical applications, among which on-chip second-order nonlinear microresonators play an important role in integrated photonic functionalities. Here we demonstrate resonant second-harmonic generation (SHG) and cascaded third-harmonic generation (THG) in a lithium niobate-on-insulator (LNOI) microdisk resonator. Efficient SHG in the visible range was obtained with only several mW input powers at telecom wavelengths. THG was also observed through a cascading process, which reveals simultaneous phase matching and strong mode coupling in the resonator. Cascading of second-order nonlinear processes gives rise to an effectively large third-order nonlinearity, which makes on-chip second-order nonlinear microresonators a promising frequency converter for integrated nonlinear photonics.
Separation and extension of cover inequalities for second-order conic knapsack constraints with GUBs
Atamtürk, Alper; Muller, Laurent Flindt; Pisinger, David
We consider the second-order conic equivalent of the classic knapsack polytope where the variables are subject to generalized upper bound constraints. We describe and compare a number of separation and extension algorithms which make use of the extra structure implied by the generalized upper bound...... constraints in order to strengthen the second-order conic equivalent of the classic cover cuts. We show that determining whether a cover can be extended with a variable is NP-hard. Computational experiments are performed comparing the proposed separation and extension algorithms. These experiments show...
Comparison of third-order plasma wave echoes with ballistic second-order plasma wave echoes
Leppert, H.D.; Schuelter, H.; Wiesemann, K.
1982-01-01
The apparent dispersion of third-order plasma wave echoes observed in a high frequency plasma is compared with that of simultaneously observed ballistic second-order echoes. Amplitude and wavelength of third-order echoes are found to be always smaller than those of second-order echoes, however, the dispersion curves of both types of echoes are very similar. These observations are in qualitative agreement with calculations of special ballistic third-order echoes. The ballistic nature of the observed third-order echoes may, therefore, be concluded from these measurements. (author)
Tahavori, Maryamsadat; Shaker, Hamid Reza
A method for model reduction of dynamical systems with the second order structure is proposed in this paper. The proposed technique preserves the second order structure of the system, and also preserves the stability of the original systems. The method uses the controllability and observability...... gramians within the time interval to build the appropriate Petrov-Galerkin projection for dynamical systems within the time interval of interest. The bound on approximation error is also derived. The numerical results are compared with the counterparts from other techniques. The results confirm...
A New Grünwald-Letnikov Derivative Derived from a Second-Order Scheme
B. A. Jacobs
2015-01-01
Full Text Available A novel derivation of a second-order accurate Grünwald-Letnikov-type approximation to the fractional derivative of a function is presented. This scheme is shown to be second-order accurate under certain modifications to account for poor accuracy in approximating the asymptotic behavior near the lower limit of differentiation. Some example functions are chosen and numerical results are presented to illustrate the efficacy of this new method over some other popular choices for discretizing fractional derivatives.
A global numerical solution of the radial Schroedinger equation by second-order perturbation theory
Adam, G.
1979-01-01
A global numerical method, which uses second-order perturbation theory, is described for the solution of the radial Schroedinger equation. The perturbative numerical (PN) solution is derived in two stages: first, the original potential is approximated by a piecewise continuous parabolic function, and second, the resulting Schroedinger equation is solved on each integration step by second-order perturbation theory, starting with a step function reference approximation for the parabolic potential. We get a manageable PN algorithm, which shows an order of accuracy equal to six in the solution of the original Schroedinger equation, and is very stable against round off errors. (author)
Second-order infinitesimal bendings of surfaces of revolution with flattening at the poles
Sabitov, I Kh
2014-01-01
We study infinitesimal bendings of surfaces of revolution with flattening at the poles. We begin by considering the minimal possible smoothness class C 1 both for surfaces and for deformation fields. Conditions are formulated for a given harmonic of a first-order infinitesimal bending to be extendable into a second order infinitesimal bending. We finish by stating a criterion for nonrigidity of second order for closed surfaces of revolution in the analytic class. We also give the first concrete example of such a nonrigid surface. Bibliography: 15 entries
Second-order infinitesimal bendings of surfaces of revolution with flattening at the poles
Sabitov, I Kh [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
2014-12-31
We study infinitesimal bendings of surfaces of revolution with flattening at the poles. We begin by considering the minimal possible smoothness class C{sup 1} both for surfaces and for deformation fields. Conditions are formulated for a given harmonic of a first-order infinitesimal bending to be extendable into a second order infinitesimal bending. We finish by stating a criterion for nonrigidity of second order for closed surfaces of revolution in the analytic class. We also give the first concrete example of such a nonrigid surface. Bibliography: 15 entries.
First- and Second-Order Full-Differential in Edge Analysis of Images
Dong-Mei Pu
2014-01-01
mathematics. We propose and reformulate them with a uniform definition framework. Based on our observation and analysis with the difference, we propose an algorithm to detect the edge from image. Experiments on Corel5K and PASCAL VOC 2007 are done to show the difference between the first order and the second order. After comparison with Canny operator and the proposed first-order differential, the main result is that the second-order differential has the better performance in analysis of changes of the context of images with good selection of control parameter.
Second-Order Controllability of Multi-Agent Systems with Multiple Leaders
Liu Bo; Han Xiao; Shi Yun-Tao; Su Hou-Sheng
2016-01-01
This paper proposes a new second-order continuous-time multi-agent model and analyzes the controllability of second-order multi-agent system with multiple leaders based on the asymmetric topology. This paper considers the more general case: velocity coupling topology is different from location coupling topology. Some sufficient and necessary conditions are presented for the controllability of the system with multiple leaders. In addition, the paper studies the controllability of the system with velocity damping gain. Simulation results are given to illustrate the correctness of theoretical results. (paper)
Massless second-order tetradic spin-3 and higher-helicity bosons
Aragone, C; La Roche, H [Universidad Simon Bolivar, Caracas (Venezuela) Dept. de Fisica
1982-11-21
The unique, uniform, second-order formulation of massless bosons of helicity >=3 is presented here in terms of tetradic fields. The actions we find are shown to coincide both with the first-order (tetradic) formulation of Vasiliev and with the symmetric second-order description of Fronsdal. We carefully analyse the gravitational coupling of the spin-3 field and find that tetradic spin-3 matter presents the same translational consistency problem as symmetric matter does. Furthermore, in the curved tetradic case the generalized Lorentz invariance can be restored by the addition of nominimal terms.
Hybrid approximations via second order combined dynamic derivatives on time scales
Qin Sheng
2007-09-01
Full Text Available This article focuses on the approximation of conventional second order derivative via the combined (diamond-$\\alpha$ dynamic derivative on time scales with necessary smoothness conditions embedded. We will show the constraints under which the second order dynamic derivative provides a consistent approximation to the conventional second derivative; the cases where the dynamic derivative approximates the derivative only via a proper modification of the existing formula; and the situations in which the dynamic derivative can never approximate consistently even with the help of available structure correction methods. Constructive error analysis will be given via asymptotic expansions for practical hybrid modeling and computational applications.
Pap-smear Classification Using Efficient Second Order Neural Network Training Algorithms
Ampazis, Nikolaos; Dounias, George; Jantzen, Jan
2004-01-01
In this paper we make use of two highly efficient second order neural network training algorithms, namely the LMAM (Levenberg-Marquardt with Adaptive Momentum) and OLMAM (Optimized Levenberg-Marquardt with Adaptive Momentum), for the construction of an efficient pap-smear test classifier. The alg......In this paper we make use of two highly efficient second order neural network training algorithms, namely the LMAM (Levenberg-Marquardt with Adaptive Momentum) and OLMAM (Optimized Levenberg-Marquardt with Adaptive Momentum), for the construction of an efficient pap-smear test classifier...
An, Honglin; Fleming, Simon
2005-05-02
The spatial distribution of second-order nonlinearity in thermally poled optical fibers was characterized by second-harmonic microscopy. The second-order nonlinearity was found to be confined to a thin layer close to the anode surface and progressed further into the silica as the poling time increased. Position uncertainty of the anode metal wire was observed to have an effect, as the nonlinear layers were found not always symmetrically located around the nearest points between the anode and cathode. Optical microscopy results were obtained on etched poled fiber cross-sections and compared with those from second-harmonic microscopy.
SECOND ORDER LEAST SQUARE ESTIMATION ON ARCH(1 MODEL WITH BOX-COX TRANSFORMED DEPENDENT VARIABLE
Herni Utami
2014-03-01
Full Text Available Box-Cox transformation is often used to reduce heterogeneity and to achieve a symmetric distribution of response variable. In this paper, we estimate the parameters of Box-Cox transformed ARCH(1 model using second-order leastsquare method and then we study the consistency and asymptotic normality for second-order least square (SLS estimators. The SLS estimation was introduced byWang (2003, 2004 to estimate the parameters of nonlinear regression models with independent and identically distributed errors
Second-order interference of two independent and tunable single-mode continuous-wave lasers
Liu Jianbin; Chen Hui; Zheng Huaibin; Xu Zhuo; Wei Dong; Zhou Yu; Gao Hong; Li Fu-Li
2016-01-01
The second-order temporal interference of two independent single-mode continuous-wave lasers is discussed by employing two-photon interference in Feynman’s path integral theory. It is concluded that whether the second-order temporal interference pattern can or cannot be retrieved via two-photon coincidence counting rate is dependent on the resolution time of the detection system and the frequency difference between these two lasers. Two identical and tunable single-mode continuous-wave diode lasers are employed to verify the predictions. These studies are helpful to understand the physics of two-photon interference with photons of different spectra. (paper)
Mancas, Stefan C. [Department of Mathematics, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosí, SLP (Mexico)
2013-09-02
We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in their first-kind form have only cubic and quadratic terms. Then, employing an old integrability criterion due to Chiellini, we introduce the corresponding integrable dissipative equations. For illustration, we present the cases of some integrable dissipative Fisher, nonlinear pendulum, and Burgers–Huxley type equations which are obtained in this way and can be of interest in applications. We also show how to obtain Abel solutions directly from the factorization of second order nonlinear equations.
Dynamical Consensus Algorithm for Second-Order Multi-Agent Systems Subjected to Communication Delay
Liu Chenglin; Liu Fei
2013-01-01
To solve the dynamical consensus problem of second-order multi-agent systems with communication delay, delay-dependent compensations are added into the normal asynchronously-coupled consensus algorithm so as to make the agents achieve a dynamical consensus. Based on frequency-domain analysis, sufficient conditions are gained for second-order multi-agent systems with communication delay under leaderless and leader-following consensus algorithms respectively. Simulation illustrates the correctness of the results. (interdisciplinary physics and related areas of science and technology)
Plyushchay, Mikhail S., E-mail: mikhail.plyushchay@usach.cl
2017-02-15
A canonical quantization scheme applied to a classical supersymmetric system with quadratic in momentum supercharges gives rise to a quantum anomaly problem described by a specific term to be quadratic in Planck constant. We reveal a close relationship between the anomaly and the Schwarzian derivative, and specify a quantization prescription which generates the anomaly-free supersymmetric quantum system with second order supercharges. We also discuss the phenomenon of a coupling-constant metamorphosis that associates quantum systems with the first-order supersymmetry to the systems with the second-order supercharges.
Plyushchay, Mikhail S.
2017-01-01
A canonical quantization scheme applied to a classical supersymmetric system with quadratic in momentum supercharges gives rise to a quantum anomaly problem described by a specific term to be quadratic in Planck constant. We reveal a close relationship between the anomaly and the Schwarzian derivative, and specify a quantization prescription which generates the anomaly-free supersymmetric quantum system with second order supercharges. We also discuss the phenomenon of a coupling-constant metamorphosis that associates quantum systems with the first-order supersymmetry to the systems with the second-order supercharges.
Coco, Armando; Russo, Giovanni
2018-05-01
In this paper we propose a second-order accurate numerical method to solve elliptic problems with discontinuous coefficients (with general non-homogeneous jumps in the solution and its gradient) in 2D and 3D. The method consists of a finite-difference method on a Cartesian grid in which complex geometries (boundaries and interfaces) are embedded, and is second order accurate in the solution and the gradient itself. In order to avoid the drop in accuracy caused by the discontinuity of the coefficients across the interface, two numerical values are assigned on grid points that are close to the interface: a real value, that represents the numerical solution on that grid point, and a ghost value, that represents the numerical solution extrapolated from the other side of the interface, obtained by enforcing the assigned non-homogeneous jump conditions on the solution and its flux. The method is also extended to the case of matrix coefficient. The linear system arising from the discretization is solved by an efficient multigrid approach. Unlike the 1D case, grid points are not necessarily aligned with the normal derivative and therefore suitable stencils must be chosen to discretize interface conditions in order to achieve second order accuracy in the solution and its gradient. A proper treatment of the interface conditions will allow the multigrid to attain the optimal convergence factor, comparable with the one obtained by Local Fourier Analysis for rectangular domains. The method is robust enough to handle large jump in the coefficients: order of accuracy, monotonicity of the errors and good convergence factor are maintained by the scheme.
Independence of First- and Second-Order Memories in Newborn Rabbits
Coureaud, Gerard; Languille, Solene; Joly, Virginie; Schaal, Benoist; Hars, Bernard
2011-01-01
The mammary pheromone promotes the acquisition of novel odorants (CS1) in newborn rabbits. Here, experiments pinpoint that CS1 becomes able to support neonatal learning of other odorants (CS2). We therefore evaluated whether these first- and second-order memories remained dependent after reactivation. Amnesia induced after CS2 recall selectively…
Pressure derivatives of the second-order elastic constants of strontium, barium, and lead nitrate
Bedi, S.S.; Verma, M.P.
