"Real-Time Optical Laboratory Linear Algebra Solution Of Partial Differential Equations"
Casasent, David; Jackson, James
1986-03-01
A Space Integrating (SI) Optical Linear Algebra Processor (OLAP) employing space and frequency-multiplexing, new partitioning and data flow, and achieving high accuracy performance with a non base-2 number system is described. Laboratory data on the performance of this system and the solution of parabolic Partial Differential Equations (PDEs) is provided. A multi-processor OLAP system is also described for the first time. It use in the solution of multiple banded matrices that frequently arise is then discussed. The utility and flexibility of this processor compared to digital systolic architectures should be apparent.
Hosseini, K.; Ayati, Z.; Ansari, R.
2018-04-01
One specific class of non-linear evolution equations, known as the Tzitzéica-type equations, has received great attention from a group of researchers involved in non-linear science. In this article, new exact solutions of the Tzitzéica-type equations arising in non-linear optics, including the Tzitzéica, Dodd-Bullough-Mikhailov and Tzitzéica-Dodd-Bullough equations, are obtained using the expa function method. The integration technique actually suggests a useful and reliable method to extract new exact solutions of a wide range of non-linear evolution equations.
Linear rotary optical delay lines
Guerboukha, Hichem; Qu, Hang; Skorobogatiy, Maksim
2016-03-01
We present a semi-analytical solution for the design of a high-speed rotary optical delay line that use a combination of two rotating curvilinear reflectors. We demonstrate that it is possible to design an infinite variety of the optical delay lines featuring linear dependence of the optical delay on the rotation angle. This is achieved via shape optimization of the rotating reflector surfaces. Moreover, a convenient spatial separation of the incoming and outgoing beams is possible. For the sake of example, we present blades that fit into a circle of 10cm diameter. Finally, a prototype of a rotary delay line is fabricated using CNC machining, and its optical properties are characterized.
Directory of Open Access Journals (Sweden)
Masatoshi Hasegawa
2017-10-01
Full Text Available This paper reviews the development of new high-temperature polymeric materials applicable to plastic substrates in image display devices with a focus on our previous results. Novel solution-processable colorless polyimides (PIs with ultra-low linear coefficients of thermal expansion (CTE are proposed in this paper. First, the principles of the coloration of PI films are briefly discussed, including the influence of the processing conditions on the film coloration, as well as the chemical and physical factors dominating the low CTE characteristics of the resultant PI films to clarify the challenges in simultaneously achieving excellent optical transparency, a very high Tg, a very low CTE, and excellent film toughness. A possible approach of achieving these target properties is to use semi-cycloaliphatic PI systems consisting of linear chain structures. However, semi-cycloaliphatic PIs obtained using cycloaliphatic diamines suffer various problems during precursor polymerization, cyclodehydration (imidization, and film preparation. In particular, when using trans-1,4-cyclohexanediamine (t-CHDA as the cycloaliphatic diamine, a serious problem emerges: salt formation in the initial stages of the precursor polymerization, which terminates the polymerization in some cases or significantly extends the reaction period. The system derived from 3,3′,4,4′-biphenyltetracarboxylic dianhydride (s-BPDA and t-CHDA can be polymerized by a controlled heating method and leads to a PI film with relatively good properties, i.e., excellent light transmittance at 400 nm (T400 = ~80%, a high Tg (>300 °C, and a very low CTE (10 ppm·K−1. However, this PI film is somewhat brittle (the maximum elongation at break, εb max is about 10%. On the other hand, the combination of cycloaliphatic tetracarboxylic dianhydrides and aromatic diamines does not result in salt formation. The steric structures of cycloaliphatic tetracarboxylic dianhydrides significantly influence
DEFF Research Database (Denmark)
Webb, Garry; Sørensen, Mads Peter; Brio, Moysey
2004-01-01
the electromagnetic momentum and energy conservation laws, corresponding to the space and time translation invariance symmetries. The symmetries are used to obtain classical similarity solutions of the equations. The traveling wave similarity solutions for the case of a cubic Kerr nonlinearity, are shown to reduce...... the properties of Maxwell's equations in nonlinear optics, without resorting to the commonly used nonlinear Schr\\"odinger (NLS) equation approximation in which a high frequency carrier wave is modulated on long length and time scales due to nonlinear sideband wave interactions. This is important in femto......-second pulse propagation in which the NLS approximation is expected to break down. The canonical Hamiltonian description of the equations involves the solution of a polynomial equation for the electric field $E$, in terms of the the canonical variables, with possible multiple real roots for $E$. In order...
Saravanan, R
2018-01-01
Non-linear optical materials have widespread and promising applications, but the efforts to understand the local structure, electron density distribution and bonding is still lacking. The present work explores the structural details, the electron density distribution and the local bond length distribution of some non-linear optical materials. It also gives estimation of the optical band gap, the particle size, crystallite size, and the elemental composition from UV-Visible analysis, SEM, XRD and EDS of some non-linear optical materials respectively.
International Nuclear Information System (INIS)
Gaudry, Jean-Baptiste
2000-01-01
This research thesis reports the study of two mechanisms of non linear interaction of a laser wave with matter. More particularly, it reports the experimental investigation of non linear optical properties of organometallic molecules in solution, as well as the damage of perfect silica under laser irradiation by using simulation codes. As far as optical properties are concerned, the author highlights the influence of the electronic configuration of the metal present in the organometallic compound, and the influence of the ligand on the second-order non-linear response. As far as the simulation is concerned, some experimental results have been reproduced. This work can be useful for the investigation of the extrinsic damage of imperfect materials, and for the design of experiments of transient measurements of excited silica [fr
Linear superposition solutions to nonlinear wave equations
International Nuclear Information System (INIS)
Liu Yu
2012-01-01
The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed
Linear zonal atmospheric prediction for adaptive optics
McGuire, Patrick C.; Rhoadarmer, Troy A.; Coy, Hanna A.; Angel, J. Roger P.; Lloyd-Hart, Michael
2000-07-01
We compare linear zonal predictors of atmospheric turbulence for adaptive optics. Zonal prediction has the possible advantage of being able to interpret and utilize wind-velocity information from the wavefront sensor better than modal prediction. For simulated open-loop atmospheric data for a 2- meter 16-subaperture AO telescope with 5 millisecond prediction and a lookback of 4 slope-vectors, we find that Widrow-Hoff Delta-Rule training of linear nets and Back- Propagation training of non-linear multilayer neural networks is quite slow, getting stuck on plateaus or in local minima. Recursive Least Squares training of linear predictors is two orders of magnitude faster and it also converges to the solution with global minimum error. We have successfully implemented Amari's Adaptive Natural Gradient Learning (ANGL) technique for a linear zonal predictor, which premultiplies the Delta-Rule gradients with a matrix that orthogonalizes the parameter space and speeds up the training by two orders of magnitude, like the Recursive Least Squares predictor. This shows that the simple Widrow-Hoff Delta-Rule's slow convergence is not a fluke. In the case of bright guidestars, the ANGL, RLS, and standard matrix-inversion least-squares (MILS) algorithms all converge to the same global minimum linear total phase error (approximately 0.18 rad2), which is only approximately 5% higher than the spatial phase error (approximately 0.17 rad2), and is approximately 33% lower than the total 'naive' phase error without prediction (approximately 0.27 rad2). ANGL can, in principle, also be extended to make non-linear neural network training feasible for these large networks, with the potential to lower the predictor error below the linear predictor error. We will soon scale our linear work to the approximately 108-subaperture MMT AO system, both with simulations and real wavefront sensor data from prime focus.
Linear and non-linear optics of condensed matter
International Nuclear Information System (INIS)
McLean, T.P.
1977-01-01
Part I - Linear optics: 1. General introduction. 2. Frequency dependence of epsilon(ω, k vector). 3. Wave-vector dependence of epsilon(ω, k vector). 4. Tensor character of epsilon(ω, k vector). Part II - Non-linear optics: 5. Introduction. 6. A classical theory of non-linear response in one dimension. 7. The generalization to three dimensions. 8. General properties of the polarizability tensors. 9. The phase-matching condition. 10. Propagation in a non-linear dielectric. 11. Second harmonic generation. 12. Coupling of three waves. 13. Materials and their non-linearities. 14. Processes involving energy exchange with the medium. 15. Two-photon absorption. 16. Stimulated Raman effect. 17. Electro-optic effects. 18. Limitations of the approach presented here. (author)
Numerical solution of large sparse linear systems
International Nuclear Information System (INIS)
Meurant, Gerard; Golub, Gene.
1982-02-01
This note is based on one of the lectures given at the 1980 CEA-EDF-INRIA Numerical Analysis Summer School whose aim is the study of large sparse linear systems. The main topics are solving least squares problems by orthogonal transformation, fast Poisson solvers and solution of sparse linear system by iterative methods with a special emphasis on preconditioned conjuguate gradient method [fr
Linear optics and quantum maps
International Nuclear Information System (INIS)
Aiello, A.; Puentes, G.; Woerdman, J. P.
2007-01-01
We present a theoretical analysis of the connection between classical polarization optics and quantum mechanics of two-level systems. First, we review the matrix formalism of classical polarization optics from a quantum information perspective. In this manner the passage from the Stokes-Jones-Mueller description of classical optical processes to the representation of one- and two-qubit quantum operations, becomes straightforward. Second, as a practical application of our classical-vs-quantum formalism, we show how two-qubit maximally entangled mixed states can be generated by using polarization and spatial modes of photons generated via spontaneous parametric down conversion
General solution of linear vector supersymmetry
International Nuclear Information System (INIS)
Blasi, Alberto; Maggiore, Nicola
2007-01-01
We give the general solution of the Ward identity for the linear vector supersymmetry which characterizes all topological models. Such a solution, whose expression is quite compact and simple, greatly simplifies the study of theories displaying a supersymmetric algebraic structure, reducing to a few lines the proof of their possible finiteness. In particular, the cohomology technology, usually involved for the quantum extension of these theories, is completely bypassed. The case of Chern-Simons theory is taken as an example
Light propagation in linear optical media
Gillen, Glen D; Guha, Shekhar
2013-01-01
Light Propagation in Linear Optical Media describes light propagation in linear media by expanding on diffraction theories beyond what is available in classic optics books. In one volume, this book combines the treatment of light propagation through various media, interfaces, and apertures using scalar and vector diffraction theories. After covering the fundamentals of light and physical optics, the authors discuss light traveling within an anisotropic crystal and present mathematical models for light propagation across planar boundaries between different media. They describe the propagation o
Progress in linear optics, non-linear optics and surface alignment of liquid crystals
Ong, H. L.; Meyer, R. B.; Hurd, A. J.; Karn, A. J.; Arakelian, S. M.; Shen, Y. R.; Sanda, P. N.; Dove, D. B.; Jansen, S. A.; Hoffmann, R.
We first discuss the progress in linear optics, in particular, the formulation and application of geometrical-optics approximation and its generalization. We then discuss the progress in non-linear optics, in particular, the enhancement of a first-order Freedericksz transition and intrinsic optical bistability in homeotropic and parallel oriented nematic liquid crystal cells. Finally, we discuss the liquid crystal alignment and surface effects on field-induced Freedericksz transition.
Optical surfacing via linear ion source
International Nuclear Information System (INIS)
Wu, Lixiang; Wei, Chaoyang; Shao, Jianda
2017-01-01
We present a concept of surface decomposition extended from double Fourier series to nonnegative sinusoidal wave surfaces, on the basis of which linear ion sources apply to the ultra-precision fabrication of complex surfaces and diffractive optics. The modified Fourier series, or sinusoidal wave surfaces, build a relationship between the fabrication process of optical surfaces and the surface characterization based on power spectral density (PSD) analysis. Also, we demonstrate that the one-dimensional scanning of linear ion source is applicable to the removal of mid-spatial frequency (MSF) errors caused by small-tool polishing in raster scan mode as well as the fabrication of beam sampling grating of high diffractive uniformity without a post-processing procedure. The simulation results show that optical fabrication with linear ion source is feasible and even of higher output efficiency compared with the conventional approach.
Optical surfacing via linear ion source
Energy Technology Data Exchange (ETDEWEB)
Wu, Lixiang, E-mail: wulx@hdu.edu.cn [Key Lab of RF Circuits and Systems of Ministry of Education, Zhejiang Provincial Key Lab of LSI Design, Microelectronics CAD Center, College of Electronics and Information, Hangzhou Dianzi University, Hangzhou (China); Wei, Chaoyang, E-mail: siomwei@siom.ac.cn [Key Laboratory of Materials for High Power Laser, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800 (China); Shao, Jianda, E-mail: jdshao@siom.ac.cn [Key Laboratory of Materials for High Power Laser, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800 (China)
2017-04-15
We present a concept of surface decomposition extended from double Fourier series to nonnegative sinusoidal wave surfaces, on the basis of which linear ion sources apply to the ultra-precision fabrication of complex surfaces and diffractive optics. The modified Fourier series, or sinusoidal wave surfaces, build a relationship between the fabrication process of optical surfaces and the surface characterization based on power spectral density (PSD) analysis. Also, we demonstrate that the one-dimensional scanning of linear ion source is applicable to the removal of mid-spatial frequency (MSF) errors caused by small-tool polishing in raster scan mode as well as the fabrication of beam sampling grating of high diffractive uniformity without a post-processing procedure. The simulation results show that optical fabrication with linear ion source is feasible and even of higher output efficiency compared with the conventional approach.
Measurement-induced nonlinearity in linear optics
International Nuclear Information System (INIS)
Scheel, Stefan; Knight, Peter L.; Nemoto, Kae; Munro, William J.
2003-01-01
We investigate the generation of nonlinear operators with single-photon sources, linear optical elements, and appropriate measurements of auxiliary modes. We provide a framework for the construction of useful single-mode and two-mode quantum gates necessary for all-optical quantum information processing. We focus our attention generally on using minimal physical resources while providing a transparent and algorithmic way of constructing these operators
Noise limitations in optical linear algebra processors.
Batsell, S G; Jong, T L; Walkup, J F; Krile, T F
1990-05-10
A general statistical noise model is presented for optical linear algebra processors. A statistical analysis which includes device noise, the multiplication process, and the addition operation is undertaken. We focus on those processes which are architecturally independent. Finally, experimental results which verify the analytical predictions are also presented.
SLAP, Large Sparse Linear System Solution Package
International Nuclear Information System (INIS)
Greenbaum, A.
1987-01-01
1 - Description of program or function: SLAP is a set of routines for solving large sparse systems of linear equations. One need not store the entire matrix - only the nonzero elements and their row and column numbers. Any nonzero structure is acceptable, so the linear system solver need not be modified when the structure of the matrix changes. Auxiliary storage space is acquired and released within the routines themselves by use of the LRLTRAN POINTER statement. 2 - Method of solution: SLAP contains one direct solver, a band matrix factorization and solution routine, BAND, and several interactive solvers. The iterative routines are as follows: JACOBI, Jacobi iteration; GS, Gauss-Seidel Iteration; ILUIR, incomplete LU decomposition with iterative refinement; DSCG and ICCG, diagonal scaling and incomplete Cholesky decomposition with conjugate gradient iteration (for symmetric positive definite matrices only); DSCGN and ILUGGN, diagonal scaling and incomplete LU decomposition with conjugate gradient interaction on the normal equations; DSBCG and ILUBCG, diagonal scaling and incomplete LU decomposition with bi-conjugate gradient iteration; and DSOMN and ILUOMN, diagonal scaling and incomplete LU decomposition with ORTHOMIN iteration
Optical linear algebra processors - Architectures and algorithms
Casasent, David
1986-01-01
Attention is given to the component design and optical configuration features of a generic optical linear algebra processor (OLAP) architecture, as well as the large number of OLAP architectures, number representations, algorithms and applications encountered in current literature. Number-representation issues associated with bipolar and complex-valued data representations, high-accuracy (including floating point) performance, and the base or radix to be employed, are discussed, together with case studies on a space-integrating frequency-multiplexed architecture and a hybrid space-integrating and time-integrating multichannel architecture.
Matrix preconditioning: a robust operation for optical linear algebra processors.
Ghosh, A; Paparao, P
1987-07-15
Analog electrooptical processors are best suited for applications demanding high computational throughput with tolerance for inaccuracies. Matrix preconditioning is one such application. Matrix preconditioning is a preprocessing step for reducing the condition number of a matrix and is used extensively with gradient algorithms for increasing the rate of convergence and improving the accuracy of the solution. In this paper, we describe a simple parallel algorithm for matrix preconditioning, which can be implemented efficiently on a pipelined optical linear algebra processor. From the results of our numerical experiments we show that the efficacy of the preconditioning algorithm is affected very little by the errors of the optical system.