1980-01-01
An interpretation is given of the measured results on the pressure derivatives of second-order elastic constants (SOEC) of strontium barium, and lead nitrate crystallizing in the fluorite type structure from the Lundquist potential. Potential parameters are determined from the experimental values of SOEC and the equilibrium condition
A note on monotone solutions for a nonconvex second-order functional differential inclusion
Aurelian Cernea
2011-12-01
Full Text Available The existence of monotone solutions for a second-order functional differential inclusion with Carath\\'{e}odory perturbation is obtained in the case when the multifunction that define the inclusion is upper semicontinuous compact valued and contained in the Fr\\'{e}chet subdifferential of a $\\phi $-convex function of order two.
Existence of solutions for nonlinear mixed type integrodifferential equation of second order
Haribhau Laxman Tidke
2010-04-01
Full Text Available In this paper, we investigate the existence of solutions for nonlinear mixed Volterra-Fredholm integrodifferential equation of second order with nonlocal conditions in Banach spaces. Our analysis is based on Leray-Schauder alternative, rely on a priori bounds of solutions and the inequality established by B. G. Pachpatte.
An Improved Second-Order Generalized Integrator Based Quadrature Signal Generator
Xin, Zhen; Wang, Xiongfei; Qin, Zian
2016-01-01
The second-order generalized integrator based quadrature signal generator (SOGI-QSG) is able to produce in-quadrature signals for many applications, such as frequency estimation, grid synchronization, and harmonic extraction. However, the SOGI-QSG is sensitive to input dc and harmonic components...
Ćaǧatay Uçgun, Filiz; Esen, Oǧul; Gümral, Hasan
2018-01-01
We present Skinner-Rusk and Hamiltonian formalisms of second order degenerate Clément and Sarıoğlu-Tekin Lagrangians. The Dirac-Bergmann constraint algorithm is employed to obtain Hamiltonian realizations of Lagrangian theories. The Gotay-Nester-Hinds algorithm is used to investigate Skinner-Rusk formalisms of these systems.
Mixed FEM for Second Order Elliptic Problems on Polygonal Meshes with BEM-Based Spaces
Efendiev, Yalchin; Galvis, Juan; Lazarov, Raytcho; Weiß er, Steffen
2014-01-01
We present a Boundary Element Method (BEM)-based FEM for mixed formulations of second order elliptic problems in two dimensions. The challenge, we would like to address, is a proper construction of H(div)-conforming vector valued trial functions
m-POINT BOUNDARY VALUE PROBLEM FOR SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATION AT RESONANCE
无
2012-01-01
In his paper,we obtain a general theorem concerning the existence of solutions to an m-point boundary value problem for the second-order differential equation with impulses.Moreover,the result can also be applied to study the usual m-point boundary value problem at resonance without impulses.
Multiple positive solutions for second order impulsive boundary value problems in Banach spaces
Zhi-Wei Lv
2010-06-01
Full Text Available By means of the fixed point index theory of strict set contraction operators, we establish new existence theorems on multiple positive solutions to a boundary value problem for second-order impulsive integro-differential equations with integral boundary conditions in a Banach space. Moreover, an application is given to illustrate the main result.
Temporal Frequency Modulates Reaction Time Responses to First-Order and Second-Order Motion
Hutchinson, Claire V.; Ledgeway, Tim
2010-01-01
This study investigated the effect of temporal frequency and modulation depth on reaction times for discriminating the direction of first-order (luminance-defined) and second-order (contrast-defined) motion, equated for visibility using equal multiples of direction-discrimination threshold. Results showed that reaction times were heavily…
Investigation of second-order optical potential for elastic π4He scattering
Mach, R.; Sapozhnikov, M.G.
1982-01-01
The calculations of elastic π - 4 He scattering within the framework of the optical model with a second-order potential were performed. The effects of recoil correlations, charge exchange and double spin (isospin) flip in the inter-- mediate states are studied. The correction of the impulse approximation is investigated. Comparison between Kerman-McManus-Thaler and Watson formalisms is made
Semantic Characterisations of Second-Order Computability over the Real Numbers
Korovina, Margarita V.; Kudinov, Oleg V.
2001-01-01
We propose semantic characterisations of second-order computability over the reals based on σ-definability theory. Notions of computability for operators and real-valued functionals defined on the class of continuous functions are introduced via domain theory. We consider the reals with and without...
Variational formulation and projectional methods for the second order transport equation
Borysiewicz, M.; Stankiewicz, R.
1979-01-01
Herein the variational problem for a second-order boundary value problem for the neutron transport equation is formulated. The projectional methods solving the problem are examined. The approach is compared with that based on the original untransformed form of the neutron transport equation
Second Order Washout filter based Power Sharing Strategy for Uninterruptible Power Supply
Lu, Jinghang; Savaghebi, Mehdi; Guerrero, Josep M.
2017-01-01
In this paper, first, the existing frequency and voltage amplitude restoration control strategies are reviewed. Moreover, the proposed second order washout filter control strategy is proposed to enhance the dynamic response under load disturbance. The physical parameter of the proposed method is ...
Tengfei Shen
2015-12-01
Full Text Available This paper deals with the multiplicity of solutions for Dirichlet boundary conditions of second-order quasilinear equations with impulsive effects. By using critical point theory, a new result is obtained. An example is given to illustrate the main result.
The Development of Perceptual Sensitivity to Second-Order Facial Relations in Children
Baudouin, Jean-Yves; Gallay, Mathieu; Durand, Karine; Robichon, Fabrice
2010-01-01
This study investigated children's perceptual ability to process second-order facial relations. In total, 78 children in three age groups (7, 9, and 11 years) and 28 adults were asked to say whether the eyes were the same distance apart in two side-by-side faces. The two faces were similar on all points except the space between the eyes, which was…
Zhou, Shiqi
2006-06-01
A second-order direct correlation function (DCF) from solving the polymer-RISM integral equation is scaled up or down by an equation of state for bulk polymer, the resultant scaling second-order DCF is in better agreement with corresponding simulation results than the un-scaling second-order DCF. When the scaling second-order DCF is imported into a recently proposed LTDFA-based polymer DFT approach, an originally associated adjustable but mathematically meaningless parameter now becomes mathematically meaningful, i.e., the numerical value lies now between 0 and 1. When the adjustable parameter-free version of the LTDFA is used instead of the LTDFA, i.e., the adjustable parameter is fixed at 0.5, the resultant parameter-free version of the scaling LTDFA-based polymer DFT is also in good agreement with the corresponding simulation data for density profiles. The parameter-free version of the scaling LTDFA-based polymer DFT is employed to investigate the density profiles of a freely jointed tangent hard sphere chain near a variable sized central hard sphere, again the predictions reproduce accurately the simulational results. Importance of the present adjustable parameter-free version lies in its combination with a recently proposed universal theoretical way, in the resultant formalism, the contact theorem is still met by the adjustable parameter associated with the theoretical way.
Application of the Lie Symmetry Analysis for second-order fractional differential equations
Mousa Ilie
2017-12-01
Full Text Available Obtaining analytical or numerical solution of fractional differential equations is one of the troublesome and challenging issue among mathematicians and engineers, specifically in recent years. The purpose of this paper Lie Symmetry method is developed to solve second-order fractional differential equations, based on conformable fractional derivative. Some numerical examples are presented to illustrate the proposed approach.
Second order evolution inclusions governed by sweeping process in Banach spaces
A. G. Ibrahim
2009-11-01
Full Text Available In this paper we prove two existence theorems concerning the existence of solutions for second order evolution inclusions governed by sweeping process with closed convex sets depending on time and state in Banach spaces. This work extends some recent existence theorems cncerning sweeping process from Hilbert spaces to Banach spaces.
Second-Order Consensus for Multiagent Systems With Directed Topologies and Nonlinear Dynamics
Yu, Wenwu; Chen, Guanrong; Cao, Ming; Kurths, Juergen; Kurths, Jürgen
This paper considers a second-order consensus problem for multiagent systems with nonlinear dynamics and directed topologies where each agent is governed by both position and velocity consensus terms with a time-varying asymptotic velocity. To describe the system's ability for reaching consensus, a
Stepwise training supports strategic second-order theory of mind in turn-taking games
Verbrugge, Laurina; Meijering, Ben; Wierda, Stefan; van Rijn, Dirk; Taatgen, Niels
People model other people's mental states in order to understand and predict their behavior. Sometimes they model what others think about them as well: "He thinks that I intend to stop." Such second-order theory of mind is needed to navigate some social situations, for example, to make optimal
Loads on a 3D body due to second order waves and a current
Skourup, Jesper; Cheung, K. F.; Bingham, Harry B.
2000-01-01
are expanded about the still-water level by Taylor series so that the solution is evaluated on a time-invariant geometry. A formulation correct to second order in the wave steepness and to first order in the current speed is used. Numerical results are obtained for the first-order and the second...
Variations in wave direction estimated using first and second order Fourier coefficients
SanilKumar, V.; Anand, N.M.
to the peak frequency are used in practice. In the present study, comparison is made on wave directions estimated based on first and second order Fourier coefficients using data collected at four locations in the west and east coasts of India. Study shows...
Large optical second-order nonlinearity of poled WO3-TeO2 glass.
Tanaka, K; Narazaki, A; Hirao, K
2000-02-15
Second-harmonic generation, one of the second-order nonlinear optical properties of thermally and electrically poled WO>(3)-TeO>(2) glasses, has been examined. We poled glass samples with two thicknesses (0.60 and 0.86 mm) at various temperatures to explore the effects of external electric field strength and poling temperature on second-order nonlinearity. The dependence of second-harmonic intensity on the poling temperature is maximum at a specific poling temperature. A second-order nonlinear susceptibility of 2.1 pm/V was attained for the 0.60-mm-thick glass poled at 250 degrees C. This value is fairly large compared with those for poled silica and tellurite glasses reported thus far. We speculate that the large third-order nonlinear susceptibility of WO>(3)- TeO>(2) glasses gives rise to the large second-order nonlinearity by means of a X((2)) = 3X((3)) E(dc) process.
Xu, Enhua; Zhao, Dongbo; Li, Shuhua
2015-10-13
A multireference second order perturbation theory based on a complete active space configuration interaction (CASCI) function or density matrix renormalized group (DMRG) function has been proposed. This method may be considered as an approximation to the CAS/A approach with the same reference, in which the dynamical correlation is simplified with blocked correlated second order perturbation theory based on the generalized valence bond (GVB) reference (GVB-BCPT2). This method, denoted as CASCI-BCPT2/GVB or DMRG-BCPT2/GVB, is size consistent and has a similar computational cost as the conventional second order perturbation theory (MP2). We have applied it to investigate a number of problems of chemical interest. These problems include bond-breaking potential energy surfaces in four molecules, the spectroscopic constants of six diatomic molecules, the reaction barrier for the automerization of cyclobutadiene, and the energy difference between the monocyclic and bicyclic forms of 2,6-pyridyne. Our test applications demonstrate that CASCI-BCPT2/GVB can provide comparable results with CASPT2 (second order perturbation theory based on the complete active space self-consistent-field wave function) for systems under study. Furthermore, the DMRG-BCPT2/GVB method is applicable to treat strongly correlated systems with large active spaces, which are beyond the capability of CASPT2.
Conformal symmetry and non-relativistic second-order fluid dynamics
Chao Jingyi; Schäfer, Thomas
2012-01-01
We study the constraints imposed by conformal symmetry on the equations of fluid dynamics at second order in the gradients of the hydrodynamic variables. At zeroth order, conformal symmetry implies a constraint on the equation of state, E 0 =2/3 P, where E 0 is the energy density and P is the pressure. At first order, conformal symmetry implies that the bulk viscosity must vanish. We show that at second order, conformal invariance requires that two-derivative terms in the stress tensor must be traceless, and that it determines the relaxation of dissipative stresses to the Navier–Stokes form. We verify these results by solving the Boltzmann equation at second order in the gradient expansion. We find that only a subset of the terms allowed by conformal symmetry appear. - Highlights: ► We derive conformal constraints for the stress tensor of a scale invariant fluid. ► We determine the relaxation time in kinetic theory. ► We compute the rate of entropy production in second-order fluid dynamics.
Comparison of Several Modes in Simple ARC Second-Order Filter
A. I. Rybin
1994-07-01
Full Text Available In this paper the popular, multiple-feedback, ARC single opamp, highpass second-order filter is proposed in several types of modes, namely voltage, current and hybrid ones. These modes are studied and compared in detail. Computer experimental results are given supporting the theory.
Time-integration methods for finite element discretisations of the second-order Maxwell equation
Sarmany, D.; Bochev, Mikhail A.; van der Vegt, Jacobus J.W.
This article deals with time integration for the second-order Maxwell equations with possibly non-zero conductivity in the context of the discontinuous Galerkin finite element method DG-FEM) and the $H(\\mathrm{curl})$-conforming FEM. For the spatial discretisation, hierarchic
Periodic solutions of singular second order differential equations : upper and lower functions
Hakl, Robert; Torres, P.J.; Zamora, M.
2011-01-01
Roč. 74, č. 18 (2011), s. 7078-7093 ISSN 0362-546X Institutional research plan: CEZ:AV0Z10190503 Keywords : second-order differential equation * singularity at the phase variable * Rayleigh-Plesset equation Subject RIV: BA - General Mathematics Impact factor: 1.536, year: 2011 http://www.sciencedirect.com/science/article/pii/S0362546X11005049
Multiple periodic solutions for a class of second-order nonlinear neutral delay equations
2006-01-01
Full Text Available By means of a variational structure and Z 2 -group index theory, we obtain multiple periodic solutions to a class of second-order nonlinear neutral delay equations of the form0, au>0$"> x ″ ( t − τ + λ ( t f ( t , x ( t , x ( t − τ , x ( t − 2 τ = x ( t , λ ( t > 0 , τ > 0 .
Boundary-value problems for first and second order functional differential inclusions
Shihuang Hong
2003-03-01
Full Text Available This paper presents sufficient conditions for the existence of solutions to boundary-value problems of first and second order multi-valued differential equations in Banach spaces. Our results obtained using fixed point theorems, and lead to new existence principles.
Matsubara, Takahiko
2003-02-01
We formulate a general method for perturbative evaluations of statistics of smoothed cosmic fields and provide useful formulae for application of the perturbation theory to various statistics. This formalism is an extensive generalization of the method used by Matsubara, who derived a weakly nonlinear formula of the genus statistic in a three-dimensional density field. After describing the general method, we apply the formalism to a series of statistics, including genus statistics, level-crossing statistics, Minkowski functionals, and a density extrema statistic, regardless of the dimensions in which each statistic is defined. The relation between the Minkowski functionals and other geometrical statistics is clarified. These statistics can be applied to several cosmic fields, including three-dimensional density field, three-dimensional velocity field, two-dimensional projected density field, and so forth. The results are detailed for second-order theory of the formalism. The effect of the bias is discussed. The statistics of smoothed cosmic fields as functions of rescaled threshold by volume fraction are discussed in the framework of second-order perturbation theory. In CDM-like models, their functional deviations from linear predictions plotted against the rescaled threshold are generally much smaller than that plotted against the direct threshold. There is still a slight meatball shift against rescaled threshold, which is characterized by asymmetry in depths of troughs in the genus curve. A theory-motivated asymmetry factor in the genus curve is proposed.
Mester, Dávid; Nagy, Péter R.; Kállay, Mihály
2018-03-01
A reduced-cost implementation of the second-order algebraic-diagrammatic construction [ADC(2)] method is presented. We introduce approximations by restricting virtual natural orbitals and natural auxiliary functions, which results, on average, in more than an order of magnitude speedup compared to conventional, density-fitting ADC(2) algorithms. The present scheme is the successor of our previous approach [D. Mester, P. R. Nagy, and M. Kállay, J. Chem. Phys. 146, 194102 (2017)], which has been successfully applied to obtain singlet excitation energies with the linear-response second-order coupled-cluster singles and doubles model. Here we report further methodological improvements and the extension of the method to compute singlet and triplet ADC(2) excitation energies and transition moments. The various approximations are carefully benchmarked, and conservative truncation thresholds are selected which guarantee errors much smaller than the intrinsic error of the ADC(2) method. Using the canonical values as reference, we find that the mean absolute error for both singlet and triplet ADC(2) excitation energies is 0.02 eV, while that for oscillator strengths is 0.001 a.u. The rigorous cutoff parameters together with the significantly reduced operation count and storage requirements allow us to obtain accurate ADC(2) excitation energies and transition properties using triple-ζ basis sets for systems of up to one hundred atoms.
Karimi, Hamid Reza; Gao, Huijun
2008-07-01
A mixed H2/Hinfinity output-feedback control design methodology is presented in this paper for second-order neutral linear systems with time-varying state and input delays. Delay-dependent sufficient conditions for the design of a desired control are given in terms of linear matrix inequalities (LMIs). A controller, which guarantees asymptotic stability and a mixed H2/Hinfinity performance for the closed-loop system of the second-order neutral linear system, is then developed directly instead of coupling the model to a first-order neutral system. A Lyapunov-Krasovskii method underlies the LMI-based mixed H2/Hinfinity output-feedback control design using some free weighting matrices. The simulation results illustrate the effectiveness of the proposed methodology.
Full Stability of Locally Optimal Solutions in Second-Order Cone Programs
Mordukhovich, B. S.; Outrata, Jiří; Sarabi, E.
2014-01-01
Roč. 24, č. 4 (2014), s. 1581-1613 ISSN 1052-6234 R&D Projects: GA ČR GAP402/12/1309 Grant - others:Australian Research Council(AU) DP-12092508; Australian Research Council(AU) DP-110102011; Portuguese Foundation of Science and Technologies(PT) MAT/11109; USA National Science Foundation(US) DMS-1007132 Institutional support: RVO:67985556 Keywords : variational analysis * second-order cone programming * full stability of local minimizers * nondegeneracy * strong regularity * quadratic growth * second-order subdifferentials * coderivatives Subject RIV: BA - General Mathematics Impact factor: 1.829, year: 2014 http://library.utia.cas.cz/separaty/2014/MTR/outrata-0434303.pdf
The second-order luminosity-redshift relation in a generic inhomogeneous cosmology
Ben-Dayan, Ido; Marozzi, Giovanni; Veneziano, Gabriele; Nugier, Fabien
2012-01-01
After recalling a general non-perturbative expression for the luminosity-redshift relation holding in a recently proposed 'geodesic light-cone' gauge, we show how it can be transformed to phenomenologically more convenient gauges in which cosmological perturbation theory is better understood. We present, in particular, the complete result on the luminosity-redshift relation in the Poisson gauge up to second order for a fairly generic perturbed cosmology, assuming that appreciable vector and tensor perturbations are only generated at second order. This relation provides a basic ingredient for the computation of the effects of stochastic inhomogeneities on precision dark-energy cosmology whose results we have anticipated in a recent letter. More generally, it can be used in connection with any physical information carried by light-like signals traveling along our past light-cone
Second-Order Perturbation Theory for Generalized Active Space Self-Consistent-Field Wave Functions.
Ma, Dongxia; Li Manni, Giovanni; Olsen, Jeppe; Gagliardi, Laura
2016-07-12
A multireference second-order perturbation theory approach based on the generalized active space self-consistent-field (GASSCF) wave function is presented. Compared with the complete active space (CAS) and restricted active space (RAS) wave functions, GAS wave functions are more flexible and can employ larger active spaces and/or different truncations of the configuration interaction expansion. With GASSCF, one can explore chemical systems that are not affordable with either CASSCF or RASSCF. Perturbation theory to second order on top of GAS wave functions (GASPT2) has been implemented to recover the remaining electron correlation. The method has been benchmarked by computing the chromium dimer ground-state potential energy curve. These calculations show that GASPT2 gives results similar to CASPT2 even with a configuration interaction expansion much smaller than the corresponding CAS expansion.
Sustainable institutionalized punishment requires elimination of second-order free-riders
Perc, Matjaž
2012-03-01
Although empirical and theoretical studies affirm that punishment can elevate collaborative efforts, its emergence and stability remain elusive. By peer-punishment the sanctioning is something an individual elects to do depending on the strategies in its neighborhood. The consequences of unsustainable efforts are therefore local. By pool-punishment, on the other hand, where resources for sanctioning are committed in advance and at large, the notion of sustainability has greater significance. In a population with free-riders, punishers must be strong in numbers to keep the ``punishment pool'' from emptying. Failure to do so renders the concept of institutionalized sanctioning futile. We show that pool-punishment in structured populations is sustainable, but only if second-order free-riders are sanctioned as well, and to a such degree that they cannot prevail. A discontinuous phase transition leads to an outbreak of sustainability when punishers subvert second-order free-riders in the competition against defectors.
Consensus Analysis of Second-Order Multiagent Systems with General Topology and Time Delay
Bo Liu
2013-01-01
Full Text Available This paper addresses the consensus of second-order multiagent systems with general topology and time delay based on the nearest neighbor rule. By using the Laplace transform technique, it is proved that the second-order multi-agent system in the presence of time-delay can reach consensus if the network topology contains a globally reachable node and time delay is bounded. The bound of time-delay only depends on eigenvalues of the Laplacian matrix of the system. The main contribution of this paper is that the accurate state of the consensus center and the upper bound of the communication delay to make the agents reach consensus are given. Some numerical simulations are given to illustrate the theoretical results.
Emergence of Lévy Walks from Second-Order Stochastic Optimization
Kuśmierz, Łukasz; Toyoizumi, Taro
2017-12-01
In natural foraging, many organisms seem to perform two different types of motile search: directed search (taxis) and random search. The former is observed when the environment provides cues to guide motion towards a target. The latter involves no apparent memory or information processing and can be mathematically modeled by random walks. We show that both types of search can be generated by a common mechanism in which Lévy flights or Lévy walks emerge from a second-order gradient-based search with noisy observations. No explicit switching mechanism is required—instead, continuous transitions between the directed and random motions emerge depending on the Hessian matrix of the cost function. For a wide range of scenarios, the Lévy tail index is α =1 , consistent with previous observations in foraging organisms. These results suggest that adopting a second-order optimization method can be a useful strategy to combine efficient features of directed and random search.
Periodic Solution of Second-Order Hamiltonian Systems with a Change Sign Potential on Time Scales
You-Hui Su
2009-01-01
Full Text Available This paper is concerned with the second-order Hamiltonian system on time scales 𝕋 of the form uΔΔ(ρ(t+μb(t|u(t|μ−2u(t+∇¯H(t,u(t=0, Δ-a.e. t∈[0,T]𝕋 , u(0−u(T=uΔ(ρ(0−uΔ(ρ(T=0, where 0,T∈𝕋. By using the minimax methods in critical theory, an existence theorem of periodic solution for the above system is established. As an application, an example is given to illustrate the result. This is probably the first time the existence of periodic solutions for second-order Hamiltonian system on time scales has been studied by critical theory.
Effect of pressure on the second-order Raman scattering intensities of zincblende semiconductors
Trallero-Giner, C.; Syassen, K. [Max-Planck-Institut fuer Festkoerperforschung, Heisenbergstrasse 1, 70569 Stuttgart (Germany)
2010-01-15
A microscopic description of the two-phonon scattering intensities in direct-gap zincblende-type semiconductors as a function of hydrostatic pressure and for non-resonant excitation is presented. The calculations were performed according to the electron-two-phonon deformation potential interaction for the {gamma}{sub 1} and {gamma}{sub 15} components of the Raman tensor. It is shown that the effect of pressure on the Raman scattering cross-section exhibits a complex behavior according to the contribution of the acoustical or optical phonons to the overtones and combinations. Second-order scattering intensities via acoustical modes could decrease or increase with increasing hydrostatic pressure, while for combinations or overtones of optical phonons a decreasing intensity is obtained. Calculations of the effect of pressure on second-order Raman intensities are compared to experimental results for ZnTe. (Abstract Copyright [2010], Wiley Periodicals, Inc.)
Second-order two-scale method for bending behaviors of composite plate with periodic configuration
Zhu Guoqing; Cui Junzhi
2010-01-01
In this paper, the second-order two-scale analysis method for bending behaviors of the plate made from composites with 3-D periodic configuration is presented by means of construction way. It can capture the microscopic 3-D mechanics behaviors caused from 3-D micro-structures. First, directly starting from the 3-D elastic plate model of composite materials with 3-D periodic configuration, three cell models are defined, and correspondingly the three classes of cell functions only defined on 3 normalized cells are constructed. And then, the effective homogenization parameters of composites are calculated from those local functions, it leads to a 2-D homogenized laminar plate problem. Next, to solve it the homogenization solution is obtained. Finally, the second-order two-scale solution is constructed from the micro-cell functions and the homogenization solution.
A second-order approximation of particle motion in the fringing field of a dipole magnet
Tarantin, N.I.
1980-01-01
The radial and axial motion of charged particles in the fringing field of an arbitrary dipole magnet has been considered with accuracy to the second-order of small quantities. The dipole magnet has an inhomogeneous field and oblique entrance and exit boundaries in the form of second-order curves. The region of the fringing field has a variable extension. A new definition of the effective boundary of the real fringing field has a variable extension. A new definition of the effective boundary of the real fringing field of the dipole magnet is used. A better understanding of the influence of the fringing magnetic field on the motion of charged particles in the pole gap of the dipole magnet has been obtained. In particular, it is shown that it is important to take into account, in the second approximation, some terms related formally to the next approximations. The results are presented in a form convenient for practical calculations. (orig.)
Kristensen, Kasper; Jørgensen, Poul; Jansik, Branislav
2012-01-01
We demonstrate that the divide-expand-consolidate (DEC) scheme – which has previously been used to determine the second-order Møller–Plesset (MP2) correlation energy – can be applied to evaluate the MP2 molecular gradient in a linear-scaling and embarrassingly parallel manner using a set of local......-box manner to ensure that the error in the DEC-MP2 correlation energy compared to a standard MP2 calculation is proportional to a single input threshold denoted the fragment optimization threshold (FOT). The FOT also implicitly controls the error in the DEC-MP2 molecular gradient as substantiated...... by a theoretical analysis and numerical results. The development of the DEC-MP2 molecular gradient is the initial step towards calculating higher order energy derivatives for large molecular systems using the DEC framework, both at the MP2 level of theory and for more accurate coupled-cluster methods....
ERRATUM: ON THE AUBIN PROPERTY OF CRITICAL POINTS TO PERTURBED SECOND-ORDER CONE PROGRAMS
Opazo, F.; Outrata, Jiří; Ramírez, H. C.
2017-01-01
Roč. 27, č. 3 (2017), s. 2143-2151 ISSN 1052-6234 R&D Projects: GA ČR GA15-00735S Institutional support: RVO:67985556 Keywords : second-order cone programming * Aubin property * nondegeneracy Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.968, year: 2016 http://library.utia.cas.cz/separaty/2017/MTR/outrata-0481868.pdf
Monotone methods for solving a boundary value problem of second order discrete system
Wang Yuan-Ming
1999-01-01
Full Text Available A new concept of a pair of upper and lower solutions is introduced for a boundary value problem of second order discrete system. A comparison result is given. An existence theorem for a solution is established in terms of upper and lower solutions. A monotone iterative scheme is proposed, and the monotone convergence rate of the iteration is compared and analyzed. The numerical results are given.