Topics in linear optical quantum computation
Glancy, Scott Charles
This thesis covers several topics in optical quantum computation. A quantum computer is a computational device which is able to manipulate information by performing unitary operations on some physical system whose state can be described as a vector (or mixture of vectors) in a Hilbert space. The basic unit of information, called the qubit, is considered to be a system with two orthogonal states, which are assigned logical values of 0 and 1. Photons make excellent candidates to serve as qubits. They have little interactions with the environment. Many operations can be performed using very simple linear optical devices such as beam splitters and phase shifters. Photons can easily be processed through circuit-like networks. Operations can be performed in very short times. Photons are ideally suited for the long-distance communication of quantum information. The great difficulty in constructing an optical quantum computer is that photons naturally interact weakly with one another. This thesis first gives a brief review of two early approaches to optical quantum computation. It will describe how any discrete unitary operation can be performed using a single photon and a network of beam splitters, and how the Kerr effect can be used to construct a two photon logic gate. Second, this work provides a thorough introduction to the linear optical quantum computer developed by Knill, Laflamme, and Milburn. It then presents this author's results on the reliability of this scheme when implemented using imperfect photon detectors. This author finds that quantum computers of this sort cannot be built using current technology. Third, this dissertation describes a method for constructing a linear optical quantum computer using nearly orthogonal coherent states of light as the qubits. It shows how a universal set of logic operations can be performed, including calculations of the fidelity with which these operations may be accomplished. It discusses methods for reducing and
Experimental quantum private queries with linear optics
International Nuclear Information System (INIS)
De Martini, Francesco; Giovannetti, Vittorio; Lloyd, Seth; Maccone, Lorenzo; Nagali, Eleonora; Sansoni, Linda; Sciarrino, Fabio
2009-01-01
The quantum private query is a quantum cryptographic protocol to recover information from a database, preserving both user and data privacy: the user can test whether someone has retained information on which query was asked and the database provider can test the amount of information released. Here we discuss a variant of the quantum private query algorithm that admits a simple linear optical implementation: it employs the photon's momentum (or time slot) as address qubits and its polarization as bus qubit. A proof-of-principle experimental realization is implemented.
Method and apparatus of highly linear optical modulation
DeRose, Christopher; Watts, Michael R.
2016-05-03
In a new optical intensity modulator, a nonlinear change in refractive index is used to balance the nonlinearities in the optical transfer function in a way that leads to highly linear optical intensity modulation.
A noble refractive optical scanner with linear response
Mega, Yair J.; Lai, Zhenhua; DiMarzio, Charles A.
2013-03-01
Many applications in various fields of science and engineering use steered optical beam systems. Currently, many methods utilize mirrors in order to steer the beam. However, this approach is an off-axis solution, which normally increases the total size of the system as well as its error and complexity. Other methods use a "Risely Prisms" based solution, which is on-axis solution, however it poses some difficulties from an engineering standpoint, and therefore isn't widely used. We present here a novel technique for steering a beam on its optical axis with a linear deflection response. We derived the formulation for the profile required of the refractive optical component necessary for preforming the beam steering. The functionality of the device was simulated analytically using Matlab, as well as using a ray-tracing software, Zemax, and showed agreement with the analytical model. An optical element was manufactured based on the proposed design and the device was tested. The results show agreement with our hypothesis. We also present some proposed geometries of the several other devices, all based on the same concept, which can be used for higher performance applications such as two-dimensional scanner, video rate scanner etc.
Polycarbonate-Based Blends for Optical Non-linear Applications
Stanculescu, F.; Stanculescu, A.
2016-02-01
This paper presents some investigations on the optical and morphological properties of the polymer (matrix):monomer (inclusion) composite materials obtained from blends of bisphenol A polycarbonate and amidic monomers. For the preparation of the composite films, we have selected monomers characterised by a maleamic acid structure and synthesised them starting from maleic anhydride and aniline derivatives with -COOH, -NO2, -N(C2H5)2 functional groups attached to the benzene ring. The composite films have been deposited by spin coating using a mixture of two solutions, one containing the matrix and the other the inclusion, both components of the composite system being dissolved in the same solvent. The optical transmission and photoluminescence properties of the composite films have been investigated in correlation with the morphology of the films. The scanning electron microscopy and atomic force microscopy have revealed a non-uniform morphology characterised by the development of two distinct phases. We have also investigated the generation of some optical non-linear (ONL) phenomena in these composite systems. The composite films containing as inclusions monomers characterised by the presence of one -COOH or two -NO2 substituent groups to the aromatic nucleus have shown the most intense second-harmonic generation (SHG). The second-order optical non-linear coefficients have been evaluated for these films, and the effect of the laser power on the ONL behaviour of these materials has also been emphasised.
Accuracy Limitations in Optical Linear Algebra Processors
Batsell, Stephen Gordon
1990-01-01
One of the limiting factors in applying optical linear algebra processors (OLAPs) to real-world problems has been the poor achievable accuracy of these processors. Little previous research has been done on determining noise sources from a systems perspective which would include noise generated in the multiplication and addition operations, noise from spatial variations across arrays, and from crosstalk. In this dissertation, we propose a second-order statistical model for an OLAP which incorporates all these system noise sources. We now apply this knowledge to determining upper and lower bounds on the achievable accuracy. This is accomplished by first translating the standard definition of accuracy used in electronic digital processors to analog optical processors. We then employ our second-order statistical model. Having determined a general accuracy equation, we consider limiting cases such as for ideal and noisy components. From the ideal case, we find the fundamental limitations on improving analog processor accuracy. From the noisy case, we determine the practical limitations based on both device and system noise sources. These bounds allow system trade-offs to be made both in the choice of architecture and in individual components in such a way as to maximize the accuracy of the processor. Finally, by determining the fundamental limitations, we show the system engineer when the accuracy desired can be achieved from hardware or architecture improvements and when it must come from signal pre-processing and/or post-processing techniques.
OPTICAL PROPERTIES OF CARBAMIDE AQUEOUS SOLUTIONS
Directory of Open Access Journals (Sweden)
E. V. Avramenko
2016-03-01
Full Text Available Subject of Research. The paper presents the results of measurements of refractometric properties (refractive index n, its temperature factor dn/dt and the ultraviolet spectral absorption in carbonic acid diamide aqueous solutions (carbamide depending on solid residue mass fraction md = 0-50 % and on temperaturet = 10-70 °C.Method of Research. Laboratory methods ofliquid-phase medium refractometry and ultraviolet spectrophotometry were applied for the research. We carried out computational modeling of electronic states spectrum for the carbonic acid diamide molecule and theoretical calculation of the fundamental electronic absorption of the molecule in the ultraviolet wavelenght region.Main Results. We have established that the solution concentration md has a nonlinear character and may be represented by the quadratic polynomial with the error Δn= ± 0,0005. We have shown the refractive indexdependence on temperature n(t changes in linear fashion att = 10-70 °C.At that, the inclination of lines n(t increases at the increase of md; so, the temperature factor dn/dt may be approximated by the quadratic polynomial. Transmission spectra of solutions in the spectral region λ= 225-760 nm have no special features except for the sharp edge in the short-wavelength region; the fundamental electronic absorptionis responsible for it. We have established that dispersion dependences of the refraction index n(λ;md in aqueous solutions of carbamide at λ= 360-760 nm and at md = 0-50 % may be calculated with the satisfactory error without additional adjustable parameters from the ultraviolet absorption data in terms of the one-dimentional oscillator Lorentz model.PracticalRelevance. Representedmeasurements of carbonic acid diamide aqueous solutions optical properties may be applied for the adjustment and calibration of commercial refractometers at processing lines of the AdBlue reagent manufacture for the selective catalytic reduction (SCR of motor transport
Minimal solution of general dual fuzzy linear systems
International Nuclear Information System (INIS)
Abbasbandy, S.; Otadi, M.; Mosleh, M.
2008-01-01
Fuzzy linear systems of equations, play a major role in several applications in various area such as engineering, physics and economics. In this paper, we investigate the existence of a minimal solution of general dual fuzzy linear equation systems. Two necessary and sufficient conditions for the minimal solution existence are given. Also, some examples in engineering and economic are considered
The linear ordering problem: an algorithm for the optimal solution ...
African Journals Online (AJOL)
In this paper we describe and implement an algorithm for the exact solution of the Linear Ordering problem. Linear Ordering is the problem of finding a linear order of the nodes of a graph such that the sum of the weights which are consistent with this order is as large as possible. It is an NP - Hard combinatorial optimisation ...
Solution of linear ill-posed problems using overcomplete dictionaries
Pensky, Marianna
2016-01-01
In the present paper we consider application of overcomplete dictionaries to solution of general ill-posed linear inverse problems. Construction of an adaptive optimal solution for such problems usually relies either on a singular value decomposition or representation of the solution via an orthonormal basis. The shortcoming of both approaches lies in the fact that, in many situations, neither the eigenbasis of the linear operator nor a standard orthonormal basis constitutes an appropriate co...
Iterative solution of large linear systems
Young, David Matheson
1971-01-01
This self-contained treatment offers a systematic development of the theory of iterative methods. Its focal point resides in an analysis of the convergence properties of the successive overrelaxation (SOR) method, as applied to a linear system with a consistently ordered matrix. The text explores the convergence properties of the SOR method and related techniques in terms of the spectral radii of the associated matrices as well as in terms of certain matrix norms. Contents include a review of matrix theory and general properties of iterative methods; SOR method and stationary modified SOR meth
Riccati transformations and principal solutions of discrete linear systems
International Nuclear Information System (INIS)
Ahlbrandt, C.D.; Hooker, J.W.
1984-01-01
Consider a second-order linear matrix difference equation. A definition of principal and anti-principal, or recessive and dominant, solutions of the equation are given and the existence of principal and anti-principal solutions and the essential uniqueness of principal solutions is proven
Navarrete-Benlloch, Carlos; Roldán, Eugenio; Chang, Yue; Shi, Tao
2014-10-06
Nonlinear optical cavities are crucial both in classical and quantum optics; in particular, nowadays optical parametric oscillators are one of the most versatile and tunable sources of coherent light, as well as the sources of the highest quality quantum-correlated light in the continuous variable regime. Being nonlinear systems, they can be driven through critical points in which a solution ceases to exist in favour of a new one, and it is close to these points where quantum correlations are the strongest. The simplest description of such systems consists in writing the quantum fields as the classical part plus some quantum fluctuations, linearizing then the dynamical equations with respect to the latter; however, such an approach breaks down close to critical points, where it provides unphysical predictions such as infinite photon numbers. On the other hand, techniques going beyond the simple linear description become too complicated especially regarding the evaluation of two-time correlators, which are of major importance to compute observables outside the cavity. In this article we provide a regularized linear description of nonlinear cavities, that is, a linearization procedure yielding physical results, taking the degenerate optical parametric oscillator as the guiding example. The method, which we call self-consistent linearization, is shown to be equivalent to a general Gaussian ansatz for the state of the system, and we compare its predictions with those obtained with available exact (or quasi-exact) methods. Apart from its operational value, we believe that our work is valuable also from a fundamental point of view, especially in connection to the question of how far linearized or Gaussian theories can be pushed to describe nonlinear dissipative systems which have access to non-Gaussian states.
Rational approximations to solutions of linear differential equations.
Chudnovsky, D V; Chudnovsky, G V
1983-08-01
Rational approximations of Padé and Padé type to solutions of differential equations are considered. One of the main results is a theorem stating that a simultaneous approximation to arbitrary solutions of linear differential equations over C(x) cannot be "better" than trivial ones implied by the Dirichlet box principle. This constitutes, in particular, the solution in the linear case of Kolchin's problem that the "Roth's theorem" holds for arbitrary solutions of algebraic differential equations. Complete effective proofs for several valuations are presented based on the Wronskian methods and graded subrings of Picard-Vessiot extensions.
Nanoplasmonic solution for nonlinear optics
DEFF Research Database (Denmark)
Bache, Morten; Lavrinenko, Andrei; Lysenko, Oleg
2014-01-01
for the silicon dioxide cladding. The blue, cyan and magenta curves correspond to the transmission spectra for the gold waveguides with the width of 10 μm and length of 2, 3, and 4 mm.The polarization of laser beam was tuned to match the transverse magnetic mode of surface plasmonpolaritons in the gold waveguides...... and is being under investigation in recent years [3].The purpose of our research is to study nonlinear optical properties of gold waveguides embedded intodielectric medium (silicon dioxide) using picosecond laser spectroscopy. The work includes modeling ofoptical properties of gold waveguides, fabrication...... of prototype samples, and optical characterization ofsamples using a picosecond laser source.The prototype samples of gold waveguides embedded into silicon dioxide were fabricated at DTUDanchip. A silicon wafer with pre-made 6.5 μm layer of silicon dioxide was used as a substrate and goldwaveguides (films...
Subroutine for series solutions of linear differential equations
International Nuclear Information System (INIS)
Tasso, H.; Steuerwald, J.
1976-02-01
A subroutine for Taylor series solutions of systems of ordinary linear differential equations is descriebed. It uses the old idea of Lie series but allows simple implementation and is time-saving for symbolic manipulations. (orig.) [de
Ghosh, A
1988-08-01
Lanczos and conjugate gradient algorithms are important in computational linear algebra. In this paper, a parallel pipelined realization of these algorithms on a ring of optical linear algebra processors is described. The flow of data is designed to minimize the idle times of the optical multiprocessor and the redundancy of computations. The effects of optical round-off errors on the solutions obtained by the optical Lanczos and conjugate gradient algorithms are analyzed, and it is shown that optical preconditioning can improve the accuracy of these algorithms substantially. Algorithms for optical preconditioning and results of numerical experiments on solving linear systems of equations arising from partial differential equations are discussed. Since the Lanczos algorithm is used mostly with sparse matrices, a folded storage scheme to represent sparse matrices on spatial light modulators is also described.
International Nuclear Information System (INIS)
Antzutkin, O.
1992-01-01
This thesis is divided into two sections. The first part covers an introduction to the Optically Detected Electron Spin Resonance (OD ESR) spectroscopy and a short description of the OD ESR spectrometer built in Linkoeping University in 1991. In the second section the following topics are discussed: Non-linear effects in OD ESR spectroscopy and Reactions and motion of organic radicals trapped in freon matrices. (19 refs.)
Vector optical fields with bipolar symmetry of linear polarization.
Pan, Yue; Li, Yongnan; Li, Si-Min; Ren, Zhi-Cheng; Si, Yu; Tu, Chenghou; Wang, Hui-Tian
2013-09-15
We focus on a new kind of vector optical field with bipolar symmetry of linear polarization instead of cylindrical and elliptical symmetries, enriching members of family of vector optical fields. We design theoretically and generate experimentally the demanded vector optical fields and then explore some novel tightly focusing properties. The geometric configurations of states of polarization provide additional degrees of freedom assisting in engineering the field distribution at the focus to the specific applications such as lithography, optical trapping, and material processing.
Oscillatory behaviour of solutions of linear neutral differential ...
African Journals Online (AJOL)
The paper considers the contribution of space-time noise to the oscillatory behaviour of solutions of a linear neutral stochastic delay differential equation. It was established that under certain conditions on the time lags and their speed of adjustments, the presence of noise generates oscillation in the solution of the equation ...
Exponential estimates for solutions of half-linear differential equations
Czech Academy of Sciences Publication Activity Database
Řehák, Pavel
2015-01-01
Roč. 147, č. 1 (2015), s. 158-171 ISSN 0236-5294 Institutional support: RVO:67985840 Keywords : half-linear differential equation * decreasing solution * increasing solution * asymptotic behavior Subject RIV: BA - General Mathematics Impact factor: 0.469, year: 2015 http://link.springer.com/article/10.1007%2Fs10474-015-0522-9
Amplitudes for multiphoton quantum processes in linear optics
International Nuclear Information System (INIS)
UrIas, Jesus
2011-01-01
The prominent role that linear optical networks have acquired in the engineering of photon states calls for physically intuitive and automatic methods to compute the probability amplitudes for the multiphoton quantum processes occurring in linear optics. A version of Wick's theorem for the expectation value, on any vector state, of products of linear operators, in general, is proved. We use it to extract the combinatorics of any multiphoton quantum processes in linear optics. The result is presented as a concise rule to write down directly explicit formulae for the probability amplitude of any multiphoton process in linear optics. The rule achieves a considerable simplification and provides an intuitive physical insight about quantum multiphoton processes. The methodology is applied to the generation of high-photon-number entangled states by interferometrically mixing coherent light with spontaneously down-converted light.
Amplitudes for multiphoton quantum processes in linear optics
Urías, Jesús
2011-07-01
The prominent role that linear optical networks have acquired in the engineering of photon states calls for physically intuitive and automatic methods to compute the probability amplitudes for the multiphoton quantum processes occurring in linear optics. A version of Wick's theorem for the expectation value, on any vector state, of products of linear operators, in general, is proved. We use it to extract the combinatorics of any multiphoton quantum processes in linear optics. The result is presented as a concise rule to write down directly explicit formulae for the probability amplitude of any multiphoton process in linear optics. The rule achieves a considerable simplification and provides an intuitive physical insight about quantum multiphoton processes. The methodology is applied to the generation of high-photon-number entangled states by interferometrically mixing coherent light with spontaneously down-converted light.
Linear and Non-Linear Optical Imaging of Cancer Cells with Silicon Nanoparticles
Tolstik, Elen; Osminkina, Liubov A.; Akimov, Denis; Gongalsky, Maksim B.; Kudryavtsev, Andrew A.; Timoshenko, Victor Yu.; Heintzmann, Rainer; Sivakov, Vladimir; Popp, Jürgen
2016-01-01
New approaches for visualisation of silicon nanoparticles (SiNPs) in cancer cells are realised by means of the linear and nonlinear optics in vitro. Aqueous colloidal solutions of SiNPs with sizes of about 10–40 nm obtained by ultrasound grinding of silicon nanowires were introduced into breast cancer cells (MCF-7 cell line). Further, the time-varying nanoparticles enclosed in cell structures were visualised by high-resolution structured illumination microscopy (HR-SIM) and micro-Raman spectroscopy. Additionally, the nonlinear optical methods of two-photon excited fluorescence (TPEF) and coherent anti-Stokes Raman scattering (CARS) with infrared laser excitation were applied to study the localisation of SiNPs in cells. Advantages of the nonlinear methods, such as rapid imaging, which prevents cells from overheating and larger penetration depth compared to the single-photon excited HR-SIM, are discussed. The obtained results reveal new perspectives of the multimodal visualisation and precise detection of the uptake of biodegradable non-toxic SiNPs by cancer cells and they are discussed in view of future applications for the optical diagnostics of cancer tumours. PMID:27626408
Fiber optic spectrophotometer with photodiode linear array
International Nuclear Information System (INIS)
Blanc, F.; Vernet, P.
1988-01-01
Spectrophotometric measurements are used in a great number of industrial processes, in nuclear environment and with optical precision components. Especially the evolution of a chemical process or of an optical coating could be followed by these measurements. Spectrophotometers, using optical fibers to transport the signal out of the instrument make possible the measurement ''in-situ'' and in real time. The advantage of using a diode array to detect the signal is an instantaneous measurement all over the spectral range without moving parts. It allows an excellent reproductibility. The instrument is controlled by a micro computer. The spectrophotometer is described and technical performance presented. An extension using optical fibers on a ''classical'' spectrophotometer (a H.P. one) is also described and technical performance presented
Oscillatory solutions of the Cauchy problem for linear differential equations
Directory of Open Access Journals (Sweden)
Gro Hovhannisyan
2015-06-01
Full Text Available We consider the Cauchy problem for second and third order linear differential equations with constant complex coefficients. We describe necessary and sufficient conditions on the data for the existence of oscillatory solutions. It is known that in the case of real coefficients the oscillatory behavior of solutions does not depend on initial values, but we show that this is no longer true in the complex case: hence in practice it is possible to control oscillatory behavior by varying the initial conditions. Our Proofs are based on asymptotic analysis of the zeros of solutions, represented as linear combinations of exponential functions.
Analytical exact solution of the non-linear Schroedinger equation
International Nuclear Information System (INIS)
Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da
2011-01-01
Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)
Linear birefringence and optical ativity in a magnetized plasma
International Nuclear Information System (INIS)
Vuolo, J.H.; Galvao, R.M.O.
1982-02-01
Linear birefringence and optical activity are considered separately to electromagnetic wave propagation in magnetized cold plasma, using frequency approximation much bigger than plasma frequency. It's showen that in some interesting cases, those phenomena could be independents. Explicit expressions are obtained for refraction indices to linear birefringency and optical activity. The correspondents indices attenuation aRe obtained in first orden of attenuation. It's showen that the characteristic states for linear dichroism coincide with the characteristic states for linear birefringence. The characteristic states for elliptic dichroism are obtained. (M.A.F.) [pt
Linear Optical Properties of Gold Colloid
Directory of Open Access Journals (Sweden)
Jingmin XIA
2015-11-01
Full Text Available Gold colloid was prepared by reducing HAuCl4·4H2O with Na3C6H5O7·2H2O. The morphology, size of gold nanoparticles and the optical property of colloid were characterized by transmission electron microscope and UV-Vis spectrophotometer, respectively. It shows that the gold nanoparticles are in the shape of spheres with diameters less than 8 nm, and the surface plasmon resonance absorption peak is located at about 438 nm. As the volume fraction of gold particles increases, the intensity of absorption peak strengthens. The optical property of gold colloid was analyzed by Maxwell-Garnett (MG effective medium theory in the company of Drude dispersion model. The results show that the matrix dielectric constant is a main factor, which influences the optical property of gold colloid.DOI: http://dx.doi.org/10.5755/j01.ms.21.4.9558
Ultra-high Frequency Linear Fiber Optic Systems
Lau, Kam
2011-01-01
This book provides an in-depth treatment of both linear fiber-optic systems and their key enabling devices. It presents a concise but rigorous treatment of the theory and practice of analog (linear) fiber-optics links and systems that constitute the foundation of Hybrid Fiber Coax infrastructure in present-day CATV distribution and cable modem Internet access. Emerging applications in remote fiber-optic feed for free-space millimeter wave enterprise campus networks are also described. Issues such as dispersion and interferometric noise are treated quantitatively, and means for mitigating them are explained. This broad but concise text will thus be invaluable not only to students of fiber-optics communication but also to practicing engineers. To the second edition of this book important new aspects of linear fiber-optic transmission technologies are added, such as high level system architectural issues, algorithms for deriving the optimal frequency assignment, directly modulated or externally modulated laser t...
Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation
Directory of Open Access Journals (Sweden)
Hamidreza Rezazadeh
2014-05-01
Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.
State-dependent linear-optical qubit amplifier
Czech Academy of Sciences Publication Activity Database
Bartkiewicz, K.; Černoch, Antonín; Lemr, K.
2013-01-01
Roč. 88, č. 6 (2013), "062304-1"-"062304-7" ISSN 1050-2947 R&D Projects: GA ČR GAP205/12/0382 Institutional support: RVO:68378271 Keywords : linear-optical qubit amplifier * quantum cloning * quantum cryptography Subject RIV: BH - Optics, Masers, Lasers Impact factor: 2.991, year: 2013
Iterative solution of linear equations in ODE codes. [Krylov subspaces
Energy Technology Data Exchange (ETDEWEB)
Gear, C. W.; Saad, Y.
1981-01-01
Each integration step of a stiff equation involves the solution of a nonlinear equation, usually by a quasi-Newton method that leads to a set of linear problems. Iterative methods for these linear equations are studied. Of particular interest are methods that do not require an explicit Jacobian, but can work directly with differences of function values using J congruent to f(x + delta) - f(x). Some numerical experiments using a modification of LSODE are reported. 1 figure, 2 tables.
Covariant electrodynamics in linear media: Optical metric
Thompson, Robert T.
2018-03-01
While the postulate of covariance of Maxwell's equations for all inertial observers led Einstein to special relativity, it was the further demand of general covariance—form invariance under general coordinate transformations, including between accelerating frames—that led to general relativity. Several lines of inquiry over the past two decades, notably the development of metamaterial-based transformation optics, has spurred a greater interest in the role of geometry and space-time covariance for electrodynamics in ponderable media. I develop a generally covariant, coordinate-free framework for electrodynamics in general dielectric media residing in curved background space-times. In particular, I derive a relation for the spatial medium parameters measured by an arbitrary timelike observer. In terms of those medium parameters I derive an explicit expression for the pseudo-Finslerian optical metric of birefringent media and show how it reduces to a pseudo-Riemannian optical metric for nonbirefringent media. This formulation provides a basis for a unified approach to ray and congruence tracing through media in curved space-times that may smoothly vary among positively refracting, negatively refracting, and vacuum.
Exact solution of some linear matrix equations using algebraic methods
Djaferis, T. E.; Mitter, S. K.
1977-01-01
A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.
Numerical solution of non-linear diffusion problems
International Nuclear Information System (INIS)
Carmen, A. del; Ferreri, J.C.
1998-01-01
This paper presents a method for the numerical solution of non-linear diffusion problems using finite-differences in moving grids. Due to the presence of steep fronts in the solution domain and to the presence of advective terms originating in the grid movement, an implicit TVD scheme, first order in time and second order in space has been developed. Some algebraic details of the derivation are given. Results are shown for the pure advection of a scalar as a test case and an example dealing with the slow spreading of viscous fluids over plane surfaces. The agreement between numerical and analytical solutions is excellent. (author). 8 refs., 3 figs
Asymptotic formulae for solutions of half-linear differential equations
Czech Academy of Sciences Publication Activity Database
Řehák, Pavel
2017-01-01
Roč. 292, January (2017), s. 165-177 ISSN 0096-3003 Institutional support: RVO:67985840 Keywords : half-linear differential equation * nonoscillatory solution * regular variation Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.738, year: 2016 http://www.sciencedirect.com/science/article/pii/S0096300316304581
On nonnegative solutions of second order linear functional differential equations
Czech Academy of Sciences Publication Activity Database
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
Radial solutions to semilinear elliptic equations via linearized operators
Directory of Open Access Journals (Sweden)
Phuong Le
2017-04-01
Full Text Available Let $u$ be a classical solution of semilinear elliptic equations in a ball or an annulus in $\\mathbb{R}^N$ with zero Dirichlet boundary condition where the nonlinearity has a convex first derivative. In this note, we prove that if the $N$-th eigenvalue of the linearized operator at $u$ is positive, then $u$ must be radially symmetric.
Minimal solution of linear formed fuzzy matrix equations
Directory of Open Access Journals (Sweden)
Maryam Mosleh
2012-10-01
Full Text Available In this paper according to the structured element method, the $mimes n$ inconsistent fuzzy matrix equation $Ailde{X}=ilde{B},$ which are linear formed by fuzzy structured element, is investigated. The necessary and sufficient condition for the existence of a fuzzy solution is also discussed. some examples are presented to illustrate the proposed method.
Linear-optical programmable quantum router
Czech Academy of Sciences Publication Activity Database
Lemr, K.; Černoch, Antonín
2013-01-01
Roč. 300, JUL (2013), s. 282-285 ISSN 0030-4018 R&D Projects: GA ČR GAP205/12/0382 Institutional research plan: CEZ:AV0Z10100522 Keywords : quantum router * quantum information processing * photon pairs * quantum communications * programmable phase gate Subject RIV: BH - Optics, Masers, Lasers Impact factor: 1.542, year: 2013 http://ac.els-cdn.com/S0030401813002563/1-s2.0-S0030401813002563-main.pdf?_tid=d1f7d17a-66e9-11e3-aa5e-00000aab0f6c&acdnat=1387264198_99aef4d40cf81f69
International Nuclear Information System (INIS)
Loock, Peter van; Nemoto, Kae; Munro, William J.; Raynal, Philippe; Luetkenhaus, Norbert
2006-01-01
We discuss the problem of implementing generalized measurements [positive operator-valued measures (POVMs)] with linear optics, either based upon a static linear array or including conditional dynamics. In our approach, a given POVM shall be identified as a solution to an optimization problem for a chosen cost function. We formulate a general principle: the implementation is only possible if a linear-optics circuit exists for which the quantum mechanical optimum (minimum) is still attainable after dephasing the corresponding quantum states. The general principle enables us, for instance, to derive a set of necessary conditions for the linear-optics implementation of the POVM that realizes the quantum mechanically optimal unambiguous discrimination of two pure nonorthogonal states. This extends our previous results on projection measurements and the exact discrimination of orthogonal states
Focal points and principal solutions of linear Hamiltonian systems revisited
Šepitka, Peter; Šimon Hilscher, Roman
2018-05-01
In this paper we present a novel view on the principal (and antiprincipal) solutions of linear Hamiltonian systems, as well as on the focal points of their conjoined bases. We present a new and unified theory of principal (and antiprincipal) solutions at a finite point and at infinity, and apply it to obtain new representation of the multiplicities of right and left proper focal points of conjoined bases. We show that these multiplicities can be characterized by the abnormality of the system in a neighborhood of the given point and by the rank of the associated T-matrix from the theory of principal (and antiprincipal) solutions. We also derive some additional important results concerning the representation of T-matrices and associated normalized conjoined bases. The results in this paper are new even for completely controllable linear Hamiltonian systems. We also discuss other potential applications of our main results, in particular in the singular Sturmian theory.
Periodic solutions of asymptotically linear Hamiltonian systems without twist conditions
Energy Technology Data Exchange (ETDEWEB)
Cheng Rong [Coll. of Mathematics and Physics, Nanjing Univ. of Information Science and Tech., Nanjing (China); Dept. of Mathematics, Southeast Univ., Nanjing (China); Zhang Dongfeng [Dept. of Mathematics, Southeast Univ., Nanjing (China)
2010-05-15
In dynamical system theory, especially in many fields of applications from mechanics, Hamiltonian systems play an important role, since many related equations in mechanics can be written in an Hamiltonian form. In this paper, we study the existence of periodic solutions for a class of Hamiltonian systems. By applying the Galerkin approximation method together with a result of critical point theory, we establish the existence of periodic solutions of asymptotically linear Hamiltonian systems without twist conditions. Twist conditions play crucial roles in the study of periodic solutions for asymptotically linear Hamiltonian systems. The lack of twist conditions brings some difficulty to the study. To the authors' knowledge, very little is known about the case, where twist conditions do not hold. (orig.)
The Linearity of Optical Tomography: Sensor Model and Experimental Verification
Directory of Open Access Journals (Sweden)
Siti Zarina MOHD. MUJI
2011-09-01
Full Text Available The aim of this paper is to show the linearization of optical sensor. Linearity of the sensor response is a must in optical tomography application, which affects the tomogram result. Two types of testing are used namely, testing using voltage parameter and testing with time unit parameter. For the former, the testing is by measuring the voltage when the obstacle is placed between transmitter and receiver. The obstacle diameters are between 0.5 until 3 mm. The latter is also the same testing but the obstacle is bigger than the former which is 59.24 mm and the testing purpose is to measure the time unit spend for the ball when it cut the area of sensing circuit. Both results show a linear relation that proves the optical sensors is suitable for process tomography application.
Entangling efficiency of linear-optical quantum gates
Czech Academy of Sciences Publication Activity Database
Lemr, Karel; Černoch, Antonín; Soubusta, Jan; Dušek, M.
2012-01-01
Roč. 86, č. 3 (2012), "032321-1"-"032321-5" ISSN 1050-2947 R&D Projects: GA ČR GAP205/12/0382 Institutional research plan: CEZ:AV0Z10100522 Keywords : linear-optical quantum gates * quantum physics Subject RIV: BH - Optics, Masers, Lasers Impact factor: 3.042, year: 2012 http://pra.aps.org/pdf/PRA/v86/i3/e032321
A Solution to the Fundamental Linear Fractional Order Differential Equation
Hartley, Tom T.; Lorenzo, Carl F.
1998-01-01
This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.
Solution methods for large systems of linear equations in BACCHUS
International Nuclear Information System (INIS)
Homann, C.; Dorr, B.
1993-05-01
The computer programme BACCHUS is used to describe steady state and transient thermal-hydraulic behaviour of a coolant in a fuel element with intact geometry in a fast breeder reactor. In such computer programmes generally large systems of linear equations with sparse matrices of coefficients, resulting from discretization of coolant conservation equations, must be solved thousands of times giving rise to large demands of main storage and CPU time. Direct and iterative solution methods of the systems of linear equations, available in BACCHUS, are described, giving theoretical details and experience with their use in the programme. Besides use of a method of lines, a Runge-Kutta-method, for solution of the partial differential equation is outlined. (orig.) [de
Asymptotic solutions and spectral theory of linear wave equations
International Nuclear Information System (INIS)
Adam, J.A.