Karimov, Ruslan Kh; Kozhevnikova, Larisa M
2010-01-01
The first mixed problem with homogeneous Dirichlet boundary condition and initial function with compact support is considered for quasilinear second order parabolic equations in a cylindrical domain D=(0,∞)xΩ. Upper bounds are obtained, which give the rate of decay of the solutions as t→∞ as a function of the geometry of the unbounded domain Ω subset of R n , n≥2. Bibliography: 18 titles.
Contrast gain control in first- and second-order motion perception.
Lu, Z L; Sperling, G
1996-12-01
A novel pedestal-plus-test paradigm is used to determine the nonlinear gain-control properties of the first-order (luminance) and the second-order (texture-contrast) motion systems, that is, how these systems' responses to motion stimuli are reduced by pedestals and other masking stimuli. Motion-direction thresholds were measured for test stimuli consisting of drifting luminance and texture-contrast-modulation stimuli superimposed on pedestals of various amplitudes. (A pedestal is a static sine-wave grating of the same type and same spatial frequency as the moving test grating.) It was found that first-order motion-direction thresholds are unaffected by small pedestals, but at pedestal contrasts above 1-2% (5-10 x pedestal threshold), motion thresholds increase proportionally to pedestal amplitude (a Weber law). For first-order stimuli, pedestal masking is specific to the spatial frequency of the test. On the other hand, motion-direction thresholds for texture-contrast stimuli are independent of pedestal amplitude (no gain control whatever) throughout the accessible pedestal amplitude range (from 0 to 40%). However, when baseline carrier contrast increases (with constant pedestal modulation amplitude), motion thresholds increase, showing that gain control in second-order motion is determined not by the modulator (as in first-order motion) but by the carrier. Note that baseline contrast of the carrier is inherently independent of spatial frequency of the modulator. The drastically different gain-control properties of the two motion systems and prior observations of motion masking and motion saturation are all encompassed in a functional theory. The stimulus inputs to both first- and second-order motion process are normalized by feedforward, shunting gain control. The different properties arise because the modulator is used to control the first-order gain and the carrier is used to control the second-order gain.
Thandapani, Ethiraju; Kannan, Manju; Pinelas, Sandra
2016-01-01
In this paper, we present some sufficient conditions for the oscillation of all solutions of a second order forced impulsive delay differential equation with damping term. Three factors-impulse, delay and damping that affect the interval qualitative properties of solutions of equations are taken into account together. The results obtained in this paper extend and generalize some of the the known results for forced impulsive differential equations. An example is provided to illustrate the main result.
Electing police and crime commissioners in England and Wales, 2012 as second-order elections
Johnston, R.; Pattie, C.
2014-01-01
The first elections to the newly created 41 posts of Police and Crime Commissioner in England and Wales were held in November 2012. The results show all the main characteristics of second-order elections. Turnout was low. The two unpopular coalition parties in the national government lost vote share compared to the outcome of the most recent general election, whereas the main opposition party's share increased substantially-as did that of a minor party (UKIP). Labour, Liberal Democrat and UKI...
Second-order phase transition in gφ42 theory
Ganbold, G.; Efimov, G.V.
1993-08-01
We have suggested a regular scheme for calculating systematically the leading term and next corrections to it up to the fourth order for the effective potential in the scalar φ 4 2 theory. The obtained results give evidence in favour of a second-order phase transition at (g/2πm 2 ) crit ≅ 0.9 in the theory under consideration. (author). 18 refs, 1 fig
The Discursive Dimension of Second-order Elections: The Case of Czech Regional Elections 2012
Vašát, Petr; Čermák, Daniel
2016-01-01
Roč. 16, č. 2 (2016), s. 121-153 ISSN 1582-456X R&D Projects: GA ČR GAP404/12/0714 Institutional support: RVO:68378025 Keywords : second-order elections theory * discursive dimension of SOE * regional elections Subject RIV: AO - Sociology, Demography Impact factor: 0.458, year: 2016 http://www.sar.org.ro/polsci/?p=1248
Second order phase transition in two dimensional sine-Gordon field theory - lattice model
Babu Joseph, K.; Kuriakose, V.C.
1978-01-01
Two dimensional sine-Gordon (SG) field theory on a lattice is studied using the single-site basis variational method of Drell and others. The nature of the phase transition associated with the spontaneous symmetry breakdown in a SG field system is clarified to be of second order. A generalisation is offered for a SG-type field theory in two dimensions with a potential of the form [cossup(n)((square root of lambda)/m)phi-1].(author)
THE STABILITY OF THE PERIODIC SOLUTIONS OF SECOND ORDER HAMILTONIAN SYSTEMS
无
2000-01-01
This paper studies the stability of the periodic solutions of the second order Hamiltonian systems with even superquadratic or subquadratic potentials. The author proves that in the subquadratic case, there exist infinite geometrically distinct elliptic periodic solutions, and in the superquadratic case, there exist infinite geometrically distinct periodic solutions with at most one instability direction if they are half period non-degenerate, otherwise they are elliptic.
Learning to fear a second-order stimulus following vicarious learning
Reynolds, G; Field, AP; Askew, C
2015-01-01
Vicarious fear learning refers to the acquisition of fear via observation of the fearful responses of others. The present study aims to extend current knowledge by exploring whether second-order vicarious fear learning can be demonstrated in children. That is, whether vicariously learnt fear responses for one stimulus can be elicited in a second stimulus associated with that initial stimulus. Results demonstrated that children’s (5–11 years) fear responses for marsupials and caterpillars incr...
Pappas, Iosif
2016-01-01
PID controllers are extensively used in industry. Although many tuning methodologies exist, finding good controller settings is not an easy task and frequently optimization-based design is preferred to satisfy more complex criteria. In this thesis, the focus was to find which tuning approaches, if any, present close to optimal behavior. Pareto-optimal controllers were found for different first and second-order processes with time delay. Performance was quantified in terms of the integrat...
Identification of Dynamic Loads Based on Second-Order Taylor-Series Expansion Method
Li, Xiaowang; Deng, Zhongmin
2016-01-01
A new method based on the second-order Taylor-series expansion is presented to identify the structural dynamic loads in the time domain. This algorithm expresses the response vectors as Taylor-series approximation and then a series of formulas are deduced. As a result, an explicit discrete equation which associates system response, system characteristic, and input excitation together is set up. In a multi-input-multi-output (MIMO) numerical simulation study, sinusoidal excitation and white no...
Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations
FAN, WESLEY C.; DRUMM, CLIFTON R.; POWELL, JENNIFER L. email wcfan@sandia.gov
2002-01-01
The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations
Existence and convergence theorems for evolutionary hemivariational inequalities of second order
Zijia Peng
2015-03-01
Full Text Available This article concerns with a class of evolutionary hemivariational inequalities in the framework of evolution triple. Based on the Rothe method, monotonicity-compactness technique and the properties of Clarke's generalized derivative and gradient, the existence and convergence theorems to these problems are established. The main idea in the proof is using the time difference to construct the approximate problems. The work generalizes the existence results on evolution inclusions and hemivariational inequalities of second order.
Combined free and forced convection flow of a second order liquid through porous parallel walls
Mishra, S.P.
1977-01-01
An analysis of the flow of a second order fluid through porous parallel walls with heat transfer under the influence of buoyancy forces is carried out. Solutions for the velocity and temperature fields have been obtained by an iterative procedure. The flow phenomena have been characterized by parameters like: R (cross flow Reynolds number), Λ (elastic parameter), G (Grashof number), σ (Prandtl number) and the effects of these numbers on the flow characteristics have been presented in several graphs and tables. (author)
Error analysis of Newmark's method for the second order equation with inhomogeneous term
Chiba, F.; Kako, T.
2000-01-01
For the second order time evolution equation with a general dissipation term, we introduce a recurrence relation of Newmark's method. Deriving an energy inequality from this relation, we consider the stability and the convergence criteria of Newmark's method. We treat a dissipation term under the assumption that the coefficient-damping matrix is constant in time and non-negative. We can relax however the assumptions for the dissipation and the rigidity matrices to be arbitrary symmetric matrices. (author)
Chen, Zhangxin; Ewing, Richard E.
1996-01-01
Multigrid algorithms for nonconforming and mixed finite element methods for second order elliptic problems on triangular and rectangular finite elements are considered. The construction of several coarse-to-fine intergrid transfer operators for nonconforming multigrid algorithms is discussed. The equivalence between the nonconforming and mixed finite element methods with and without projection of the coefficient of the differential problems into finite element spaces is described.
Second-order Born approximation for the ionization of molecules by electron and positron impact
Dal Cappello, C. [Universite Paul Verlaine-Metz, Laboratoire de Physique Moleculaire et des Collisions, Institut Jean Barriol (FR2843), 1 Boulevard Arago, F-57078 Metz Cedex 3 (France); Rezkallah, Z.; Houamer, S. [Laboratoire de Physique Quantique et Systemes Dynamiques, Departement de Physique, Faculte des Sciences Universite Ferhat Abbas, Setif 19000 (Algeria); Charpentier, I. [Universite Paul Verlaine-Metz, Laboratoire de Physique et Mecanique des Materiaux UMR 7554, Ile du Saulcy, F-57045 Metz Cedex 1 (France); Hervieux, P. A. [Institut de Physique et Chimie des Materiaux de Strasbourg, 23 Rue du Loess, BP 43, F-67034 Strasbourg Cedex 2 (France); Ruiz-Lopez, M. F. [Nancy-University, Equipe de Chimie et Biochimie Theoriques, UMR CNRS-UHP 7565, BP 239, F-54506 Vandoeuvre-les-Nancy (France); Dey, R. [Max-Planck Institut fuer Plasmaphysik, Boltzmannstr. 2, D-85748 Garching (Germany); Roy, A. C. [School of Mathematical Sciences, Ramakrishna Mission Vivekananda University, Belur Math 711202, West Bengal (India)
2011-09-15
Second-order Born approximation is applied to study the ionization of molecules. The initial and final states are described by single-center wave functions. For the initial state a Gaussian wave function is used while for the ejected electron it is a distorted wave. Results of the present model are compared with recent (e,2e) experiments on the water molecule. Preliminary results are also presented for the ionization of the thymine molecule by electrons and positrons.
Second-order Hydrodynamics in QCD at NLO arXiv
Ghiglieri, Jacopo; Teaney, Derek
We compute the hydrodynamic relaxation times $\\tau_\\pi$ and $\\tau_j$ for hot QCD at next-to-leading order in the coupling by using kinetic theory. We show that certain dimensionless ratios of second-order to first-order transport coefficients obey bounds which apply whenever a kinetic theory description is possible; the computed values lie somewhat above these bounds. Strongly coupled theories with holographic duals strongly violate these bounds, highlighting their distance from a quasiparticle description.
Dynamics of second order in time evolution equations with state-dependent delay
Chueshov, I.; Rezunenko, Oleksandr
123-124, č. 1 (2015), s. 126-149 ISSN 0362-546X R&D Projects: GA ČR GAP103/12/2431 Institutional support: RVO:67985556 Keywords : Second order evolution equations * State dependent delay * Nonlinear plate * Finite-dimensional attractor Subject RIV: BD - Theory of Information Impact factor: 1.125, year: 2015 http://library.utia.cas.cz/separaty/2015/AS/rezunenko-0444708.pdf
Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations
Fan, W C; Powell, J L
2002-01-01
The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations.
Salih Yalcinbas
2016-01-01
Full Text Available In this study, a numerical approach is proposed to obtain approximate solutions of nonlinear system of second order boundary value problem. This technique is essentially based on the truncated Fermat series and its matrix representations with collocation points. Using the matrix method, we reduce the problem system of nonlinear algebraic equations. Numerical examples are also given to demonstrate the validity and applicability of the presented technique. The method is easy to implement and produces accurate results.
A Unified Introduction to Ordinary Differential Equations
Lutzer, Carl V.
2006-01-01
This article describes how a presentation from the point of view of differential operators can be used to (partially) unify the myriad techniques in an introductory course in ordinary differential equations by providing students with a powerful, flexible paradigm that extends into (or from) linear algebra. (Contains 1 footnote.)
Expressions for optical scalars and deflection angle at second order in terms of curvature scalars
Crisnejo, Gabriel; Gallo, Emanuel
2018-04-01
We present formal expressions for the optical scalars in terms of the curvature scalars in the weak gravitational lensing regime at second order in perturbations of a flat background without mentioning the extension of the lens or their shape. Also, by considering the thin lens approximation for static and axially symmetric configurations we obtain an expression for the second-order deflection angle which generalizes our previous result presented by Gallo and Moreschi [Phys. Rev. D 83, 083007 (2011)., 10.1103/PhysRevD.83.083007]. As applications of these formulas we compute the optical scalars for some known family of metrics, and we recover expressions for the deflection angle. In contrast to other works in the subject, our formalism allows a straightforward identification of how the different components of the curvature tensor contribute to the optical scalars and deflection angle. We also discuss in what sense the Schwarzschild solution can be thought as a true thin lens at second order.
An exactly solvable model for first- and second-order transitions
Klushin, L I; Skvortsov, A M; Gorbunov, A A
1998-01-01
The possibility of an exact analytical description of first-order and second-order transitions is demonstrated using a specific microscopic model. Predictions using the exactly calculated partition function are compared with those based on the Landau and Yang-Lee approaches. The model employed is an adsorbed polymer chain with an arbitrary number of links and an external force applied to its end, for which the variation of the partition function with the adsorption interaction parameter and the magnitude of the applied force is calculated. In the thermodynamic limit, the system has one isotropic and two anisotropic, ordered phases, each of which is characterized by two order parameters and between which first-order and second-order transitions occur and a bicritical point exists. The Landau free energy is found exactly as a function of each order parameter separately and, near the bicritical point, as a function of both of them simultaneously. An exact analytical formula is found for the distribution of the complex zeros of the partition function in first-order and second-order phase transitions. Hypotheses concerning the way in which the free energy and the positions of the complex zeros scale with the number of particles N in the system are verified. (reviews of topical problems)
A novel nonlinear adaptive filter using a pipelined second-order Volterra recurrent neural network.