1982-01-01
This review contains two closely related strands. Firstly the asymptotic solution of systems of linear partial differential equations is discussed, with particular reference to Lighthill's method for obtaining the asymptotic functional form of the solution of a scalar wave equation with constant coefficients. Many of the applications of this technique are highlighted. Secondly, the methods and applications of the theory of the reduced (one-dimensional) wave equation - particularly spectral theory - are discussed. While the breadth of application and power of the techniques is emphasised throughout, the opportunity is taken to present to a wider readership, developments of the methods which have occured in some aspects of astrophysical (particularly solar) and geophysical fluid dynamics. It is believed that the topics contained herein may be of relevance to the applied mathematician or theoretical physicist interest in problems of linear wave propagation in these areas. (orig./HSI)
A general method for enclosing solutions of interval linear equations
Czech Academy of Sciences Publication Activity Database
Rohn, Jiří
2012-01-01
Roč. 6, č. 4 (2012), s. 709-717 ISSN 1862-4472 R&D Projects: GA ČR GA201/09/1957; GA ČR GC201/08/J020 Institutional research plan: CEZ:AV0Z10300504 Keywords : interval linear equations * solution set * enclosure * absolute value inequality Subject RIV: BA - General Mathematics Impact factor: 1.654, year: 2012
From linear optical quantum computing to Heisenberg-limited interferometry
International Nuclear Information System (INIS)
Lee, Hwang; Kok, Pieter; Williams, Colin P; Dowling, Jonathan P
2004-01-01
The working principles of linear optical quantum computing are based on photodetection, namely, projective measurements. The use of photodetection can provide efficient nonlinear interactions between photons at the single-photon level, which is technically problematic otherwise. We report an application of such a technique to prepare quantum correlations as an important resource for Heisenberg-limited optical interferometry, where the sensitivity of phase measurements can be improved beyond the usual shot-noise limit. Furthermore, using such nonlinearities, optical quantum non-demolition measurements can now be carried out easily at the single-photon level
Linear and Nonlinear Optical Properties of Micrometer-Scale Gold Nanoplates
International Nuclear Information System (INIS)
Liu Xiao-Lan; Peng Xiao-Niu; Yang Zhong-Jian; Li Min; Zhou Li
2011-01-01
Micrometer-scale gold nanoplates have been synthesized in high yield through a polyol process. The morphology, crystal structure and linear optical extinction of the gold nanoplates have been characterized. These gold nanoplates are single-crystalline with triangular, truncated triangular and hexagonal shapes, exhibiting strong surface plasmon resonance (SPR) extinction in the visible and near-infrared (NIR) region. The linear optical properties of gold nanoplates are also investigated by theoretical calculations. We further investigate the nonlinear optical properties of the gold nanoplates in solution by Z-scan technique. The nonlinear absorption (NLA) coefficient and nonlinear refraction (NLR) index are measured to be 1.18×10 2 cm/GW and −1.04×10 −3 cm 2 /GW, respectively. (condensed matter: electronic structure, electrical, magnetic, and optical properties)
Adaptive phase measurements in linear optical quantum computation
International Nuclear Information System (INIS)
Ralph, T C; Lund, A P; Wiseman, H M
2005-01-01
Photon counting induces an effective non-linear optical phase shift in certain states derived by linear optics from single photons. Although this non-linearity is non-deterministic, it is sufficient in principle to allow scalable linear optics quantum computation (LOQC). The most obvious way to encode a qubit optically is as a superposition of the vacuum and a single photon in one mode-so-called 'single-rail' logic. Until now this approach was thought to be prohibitively expensive (in resources) compared to 'dual-rail' logic where a qubit is stored by a photon across two modes. Here we attack this problem with real-time feedback control, which can realize a quantum-limited phase measurement on a single mode, as has been recently demonstrated experimentally. We show that with this added measurement resource, the resource requirements for single-rail LOQC are not substantially different from those of dual-rail LOQC. In particular, with adaptive phase measurements an arbitrary qubit state α vertical bar 0>+β vertical bar 1> can be prepared deterministically
Optical linear algebra processors - Noise and error-source modeling
Casasent, D.; Ghosh, A.
1985-01-01
The modeling of system and component noise and error sources in optical linear algebra processors (OLAPs) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.
Optical linear algebra processors: noise and error-source modeling.
Casasent, D; Ghosh, A
1985-06-01
The modeling of system and component noise and error sources in optical linear algebra processors (OLAP's) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.
Silver Nanoparticles with Broad Multiband Linear Optical Absorption
Bakr, Osman M.
2009-07-06
A simple one-pot method produces silver nanoparticles coated with aryl thiols that show intense, broad nonplasmonic optical properties. The synthesis works with many aryl-thiol capping ligands, including water-soluble 4-mercaptobenzoic acid. The nanoparticles produced show linear absorption that is broader, stronger, and more structured than most conventional organic and inorganic dyes.
Silver Nanoparticles with Broad Multiband Linear Optical Absorption
Bakr, Osman M.; Amendola, Vincenzo; Aikens, Christine M.; Wenseleers, Wim; Li, Rui; Dal Negro, Luca; Schatz, George C.; Stellacci, Francesco
2009-01-01
A simple one-pot method produces silver nanoparticles coated with aryl thiols that show intense, broad nonplasmonic optical properties. The synthesis works with many aryl-thiol capping ligands, including water-soluble 4-mercaptobenzoic acid. The nanoparticles produced show linear absorption that is broader, stronger, and more structured than most conventional organic and inorganic dyes.
Proposal of Realization Restricted Quantum Game with Linear Optic Method
International Nuclear Information System (INIS)
Zhao Haijun; Fang Ximing
2006-01-01
We present a quantum game with the restricted strategic space and its realization with linear optical system, which can be played by two players who are separated remotely. This game can also be realized on any other quantum computers. We find that the constraint brings some interesting properties that are useful for making game models.
Utilizing encoding in scalable linear optics quantum computing
International Nuclear Information System (INIS)
Hayes, A J F; Gilchrist, A; Myers, C R; Ralph, T C
2004-01-01
We present a scheme which offers a significant reduction in the resources required to implement linear optics quantum computing. The scheme is a variation of the proposal of Knill, Laflamme and Milburn, and makes use of an incremental approach to the error encoding to boost probability of success
Linear and nonlinear optical spectroscopy: Spectral, temporal and spatial resolution
DEFF Research Database (Denmark)
Hvam, Jørn Marcher
1997-01-01
Selected linear and nonlinear optical spectroscopies are being described with special emphasis on the possibility of obtaining simultaneous spectral, temporal and spatial resolution. The potential of various experimental techniques is being demonstrated by specific examples mostly taken from inve...... investigations of the electronic, and opto-electronic, properties of semiconductor nanostructures....
Instrumentation for Linear and Nonlinear Optical Device Characterization
2018-01-31
distribution is Unlimited 13. SUPPLEMENTARY NOTES 14. ABSTRACT The Pl has acquired six pieces of equipment to extend capabilities for linear and nonlinear...optical spectral analysis • Frequency comb generation in mid-infrared Accomplishments Six major pieces of equipment have been ordered and received
McDONALD OBSERVATORY ARCHIVE OF OPTICAL LINEAR POLARIZATION MEASUREMENTS
International Nuclear Information System (INIS)
Wills, Beverley J.; Wills, D.; Breger, M.
2011-01-01
We present 990 previously unpublished optical linear polarization measurements of quasars, active galactic nuclei, and some stars observed for interstellar polarization. The observations, covering the period 1981-2000, were made with McDonald Observatory's 2.1 m Struve reflector and the Breger photopolarimeter.
Linear optical response of carbon nanotubes under axial magnetic field
Moradian, Rostam; Chegel, Raad; Behzad, Somayeh
2010-04-01
We considered single walled carbon naotubes (SWCNTs) as real three dimensional (3D) systems in a cylindrical coordinate. The optical matrix elements and linear susceptibility, χ(ω), in the tight binding approximation in terms of one-dimensional wave vector, kz and subband index, l are calculated. In an external axial magnetic field optical frequency dependence of linear susceptibility are investigated. We found that axial magnetic field has two effects on the imaginary part of the linear susceptibility spectrum, in agreement with experimental results. The first effect is broadening and the second, splitting. Also we found that for all metallic zigzag and armchair SWCNTs, the axial magnetic field leads to the creation of a peak with energy less than 1.5 eV, contrary to what is observed in the absence of a magnetic field.
Small-scale quantum information processing with linear optics
International Nuclear Information System (INIS)
Bergou, J.A.; Steinberg, A.M.; Mohseni, M.
2005-01-01
Full text: Photons are the ideal systems for carrying quantum information. Although performing large-scale quantum computation on optical systems is extremely demanding, non scalable linear-optics quantum information processing may prove essential as part of quantum communication networks. In addition efficient (scalable) linear-optical quantum computation proposal relies on the same optical elements. Here, by constructing multirail optical networks, we experimentally study two central problems in quantum information science, namely optimal discrimination between nonorthogonal quantum states, and controlling decoherence in quantum systems. Quantum mechanics forbids deterministic discrimination between nonorthogonal states. This is one of the central features of quantum cryptography, which leads to secure communications. Quantum state discrimination is an important primitive in quantum information processing, since it determines the limitations of a potential eavesdropper, and it has applications in quantum cloning and entanglement concentration. In this work, we experimentally implement generalized measurements in an optical system and demonstrate the first optimal unambiguous discrimination between three non-orthogonal states with a success rate of 55 %, to be compared with the 25 % maximum achievable using projective measurements. Furthermore, we present the first realization of unambiguous discrimination between a pure state and a nonorthogonal mixed state. In a separate experiment, we demonstrate how decoherence-free subspaces (DFSs) may be incorporated into a prototype optical quantum algorithm. Specifically, we present an optical realization of two-qubit Deutsch-Jozsa algorithm in presence of random noise. By introduction of localized turbulent airflow we produce a collective optical dephasing, leading to large error rates and demonstrate that using DFS encoding, the error rate in the presence of decoherence can be reduced from 35 % to essentially its pre
Ultra-high Frequency Linear Fiber Optic Systems
Lau, Kam Y
2009-01-01
Designed for a one-semester course on fiber-optics systems and communication links, this book provides a concise but rigorous treatment of the theory and practice of analog (linear) fiber-optics links and systems that constitute the foundation of Hybrid Fiber Coax infrastructure in present-day CATV distribution and cable modem Internet access. Emerging applications in remote fiber-optic feed for free-space millimeter wave enterprise campus networks are also described. Issues such as dispersion and interferometric noise are treated quantitatively, and means for mitigating them are explained. This broad but concise text will thus be invaluable not only to students of fiber-optics communication but also to practicing engineers.
Solution of the fully fuzzy linear systems using iterative techniques
International Nuclear Information System (INIS)
Dehghan, Mehdi; Hashemi, Behnam; Ghatee, Mehdi
2007-01-01
This paper mainly intends to discuss the iterative solution of fully fuzzy linear systems which we call FFLS. We employ Dubois and Prade's approximate arithmetic operators on LR fuzzy numbers for finding a positive fuzzy vector x-tilde which satisfies A-tildex-tilde=b, where A-tilde and b-tilde are a fuzzy matrix and a fuzzy vector, respectively. Please note that the positivity assumption is not so restrictive in applied problems. We transform FFLS and propose iterative techniques such as Richardson, Jacobi, Jacobi overrelaxation (JOR), Gauss-Seidel, successive overrelaxation (SOR), accelerated overrelaxation (AOR), symmetric and unsymmetric SOR (SSOR and USSOR) and extrapolated modified Aitken (EMA) for solving FFLS. In addition, the methods of Newton, quasi-Newton and conjugate gradient are proposed from nonlinear programming for solving a fully fuzzy linear system. Various numerical examples are also given to show the efficiency of the proposed schemes
Spin and diamagnetism in linear and nonlinear optics
International Nuclear Information System (INIS)
Andersen, Torsten; Keller, Ole; Huebner, Wolfgang; Johansson, Boerje
2004-01-01
We present a local-field theory for spin and diamagnetism in linear and nonlinear optics. We examine all the processes contained in the Pauli Hamiltonian and its corresponding microscopic current density, including the terms depending on the electron spin. The resulting general real-space conductivities are presented and discussed. To quantify the implications of including the spin, we study the linear and nonlinear optical properties of free-electron metals, represented by the screened homogeneous electron gas. The real-space formalism is transformed into Fourier space, and the symmetries of the linear and nonlinear optical conductivities in a homogeneous electron gas are discussed. Numerical results are presented for the homogeneous electron gas, in which we treat ω and q as independent variables, thereby opening the theory to near-field optics and the study of evanescent waves. We show that in regions of the ω-q spectrum, the presence of diamagnetism and spin dynamics significantly alters the response in comparison to considering only the paramagnetic response. Additionally, we discuss the effects of screening, and we finish our treatment by a discussion of how to connect the present theory to existing methods in ab initio solid-state physics
Linear perturbations of a self-similar solution of hydrodynamics with non-linear heat conduction
International Nuclear Information System (INIS)
Dubois-Boudesocque, Carine
2000-01-01
The stability of an ablative flow, where a shock wave is located upstream a thermal front, is of importance in inertial confinement fusion. The present model considers an exact self-similar solution to the hydrodynamic equations with non-linear heat conduction for a semi-infinite slab. For lack of an analytical solution, a high resolution numerical procedure is devised, which couples a finite difference method with a relaxation algorithm using a two-domain pseudo-spectral method. Stability of this solution is studied by introducing linear perturbation method within a Lagrangian-Eulerian framework. The initial and boundary value problem is solved by a splitting of the equations between a hyperbolic system and a parabolic equation. The boundary conditions of the hyperbolic system are treated, in the case of spectral methods, according to Thompson's approach. The parabolic equation is solved by an influence matrix method. These numerical procedures have been tested versus exact solutions. Considering a boundary heat flux perturbation, the space-time evolution of density, velocity and temperature are shown. (author) [fr
Oscillation of solutions of some higher order linear differential equations
Directory of Open Access Journals (Sweden)
Hong-Yan Xu
2009-11-01
Full Text Available In this paper, we deal with the order of growth and the hyper order of solutions of higher order linear differential equations $$f^{(k}+B_{k-1}f^{(k-1}+\\cdots+B_1f'+B_0f=F$$ where $B_j(z (j=0,1,\\ldots,k-1$ and $F$ are entire functions or polynomials. Some results are obtained which improve and extend previous results given by Z.-X. Chen, J. Wang, T.-B. Cao and C.-H. Li.
Description of All Solutions of a Linear Complementarity Problem
Czech Academy of Sciences Publication Activity Database
Rohn, Jiří
2009-01-01
Roč. 18, - (2009), s. 246-252 E-ISSN 1081-3810 R&D Projects: GA ČR GA201/09/1957; GA ČR GC201/08/J020 Institutional research plan: CEZ:AV0Z10300504 Keywords : linear complementarity problem * Moore-Penrose inverse * verified solution * absolute value equation Subject RIV: BA - General Mathematics Impact factor: 0.892, year: 2009 http://www.math.technion.ac.il/iic/ ela / ela -articles/articles/vol18_pp246-252.pdf
Optical solutions for unbundled access network
Bacîş Vasile, Irina Bristena
2015-02-01
The unbundling technique requires finding solutions to guarantee the economic and technical performances imposed by the nature of the services that can be offered. One of the possible solutions is the optic one; choosing this solution is justified for the following reasons: it optimizes the use of the access network, which is the most expensive part of a network (about 50% of the total investment in telecommunications networks) while also being the least used (telephone traffic on the lines has a low cost); it increases the distance between the master station/central and the terminal of the subscriber; the development of the services offered to the subscribers is conditioned by the subscriber network. For broadband services there is a need for support for the introduction of high-speed transport. A proper identification of the factors that must be satisfied and a comprehensive financial evaluation of all resources involved, both the resources that are in the process of being bought as well as extensions are the main conditions that would lead to a correct choice. As there is no single optimal technology for all development scenarios, which can take into account all access systems, a successful implementation is always done by individual/particularized scenarios. The method used today for the selection of an optimal solution is based on statistics and analysis of the various, already implemented, solutions, and on the experience that was already gained; the main evaluation criterion and the most unbiased one is the ratio between the cost of the investment and the quality of service, while serving an as large as possible number of customers.
Fault tolerance in parity-state linear optical quantum computing
International Nuclear Information System (INIS)
Hayes, A. J. F.; Ralph, T. C.; Haselgrove, H. L.; Gilchrist, Alexei
2010-01-01
We use a combination of analytical and numerical techniques to calculate the noise threshold and resource requirements for a linear optical quantum computing scheme based on parity-state encoding. Parity-state encoding is used at the lowest level of code concatenation in order to efficiently correct errors arising from the inherent nondeterminism of two-qubit linear-optical gates. When combined with teleported error-correction (using either a Steane or Golay code) at higher levels of concatenation, the parity-state scheme is found to achieve a saving of approximately three orders of magnitude in resources when compared to the cluster state scheme, at a cost of a somewhat reduced noise threshold.
One-step deterministic multipartite entanglement purification with linear optics
Energy Technology Data Exchange (ETDEWEB)
Sheng, Yu-Bo [Department of Physics, Tsinghua University, Beijing 100084 (China); Long, Gui Lu, E-mail: gllong@tsinghua.edu.cn [Department of Physics, Tsinghua University, Beijing 100084 (China); Center for Atomic and Molecular NanoSciences, Tsinghua University, Beijing 100084 (China); Key Laboratory for Quantum Information and Measurements, Beijing 100084 (China); Deng, Fu-Guo [Department of Physics, Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875 (China)
2012-01-09
We present a one-step deterministic multipartite entanglement purification scheme for an N-photon system in a Greenberger–Horne–Zeilinger state with linear optical elements. The parties in quantum communication can in principle obtain a maximally entangled state from each N-photon system with a success probability of 100%. That is, it does not consume the less-entangled photon systems largely, which is far different from other multipartite entanglement purification schemes. This feature maybe make this scheme more feasible in practical applications. -- Highlights: ► We proposed a deterministic entanglement purification scheme for GHZ states. ► The scheme uses only linear optical elements and has a success probability of 100%. ► The scheme gives a purified GHZ state in just one-step.
Synthesis of polymeric micro- and nanostructural materials for application in non-linear optics
International Nuclear Information System (INIS)
Kravets, Lyubov; Palistrant, Natalia; Bivol, Valerii; Robu, Stepan; Barba, Nikolai; Orelovitch, Oleg
2007-01-01
The present paper describes a new approach developed for the preparation of micro- and nanostructural materials on the basis of polymeric compositions used as a matrix in non-linear optics. This approach consists in filling the pores of poly(ethylene terephthalate) track membranes (PET TM) from polymeric compositions using an impregnation method. It is shown that depending on the concentration of polymeric compositions in the solution it is possible to form a variety of micro- and nanostructural materials (tubules and wires as well as composite membranes) with a wide spectrum of characteristics. The developed method of producing micro- and nanostructural materials provides a possible way for creating polymeric objects with non-linear optic properties which can be used to design electronic micro- and nanodevices and to obtain chemical and optical sensors
An algorithm for the solution of dynamic linear programs
Psiaki, Mark L.
1989-01-01
The algorithm's objective is to efficiently solve Dynamic Linear Programs (DLP) by taking advantage of their special staircase structure. This algorithm constitutes a stepping stone to an improved algorithm for solving Dynamic Quadratic Programs, which, in turn, would make the nonlinear programming method of Successive Quadratic Programs more practical for solving trajectory optimization problems. The ultimate goal is to being trajectory optimization solution speeds into the realm of real-time control. The algorithm exploits the staircase nature of the large constraint matrix of the equality-constrained DLPs encountered when solving inequality-constrained DLPs by an active set approach. A numerically-stable, staircase QL factorization of the staircase constraint matrix is carried out starting from its last rows and columns. The resulting recursion is like the time-varying Riccati equation from multi-stage LQR theory. The resulting factorization increases the efficiency of all of the typical LP solution operations over that of a dense matrix LP code. At the same time numerical stability is ensured. The algorithm also takes advantage of dynamic programming ideas about the cost-to-go by relaxing active pseudo constraints in a backwards sweeping process. This further decreases the cost per update of the LP rank-1 updating procedure, although it may result in more changes of the active set that if pseudo constraints were relaxed in a non-stagewise fashion. The usual stability of closed-loop Linear/Quadratic optimally-controlled systems, if it carries over to strictly linear cost functions, implies that the saving due to reduced factor update effort may outweigh the cost of an increased number of updates. An aerospace example is presented in which a ground-to-ground rocket's distance is maximized. This example demonstrates the applicability of this class of algorithms to aerospace guidance. It also sheds light on the efficacy of the proposed pseudo constraint relaxation
Unconditional quantum cloning of coherent states with linear optics
International Nuclear Information System (INIS)
Leuchs, G.; Andersen, U.L.; Josse, V.
2005-01-01
Intense light pulses with non-classical properties are used to implement protocols for quantum communication. Most of the elements in the tool box needed to assemble the experimental set-ups for these protocols are readily described by Bogoliubov transformations corresponding to Gaussian transformations that map Gaussian states onto Gaussian states. One particularly interesting application is quantum cloning of a coherent state. A scheme for optimal Gaussian cloning of optical coherent states is proposed and experimentally demonstrated. Its optical realization is based entirely on simple linear optical elements and homodyne detection. The optimality of the presented scheme is only limited by detection inefficiencies. Experimentally we achieved a cloning fidelity of about 65%, which almost touches the optimal value of 2/3. (author)
Preserving Simplecticity in the Numerical Integration of Linear Beam Optics
Energy Technology Data Exchange (ETDEWEB)
Allen, Christopher K. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2017-07-01
Presented are mathematical tools and methods for the development of numerical integration techniques that preserve the symplectic condition inherent to mechanics. The intended audience is for beam physicists with backgrounds in numerical modeling and simulation with particular attention to beam optics applications. The paper focuses on Lie methods that are inherently symplectic regardless of the integration accuracy order. Section 2 provides the mathematically tools used in the sequel and necessary for the reader to extend the covered techniques. Section 3 places those tools in the context of charged-particle beam optics; in particular linear beam optics is presented in terms of a Lie algebraic matrix representation. Section 4 presents numerical stepping techniques with particular emphasis on a third-order leapfrog method. Section 5 discusses the modeling of field imperfections with particular attention to the fringe fields of quadrupole focusing magnets. The direct computation of a third order transfer matrix for a fringe field is shown.
A Linear Birefringence Measurement Method for an Optical Fiber Current Sensor.
Xu, Shaoyi; Shao, Haiming; Li, Chuansheng; Xing, Fangfang; Wang, Yuqiao; Li, Wei
2017-07-03
In this work, a linear birefringence measurement method is proposed for an optical fiber current sensor (OFCS). First, the optical configuration of the measurement system is presented. Then, the elimination method of the effect of the azimuth angles between the sensing fiber and the two polarizers is demonstrated. Moreover, the relationship of the linear birefringence, the Faraday rotation angle and the final output is determined. On these bases, the multi-valued problem on the linear birefringence is simulated and its solution is illustrated when the linear birefringence is unknown. Finally, the experiments are conducted to prove the feasibility of the proposed method. When the numbers of turns of the sensing fiber in the OFCS are about 15, 19, 23, 27, 31, 35, and 39, the measured linear birefringence obtained by the proposed method are about 1.3577, 1.8425, 2.0983, 2.5914, 2.7891, 3.2003 and 3.5198 rad. Two typical methods provide the references for the proposed method. The proposed method is proven to be suitable for the linear birefringence measurement in the full range without the limitation that the linear birefringence must be smaller than π/2.
Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices
International Nuclear Information System (INIS)
Luz, H. L. F. da; Gammal, A.; Abdullaev, F. Kh.; Salerno, M.; Tomio, Lauro
2010-01-01
The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.
Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices
da Luz, H. L. F.; Abdullaev, F. Kh.; Gammal, A.; Salerno, M.; Tomio, Lauro
2010-10-01
The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.
Approximate solution to neutron transport equation with linear anisotropic scattering
International Nuclear Information System (INIS)
Coppa, G.; Ravetto, P.; Sumini, M.
1983-01-01
A method to obtain an approximate solution to the transport equation, when both sources and collisions show a linearly anisotropic behavior, is outlined and the possible implications for numerical calculations in applied neutronics as well as shielding evaluations are investigated. The form of the differential system of equations taken by the method is quite handy and looks simpler and more manageable than any other today available technique. To go deeper into the efficiency of the method, some typical calculations concerning critical dimension of multiplying systems are then performed and the results are compared with the ones coming from the classical Ssub(N) approximations. The outcome of such calculations leads us to think of interesting developments of the method which could be quite useful in alternative to other today widespread approximate procedures, for any geometry, but especially for curved ones. (author)
High-Dimensional Quantum Information Processing with Linear Optics
Fitzpatrick, Casey A.
Quantum information processing (QIP) is an interdisciplinary field concerned with the development of computers and information processing systems that utilize quantum mechanical properties of nature to carry out their function. QIP systems have become vastly more practical since the turn of the century. Today, QIP applications span imaging, cryptographic security, computation, and simulation (quantum systems that mimic other quantum systems). Many important strategies improve quantum versions of classical information system hardware, such as single photon detectors and quantum repeaters. Another more abstract strategy engineers high-dimensional quantum state spaces, so that each successful event carries more information than traditional two-level systems allow. Photonic states in particular bring the added advantages of weak environmental coupling and data transmission near the speed of light, allowing for simpler control and lower system design complexity. In this dissertation, numerous novel, scalable designs for practical high-dimensional linear-optical QIP systems are presented. First, a correlated photon imaging scheme using orbital angular momentum (OAM) states to detect rotational symmetries in objects using measurements, as well as building images out of those interactions is reported. Then, a statistical detection method using chains of OAM superpositions distributed according to the Fibonacci sequence is established and expanded upon. It is shown that the approach gives rise to schemes for sorting, detecting, and generating the recursively defined high-dimensional states on which some quantum cryptographic protocols depend. Finally, an ongoing study based on a generalization of the standard optical multiport for applications in quantum computation and simulation is reported upon. The architecture allows photons to reverse momentum inside the device. This in turn enables realistic implementation of controllable linear-optical scattering vertices for
Applied research of quantum information based on linear optics
International Nuclear Information System (INIS)
Xu, Xiao-Ye
2016-01-01
This thesis reports on outstanding work in two main subfields of quantum information science: one involves the quantum measurement problem, and the other concerns quantum simulation. The thesis proposes using a polarization-based displaced Sagnac-type interferometer to achieve partial collapse measurement and its reversal, and presents the first experimental verification of the nonlocality of the partial collapse measurement and its reversal. All of the experiments are carried out in the linear optical system, one of the earliest experimental systems to employ quantum communication and quantum information processing. The thesis argues that quantum measurement can yield quantum entanglement recovery, which is demonstrated by using the frequency freedom to simulate the environment. Based on the weak measurement theory, the author proposes that white light can be used to precisely estimate phase, and effectively demonstrates that the imaginary part of the weak value can be introduced by means of weak measurement evolution. Lastly, a nine-order polarization-based displaced Sagnac-type interferometer employing bulk optics is constructed to perform quantum simulation of the Landau-Zener evolution, and by tuning the system Hamiltonian, the first experiment to research the Kibble-Zurek mechanism in non-equilibrium kinetics processes is carried out in the linear optical system.
Applied research of quantum information based on linear optics
Energy Technology Data Exchange (ETDEWEB)
Xu, Xiao-Ye
2016-08-01
This thesis reports on outstanding work in two main subfields of quantum information science: one involves the quantum measurement problem, and the other concerns quantum simulation. The thesis proposes using a polarization-based displaced Sagnac-type interferometer to achieve partial collapse measurement and its reversal, and presents the first experimental verification of the nonlocality of the partial collapse measurement and its reversal. All of the experiments are carried out in the linear optical system, one of the earliest experimental systems to employ quantum communication and quantum information processing. The thesis argues that quantum measurement can yield quantum entanglement recovery, which is demonstrated by using the frequency freedom to simulate the environment. Based on the weak measurement theory, the author proposes that white light can be used to precisely estimate phase, and effectively demonstrates that the imaginary part of the weak value can be introduced by means of weak measurement evolution. Lastly, a nine-order polarization-based displaced Sagnac-type interferometer employing bulk optics is constructed to perform quantum simulation of the Landau-Zener evolution, and by tuning the system Hamiltonian, the first experiment to research the Kibble-Zurek mechanism in non-equilibrium kinetics processes is carried out in the linear optical system.
Linear homotopy solution of nonlinear systems of equations in geodesy
Paláncz, Béla; Awange, Joseph L.; Zaletnyik, Piroska; Lewis, Robert H.
2010-01-01
A fundamental task in geodesy is solving systems of equations. Many geodetic problems are represented as systems of multivariate polynomials. A common problem in solving such systems is improper initial starting values for iterative methods, leading to convergence to solutions with no physical meaning, or to convergence that requires global methods. Though symbolic methods such as Groebner bases or resultants have been shown to be very efficient, i.e., providing solutions for determined systems such as 3-point problem of 3D affine transformation, the symbolic algebra can be very time consuming, even with special Computer Algebra Systems (CAS). This study proposes the Linear Homotopy method that can be implemented easily in high-level computer languages like C++ and Fortran that are faster than CAS by at least two orders of magnitude. Using Mathematica, the power of Homotopy is demonstrated in solving three nonlinear geodetic problems: resection, GPS positioning, and affine transformation. The method enlarging the domain of convergence is found to be efficient, less sensitive to rounding of numbers, and has lower complexity compared to other local methods like Newton-Raphson.
DEFF Research Database (Denmark)
Johnsen, Kristinn; Jauho, Antti-Pekka
1998-01-01
We theoretically study the effect of THz radiation on the linear optical absorption spectra of semiconductor structures. A general theoretical framework, based on nonequilibrium Green functions, is formulated and applied to the calculation of linear optical absorption spectrum for several...
Resource-efficient generation of linear cluster states by linear optics with postselection
International Nuclear Information System (INIS)
Uskov, D B; Alsing, P M; Fanto, M L; Szep, A; Smith, A M; Kaplan, L; Kim, R
2015-01-01
We report on theoretical research in photonic cluster-state computing. Finding optimal schemes of generating non-classical photonic states is of critical importance for this field as physically implementable photon–photon entangling operations are currently limited to measurement-assisted stochastic transformations. A critical parameter for assessing the efficiency of such transformations is the success probability of a desired measurement outcome. At present there are several experimental groups that are capable of generating multi-photon cluster states carrying more than eight qubits. Separate photonic qubits or small clusters can be fused into a single cluster state by a probabilistic optical CZ gate conditioned on simultaneous detection of all photons with 1/9 success probability for each gate. This design mechanically follows the original theoretical scheme of cluster state generation proposed more than a decade ago by Raussendorf, Browne and Briegel. The optimality of the destructive CZ gate in application to linear optical cluster state generation has not been analyzed previously. Our results reveal that this method is far from the optimal one. Employing numerical optimization we have identified that the maximal success probability of fusing n unentangled dual-rail optical qubits into a linear cluster state is equal to (1/2) n−1 ; an m-tuple of photonic Bell pair states, commonly generated via spontaneous parametric down-conversion, can be fused into a single cluster with the maximal success probability of (1/4) m−1 . (paper)
Linear Optics From Closed Orbits (LOCO): An Introduction
International Nuclear Information System (INIS)
Safranek, James
2009-01-01
The LOCO code is used to find and correct errors in the linear optics of storage rings. The original FORTRAN code was written to correct the optics of the NSLS X-Ray ring, and was applied soon thereafter to debug problems with the ALS optics. The ideas used in the code were developed from previous work at SLAC. Several years ago, LOCO was rewritten in MATLAB. As described in this newsletter, the MATLAB version includes a user-friendly interface, with many useful fitting and analysis options. LOCO has been used at many accelerators. Presently, a search for LOCO in the text of papers on the Joint Accelerator Conferences Website yields 107 papers. A comprehensive survey of applications will not be included here. Details of recent results at a few light sources are included in this newsletter. In the past, the quality of LOCO fitting results varied significantly, depending on the storage ring. In particular, the results were mixed for colliding beam facilities, where there tend to be fewer BPMs that in light sources. Fitting rings with less BPM data to constrain the fit optics parameters often led to unreasonably large fit quadrupole gradient variations. Recently, modifications have been made to the LOCO fitting algorithm which leads to much better results when the BPM data does not tightly constrain the fit parameters. The modifications are described in this newsletter, and an example of results with this new algorithm is included.
Wavefront Sensing for WFIRST with a Linear Optical Model
Jurling, Alden S.; Content, David A.
2012-01-01
In this paper we develop methods to use a linear optical model to capture the field dependence of wavefront aberrations in a nonlinear optimization-based phase retrieval algorithm for image-based wavefront sensing. The linear optical model is generated from a ray trace model of the system and allows the system state to be described in terms of mechanical alignment parameters rather than wavefront coefficients. This approach allows joint optimization over images taken at different field points and does not require separate convergence of phase retrieval at individual field points. Because the algorithm exploits field diversity, multiple defocused images per field point are not required for robustness. Furthermore, because it is possible to simultaneously fit images of many stars over the field, it is not necessary to use a fixed defocus to achieve adequate signal-to-noise ratio despite having images with high dynamic range. This allows high performance wavefront sensing using in-focus science data. We applied this technique in a simulation model based on the Wide Field Infrared Survey Telescope (WFIRST) Intermediate Design Reference Mission (IDRM) imager using a linear optical model with 25 field points. We demonstrate sub-thousandth-wave wavefront sensing accuracy in the presence of noise and moderate undersampling for both monochromatic and polychromatic images using 25 high-SNR target stars. Using these high-quality wavefront sensing results, we are able to generate upsampled point-spread functions (PSFs) and use them to determine PSF ellipticity to high accuracy in order to reduce the systematic impact of aberrations on the accuracy of galactic ellipticity determination for weak-lensing science.
Linear optical response of finite systems using multishift linear system solvers
Energy Technology Data Exchange (ETDEWEB)
Hübener, Hannes; Giustino, Feliciano [Department of Materials, University of Oxford, Oxford OX1 3PH (United Kingdom)
2014-07-28
We discuss the application of multishift linear system solvers to linear-response time-dependent density functional theory. Using this technique the complete frequency-dependent electronic density response of finite systems to an external perturbation can be calculated at the cost of a single solution of a linear system via conjugate gradients. We show that multishift time-dependent density functional theory yields excitation energies and oscillator strengths in perfect agreement with the standard diagonalization of the response matrix (Casida's method), while being computationally advantageous. We present test calculations for benzene, porphin, and chlorophyll molecules. We argue that multishift solvers may find broad applicability in the context of excited-state calculations within density-functional theory and beyond.
Negative base encoding in optical linear algebra processors
Perlee, C.; Casasent, D.
1986-01-01
In the digital multiplication by analog convolution algorithm, the bits of two encoded numbers are convolved to form the product of the two numbers in mixed binary representation; this output can be easily converted to binary. Attention is presently given to negative base encoding, treating base -2 initially, and then showing that the negative base system can be readily extended to any radix. In general, negative base encoding in optical linear algebra processors represents a more efficient technique than either sign magnitude or 2's complement encoding, when the additions of digitally encoded products are performed in parallel.
IR Optics Measurement with Linear Coupling's Action-Angle Parameterization
Luo, Yun; Pilat, Fulvia Caterina; Satogata, Todd; Trbojevic, Dejan
2005-01-01
The interaction region (IP) optics are measured with the two DX/BPMs close to the IPs at the Relativistic Heavy Ion Collider (RHIC). The beta functions at IP are measured with the two eigenmodes' phase advances between the two BPMs. And the beta waists are also determined through the beta functions at the two BPMs. The coupling parameters at the IPs are also given through the linear coupling's action-angle parameterization. All the experimental data are taken during the driving oscillations with the AC dipole. The methods to do these measurements are discussed. And the measurement results during the beta*
Structure/property relationships in non-linear optical materials
Energy Technology Data Exchange (ETDEWEB)
Cole, J M [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France); [Durham Univ. (United Kingdom); Howard, J A.K. [Durham Univ. (United Kingdom); McIntyre, G J [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)
1997-04-01
The application of neutrons to the study of structure/property relationships in organic non-linear optical materials (NLOs) is described. In particular, charge-transfer effects and intermolecular interactions are investigated. Charge-transfer effects are studied by charge-density analysis and an example of one such investigation is given. The study of intermolecular interactions concentrates on the effects of hydrogen-bonding and an example is given of two structurally similar molecules with very disparate NLO properties, as a result of different types of hydrogen-bonding. (author). 3 refs.