Zhao, Haiquan; Zhang, Jiashu
2009-12-01
To enhance the performance and overcome the heavy computational complexity of recurrent neural networks (RNN), a novel nonlinear adaptive filter based on a pipelined second-order Volterra recurrent neural network (PSOVRNN) is proposed in this paper. A modified real-time recurrent learning (RTRL) algorithm of the proposed filter is derived in much more detail. The PSOVRNN comprises of a number of simple small-scale second-order Volterra recurrent neural network (SOVRNN) modules. In contrast to the standard RNN, these modules of a PSOVRNN can be performed simultaneously in a pipelined parallelism fashion, which can lead to a significant improvement in its total computational efficiency. Moreover, since each module of the PSOVRNN is a SOVRNN in which nonlinearity is introduced by the recursive second-order Volterra (RSOV) expansion, its performance can be further improved. Computer simulations have demonstrated that the PSOVRNN performs better than the pipelined recurrent neural network (PRNN) and RNN for nonlinear colored signals prediction and nonlinear channel equalization. However, the superiority of the PSOVRNN over the PRNN is at the cost of increasing computational complexity due to the introduced nonlinear expansion of each module.
Practical considerations for a second-order directional hearing aid microphone system
Thompson, Stephen C.
2003-04-01
First-order directional microphone systems for hearing aids have been available for several years. Such a system uses two microphones and has a theoretical maximum free-field directivity index (DI) of 6.0 dB. A second-order microphone system using three microphones could provide a theoretical increase in free-field DI to 9.5 dB. These theoretical maximum DI values assume that the microphones have exactly matched sensitivities at all frequencies of interest. In practice, the individual microphones in the hearing aid always have slightly different sensitivities. For the small microphone separation necessary to fit in a hearing aid, these sensitivity matching errors degrade the directivity from the theoretical values, especially at low frequencies. This paper shows that, for first-order systems the directivity degradation due to sensitivity errors is relatively small. However, for second-order systems with practical microphone sensitivity matching specifications, the directivity degradation below 1 kHz is not tolerable. A hybrid order directive system is proposed that uses first-order processing at low frequencies and second-order directive processing at higher frequencies. This hybrid system is suggested as an alternative that could provide improved directivity index in the frequency regions that are important to speech intelligibility.
Charge and finite size corrections for virtual photon spectra in second order Born approximation
Durgapal, P.
1982-01-01
The purpose of this work is to investigate the effects of finite nuclear size and charge on the spectrum of virtual photons emitted when a relativistic electron is scattered in the field of an atomic nucleus. The method consisted in expanding the scattering cross section in terms of integrals over the nuclear inelastic form factor with a kernel which was evaluated in second order Born approximation and was derived from the elastic-electron scattering form factor. The kernel could be evaluated analytically provided the elastic form factor contained only poles. For this reason the author used a Yukawa form factor. Before calculating the second order term the author studied the first order term containing finite size effects in the inelastic form factor. The author observed that the virtual photon spectrum is insensitive to the details of the inelastic distribution over a large range of energies and depends only on the transition radius. This gave the author the freedom of choosing an inelastic distribution for which the form factor has only poles and the author chose a modified form of the exponential distribution, which enabled the author to evaluate the matrix element analytically. The remaining integral over the physical momentum transfer was performed numerically. The author evaluated the virtual photon spectra for E1 and M1 transitions for a variety of electron energies using several nuclei and compared the results with the distorted wave calculations. Except for low energy and high Z, the second order results compared well with the distorted wave calculations
Meng, Shukai; Mo, Yu L.
2001-09-01
Image segmentation is one of the most important operations in many image analysis problems, which is the process that subdivides an image into its constituents and extracts those parts of interest. In this paper, we present a new second order difference gray-scale image segmentation algorithm based on cellular neural networks. A 3x3 CNN cloning template is applied, which can make smooth processing and has a good ability to deal with the conflict between the capability of noise resistance and the edge detection of complex shapes. We use second order difference operator to calculate the coefficients of the control template, which are not constant but rather depend on the input gray-scale values. It is similar to Contour Extraction CNN in construction, but there are some different in algorithm. The result of experiment shows that the second order difference CNN has a good capability in edge detection. It is better than Contour Extraction CNN in detail detection and more effective than the Laplacian of Gauss (LOG) algorithm.
Ordinary differential equations
Greenberg, Michael D
2014-01-01
Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps
Domoshnitsky, Alexander; Maghakyan, Abraham; Berezansky, Leonid
2017-01-01
In this paper a method for studying stability of the equation [Formula: see text] not including explicitly the first derivative is proposed. We demonstrate that although the corresponding ordinary differential equation [Formula: see text] is not exponentially stable, the delay equation can be exponentially stable.
Ordinary differential equations
Cox, William
1995-01-01
Building on introductory calculus courses, this text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts, including uniqueness and existence theorems, are worked through in detail and the student is encouraged to develop much of the routine material themselves, thus helping to ensure a solid understanding of the fundamentals required.The wide use of exercises, problems and self-assessment questions helps to promote a deeper understanding of the material and it is developed in such a way that it lays the groundwork for further
Ordinary differential equations
Miller, Richard K
1982-01-01
Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments. It is intended as a text for a first graduate course in differential equations for students in mathematics, engineering, and the sciences. Although differential equations is an old, traditional, and well-established subject, the diverse backgrounds and interests of the students in a typical modern-day course cause problems in the selection and method of presentation of material. In order to compensate for this diversity,
Jessica C Lee
Full Text Available In human causal learning, excitatory and inhibitory learning effects can sometimes be found in the same paradigm by altering the learning conditions. This study aims to explore whether learning in the feature negative paradigm can be dissociated by emphasising speed over accuracy. In two causal learning experiments, participants were given a feature negative discrimination in which the outcome caused by one cue was prevented by the addition of another. Participants completed training trials either in a self-paced fashion with instructions emphasising accuracy, or under strict time constraints with instructions emphasising speed. Using summation tests in which the preventative cue was paired with another causal cue, participants in the accuracy groups correctly rated the preventative cue as if it reduced the probability of the outcome. However, participants in the speed groups rated the preventative cue as if it increased the probability of the outcome. In Experiment 1, both speed and accuracy groups later judged the same cue to be preventative in a reasoned inference task. Experiment 2 failed to find evidence of similar dissociations in retrospective revaluation (release from overshadowing vs. mediated extinction or learning about a redundant cue (blocking vs. augmentation. However in the same experiment, the tendency for the accuracy group to show conditioned inhibition and the speed group to show second-order conditioning was consistent even across sub-sets of the speed and accuracy groups with equivalent accuracy in training, suggesting that second-order conditioning is not merely a consequence of poorer acquisition. This dissociation mirrors the trade-off between second-order conditioning and conditioned inhibition observed in animal conditioning when training is extended.
Second-Order Free-Riding on Antisocial Punishment Restores the Effectiveness of Prosocial Punishment
Szolnoki, Attila; Perc, Matjaž
2017-10-01
Economic experiments have shown that punishment can increase public goods game contributions over time. However, the effectiveness of punishment is challenged by second-order free-riding and antisocial punishment. The latter implies that noncooperators punish cooperators, while the former implies unwillingness to shoulder the cost of punishment. Here, we extend the theory of cooperation in the spatial public goods game by considering four competing strategies, which are traditional cooperators and defectors, as well as cooperators who punish defectors and defectors who punish cooperators. We show that if the synergistic effects are high enough to sustain cooperation based on network reciprocity alone, antisocial punishment does not deter public cooperation. Conversely, if synergistic effects are low and punishment is actively needed to sustain cooperation, antisocial punishment does is viable, but only if the cost-to-fine ratio is low. If the costs are relatively high, cooperation again dominates as a result of spatial pattern formation. Counterintuitively, defectors who do not punish cooperators, and are thus effectively second-order free-riding on antisocial punishment, form an active layer around punishing cooperators, which protects them against defectors that punish cooperators. A stable three-strategy phase that is sustained by the spontaneous emergence of cyclic dominance is also possible via the same route. The microscopic mechanism behind the reported evolutionary outcomes can be explained by the comparison of invasion rates that determine the stability of subsystem solutions. Our results reveal an unlikely evolutionary escape from adverse effects of antisocial punishment, and they provide a rationale for why second-order free-riding is not always an impediment to the evolutionary stability of punishment.
A second-order unconstrained optimization method for canonical-ensemble density-functional methods
Nygaard, Cecilie R.; Olsen, Jeppe
2013-03-01
A second order converging method of ensemble optimization (SOEO) in the framework of Kohn-Sham Density-Functional Theory is presented, where the energy is minimized with respect to an ensemble density matrix. It is general in the sense that the number of fractionally occupied orbitals is not predefined, but rather it is optimized by the algorithm. SOEO is a second order Newton-Raphson method of optimization, where both the form of the orbitals and the occupation numbers are optimized simultaneously. To keep the occupation numbers between zero and two, a set of occupation angles is defined, from which the occupation numbers are expressed as trigonometric functions. The total number of electrons is controlled by a built-in second order restriction of the Newton-Raphson equations, which can be deactivated in the case of a grand-canonical ensemble (where the total number of electrons is allowed to change). To test the optimization method, dissociation curves for diatomic carbon are produced using different functionals for the exchange-correlation energy. These curves show that SOEO favors symmetry broken pure-state solutions when using functionals with exact exchange such as Hartree-Fock and Becke three-parameter Lee-Yang-Parr. This is explained by an unphysical contribution to the exact exchange energy from interactions between fractional occupations. For functionals without exact exchange, such as local density approximation or Becke Lee-Yang-Parr, ensemble solutions are favored at interatomic distances larger than the equilibrium distance. Calculations on the chromium dimer are also discussed. They show that SOEO is able to converge to ensemble solutions for systems that are more complicated than diatomic carbon.
Second-Order Free-Riding on Antisocial Punishment Restores the Effectiveness of Prosocial Punishment
Attila Szolnoki
2017-10-01
Full Text Available Economic experiments have shown that punishment can increase public goods game contributions over time. However, the effectiveness of punishment is challenged by second-order free-riding and antisocial punishment. The latter implies that noncooperators punish cooperators, while the former implies unwillingness to shoulder the cost of punishment. Here, we extend the theory of cooperation in the spatial public goods game by considering four competing strategies, which are traditional cooperators and defectors, as well as cooperators who punish defectors and defectors who punish cooperators. We show that if the synergistic effects are high enough to sustain cooperation based on network reciprocity alone, antisocial punishment does not deter public cooperation. Conversely, if synergistic effects are low and punishment is actively needed to sustain cooperation, antisocial punishment does is viable, but only if the cost-to-fine ratio is low. If the costs are relatively high, cooperation again dominates as a result of spatial pattern formation. Counterintuitively, defectors who do not punish cooperators, and are thus effectively second-order free-riding on antisocial punishment, form an active layer around punishing cooperators, which protects them against defectors that punish cooperators. A stable three-strategy phase that is sustained by the spontaneous emergence of cyclic dominance is also possible via the same route. The microscopic mechanism behind the reported evolutionary outcomes can be explained by the comparison of invasion rates that determine the stability of subsystem solutions. Our results reveal an unlikely evolutionary escape from adverse effects of antisocial punishment, and they provide a rationale for why second-order free-riding is not always an impediment to the evolutionary stability of punishment.
Enhancing second-order conditioning with lesions of the basolateral amygdala.
Holland, Peter C
2016-04-01
Because the occurrence of primary reinforcers in natural environments is relatively rare, conditioned reinforcement plays an important role in many accounts of behavior, including pathological behaviors such as the abuse of alcohol or drugs. As a result of pairing with natural or drug reinforcers, initially neutral cues acquire the ability to serve as reinforcers for subsequent learning. Accepting a major role for conditioned reinforcement in everyday learning is complicated by the often-evanescent nature of this phenomenon in the laboratory, especially when primary reinforcers are entirely absent from the test situation. Here, I found that under certain conditions, the impact of conditioned reinforcement could be extended by lesions of the basolateral amygdala (BLA). Rats received first-order Pavlovian conditioning pairings of 1 visual conditioned stimulus (CS) with food prior to receiving excitotoxic or sham lesions of the BLA, and first-order pairings of another visual CS with food after that surgery. Finally, each rat received second-order pairings of a different auditory cue with each visual first-order CS. As in prior studies, relative to sham-lesioned control rats, lesioned rats were impaired in their acquisition of second-order conditioning to the auditory cue paired with the first-order CS that was trained after surgery. However, lesioned rats showed enhanced and prolonged second-order conditioning to the auditory cue paired with the first-order CS that was trained before amygdala damage was made. Implications for an enhanced role for conditioned reinforcement by drug-related cues after drug-induced alterations in neural plasticity are discussed. (PsycINFO Database Record (c) 2016 APA, all rights reserved).
Pegalajar Jurado, Antonio Manuel; Borg, Michael; Robertson, Amy
2017-01-01
In this study, we assess the impact of different wave kinematics models on the dynamic response of a tension-leg-platform wind turbine. Aero-hydro-elastic simulations of the floating wind turbine are carried out employing linear, second-order, and fully nonlinear kinematics using the Morison equa...... damping coefficients in the model by a more detailed, customizable definition of the user-defined numerical damping....
Bond index: relation to second-order density matrix and charge fluctuations
Giambiagi, M.S. de; Giambiagi, M.; Jorge, F.E.