Accuracy requirements of optical linear algebra processors in adaptive optics imaging systems
Downie, John D.; Goodman, Joseph W.
1989-10-01
The accuracy requirements of optical processors in adaptive optics systems are determined by estimating the required accuracy in a general optical linear algebra processor (OLAP) that results in a smaller average residual aberration than that achieved with a conventional electronic digital processor with some specific computation speed. Special attention is given to an error analysis of a general OLAP with regard to the residual aberration that is created in an adaptive mirror system by the inaccuracies of the processor, and to the effect of computational speed of an electronic processor on the correction. Results are presented on the ability of an OLAP to compete with a digital processor in various situations.
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…
Kuindersma, P.I.; Leijtens, X.J.M.; Zantvoort, van J.H.C.; Waardt, de H.
2012-01-01
We characterize integrated InP circuits for high speed ‘all-optical’ signal processing. Single chip circuits act as optical transistors. Transmodulation is performed by non-linear gain sections. Integrated tunable filters give signal equalization in time domain.
General solutions of second-order linear difference equations of Euler type
Directory of Open Access Journals (Sweden)
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.
Linear regression crash prediction models : issues and proposed solutions.
2010-05-01
The paper develops a linear regression model approach that can be applied to : crash data to predict vehicle crashes. The proposed approach involves novice data aggregation : to satisfy linear regression assumptions; namely error structure normality ...
Optical Networks Solutions planning - performances - management
DEFF Research Database (Denmark)
Fenger, Christian
2002-01-01
It has been a decisive goal in the compilation of this thesis to make us capable of realizing the future national and regional telecommunication networks in an efficient and resource optimal way. By future telecommunication network is assumed an all optical network where the information in transit...... are kept optical and not converted into the optical domain. The focus is on the scientific results achieved throughout the Ph.D. period. Five subjects – all increasing the understanding of optical networks – are studied. Static wavelength routed optical networks are studied. Management on terms...... of lightpath allocation and design is considered. By using statistical models (simultaneous analysis of many networks) the correspondence between parameters determining the network topology and the performance of the optical network is found. These dependencies are important knowledge in the process...
Real-time optical laboratory solution of parabolic differential equations
Casasent, David; Jackson, James
1988-01-01
An optical laboratory matrix-vector processor is used to solve parabolic differential equations (the transient diffusion equation with two space variables and time) by an explicit algorithm. This includes optical matrix-vector nonbase-2 encoded laboratory data, the combination of nonbase-2 and frequency-multiplexed data on such processors, a high-accuracy optical laboratory solution of a partial differential equation, new data partitioning techniques, and a discussion of a multiprocessor optical matrix-vector architecture.
Adaptive matching of the iota ring linear optics for space charge compensation
Energy Technology Data Exchange (ETDEWEB)
Romanov, A. [Fermilab; Bruhwiler, D. L. [RadiaSoft, Boulder; Cook, N. [RadiaSoft, Boulder; Hall, C. [RadiaSoft, Boulder
2016-10-09
Many present and future accelerators must operate with high intensity beams when distortions induced by space charge forces are among major limiting factors. Betatron tune depression of above approximately 0.1 per cell leads to significant distortions of linear optics. Many aspects of machine operation depend on proper relations between lattice functions and phase advances, and can be i proved with proper treatment of space charge effects. We implement an adaptive algorithm for linear lattice re matching with full account of space charge in the linear approximation for the case of Fermilab’s IOTA ring. The method is based on a search for initial second moments that give closed solution and, at the same predefined set of goals for emittances, beta functions, dispersions and phase advances at and between points of interest. Iterative singular value decomposition based technique is used to search for optimum by varying wide array of model parameters
IR OPTICS MEASUREMENT WITH LINEAR COUPLING'S ACTION-ANGLE PARAMETERIZATION
International Nuclear Information System (INIS)
LUO, Y.; BAI, M.; PILAT, R.; SATOGATA, T.; TRBOJEVIC, D.
2005-01-01
A parameterization of linear coupling in action-angle coordinates is convenient for analytical calculations and interpretation of turn-by-turn (TBT) beam position monitor (BPM) data. We demonstrate how to use this parameterization to extract the twiss and coupling parameters in interaction regions (IRs), using BPMs on each side of the long IR drift region. The example of TBT BPM analysis was acquired at the Relativistic Heavy Ion Collider (RHIC), using an AC dipole to excite a single eigenmode. Besides the full treatment, a fast estimate of beta*, the beta function at the interaction point (IP), is provided, along with the phase advance between these BPMs. We also calculate and measure the waist of the beta function and the local optics
Linear optical quantum computing in a single spatial mode.
Humphreys, Peter C; Metcalf, Benjamin J; Spring, Justin B; Moore, Merritt; Jin, Xian-Min; Barbieri, Marco; Kolthammer, W Steven; Walmsley, Ian A
2013-10-11
We present a scheme for linear optical quantum computing using time-bin-encoded qubits in a single spatial mode. We show methods for single-qubit operations and heralded controlled-phase (cphase) gates, providing a sufficient set of operations for universal quantum computing with the Knill-Laflamme-Milburn [Nature (London) 409, 46 (2001)] scheme. Our protocol is suited to currently available photonic devices and ideally allows arbitrary numbers of qubits to be encoded in the same spatial mode, demonstrating the potential for time-frequency modes to dramatically increase the quantum information capacity of fixed spatial resources. As a test of our scheme, we demonstrate the first entirely single spatial mode implementation of a two-qubit quantum gate and show its operation with an average fidelity of 0.84±0.07.
Classical and quantum non-linear optical applications using the Mach-Zehnder interferometer
Prescod, Andru
Mach Zehnder (MZ) modulators are widely employed in a variety of applications, such as optical communications, optical imaging, metrology and encryption. In this dissertation, we explore two non-linear MZ applications; one classified as classical and one as quantum, in which the Mach Zehnder interferometer is used. In the first application, a classical non-linear application, we introduce and study a new electro-optic highly linear (e.g., >130 dB) modulator configuration. This modulator makes use of a phase modulator (PM) in one arm of the MZ interferometer (MZI) and a ring resonator (RR) located on the other arm. The modulator performance is obtained through the control of a combination of internal and external parameters. These parameters include the RR-coupling ratio (internal parameter); the RF power split ratio and the RF phase bias (external parameters). Results show the unique and superior features, such as high linearity (SFDR˜133 dB), modulation bandwidth extension (as much as 70%) over the previously proposed and demonstrated Resonator-Assisted Mach Zehnder (RAMZ) design. Furthermore the proposed electro-optic modulator of this dissertation also provides an inherent SFDR compensation capability, even in cases where a significant waveguide optical loss exists. This design also shows potential for increased flexibility, practicality and ease of use. In the second application, a quantum non-linear application, we experimentally demonstrate quantum optical coherence tomography (QOCT) using a type II non-linear crystal (periodically-poled potassium titanyl phosphate (KTiOPO4) or PPKTP). There have been several publications discussing the merits and disadvantages of QOCT compared to OCT and other imaging techniques. First, we discuss the issues and solutions for increasing the efficiency of the quantum entangled photons. Second, we use a free space QOCT experiment to generate a high flux of these quantum entangled photons in two orthogonal polarizations, by
Localized solutions of non-linear Klein--Gordon equations
International Nuclear Information System (INIS)
Werle, J.
1977-05-01
Nondissipative, stationary solutions for a class of nonlinear Klein-Gordon equations for a scalar field were found explicitly. Since the field is different from zero only inside a sphere of definite radius, the solutions are called quantum droplets
Linear Optical Response of Silicon Nanotubes Under Axial Magnetic Field
Chegel, Raad; Behzad, Somayeh
2013-01-01
We investigated the optical properties of silicon nanotubes (SiNTs) in the low energy region, E < 0.5 eV, and middle energy region, 1.8 eV < E < 2 eV. The dependence of optical matrix elements and linear susceptibility on radius and magnetic field, in terms of one-dimensional (1-d) wavevector and subband index, is calculated using the tight-binding approximation. It is found that, on increasing the nanotube diameter, the low-energy peaks show red-shift and their intensities are decreased. Also, we found that in the middle energy region all tubes have two distinct peaks, where the energy position of the second peak is approximately constant and independent of the nanotube diameter. Comparing the band structure of these tubes in different magnetic fields, several differences are clearly seen, such as splitting of degenerate bands, creation of additional band-edge states, and bandgap modification. It is found that applying the magnetic field leads to a phase transition in zigzag silicon hexagonal nanotubes (Si h-NTs), unlike in zigzag silicon gear-like nanotubes (Si g-NTs), which remain semiconducting in any magnetic field. We found that the axial magnetic field has two effects on the linear susceptibility spectrum, namely broadening and splitting. The axial magnetic field leads to the creation of a peak with energy less than 0.2 eV in metallic Si h-NTs, whereas in the absence of a magnetic field such a transition is not allowed.
Fundamental solution of the problem of linear programming and method of its determination
Petrunin, S. V.
1978-01-01
The idea of a fundamental solution to a problem in linear programming is introduced. A method of determining the fundamental solution and of applying this method to the solution of a problem in linear programming is proposed. Numerical examples are cited.
Linear position sensitive neutron detector using fiber optic encoded scintillators
International Nuclear Information System (INIS)
Davidson, P.L.; Wroe, H.
1983-01-01
A linear position sensitive slow neutron detector with 3 mm resolution is described. It uses the fiber optic coding principle in which the resolution elements are separate pieces of lithium loaded glass scintillator each coupled by means of flexible polymer optical fibers to a unique combination of 3 photo multipliers (PM's) out of a bank of 12. A decoder circuit repsponds to a triple coincidence between PM outputs and generates a 12 bit work which identifies the scintillator element which stopped the incident neutron. Some details of the construction and decoding electronics are given together with test results obtained using a laboratory isotope neutron source and a monochomated, collimated neutron beam from a reactor. The count rate in the absence of neutron sources is 2 to 3 c min - 1 per element; the element to element variation in response to a uniform flux is a few percent for 95% of the elements; the resolution as measured by a 1 mm wide prode neutron beam is 3 mm; the relative long term stability is about 0.1% over 3 days and the detection efficiency measured by comparison with an end windowed, high pressure gas counter is about 65% at a neutron wavelength of 0.9A 0
Northwestern University trial emerging optical solutions
2001-01-01
Nortel Networks, SBC Ameritech and Northwestern University announced the creation of OMNInet (Optical Metro Network Initiative), a collaborative experimental network. The OMNInet technology trial, a four-site network located in Chicago, will provide a test bed for all-optical switching, advanced high-speed technology such as 10 gigabit Ethernet (10GE) and will test next-generation applications in healthcare, industrial design, finance and commerce.
Whispering Gallery Mode Based Optical Fiber Sensor for Measuring Concentration of Salt Solution
Directory of Open Access Journals (Sweden)
Chia-Chin Chiang
2013-01-01
Full Text Available An optical fiber solution-concentration sensor based on whispering gallery mode (WGM is proposed in this paper. The WGM solution-concentration sensors were used to measure salt solutions, in which the concentrations ranged from 1% to 25% and the wavelength drifted from the left to the right. The experimental results showed an average sensitivity of approximately 0.372 nm/% and an R2 linearity of 0.8835. The proposed WGM sensors are of low cost, feasible for mass production, and durable for solution-concentration sensing.
Superradiance Effects in the Linear and Nonlinear Optical Response of Quantum Dot Molecules
Sitek, A.; Machnikowski, P.
2008-11-01
We calculate the linear optical response from a single quantum dot molecule and the nonlinear, four-wave-mixing response from an inhomogeneously broadened ensemble of such molecules. We show that both optical signals are affected by the coupling-dependent superradiance effect and by optical interference between the two polarizations. As a result, the linear and nonlinear responses are not identical.
A note on the time decay of solutions for the linearized Wigner-Poisson system
Gamba, Irene; Gualdani, Maria; Sparber, Christof
2009-01-01
We consider the one-dimensional Wigner-Poisson system of plasma physics, linearized around a (spatially homogeneous) Lorentzian distribution and prove that the solution of the corresponding linearized problem decays to zero in time. We also give
Numerical solution of two-dimensional non-linear partial differential ...
African Journals Online (AJOL)
linear partial differential equations using a hybrid method. The solution technique involves discritizing the non-linear system of partial differential equations (PDEs) to obtain a corresponding nonlinear system of algebraic difference equations to be ...
Dextran solution optical activity in Tb (III) ion presence
International Nuclear Information System (INIS)
Vasconcellos, Sandra S.; Rodrigues, J.F.; Faljoni-Alario, A.
1984-01-01
Optical activity studies of aqueous solutions of dextrana in presence of Tb (III) or without it shows the complex with the hidroxyl groups of C 2 and C 3 of monomeric unit participation is formed. (L.M.J.) [pt
Analytical solution of dispersion relations for the nuclear optical model
Energy Technology Data Exchange (ETDEWEB)
VanderKam, J.M. [Center for Communications Research, Thanet Road, Princeton, NJ 08540 (United States); Weisel, G.J. [Triangle Universities Nuclear Laboratory, and Duke University, Box 90308, Durham, NC 27708-0308 (United States); Penn State Altoona, 3000 Ivyside Park, Altoona, PA 16601-3760 (United States); Tornow, W. [Triangle Universities Nuclear Laboratory, and Duke University, Box 90308, Durham, NC 27708-0308 (United States)
2000-12-01
Analytical solutions of dispersion integral relations, linking the real and imaginary parts of the nuclear optical model, have been derived. These are displayed for some widely used forms of the volume- and surface-absorptive nuclear potentials. When the analytical solutions are incorporated into the optical-model search code GENOA, replacing a numerical integration, the code runs three and a half to seven times faster, greatly aiding the analysis of direct-reaction, elastic scattering data. (author)
Solution of generalized shifted linear systems with complex symmetric matrices
International Nuclear Information System (INIS)
Sogabe, Tomohiro; Hoshi, Takeo; Zhang, Shao-Liang; Fujiwara, Takeo
2012-01-01
We develop the shifted COCG method [R. Takayama, T. Hoshi, T. Sogabe, S.-L. Zhang, T. Fujiwara, Linear algebraic calculation of Green’s function for large-scale electronic structure theory, Phys. Rev. B 73 (165108) (2006) 1–9] and the shifted WQMR method [T. Sogabe, T. Hoshi, S.-L. Zhang, T. Fujiwara, On a weighted quasi-residual minimization strategy of the QMR method for solving complex symmetric shifted linear systems, Electron. Trans. Numer. Anal. 31 (2008) 126–140] for solving generalized shifted linear systems with complex symmetric matrices that arise from the electronic structure theory. The complex symmetric Lanczos process with a suitable bilinear form plays an important role in the development of the methods. The numerical examples indicate that the methods are highly attractive when the inner linear systems can efficiently be solved.
Unbounded solutions of quasi-linear difference equations
Czech Academy of Sciences Publication Activity Database
Cecchi, M.; Došlá, Zuzana; Marini, M.
2003-01-01
Roč. 45, 10-11 (2003), s. 1113-1123 ISSN 0898-1221 Institutional research plan: CEZ:AV0Z1019905 Keywords : nonlinear difference equation * possitive increasing solution * strongly increasing solution Subject RIV: BA - General Mathematics Impact factor: 0.498, year: 2003
Non linear photons: a non singular cosmological solution
International Nuclear Information System (INIS)
Alves, G.A.
1986-01-01
The validity of equivalence principle as principle of minimum coupling between field interactions, is discussed. The non minimum coupling between vector field and gravitational field, and some consequences of this coupling are analysed. Starting from spherical symmetry metric, the coupled field equations, obtaining exact solutions and interpreting these solutions, are solved. (M.C.K.) [pt
International Nuclear Information System (INIS)
Alvarez-Estrada, R.F.
1979-01-01
A comprehensive review of the inverse scattering solution of certain non-linear evolution equations of physical interest in one space dimension is presented. We explain in some detail the interrelated techniques which allow to linearize exactly the following equations: (1) the Korteweg and de Vries equation; (2) the non-linear Schrodinger equation; (3) the modified Korteweg and de Vries equation; (4) the Sine-Gordon equation. We concentrate in discussing the pairs of linear operators which accomplish such an exact linearization and the solution of the associated initial value problem. The application of the method to other non-linear evolution equations is reviewed very briefly
Some problems on non-linear semigroups and the blow-up of integral solutions
International Nuclear Information System (INIS)
Pavel, N.H.
1983-07-01
After some introductory remarks, this highly mathematical document considers a unifying approach in the theory of non-linear semigroups. Then a brief survey is given on blow-up of mild solutions from the semilinear case. Finally, the global behavior of solutions to non-linear evolution equations is addressed; it is found that classical results on the behavior of the maximal solution u as t up-arrow tsub(max) hold also for integral solutions
Optically stimulated luminescence from quartz measured using the linear modulation technique
DEFF Research Database (Denmark)
Bulur, E.; Bøtter-Jensen, L.; Murray, A.S.
2000-01-01
The optically stimulated luminescence (OSL) from heated natural quartz has been investigated using the linear modulation technique (LMT), in which the excitation light intensity is increased linearly during stimulation. In contrast to conventional stimulation, which usually produces a monotonical...
General guidelines solution for linear programming with fuzzy coefficients
Directory of Open Access Journals (Sweden)
Sergio Gerardo de los Cobos Silva
2013-08-01
Full Text Available This work introduce to the Possibilistic Programming and the Fuzzy Programming as paradigms that allow to resolve problems of linear programming when the coefficients of the model or the restrictions on the same are presented as fuzzy numbers, rather than exact numbers (crisp. This work presents some examples based on [1].
POSITIVE SOLUTIONS TO SEMI-LINEAR SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACE
Institute of Scientific and Technical Information of China (English)
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.
No-signaling quantum key distribution: solution by linear programming
Hwang, Won-Young; Bae, Joonwoo; Killoran, Nathan
2015-02-01
We outline a straightforward approach for obtaining a secret key rate using only no-signaling constraints and linear programming. Assuming an individual attack, we consider all possible joint probabilities. Initially, we study only the case where Eve has binary outcomes, and we impose constraints due to the no-signaling principle and given measurement outcomes. Within the remaining space of joint probabilities, by using linear programming, we get bound on the probability of Eve correctly guessing Bob's bit. We then make use of an inequality that relates this guessing probability to the mutual information between Bob and a more general Eve, who is not binary-restricted. Putting our computed bound together with the Csiszár-Körner formula, we obtain a positive key generation rate. The optimal value of this rate agrees with known results, but was calculated in a more straightforward way, offering the potential of generalization to different scenarios.
Solution of a System of Linear Equations with Fuzzy Numbers
Czech Academy of Sciences Publication Activity Database
Horčík, Rostislav
2008-01-01
Roč. 159, č. 14 (2008), s. 1788-1810 ISSN 0165-0114 R&D Projects: GA AV ČR KJB100300502 Institutional research plan: CEZ:AV0Z10300504 Keywords : fuzzy number * fuzzy interval * interval analysis * fuzzy arithmetic * fuzzy class theory * united solution set Subject RIV: BA - General Mathematics Impact factor: 1.833, year: 2008
Linear and nonlinear optical properties of borate crystals as ...
Indian Academy of Sciences (India)
Unknown
crystal series, with an accuracy acceptable for materials development/design, and answer the questions often ... Optical property; nonlinear optical crystals; first principles calculation. 1. ..... system, and is not in concept suitable to excitation pro-.
Non-linear optical imaging – Introduction and pharmaceutical applications
Fussell, A.L.; Isomaki, Antti; Strachan, Clare J.
2013-01-01
Nonlinear optical imaging is an emerging technology with much potential in pharmaceutical analysis. The technique encompasses a range of optical phenomena, including coherent anti-Stokes Raman scattering (CARS), second harmonic generation (SHG), and twophoton excited fluorescence (TPEF). The
Quantitative analysis of eyes and other optical systems in linear optics.
Harris, William F; Evans, Tanya; van Gool, Radboud D
2017-05-01
To show that 14-dimensional spaces of augmented point P and angle Q characteristics, matrices obtained from the ray transference, are suitable for quantitative analysis although only the latter define an inner-product space and only on it can one define distances and angles. The paper examines the nature of the spaces and their relationships to other spaces including symmetric dioptric power space. The paper makes use of linear optics, a three-dimensional generalization of Gaussian optics. Symmetric 2 × 2 dioptric power matrices F define a three-dimensional inner-product space which provides a sound basis for quantitative analysis (calculation of changes, arithmetic means, etc.) of refractive errors and thin systems. For general systems the optical character is defined by the dimensionally-heterogeneous 4 × 4 symplectic matrix S, the transference, or if explicit allowance is made for heterocentricity, the 5 × 5 augmented symplectic matrix T. Ordinary quantitative analysis cannot be performed on them because matrices of neither of these types constitute vector spaces. Suitable transformations have been proposed but because the transforms are dimensionally heterogeneous the spaces are not naturally inner-product spaces. The paper obtains 14-dimensional spaces of augmented point P and angle Q characteristics. The 14-dimensional space defined by the augmented angle characteristics Q is dimensionally homogenous and an inner-product space. A 10-dimensional subspace of the space of augmented point characteristics P is also an inner-product space. The spaces are suitable for quantitative analysis of the optical character of eyes and many other systems. Distances and angles can be defined in the inner-product spaces. The optical systems may have multiple separated astigmatic and decentred refracting elements. © 2017 The Authors Ophthalmic & Physiological Optics © 2017 The College of Optometrists.
Liao, Ruolin; Wu, Zhichao; Fu, Songnian; Zhu, Shengnan; Yu, Zhe; Tang, Ming; Liu, Deming
2018-02-01
Although the linear optical sampling (LOS) technique is powerful enough to characterize various advanced modulation formats with high symbol rates, the central wavelength of a pulsed local oscillator (LO) needs to be carefully set according to that of the signal under test, due to the coherent mixing operation. Here, we experimentally demonstrate wideband LOS enabled by a fiber optics frequency comb (FOFC). Meanwhile, when the broadband FOFC acts as the pulsed LO, we propose a scheme to mitigate the enhanced sampling error arising in the non-ideal response of a balanced photodetector. Finally, precise characterizations of arbitrary 128 Gbps PDM-QPSK wavelength channels from 1550 to 1570 nm are successfully achieved, when a 101.3 MHz frequency spaced comb with a 3 dB spectral power ripple of 20 nm is used.
Optical fibre sensing: a solution for industry
Sun, T.; Fabian, M.; Chen, Y.; Vidakovic, M.; Javdani, S.; Grattan, K. T. V.; Carlton, J.; Gerada, C.; Brun, L.
2017-04-01
Optical fibres have been explored widely for their sensing capability to meet increasing industrial needs, building on their success in telecommunications. This paper provides a review of research activities at City University of London in response to industrial challenges through the development of a range of fibre Bragg grating (FBG)-based sensors for transportation structural monitoring. For marine propellers, arrays of FBGs mapped onto the surface of propeller blades allow for capturing vibrational modes, with reference to simulation data. The research funded by EU Cleansky programme enables the development of self-sensing electric motor drives to support `More Electric Aircraft' concept. The partnership with Faiveley Brecknell Willis in the UK enables the integration of FBG sensors into the railway current-collecting pantographs for real-time condition monitoring when they are operating under 25kV conditions.
Johnson, Thomas
2018-01-01
In a recent seminal paper \\cite{D--H--R} of Dafermos, Holzegel and Rodnianski the linear stability of the Schwarzschild family of black hole solutions to the Einstein vacuum equations was established by imposing a double null gauge. In this paper we shall prove that the Schwarzschild family is linearly stable as solutions to the Einstein vacuum equations by imposing instead a generalised wave gauge: all sufficiently regular solutions to the system of equations that result from linearising the...
Linear facility location in three dimensions - Models and solution methods
DEFF Research Database (Denmark)
Brimberg, Jack; Juel, Henrik; Schöbel, Anita
2002-01-01
We consider the problem of locating a line or a line segment in three-dimensional space, such that the sum of distances from the facility represented by the line (segment) to a given set of points is minimized. An example is planning the drilling of a mine shaft, with access to ore deposits through...... horizontal tunnels connecting the deposits and the shaft. Various models of the problem are developed and analyzed, and efficient solution methods are given....
Linear electro-optical properties of tetragonal BaTiO 3
Indian Academy of Sciences (India)
Linear optical susceptibility and clamped linear electro-optical tensor coefﬁcients of tetragonal BaTiO3 are calculated using a formalism based on bond charge theory. Calculated values are in close agreement with experimental data. The covalent Ti–O bonds constituting distorted TiO6 octahedral groups are found to be ...
Tisdell, Christopher C.
2017-01-01
For over 50 years, the learning of teaching of "a priori" bounds on solutions to linear differential equations has involved a Euclidean approach to measuring the size of a solution. While the Euclidean approach to "a priori" bounds on solutions is somewhat manageable in the learning and teaching of the proofs involving…
A study on linear and non-linear optical constants of Rhodamine B thin film deposited on FTO glass
Yahia, I. S.; Jilani, Asim; Abutalib, M. M.; AlFaify, S.; Shkir, M.; Abdel-wahab, M. Sh.; Al-Ghamdi, Attieh A.; El-Naggar, A. M.
2016-06-01
The aim of this research was to fabricate/deposit the good quality thin film of Rhodamine B dye on fluorine doped tin oxide glass substrate by the low cost spin coating technique and study their linear and nonlinear optical parameters. The thickness of the thin film was measured about 300 nm with alpha step system. The transmittance of the fabricated thin film was found to be above 75% corresponding to the fluorine doped tin oxide layer. The structural analysis was performed with X-rays diffraction spectroscopy. Atomic force microscope showed the topographic image of deposited thin film. Linear optical constant like absorption coefficient, band gap, and extinction index was calculated. The dielectric constant was calculated to know the optical response of Rhodamine B dye over fluorine doped tin oxide substrate. The nonlinear optical constant like linear optical susceptibility χ(1), nonlinear optical susceptibility χ(3), nonlinear refractive index (n2) were calculated by spectroscopic method. This method has advantage over the experimental method like Z-Scan for organic dye base semiconductors for future advance optoelectronics applications like dye synthesis solar cell.
A study on linear and non-linear optical constants of Rhodamine B thin film deposited on FTO glass
Energy Technology Data Exchange (ETDEWEB)
Yahia, I.S. [Nano-Science & Semiconductor Labs, Physics Department, Faculty of Education, Ain Shams University, Roxy, Cairo (Egypt); Department of Physics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha (Saudi Arabia); Jilani, Asim, E-mail: asim.jilane@gmail.com [Centre of Nanotechnology, Physics Department-Faculty of Science-AL Faisaliah Campus, King Abdulaziz University, P.O. Box 80200, Jeddah 21589 (Saudi Arabia); Abutalib, M.M. [Centre of Nanotechnology, Physics Department-Faculty of Science-AL Faisaliah Campus, King Abdulaziz University, P.O. Box 80200, Jeddah 21589 (Saudi Arabia); AlFaify, S. [Nano-Science & Semiconductor Labs, Physics Department, Faculty of Education, Ain Shams University, Roxy, Cairo (Egypt); Shkir, M. [Department of Physics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha (Saudi Arabia); Abdel-wahab, M.Sh.; Al-Ghamdi, Attieh A. [Centre of Nanotechnology, Physics Department-Faculty of Science-AL Faisaliah Campus, King Abdulaziz University, P.O. Box 80200, Jeddah 21589 (Saudi Arabia); El-Naggar, A.M. [Exploitation of Renewable Energy Applications in Saudi Arabia, Physics & Astronomy Department, College of Science, King Saud University, P.O.Box 2455, Riyadh 11451 (Saudi Arabia)
2016-06-01
The aim of this research was to fabricate/deposit the good quality thin film of Rhodamine B dye on fluorine doped tin oxide glass substrate by the low cost spin coating technique and study their linear and nonlinear optical parameters. The thickness of the thin film was measured about 300 nm with alpha step system. The transmittance of the fabricated thin film was found to be above 75% corresponding to the fluorine doped tin oxide layer. The structural analysis was performed with X-rays diffraction spectroscopy. Atomic force microscope showed the topographic image of deposited thin film. Linear optical constant like absorption coefficient, band gap, and extinction index was calculated. The dielectric constant was calculated to know the optical response of Rhodamine B dye over fluorine doped tin oxide substrate. The nonlinear optical constant like linear optical susceptibility χ{sup (1)}, nonlinear optical susceptibility χ{sup (3)}, nonlinear refractive index (n{sub 2}) were calculated by spectroscopic method. This method has advantage over the experimental method like Z-Scan for organic dye base semiconductors for future advance optoelectronics applications like dye synthesis solar cell.
Large-time asymptotic behaviour of solutions of non-linear Sobolev-type equations
International Nuclear Information System (INIS)
Kaikina, Elena I; Naumkin, Pavel I; Shishmarev, Il'ya A
2009-01-01
The large-time asymptotic behaviour of solutions of the Cauchy problem is investigated for a non-linear Sobolev-type equation with dissipation. For small initial data the approach taken is based on a detailed analysis of the Green's function of the linear problem and the use of the contraction mapping method. The case of large initial data is also closely considered. In the supercritical case the asymptotic formulae are quasi-linear. The asymptotic behaviour of solutions of a non-linear Sobolev-type equation with a critical non-linearity of the non-convective kind differs by a logarithmic correction term from the behaviour of solutions of the corresponding linear equation. For a critical convective non-linearity, as well as for a subcritical non-convective non-linearity it is proved that the leading term of the asymptotic expression for large times is a self-similar solution. For Sobolev equations with convective non-linearity the asymptotic behaviour of solutions in the subcritical case is the product of a rarefaction wave and a shock wave. Bibliography: 84 titles.
Non-linear optical techniques and optical properties of condensed molecular systems
Citroni, Margherita
2013-06-01
Structure, dynamics, and optical properties of molecular systems can be largely modified by the applied pressure, with remarkable consequences on their chemical stability. Several examples of selective reactions yielding technologically attractive products can be cited, which are particularly efficient when photochemical effects are exploited in conjunction with the structural conditions attained at high density. Non-linear optical techniques are a basic tool to unveil key aspects of the chemical reactivity and dynamic properties of molecules. Their application to high-pressure samples is experimentally challenging, mainly because of the small sample dimensions and of the non-linear effects generated in the anvil materials. In this talk I will present results on the electronic spectra of several aromatic crystals obtained through two-photon induced fluorescence and two-photon excitation profiles measured as a function of pressure (typically up to about 25 GPa), and discuss the relationship between the pressure-induced modifications of the electronic structure and the chemical reactivity at high pressure. I will also present the first successful pump-probe infrared measurement performed as a function of pressure on a condensed molecular system. The system under examination is liquid water, in a sapphire anvil cell, up to 1 GPa along isotherms at 298 and 363 K. These measurements give a new enlightening insight into the dynamical properties of low- and high-density water allowing a definition of the two structures.
DEFF Research Database (Denmark)
Ahmadi, Mohamadreza; Mojallali, Hamed; Wisniewski, Rafal
2012-01-01
This paper addresses the robust stability and control problem of uncertain piecewise linear switched systems where, instead of the conventional Carathe ́odory solutions, we allow for Filippov solutions. In other words, in contrast to the previous studies, solutions with infinite switching in fini...... algorithm is proposed to surmount the aforementioned matrix inequality conditions....... time along the facets and on faces of arbitrary dimensions are also taken into account. Firstly, based on earlier results, the stability problem of piecewise linear systems with Filippov solutions is translated into a number of linear matrix inequality feasibility tests. Subsequently, a set of matrix...... inequalities are brought forward, which determines the asymptotic stability of the Filippov solutions of a given uncertain piecewise linear system. Afterwards, bilinear matrix inequality conditions for synthesizing a robust controller with a guaranteed H∞ per- formance are formulated. Finally, a V-K iteration...
Passive linear-optics 640 Gbit/s logic NOT gate
DEFF Research Database (Denmark)
Maram, Reza; Kong, Deming; Galili, Michael
2015-01-01
We experimentally demonstrate a 640 Gbit/s all-optical NOT gate for high-speed telecommunication on-off-keying (OOK) data signals. We employ linear optical signal processing based on spectral phase-only (all-pass) optical filtering to perform the target logic NOT operation....
Sub-wavelength plasmonic readout for direct linear analysis of optically tagged DNA
Varsanik, Jonathan; Teynor, William; LeBlanc, John; Clark, Heather; Krogmeier, Jeffrey; Yang, Tian; Crozier, Kenneth; Bernstein, Jonathan
2010-02-01
This work describes the development and fabrication of a novel nanofluidic flow-through sensing chip that utilizes a plasmonic resonator to excite fluorescent tags with sub-wavelength resolution. We cover the design of the microfluidic chip and simulation of the plasmonic resonator using Finite Difference Time Domain (FDTD) software. The fabrication methods are presented, with testing procedures and preliminary results. This research is aimed at improving the resolution limits of the Direct Linear Analysis (DLA) technique developed by US Genomics [1]. In DLA, intercalating dyes which tag a specific 8 base-pair sequence are inserted in a DNA sample. This sample is pumped though a nano-fluidic channel, where it is stretched into a linear geometry and interrogated with light which excites the fluorescent tags. The resulting sequence of optical pulses produces a characteristic "fingerprint" of the sample which uniquely identifies any sample of DNA. Plasmonic confinement of light to a 100 nm wide metallic nano-stripe enables resolution of a higher tag density compared to free space optics. Prototype devices have been fabricated and are being tested with fluorophore solutions and tagged DNA. Preliminary results show evanescent coupling to the plasmonic resonator is occurring with 0.1 micron resolution, however light scattering limits the S/N of the detector. Two methods to reduce scattered light are presented: index matching and curved waveguides.