1985-01-01
It is shown that, in the same way as the atomic charge is an invariant built from the first-order density matrix, the closed-shell generalized bond index is an invariant associated with the second-order reduced density matrix. The active charge of an atom (sum of bond indices) is shown to be the sum of all density correlation functions between it and the other atoms in the molecule; similarly, the self-charge is the fluctuation of its total charge. (Author) [pt
An efficient second-order SQP method for structural topology optimization
Rojas Labanda, Susana; Stolpe, Mathias
2016-01-01
This article presents a Sequential Quadratic Programming (SQP) solver for structural topology optimization problems named TopSQP. The implementation is based on the general SQP method proposed in Morales et al. J Numer Anal 32(2):553–579 (2010) called SQP+. The topology optimization problem...... nonlinear solvers IPOPT and SNOPT. Numerical experiments on a large set of benchmark problems show good performance of TopSQP in terms of number of function evaluations. In addition, the use of second-order information helps to decrease the objective function value....
Mohammad Mokim
2017-10-01
Full Text Available We demonstrate an effective microspectroscopy technique by tracing the dispersion of second order nonlinear susceptibility (χ(2 in a monolayer tungsten diselenide (WSe2. The χ(2 dispersion obtained with better than 3 meV photon energy resolution showed peak value being within 6.3-8.4×10-19 m2/V range. We estimate the fundamental bandgap to be at 2.2 eV. Sub-structure in the χ(2 dispersion reveals a contribution to the nonlinearity due to exciton transitions with exciton binding energy estimated to be at 0.7 eV.
Non-commutative gauge Gravity: Second- order Correction and Scalar Particles Creation
Zaim, S.
2009-01-01
A noncommutative gauge theory for a charged scalar field is constructed. The invariance of this model under local Poincare and general coordinate transformations is verified. Using the general modified field equation, a general Klein-Gordon equation up to the second order of the noncommu- tativity parameter is derived. As an application, we choose the Bianchi I universe. Using the Seiberg-Witten maps, the deformed noncommutative metric is obtained and a particle production process is studied. It is shown that the noncommutativity plays the same role as an electric field, gravity and chemical potential.
Kepner, Gordon R
2010-04-13
The numerous natural phenomena that exhibit saturation behavior, e.g., ligand binding and enzyme kinetics, have been approached, to date, via empirical and particular analyses. This paper presents a mechanism-free, and assumption-free, second-order differential equation, designed only to describe a typical relationship between the variables governing these phenomena. It develops a mathematical model for this relation, based solely on the analysis of the typical experimental data plot and its saturation characteristics. Its utility complements the traditional empirical approaches. For the general saturation curve, described in terms of its independent (x) and dependent (y) variables, a second-order differential equation is obtained that applies to any saturation phenomena. It shows that the driving factor for the basic saturation behavior is the probability of the interactive site being free, which is described quantitatively. Solving the equation relates the variables in terms of the two empirical constants common to all these phenomena, the initial slope of the data plot and the limiting value at saturation. A first-order differential equation for the slope emerged that led to the concept of the effective binding rate at the active site and its dependence on the calculable probability the interactive site is free. These results are illustrated using specific cases, including ligand binding and enzyme kinetics. This leads to a revised understanding of how to interpret the empirical constants, in terms of the variables pertinent to the phenomenon under study. The second-order differential equation revealed the basic underlying relations that describe these saturation phenomena, and the basic mathematical properties of the standard experimental data plot. It was shown how to integrate this differential equation, and define the common basic properties of these phenomena. The results regarding the importance of the slope and the new perspectives on the empirical
Sturm-Picone type theorems for second-order nonlinear differential equations
Aydin Tiryaki
2014-06-01
Full Text Available The aim of this article is to give Sturm-Picone type theorems for the pair of second-order nonlinear differential equations $$\\displaylines{ (p_1(t|x'|^{\\alpha-1}x''+q_1(tf_1(x=0 \\cr (p_2(t|y'|^{\\alpha-1}y''+q_2(tf_2(y=0,\\quad t_1
Origin of second-order transverse magnetic anisotropy in Mn12-acetate
Cornia, A.; Sessoli, R.; Sorace, L.; Gatteschi, D.; Barra, A. L.; Daiguebonne, C.
2002-01-01
The symmetry breaking effects for quantum tunneling of the magnetization in Mn 12 -acetate, a molecular nanomagnet, represent an open problem. We present structural evidence that the disorder of the acetic acid of crystallization induces sizable distortion of the Mn(III) sites, giving rise to six different isomers. Four isomers have symmetry lower than tetragonal and a nonzero second-order transverse magnetic anisotropy, which has been evaluated using a ligand field approach. The result of the calculation leads to an improved simulation of electron paramagnetic resonance spectra and justifies the tunnel splitting distribution derived from the field sweep rate dependence of the hysteresis loops
A new simple model for composite fading channels: Second order statistics and channel capacity
Yilmaz, Ferkan
2010-09-01
In this paper, we introduce the most general composite fading distribution to model the envelope and the power of the received signal in such fading channels as millimeter wave (60 GHz or above) fading channels and free-space optical channels, which we term extended generalized-K (EGK) composite fading distribution. We obtain the second-order statistics of the received signal envelope characterized by the EGK composite fading distribution. Expressions for probability density function, cumulative distribution function, level crossing rate and average fade duration, moments, amount of fading and average capacity are derived. Numerical and computer simulation examples validate the accuracy of the presented mathematical analysis. © 2010 IEEE.
Effect of Second-Order Hydrodynamics on a Floating Offshore Wind Turbine
Roald, L.; Jonkman, J.; Robertson, A.
2014-05-01
The design of offshore floating wind turbines uses design codes that can simulate the entire coupled system behavior. At the present, most codes include only first-order hydrodynamics, which induce forces and motions varying with the same frequency as the incident waves. Effects due to second- and higher-order hydrodynamics are often ignored in the offshore industry, because the forces induced typically are smaller than the first-order forces. In this report, first- and second-order hydrodynamic analysis used in the offshore oil and gas industry is applied to two different wind turbine concepts--a spar and a tension leg platform.
Four New Applications of Second-Order Generalized Integrator Quadrature Signal Generator
Xin, Zhen; Zhao, Rende; Wang, Xiongfei
2016-01-01
The Second-Order Generalized Integrator (SOGI) was used as a building block for the SOGI-Quadrature-Signal Generator (SOGI-QSG) which has been widely used for grid synchronization, frequency estimation, and harmonic extraction over the past decade. This paper further investigates its integration...... and differentiation characteristics, with four new integrators and differentiators proposed. Theoretical analysis shows that the proposed SOGI-QSG based integration and differentiation methods can effectively overcome the drawbacks of the pure integrator and differentiator. The proposed four new methods...
Heighway, E.A.
1980-07-01
A second order beam transport design code with parametric optimization is described. The code analyzes the transport of charged particle beams through a user defined magnet system. The magnet system parameters are varied (within user defined limits) until the properties of the transported beam and/or the system transport matrix match those properties requested by the user. The code uses matrix formalism to represent the transport elements and optimization is achieved using the variable metric method. Any constraints that can be expressed algebraically may be included by the user as part of his design. Instruction in the use of the program is given. (auth)
Xin, Zhen; Qin, Zian; Lu, Minghui
2016-01-01
Due to the simplicity and flexibility of the structure of the Second-Order Generalized Integrator based Quadrature Signal Generator (SOGI-QSG), it has been widely used over the past decade for many applications such as frequency estimation, grid synchronization, and harmonic extraction. However......, the SOGI-QSG will produce errors when its input signal contains a dc component or harmonic components with unknown frequencies. The accuracy of the signal detection methods using it may hence be compromised. To overcome the drawback, the First-Order System (FOS) concept is first used to illustrate...
Adaptive Second-Order Total Variation: An Approach Aware of Slope Discontinuities
Lenzen, Frank; Becker, Florian; Lellmann, Jan
2013-01-01
Total variation (TV) regularization, originally introduced by Rudin, Osher and Fatemi in the context of image denoising, has become widely used in the field of inverse problems. Two major directions of modifications of the original approach were proposed later on. The first concerns adaptive variants of TV regularization, the second focuses on higher-order TV models. In the present paper, we combine the ideas of both directions by proposing adaptive second-order TV models, including one anisotropic model. Experiments demonstrate that introducing adaptivity results in an improvement of the reconstruction error. © 2013 Springer-Verlag.
A second-order shock-expansion method applicable to bodies of revolution near zero lift
1957-01-01
A second-order shock-expansion method applicable to bodies of revolution is developed by the use of the predictions of the generalized shock-expansion method in combination with characteristics theory. Equations defining the zero-lift pressure distributions and the normal-force and pitching-moment derivatives are derived. Comparisons with experimental results show that the method is applicable at values of the similarity parameter, the ratio of free-stream Mach number to nose fineness ratio, from about 0.4 to 2.
Practical Calculation of Second-order Supersonic Flow past Nonlifting Bodies of Revolution
Van Dyke, Milton D
1952-01-01
Calculation of second-order supersonic flow past bodies of revolution at zero angle of attack is described in detail, and reduced to routine computation. Use of an approximate tangency condition is shown to increase the accuracy for bodies with corners. Tables of basic functions and standard computing forms are presented. The procedure is summarized so that one can apply it without necessarily understanding the details of the theory. A sample calculation is given, and several examples are compared with solutions calculated by the method of characteristics.
Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides
Reddy, D. V.; Raymer, M. G.; McKinstrie, C. J.
2013-01-01
in a transparent optical network using temporally orthogonal waveforms to encode different channels. We model the process using coupled-mode equations appropriate for wave mixing in a uniform second-order nonlinear optical medium pumped by a strong laser pulse. We find Green functions describing the process...... in this optimal regime. We also find an operating regime in which high-efficiency frequency conversion without temporal-shape selectivity can be achieved while preserving the shapes of a wide class of input pulses. The results are applicable to both classical and quantum frequency conversion....
Ermolaev, P; Volynsky, M
2014-01-01
Recurrent stochastic data processing algorithms using representation of interferometric signal as output of a dynamic system, which state is described by vector of parameters, in some cases are more effective, compared with conventional algorithms. Interferometric signals depend on phase nonlinearly. Consequently it is expedient to apply algorithms of nonlinear stochastic filtering, such as Kalman type filters. An application of the second order extended Kalman filter and Markov nonlinear filter that allows to minimize estimation error is described. Experimental results of signals processing are illustrated. Comparison of the algorithms is presented and discussed.
Instrumentation amplifier implements second-order active low-pass filter with high gain factor
Blomqvist, Kim H; Eskelinen, Pekka; Sepponen, Raimo E
2011-01-01
A single-ended second-order active low-pass filter can simultaneously provide high gain factor and dc voltage subtraction. This makes it possible to reduce the number of components and signal processing stages needed in an application where small voltage changes are measured on the top of large dc voltage masked by a large amplitude oscillating carrier. The filter described in this paper is constructed from a conventional 3-op-amp instrumentation amplifier and five passive circuit elements. (technical design note)
Exceptional points near first- and second-order quantum phase transitions.
Stránský, Pavel; Dvořák, Martin; Cejnar, Pavel
2018-01-01
We study the impact of quantum phase transitions (QPTs) on the distribution of exceptional points (EPs) of the Hamiltonian in the complex-extended parameter domain. Analyzing first- and second-order QPTs in the Lipkin-Meshkov-Glick model we find an exponentially and polynomially close approach of EPs to the respective critical point with increasing size of the system. If the critical Hamiltonian is subject to random perturbations of various kinds, the averaged distribution of EPs close to the critical point still carries decisive information on the QPT type. We therefore claim that properties of the EP distribution represent a parametrization-independent signature of criticality in quantum systems.
Stochastic bounded consensus of second-order multi-agent systems in noisy environment
Ren Hong-Wei; Deng Fei-Qi
2017-01-01
This paper investigates the stochastic bounded consensus of leader-following second-order multi-agent systems in a noisy environment. It is assumed that each agent received the information of its neighbors corrupted by noises and time delays. Based on the graph theory, stochastic tools, and the Lyapunov function method, we derive the sufficient conditions under which the systems would reach stochastic bounded consensus in mean square with the protocol we designed. Finally, a numerical simulation is illustrated to check the effectiveness of the proposed algorithms. (paper)
Team Resilience as a Second-Order Emergent State: A Theoretical Model and Research Directions
Clint Bowers
2017-08-01
Full Text Available Resilience has been recognized as an important phenomenon for understanding how individuals overcome difficult situations. However, it is not only individuals who face difficulties; it is not uncommon for teams to experience adversity. When they do, they must be able to overcome these challenges without performance decrements.This manuscript represents a theoretical model that might be helpful in conceptualizing this important construct. Specifically, it describes team resilience as a second-order emergent state. We also include research propositions that follow from the model.
Second-order domain derivative of normal-dependent boundary integrals
Balzer, Jonathan
2010-03-17
Numerous reconstruction tasks in (optical) surface metrology allow for a variational formulation. The occurring boundary integrals may be interpreted as shape functions. The paper is concerned with the second-order analysis of such functions. Shape Hessians of boundary integrals are considered difficult to find analytically because they correspond to third-order derivatives of an, in a sense equivalent, domain integral. We complement previous results by considering cost functions depending explicitly on the surface normal. The correctness and practicability of our calculations are verified in the context of a Newton-type shape reconstruction method. © 2010 Birkhäuser / Springer Basel AG.
Solution of Euler unsteady equations using a second order numerical scheme
Devos, J.P.
1992-08-01
In thermal power plants, the steam circuits experience incidents due to the noise and vibration induced by trans-sonic flow. In these configurations, the compressible fluid can be considered the perfect ideal. Euler equations therefore constitute a good model. However, processing of the discontinuities induced by the shockwaves are a particular problem. We give a bibliographical synthesis of the work done on this subject. The research by Roe and Harten leads to TVD (Total Variation Decreasing) type schemes. These second order schemes generate no oscillation and converge towards physically acceptable weak solutions. (author). 12 refs
Bartosz, Krzysztof; Denkowski, Zdzisław; Kalita, Piotr
In this paper the sensitivity of optimal solutions to control problems described by second order evolution subdifferential inclusions under perturbations of state relations and of cost functionals is investigated. First we establish a new existence result for a class of such inclusions. Then, based on the theory of sequential [Formula: see text]-convergence we recall the abstract scheme concerning convergence of minimal values and minimizers. The abstract scheme works provided we can establish two properties: the Kuratowski convergence of solution sets for the state relations and some complementary [Formula: see text]-convergence of the cost functionals. Then these two properties are implemented in the considered case.
Calculation of three-dimensional groundwater transport using second-order moments
Pepper, D.W.; Stephenson, D.E.
1987-01-01
Groundwater transport of contaminants from the F-Area seepage basin at the Savannah River Plant (SRP) was calculated using a three-dimensional, second-order moment technique. The numerical method calculates the zero, first, and second moment distributions of concentration within a cell volume. By summing the moments over the entire solution domain, and using a Lagrangian advection scheme, concentrations are transported without numerical dispersion errors. Velocities obtained from field tests are extrapolated and interpolated to all nodal points; a variational analysis is performed over the three-dimensional velocity field to ensure mass consistency. Transport predictions are calculated out to 12,000 days. 28 refs., 9 figs
Fairouz Zouyed
2015-01-01
Full Text Available This paper discusses the inverse problem of determining an unknown source in a second order differential equation from measured final data. This problem is ill-posed; that is, the solution (if it exists does not depend continuously on the data. In order to solve the considered problem, an iterative method is proposed. Using this method a regularized solution is constructed and an a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, numerical results are presented to illustrate the accuracy and efficiency of this method.
Kinetics of two simultaneous second-order reactions occurring in different zones
Dole, M.; Hsu, C.S.; Patel, V.M.; Patel, G.N.
1975-01-01
Equations have been derived for the case of free radicals recombining according to the second-order kinetics with or without diffusion control under the conditions that there are two simultaneous spatially separated recombination reactions but that only the overall free-radical concentration can be observed. The properties of these equations are discussed and methods for determining the three independent parameters in the first case and five in the second developed. The resulting equations have been applied to the interpretation of data obtained in studying the decay of allyl chain free radicals in irradiated extended chain crystalline polyethylene
Semantic Characterisations of Second-Order Computability over the Real Numbers
Korovina, Margarita V.; Kudinov, Oleg V.
2001-01-01
equality and prove theorems which connect computable operators and real-valued functionals with validity of finite σ-formulas. This research was supported in part by the RFBR (grants N 99-01-00485, N 00-01-00810) and by the Siberian Division of RAS (a grant for young researchers, 2000)......We propose semantic characterisations of second-order computability over the reals based on σ-definability theory. Notions of computability for operators and real-valued functionals defined on the class of continuous functions are introduced via domain theory. We consider the reals with and without...
Brandt, H.E.
1983-01-01
A new exact symmetry is proved for the complete second-order nonlinear conductivity tensor of an unmagnetized relativistic turbulent plasma. The symmetry is not limited to principal parts. If Cerenkov resonance is ignored, the new symmetry reduces to the well-known symmetry related to the Manley--Rowe relations, crossing symmetry, and nondissipation of the principal part of the nonlinear current. Also, a new utilitarian representation for the complete tensor is obtained in which all derivatives are removed and the pole structure is clearly exhibited
The mass polarization effect in He-like ions: first and second order
Bhatia, A K; Drachman, Richard J
2003-01-01
In a paper with a similar title, Yamanaka has calculated the mass polarization effect (to first order in μ/M) for several low-lying states of the two-electron atoms and ions with atomic number Z from 2 to 10. Here we improve the previous results by using Hylleraas variational wavefunctions with up to 560 terms and extend the calculation to include some additional states and the Z = 1 ground state. In addition, we compute the second-order effect using the method of pseudostate summation. A nonperturbative method of computation is also discussed and used as a check
Kohn–Sham exchange-correlation potentials from second-order reduced density matrices
Cuevas-Saavedra, Rogelio; Staroverov, Viktor N., E-mail: vstarove@uwo.ca [Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7 (Canada); Ayers, Paul W. [Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1 (Canada)
2015-12-28
We describe a practical algorithm for constructing the Kohn–Sham exchange-correlation potential corresponding to a given second-order reduced density matrix. Unlike conventional Kohn–Sham inversion methods in which such potentials are extracted from ground-state electron densities, the proposed technique delivers unambiguous results in finite basis sets. The approach can also be used to separate approximately the exchange and correlation potentials for a many-electron system for which the reduced density matrix is known. The algorithm is implemented for configuration-interaction wave functions and its performance is illustrated with numerical examples.
Second-Order Statistics for Wave Propagation through Complex Optical Systems
Yura, H.T.; Hanson, Steen Grüner
1989-01-01
Closed-form expressions are derived for various statistical functions that arise in optical propagation through arbitrary optical systems that can be characterized by a complex ABCD matrix in the presence of distributed random inhomogeneities along the optical path. Specifically, within the second......-order Rytov approximation, explicit general expressions are presented for the mutual coherence function, the log-amplitude and phase correlation functions, and the mean-square irradiance that are obtained in propagation through an arbitrary paraxial ABCD optical system containing Gaussian-shaped limiting...
Second-Order Moller-Plesset Perturbation Theory for Molecular Dirac-Hartree-Fock Wave Functions
Dyall, Kenneth G.; Arnold, James O. (Technical Monitor)
1994-01-01
Moller-Plesset perturbation theory is developed to second order for a selection of Kramers restricted Dirac-Hartree-Fock closed and open-shell reference wave functions. The open-shell wave functions considered are limited to those with no more than two electrons in open shells, but include the case of a two-configuration SCF reference. Denominator shifts are included in the style of Davidson's OPT2 method. An implementation which uses unordered integrals with labels is presented, and results are given for a few test cases.
Mixed FEM for Second Order Elliptic Problems on Polygonal Meshes with BEM-Based Spaces
Efendiev, Yalchin
2014-01-01
We present a Boundary Element Method (BEM)-based FEM for mixed formulations of second order elliptic problems in two dimensions. The challenge, we would like to address, is a proper construction of H(div)-conforming vector valued trial functions on arbitrary polygonal partitions of the domain. The proposed construction generates trial functions on polygonal elements which inherit some of the properties of the unknown solution. In the numerical realization, the relevant local problems are treated by means of boundary integral formulations. We test the accuracy of the method on two model problems. © 2014 Springer-Verlag.
Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations
Abdulle, Assyr
2013-01-01
We introduce a new family of explicit integrators for stiff Itô stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer from the step size reduction faced by standard explicit methods. The family is based on the standard second order orthogonal Runge-Kutta-Chebyshev (ROCK2) methods for deterministic problems. The convergence, meansquare, and asymptotic stability properties of the methods are analyzed. Numerical experiments, including applications to nonlinear SDEs and parabolic stochastic partial differential equations are presented and confirm the theoretical results. © 2013 Society for Industrial and Applied Mathematics.
A canonical form of the equation of motion of linear dynamical systems
Kawano, Daniel T.; Salsa, Rubens Goncalves; Ma, Fai; Morzfeld, Matthias
2018-03-01
The equation of motion of a discrete linear system has the form of a second-order ordinary differential equation with three real and square coefficient matrices. It is shown that, for almost all linear systems, such an equation can always be converted by an invertible transformation into a canonical form specified by two diagonal coefficient matrices associated with the generalized acceleration and displacement. This canonical form of the equation of motion is unique up to an equivalence class for non-defective systems. As an important by-product, a damped linear system that possesses three symmetric and positive definite coefficients can always be recast as an undamped and decoupled system.
Batty, Christopher
2017-02-01
This paper introduces a two-dimensional cell-centred finite volume discretization of the Poisson problem on adaptive Cartesian quadtree grids which exhibits second order accuracy in both the solution and its gradients, and requires no grading condition between adjacent cells. At T-junction configurations, which occur wherever resolution differs between neighboring cells, use of the standard centred difference gradient stencil requires that ghost values be constructed by interpolation. To properly recover second order accuracy in the resulting numerical gradients, prior work addressing block-structured grids and graded trees has shown that quadratic, rather than linear, interpolation is required; the gradients otherwise exhibit only first order convergence, which limits potential applications such as fluid flow. However, previous schemes fail or lose accuracy in the presence of the more complex T-junction geometries arising in the case of general non-graded quadtrees, which place no restrictions on the resolution of neighboring cells. We therefore propose novel quadratic interpolant constructions for this case that enable second order convergence by relying on stencils oriented diagonally and applied recursively as needed. The method handles complex tree topologies and large resolution jumps between neighboring cells, even along the domain boundary, and both Dirichlet and Neumann boundary conditions are supported. Numerical experiments confirm the overall second order accuracy of the method in the L∞ norm.
Relation between second-order moment radius of focal spot and near field distribution of laser beam
Gao Xueyan; Su Yi; Ye Yidong; Guan Youguang
2011-01-01
In order to analyze the effect of aberration of amplitude and phase of laser beam on second-order moment radius of focal spot, based on the Fraunhofer formula for light wave scalar diffraction theory and the definition of second-order moment radius, the general expression for focal spot second-order moment radius depending on the complex amplitude of near field is derived. The second-order moment radius of the focal spot depending on intensity distribution and phase distribution of near field is derived, and its clear physical meaning is described. The second-order moment radius and the divergence angle of focal spot may be easily calculated with the second-order moment radius expression of focal spot. At last, the divergence angles of focal spots of several kinds of Gaussian laser beams are calculated directly, and the results are in accordance with those in the related references. (authors)
Staff Association
2011-01-01
Tuesday 12 April at 14.00 Council Chamber, Bldg 503 In conformity with the Statutes of the Staff Association, an ordinary General Assembly is organized once a year (article IV.2.1). Agenda Adoption of the Agenda Approval of the Draft Minutes of the Ordinary General Assembly of 20 April 2010 Presentation and approval of the Activity Report 2010 Presentation and approval of the Financial Report 2010 Presentation and approval of the Auditors Report 2010 Programme for 2011 Presentation et and approval of the draft budget and subscription rate 2012 Election of the Election Committee Election of the Board of Auditors Miscellaneous We remind members of article IV.3.4 in the Statutes of the Association which reads: “After having dealt with all the items on the agenda, the members may, with the consent of the Assembly, have other matters discussed, but decisions may be taken only on the items listed on the agenda. Nevertheless, the Assembly ma...
Association du personnel
2010-01-01
Tuesday 20 April at 10.00 Council Chamber, Bldg 503 In conformity with the Statutes of the Staff Association, an ordinary General Assembly is organized once a year (article IV.2.1). Agenda Adoption of the Agenda Approval of the Draft Minutes of the Ordinary General Assembly of 12 May 2009 Presentation and approval of the Activity Report 2009 Presentation and approval of the Financial Report 2009 Presentation and approval of the Auditors Report 2009 Programme for 2010 Presentation et and approval of the draft budget and subscription rate 2010 Modifications to the statutes of the association Election of the Election Committee Election of the Board of Auditors Miscellaneous We remind members of article IV.3.4 in the Statutes of the Association which reads: “After having dealt with all the items on the agenda, the members may, with the consent of the Assembly, have other matters discussed, but decisions may be taken only on the items listed on the agenda...
Staff Association
2011-01-01
Tuesday 12 April at 14.00 Council Chamber, Bldg 503 In conformity with the Statutes of the Staff Association, an ordinary General Assembly is organized once a year (article IV.2.1). Agenda Adoption of the Agenda Approval of the Draft Minutes of the Ordinary General Assembly of 20 April 2010 Presentation and approval of the Activity Report 2010 Presentation and approval of the Financial Report 2010 Presentation and approval of the Auditors Report 2010 Programme for 2011 Presentation and approval of the draft budget and subscription rate 2012 Election of the Election Committee Election of the Board of Auditors Miscellaneous We remind members of article IV.3.4 in the Statutes of the Association which reads: “After having dealt with all the items on the agenda, the members may, with the consent of the Assembly, have other matters discussed, but decisions may be taken only on the items listed on the agenda. Nevertheless, the Assembly may r...
Staff Association
2010-01-01
Tuesday 20 April at 10.00 Council Chamber, Bldg 503 In conformity with the Statutes of the Staff Association, an ordinary General Assembly is organized once a year (article IV.2.1). Agenda Adoption of the Agenda Approval of the Draft Minutes of the Ordinary General Assembly of 12 May 2009 Presentation and approval of the Activity Report 2009 Presentation and approval of the Financial Report 2009 Presentation and approval of the Auditors Report 2009 Programme for 2010 Presentation et and approval of the draft budget and subscription rate 2010 Election of the Election Committee Election of the Board of Auditors Miscellaneous We remind members of article IV.3.4 in the Statutes of the Association which reads: “After having dealt with all the items on the agenda, the members may, with the consent of the Assembly, have other matters discussed, but decisions may be taken only on the items listed on the agenda. Nevertheless, the Assembly may require t...
Learning to fear a second-order stimulus following vicarious learning.
Reynolds, Gemma; Field, Andy P; Askew, Chris
2017-04-01
Vicarious fear learning refers to the acquisition of fear via observation of the fearful responses of others. The present study aims to extend current knowledge by exploring whether second-order vicarious fear learning can be demonstrated in children. That is, whether vicariously learnt fear responses for one stimulus can be elicited in a second stimulus associated with that initial stimulus. Results demonstrated that children's (5-11 years) fear responses for marsupials and caterpillars increased when they were seen with fearful faces compared to no faces. Additionally, the results indicated a second-order effect in which fear-related learning occurred for other animals seen together with the fear-paired animal, even though the animals were never observed with fearful faces themselves. Overall, the findings indicate that for children in this age group vicariously learnt fear-related responses for one stimulus can subsequently be observed for a second stimulus without it being experienced in a fear-related vicarious learning event. These findings may help to explain why some individuals do not recall involvement of a traumatic learning episode in the development of their fear of a specific stimulus.
Second-order hydrodynamics and universality in non-conformal holographic fluids
Kleinert, Philipp; Probst, Jonas
2016-01-01
We study second-order hydrodynamic transport in strongly coupled non-conformal field theories with holographic gravity duals in asymptotically anti-de Sitter space. We first derive new Kubo formulae for five second-order transport coefficients in non-conformal fluids in (3+1) dimensions. We then apply them to holographic RG flows induced by scalar operators of dimension Δ=3. For general background solutions of the dual bulk geometry, we find explicit expressions for the five transport coefficients at infinite coupling and show that a specific combination, H̃=2ητ π −2(κ−κ ∗ )−λ 2 , always vanishes. We prove analytically that the Haack-Yarom identity H=2ητ π −4λ 1 −λ 2 =0, which is known to be true for conformal holographic fluids at infinite coupling, also holds when taking into account leading non-conformal corrections. The numerical results we obtain for two specific families of RG flows suggest that H vanishes regardless of conformal symmetry. Our work provides further evidence that the Haack-Yarom identity H=0 may be universally satisfied by strongly coupled fluids.
Second order numerical method of two-fluid model of air-water flow
Tiselj, I.; Petelin, S.
1995-01-01
Model considered in this paper is six-equation two-fluid model used in computer code RELAP5. Air-water equations were taken in a code named PDE to avoid additional problems caused by condensation or vaporization. Terms with space derivatives were added in virtual mass term in momentum equations to ensure the hyperbolicity of the equations. Numerical method in PDE code is based on approximate Riemann solvers. Equations are solved on non-staggered grid with explicit time advancement and with upwind discretization of the convective terms in characteristic form of the equations. Flux limiters are used to find suitable combinations of the first (upwind) and the second order (Lax-Wendroff) discretization s which ensure second order accuracy on smooth solutions and damp oscillations around the discontinuities. Because of the small time steps required and because of its non-dissipative nature the scheme is suitable for the prediction of the fast transients: pressure waves, shock and rarefaction waves, water hammer or critical flow. Some preliminary results are presented for a shock tube problem and for Water Faucet problem - problems usually used as benchmarks for two-fluid computer codes. (author)
First and second order derivatives for optimizing parallel RF excitation waveforms.
Majewski, Kurt; Ritter, Dieter
2015-09-01
For piecewise constant magnetic fields, the Bloch equations (without relaxation terms) can be solved explicitly. This way the magnetization created by an excitation pulse can be written as a concatenation of rotations applied to the initial magnetization. For fixed gradient trajectories, the problem of finding parallel RF waveforms, which minimize the difference between achieved and desired magnetization on a number of voxels, can thus be represented as a finite-dimensional minimization problem. We use quaternion calculus to formulate this optimization problem in the magnitude least squares variant and specify first and second order derivatives of the objective function. We obtain a small tip angle approximation as first order Taylor development from the first order derivatives and also develop algorithms for first and second order derivatives for this small tip angle approximation. All algorithms are accompanied by precise floating point operation counts to assess and compare the computational efforts. We have implemented these algorithms as callback functions of an interior-point solver. We have applied this numerical optimization method to example problems from the literature and report key observations. Copyright © 2015 Elsevier Inc. All rights reserved.
First and second order derivatives for optimizing parallel RF excitation waveforms
Majewski, Kurt; Ritter, Dieter
2015-09-01
For piecewise constant magnetic fields, the Bloch equations (without relaxation terms) can be solved explicitly. This way the magnetization created by an excitation pulse can be written as a concatenation of rotations applied to the initial magnetization. For fixed gradient trajectories, the problem of finding parallel RF waveforms, which minimize the difference between achieved and desired magnetization on a number of voxels, can thus be represented as a finite-dimensional minimization problem. We use quaternion calculus to formulate this optimization problem in the magnitude least squares variant and specify first and second order derivatives of the objective function. We obtain a small tip angle approximation as first order Taylor development from the first order derivatives and also develop algorithms for first and second order derivatives for this small tip angle approximation. All algorithms are accompanied by precise floating point operation counts to assess and compare the computational efforts. We have implemented these algorithms as callback functions of an interior-point solver. We have applied this numerical optimization method to example problems from the literature and report key observations.
Kalpeshkumar Rohitbhai Patil
2016-10-01
Full Text Available Proper synchronization of Distributed Generator with grid and its performance in grid-connected mode relies on fast and precise estimation of phase and amplitude of the fundamental component of grid voltage. However, the accuracy with which the frequency is estimated is dependent on the type of grid voltage abnormalities and structure of the phase-locked loop or frequency locked loop control schemes. Among various control schemes, second-order generalized integrator based frequency- locked loop (SOGI-FLL is reported to have the most promising performance. It tracks the frequency of grid voltage accurately even when grid voltage is characterized by sag, swell, harmonics, imbalance, frequency variations etc. However, estimated frequency contains low frequency oscillations in case when sensed grid-voltage has a dc offset. This paper presents a modified dual second-order generalized integrator frequency-locked loop (MDSOGI-FLL for three-phase systems to cope with the non-ideal three-phase grid voltages having all type of abnormalities including the dc offset. The complexity in control scheme is almost the same as the standard dual SOGI-FLL, but the performance is enhanced. Simulation results show that the proposed MDSOGI-FLL is effective under all abnormal grid voltage conditions. The results are validated experimentally to justify the superior performance of MDSOGI-FLL under adverse conditions.
Radiation-reaction force on a small charged body to second order
Moxon, Jordan; Flanagan, Éanna
2018-05-01
In classical electrodynamics, an accelerating charged body emits radiation and experiences a corresponding radiation-reaction force, or self-force. We extend to higher order in the total charge a previous rigorous derivation of the electromagnetic self-force in flat spacetime by Gralla, Harte, and Wald. The method introduced by Gralla, Harte, and Wald computes the self-force from the Maxwell field equations and conservation of stress-energy in a limit where the charge, size, and mass of the body go to zero, and it does not require regularization of a singular self-field. For our higher-order computation, an adjustment of the definition of the mass of the body is necessary to avoid including self-energy from the electromagnetic field sourced by the body in the distant past. We derive the evolution equations for the mass, spin, and center-of-mass position of the body through second order. We derive, for the first time, the second-order acceleration dependence of the evolution of the spin (self-torque), as well as a mixing between the extended body effects and the acceleration-dependent effects on the overall body motion.
Block correlated second order perturbation theory with a generalized valence bond reference function
Xu, Enhua; Li, Shuhua
2013-01-01
The block correlated second-order perturbation theory with a generalized valence bond (GVB) reference (GVB-BCPT2) is proposed. In this approach, each geminal in the GVB reference is considered as a “multi-orbital” block (a subset of spin orbitals), and each occupied or virtual spin orbital is also taken as a single block. The zeroth-order Hamiltonian is set to be the summation of the individual Hamiltonians of all blocks (with explicit two-electron operators within each geminal) so that the GVB reference function and all excited configuration functions are its eigenfunctions. The GVB-BCPT2 energy can be directly obtained without iteration, just like the second order Møller–Plesset perturbation method (MP2), both of which are size consistent. We have applied this GVB-BCPT2 method to investigate the equilibrium distances and spectroscopic constants of 7 diatomic molecules, conformational energy differences of 8 small molecules, and bond-breaking potential energy profiles in 3 systems. GVB-BCPT2 is demonstrated to have noticeably better performance than MP2 for systems with significant multi-reference character, and provide reasonably accurate results for some systems with large active spaces, which are beyond the capability of all CASSCF-based methods
Adib, M.; Abdel Kawy, A.; Habib, N.; El Mesiry, M.
2010-01-01
An investigation of pyrolytic graphite (PG) crystal as an efficient second order neutron filter at tuned boundary crossings has been carried out. The neutron transmission through PG crystal at these tuned crossing points as a function of first- and second-order wavelengths were calculated in terms of PG mosaic spread and thickness. The filtering features of PG crystals at these tuned boundary crossings were deduced. It was shown that, there are a large number of tuned positions at double and triple boundary crossings of the curves (hkl) are very promising as tuned filter positions. However, only fourteen of them are found to be most promising ones. These tuned positions are found to be within the neutron wavelengths from 0.133 up to 0.4050 nm. A computer package GRAPHITE has been used in order to provide the required calculations in the whole neutron wavelength range in terms of PG mosaic spread and its orientation with respect to incident neutron beam direction. It was shown that 0.5 cm thick PG crystal with angular mosaic spread of 2 0 is sufficient to remove 2nd-order neutrons at the wavelengths corresponding to the positions of the intersection boundaries curves (hkl).
A parallel second-order adaptive mesh algorithm for incompressible flow in porous media.
Pau, George S H; Almgren, Ann S; Bell, John B; Lijewski, Michael J
2009-11-28
In this paper, we present a second-order accurate adaptive algorithm for solving multi-phase, incompressible flow in porous media. We assume a multi-phase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting, the total velocity, defined to be the sum of the phase velocities, is divergence free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized. The single-grid algorithm is described briefly, but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behaviour of the method.
The second-order description of rotational non-equilibrium effects in polyatomic gases
Myong, Rho Shin
2017-11-01
The conventional description of gases is based on the physical laws of conservation (mass, momentum, and energy) in conjunction with the first-order constitutive laws, the two-century old so-called Navier-Stokes-Fourier (NSF) equation based on a critical assumption made by Stokes in 1845 that the bulk viscosity vanishes. While the Stokes' assumption is certainly legitimate in the case of dilute monatomic gases, ever increasing evidences, however, now indicate that such is not the case, in particular, in the case of polyatomic gases-like nitrogen and carbon dioxide-far-from local thermal equilibrium. It should be noted that, from room temperature acoustic attenuation data, the bulk viscosity for carbon dioxide is three orders of magnitude larger than its shear viscosity. In this study, this fundamental issue in compressible gas dynamics is revisited and the second-order constitutive laws are derived by starting from the Boltzmann-Curtiss kinetic equation. Then the topology of the second-order nonlinear coupled constitutive relations in phase space is investigated. Finally, the shock-vortex interaction problem where the strong interaction of two important thermal (translational and rotational) non-equilibrium phenomena occurs is considered in order to highlight the rotational non-equilibrium effects in polyatomic gases. This work was supported by the National Research Foundation of South Korea (NRF 2017-R1A2B2-007634).
Chaichian, M.; Hayashi, M.; Honkaranta, T.
1980-01-01
We consider in QCD the second order, in gluon-quark coupling constant, contribution of the quark-quark scatte-ring (bremsstrahlung) to the transverse momentum distribution of muon pairs produced in proton-proton collisions. In certain kinematical regions accesible to experimental tests, this contribution is quite large in comparison with the first order calculations. This happens for a specific choice of scale violating structure functions which fit the deep inelastic data. Thus the first order QCD calcula-tion alone is not conclusive in trying to fit the data -one must necessarily check the effect of the second order quark-quark scattering as compared with the first order quark-gluon and the quark-antiquark scattering. This remark concerns also the case when in the first order diagrams the effect of primordial transverse momentum of partons is included as well as the case when the first order is replaced by DDT type of formulae. Mass regularization and different prescriptions for the constant term in q → g + q vertex are considered. Results are presented for the energies √s=6.5, 27, 63, 800 GeV and are compared with experiment. Implications of these results for the detection of W +- -mesons via psub(T) distribution of their decay products μ +- in proton-proton collisions are mentioned. (author)
Transport coefficients in second-order non-conformal viscous hydrodynamics
Ryblewski, Radoslaw
2015-01-01
Based on the exact solution of Boltzmann kinetic equation in the relaxation-time approximation, the precision of the two most recent formulations of relativistic second-order non-conformal viscous hydrodynamics (14-moment approximation and causal Chapman-Enskog method), standard Israel-Stewart theory, and anisotropic hydrodynamics framework, in the simple case of one-dimensional Bjorken expansion, is tested. It is demonstrated that the failure of Israel-Stewart theory in reproducing exact solutions of the Boltzmann kinetic equation occurs due to neglecting and/or choosing wrong forms of some of the second-order transport coefficients. In particular, the importance of shear-bulk couplings in the evolution equations for dissipative quantities is shown. One finds that, in the case of the bulk viscous pressure correction, such coupling terms are as important as the corresponding first-order Navier-Stokes term and must be included in order to obtain, at least qualitative, overall agreement with the kinetic theory. (paper)
Studies of Second Order Optical Nonlinearities of 4-Aminobenzophenone (ABP) Single Crystal Films
Bhowmik, Achintya; Thakur, Mrinal
1998-03-01
Specific organic materials exhibit very high second order optical susceptibilities. Growth of single crystal films of these materials and characterization of nonlinear optical properties are necessary for implementation of device applications. We have grown large-area films ( 1 cm^2 area, 4 μm thick) of ABP by a modification of the shear method. Single crystal nature of the films was confirmed by polarized optical microscopy. X-ray diffraction analysis showed a [100] surface orientation. The absorption spectra revealed transparency from 390 nm to 1940 nm. Significant elements of the second order optical susceptibility tensor were measured by detailed SHG experiments using a Nd:YAG laser (1064 nm, 100 ps, 82 MHz). Second-harmonic power was measured using lock-in detection with carefully selected polarization conditions while the film was rotated about the propagation direction. Using LiNbØas the reference, d-coefficients of ABP were found to be d_23=7.2 pm/V and d_22=0.7 pm/V. Type-I and type-II phase-matching directions were identified on the film by analyzing the optical indicatrix surfaces at fundamental and second-harmonic frequencies.