A fast method for linear waves based on geometrical optics
Stolk, C.C.
2009-01-01
We develop a fast method for solving the one-dimensional wave equation based on geometrical optics. From geometrical optics (e.g., Fourier integral operator theory or WKB approximation) it is known that high-frequency waves split into forward and backward propagating parts, each propagating with the
Extreme non-linear elasticity and transformation optics
DEFF Research Database (Denmark)
Gersborg, Allan Roulund; Sigmund, Ole
2010-01-01
realizations correspond to minimizers of elastic energy potentials for extreme values of the mechanical Poisson's ratio ν . For TE (Hz) polarized light an incompressible transformation ν = 1/2 is ideal and for TM (E z) polarized light one should use a compressible transformation with negative Poissons's ratio......Transformation optics is a powerful concept for designing novel optical components such as high transmission waveguides and cloaking devices. The selection of specific transformations is a non-unique problem. Here we reveal that transformations which allow for all dielectric and broadband optical...... ν = -1. For the TM polarization the mechanical analogy corresponds to a modified Liao functional known from the transformation optics literature. Finally, the analogy between ideal transformations and solid mechanical material models automates and broadens the concept of transformation optics...
Directory of Open Access Journals (Sweden)
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.
Femtosecond Non-Markovian Optical Dynamics in Solution
Nibbering, Erik T.J.; Wiersma, Douwe A.; Duppen, Koos
1991-01-01
Femtosecond photon-echo experiments on sodium resorufin in dimethylsulfoxide at room temperature show that optical dephasing in solution is of non-Markovian character. A single Gauss-Markov stochastic modulation process is used to interpret both the femtosecond light-scattering results and the
Cappi, R; Martini, M; Métral, Elias; Métral, G; Steerenberg, R; Müller, A S
2003-01-01
The CERN Proton Synchrotron machine is built using combined function magnets. The control of the linear tune as well as the chromaticity in both planes is achieved by means of special coils added to the main magnets, namely two pole-face-windings and one figure-of-eight loop. As a result, the overall magnetic field configuration is rather complex not to mention the saturation effects induced at top-energy. For these reasons a linear model of the PS main magnet does not provide sufficient precision to model particle dynamics. On the other hand, a sophisticated optical model is the key element for the foreseen intensity upgrade and, in particular, for the novel extraction mode based on adiabatic capture of beam particles inside stable islands in transverse phase space. A solution was found by performing accurate measurement of the nonlinear tune as a function of both amplitude and momentum offset so to extract both linear and nonlinear properties of the lattice. In this paper the measurement results are present...
Optical wireless links with enhanced linearity and selectivity [Invited
Green, Roger J.; Sweet, C.; Idrus, S.
2005-10-01
Optical wireless is an attractive medium as an alternative to optical fiber communications, and also to RF, because of its high bandwidth and relative ease of use, especially when it comes to deployment in new physical situations. We describe an optical wireless link approach that offers a performance that gives analog transmission with significantly reduced distortion levels and enhanced reception sensitivity by combining a novel hybrid detector-amplifier technique. Reduction of distortion by 40 dB and improvement in sensitivity of 20-30 dB is possible, using the techniques described.
On the completeness of the set of Bethe-Hulthen solutions of the linear Heisenberg system
International Nuclear Information System (INIS)
Caspers, W J; Labuz, M; Wal, A
2006-01-01
In this work we formulate the standard form of the solutions of the Heisenberg chain with periodic boundary conditions and show that these solutions can be transformed into the well-known Bethe-Hulthen solutions. The standard form is found by solving the secular problem, separated according to the irreducible representations of the translation group. The relevant parameters exp(ik j ) of the Bethe-Hulthen solutions are found from a set of linear equations with coefficients derived from the standard solutions. This correspondence between standard and Bethe-Hulthen solutions realizes the completeness of the Bethe-Hulthen method
DEFF Research Database (Denmark)
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....
TITLE PAGE Linear and nonlinear optical properties of 4 ...
Indian Academy of Sciences (India)
57
optical effects viz. reverse saturable absorption and self-defocusing of laser beam. ... Defect Analysis, Mechanical stability, UV-visible spectroscopy, Refractive index .... for geometry optimization in gas phase and in the solvent phase (ethanol).
Malykin, G. B.; Pozdnyakova, V. I.
2018-03-01
A linear transformation of orthogonal polarization modes in coiled optical spun-fibers with strong unperturbed linear birefringence, which causes the emergence of the dependences of the integrated elliptical birefringence and the ellipticity and azimuth of the major axis of the ellipse, as well as the polarization state of radiation (PSR), on the length of optical fiber has been considered. Optical spun-fibers are subjected to a strong mechanical twisting, which is frozen into the structure of the optical fiber upon cooling, in the process of being drawn out from the workpiece. Since the values of the local polarization parameters of coiled spunwaveguides vary according to a rather complex law, the calculations were carried out by numerical modeling of the parameters of the Jones matrices. Since the rotation speed of the axes of the birefringence is constant on a relatively short segment of a coiled optical spun-fiber in the accompanying torsion (helical) coordinate system, the so-called "Ginzburg helical polarization modes" (GHPMs)—two mutually orthogonal ellipses with the opposite directions of traversal, the axis of which rotate relative to the fixed coordinate system uniformly and unidirectionally—are approximately the local normal polarization modes of such optical fiber. It has been shown that, despite the fact that the unperturbed linear birefringence of the spun-fibers significantly exceeds the linear birefringence, which is caused by the winding on a coil, the integral birefringence of an extended segment of such a fiber coincides in order of magnitude with the linear birefringence, which is caused by the winding on the coil, and the integral polarization modes tend asymptotically to circular ones. It has been also shown that the values of the circular birefringence of twisted single-mode fibers, which were calculated in a nonrotating and torsion helical coordinate systems, differ significantly. It has been shown that the polarization phenomena occur
Directory of Open Access Journals (Sweden)
Hongchun Sun
2012-01-01
Full Text Available For the extended mixed linear complementarity problem (EML CP, we first present the characterization of the solution set for the EMLCP. Based on this, its global error bound is also established under milder conditions. The results obtained in this paper can be taken as an extension for the classical linear complementarity problems.
A note on the time decay of solutions for the linearized Wigner-Poisson system
Gamba, Irene
2009-01-01
We consider the one-dimensional Wigner-Poisson system of plasma physics, linearized around a (spatially homogeneous) Lorentzian distribution and prove that the solution of the corresponding linearized problem decays to zero in time. We also give an explicit algebraic decay rate.
International Nuclear Information System (INIS)
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)
Solution of systems of linear algebraic equations by the method of summation of divergent series
International Nuclear Information System (INIS)
Kirichenko, G.A.; Korovin, Ya.S.; Khisamutdinov, M.V.; Shmojlov, V.I.
2015-01-01
A method for solving systems of linear algebraic equations has been proposed on the basis on the summation of the corresponding continued fractions. The proposed algorithm for solving systems of linear algebraic equations is classified as direct algorithms providing an exact solution in a finite number of operations. Examples of solving systems of linear algebraic equations have been presented and the effectiveness of the algorithm has been estimated [ru
Widely Linear Equalization for IQ Imbalance and Skew Compensation in Optical Coherent Receivers
DEFF Research Database (Denmark)
Porto da Silva, Edson; Zibar, Darko
2016-01-01
In this paper, an alternative approach to design linear equalization algorithms for optical coherent receivers is introduced. Using widely linear complex analysis, a general analytical model it is shown, where In-phase/quadrature (IQ) imbalances and IQ skew at the coherent receiver front-end are ......In this paper, an alternative approach to design linear equalization algorithms for optical coherent receivers is introduced. Using widely linear complex analysis, a general analytical model it is shown, where In-phase/quadrature (IQ) imbalances and IQ skew at the coherent receiver front...
Oscillation and nonoscillation results for solutions of half-linear equations with deviated argument
Czech Academy of Sciences Publication Activity Database
Drábek, P.; Kufner, Alois; Kuliev, K.
2017-01-01
Roč. 447, č. 1 (2017), s. 371-382 ISSN 0022-247X Institutional support: RVO:67985840 Keywords : half-linear equation * oscillatory solution * nonoscillatory solution Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.064, year: 2016 http://www.sciencedirect.com/science/article/pii/S0022247X16306059
Directory of Open Access Journals (Sweden)
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.
Some examples of non-linear systems and characteristics of their solutions
CSIR Research Space (South Africa)
Greben, JM
2006-07-01
Full Text Available . In contrast to certain other applications in complexity theory, these non-linear solutions are characterized by great stability. To go beyond the dominant non-perturbative solution one has to consider the source term as well. The parameter freedom...
Construction of a quantum repeater with linear optics
International Nuclear Information System (INIS)
Kok, Pieter; Williams, Colin P.; Dowling, Jonathan P.
2003-01-01
We study the mechanism and complexity of an efficient quantum repeater, employing double-photon guns, for long-distance optical quantum communication. The guns create polarization-entangled photon pairs on demand. One such source might be a semiconducter quantum dot, which has the distinct advantage over parametric down-conversion that the probability of creating a photon pair is close to 1, while the probability of creating multiple pairs vanishes. The swapping and purifying components are implemented by polarizing beam splitters and probabilistic optical controlled-NOT gates. We also show that the bottleneck in the efficiency of this repeater is due to detector losses
Arshad, Muhammad; Seadawy, Aly R.; Lu, Dianchen
2018-01-01
In mono-mode optical fibers, the higher order non-linear Schrödinger equation (NLSE) describes the propagation of enormously short light pulses. We constructed optical solitons and, solitary wave solutions of higher order NLSE mono-mode optical fibers via employing modified extended mapping method which has important applications in Mathematics and physics. Furthermore, the formation conditions are also given on parameters in which optical bright and dark solitons can exist for this media. The moment of the obtained solutions are also given graphically, that helps to realize the physical phenomena's of this model. The modulation instability analysis is utilized to discuss the model stability, which verifies that all obtained solutions are exact and stable. Many other such types of models arising in applied sciences can also be solved by this reliable, powerful and effective method. The method can also be functional to other sorts of higher order nonlinear problems in contemporary areas of research.
Solutions of the linearized Bach-Einstein equation in the static spherically symmetric case
International Nuclear Information System (INIS)
Schmidt, H.J.
1985-01-01
The Bach-Einstein equation linearized around Minkowski space-time is completely solved. The set of solutions depends on three parameters; a two-parameter subset of it becomes asymptotically flat. In that region the gravitational potential is of the type phi = -m/r + epsilon exp (-r/l). Because of the different asymptotic behaviour of both terms, it became necessary to linearize also around the Schwarzschild solution phi = -m/r. The linearized equation resulting in this case is discussed using qualitative methods. The result is that for m = 2l phi = -m/r + epsilon r -2 exp (-r/l) u, where u is some bounded function; m is arbitrary and epsilon again small. Further, the relation between the solution of the linearized and the full equation is discussed. (author)
On the summability of divergent power series solutions for certain first-order linear PDEs
Directory of Open Access Journals (Sweden)
Masaki Hibino
2015-01-01
Full Text Available This article is concerned with the study of the Borel summability of divergent power series solutions for certain singular first-order linear partial differential equations of nilpotent type. Our main purpose is to obtain conditions which coefficients of equations should satisfy in order to ensure the Borel summability of divergent solutions. We will see that there is a close affinity between the Borel summability of divergent solutions and global analytic continuation properties for coefficients of equations.
Entanglement-based linear-optical qubit amplifier
Czech Academy of Sciences Publication Activity Database
Meyer-Scott, E.; Bula, M.; Bartkiewicz, K.; Černoch, Antonín; Soubusta, Jan; Jennewein, T.; Lemr, Karel
2013-01-01
Roč. 87, č. 1 (2013), "012327-1"-"012327-7" ISSN 1050-2947 R&D Projects: GA ČR GAP205/12/0382 Institutional support: RVO:68378271 Keywords : quantum physics * photonics qubits * qubit amplifier Subject RIV: BH - Optics, Masers, Lasers Impact factor: 2.991, year: 2013
Experimental realization of linear-optical partial SWAP gates
Czech Academy of Sciences Publication Activity Database
Černoch, Antonín; Soubusta, Jan; Bartůšková, L.; Dušek, M.; Fiurášek, J.
2008-01-01
Roč. 100, č. 18 (2008), 180501/1-180501/4 ISSN 0031-9007 R&D Projects: GA MŠk(CZ) 1M06002 Institutional research plan: CEZ:AV0Z10100522 Keywords : two-qubit gates * Mach-Zehnder interferomeret * quantum information processing Subject RIV: BH - Optics, Masers, Lasers Impact factor: 7.180, year: 2008
Resource-efficient linear-optical quantum router
Czech Academy of Sciences Publication Activity Database
Lemr, K.; Bartkiewicz, K.; Černoch, A.; Soubusta, Jan
2013-01-01
Roč. 87, č. 6 (2013), "062333-1"-"062333-7" ISSN 1050-2947 Institutional research plan: CEZ:AV0Z10100522 Keywords : quantum router * signal qubit * quantum communications Subject RIV: BH - Optics, Masers, Lasers Impact factor: 2.991, year: 2013
Enhanced linear photonic nanojet generated by core-shell optical microfibers
Liu, Cheng-Yang; Yen, Tzu-Ping; Chen, Chien-Wen
2017-05-01
The generation of linear photonic nanojet using core-shell optical microfiber is demonstrated numerically and experimentally in the visible light region. The power flow patterns for the core-shell optical microfiber are calculated by using the finite-difference time-domain method. The focusing properties of linear photonic nanojet are evaluated in terms of length and width along propagation and transversal directions. In experiment, the silica optical fiber is etched chemically down to 6 μm diameter and coated with metallic thin film by using glancing angle deposition. We show that the linear photonic nanojet is enhanced clearly by metallic shell due to surface plasmon polaritons. The large-area superresolution imaging can be performed by using a core-shell optical microfiber in the far-field system. The potential applications of this core-shell optical microfiber include micro-fluidics and nano-structure measurements.
Ultrabroadband optical chirp linearization for precision metrology applications.
Roos, Peter A; Reibel, Randy R; Berg, Trenton; Kaylor, Brant; Barber, Zeb W; Babbitt, Wm Randall
2009-12-01
We demonstrate precise linearization of ultrabroadband laser frequency chirps via a fiber-based self-heterodyne technique to enable extremely high-resolution, frequency-modulated cw laser-radar (LADAR) and a wide range of other metrology applications. Our frequency chirps cover bandwidths up to nearly 5 THz with frequency errors as low as 170 kHz, relative to linearity. We show that this performance enables 31-mum transform-limited LADAR range resolution (FWHM) and 86 nm range precisions over a 1.5 m range baseline. Much longer range baselines are possible but are limited by atmospheric turbulence and fiber dispersion.
Non-linear optical studies of adsorbates: Spectroscopy and dynamics
International Nuclear Information System (INIS)
Zhu, Xiangdong.
1989-08-01
In the first part of this thesis, we have established a systematic procedure to apply the surface optical second-harmonic generation (SHG) technique to study surface dynamics of adsorbates. In particular, we have developed a novel technique for studies of molecular surface diffusions. In this technique, the laser-induced desorption with two interfering laser beams is used to produce a monolayer grating of adsorbates. The monolayer grating is detected with diffractions of optical SHG. By monitoring the first-order second-harmonic diffraction, we can follow the time evolution of the grating modulation from which we are able to deduce the diffusion constant of the adsorbates on the surface. We have successfully applied this technique to investigate the surface diffusion of CO on Ni(111). The unique advantages of this novel technique will enable us to readily study anisotropy of a surface diffusion with variable grating orientation, and to investigate diffusion processes of a large dynamic range with variable grating spacings. In the second part of this work, we demonstrate that optical infrared-visible sum-frequency generation (SFG) from surfaces can be used as a viable surface vibrational spectroscopic technique. We have successfully recorded the first vibrational spectrum of a monolayer of adsorbates using optical infrared-visible SFG. The qualitative and quantitative correlation of optical SFG with infrared absorption and Raman scattering spectroscopies are examined and experimentally demonstrated. We have further investigated the possibility to use transient infrared-visible SFG to probe vibrational transients and ultrafast relaxations on surfaces. 146 refs
Non-linear optical studies of adsorbates: Spectroscopy and dynamics
Energy Technology Data Exchange (ETDEWEB)
Zhu, Xiangdong.
1989-08-01
In the first part of this thesis, we have established a systematic procedure to apply the surface optical second-harmonic generation (SHG) technique to study surface dynamics of adsorbates. In particular, we have developed a novel technique for studies of molecular surface diffusions. In this technique, the laser-induced desorption with two interfering laser beams is used to produce a monolayer grating of adsorbates. The monolayer grating is detected with diffractions of optical SHG. By monitoring the first-order second-harmonic diffraction, we can follow the time evolution of the grating modulation from which we are able to deduce the diffusion constant of the adsorbates on the surface. We have successfully applied this technique to investigate the surface diffusion of CO on Ni(111). The unique advantages of this novel technique will enable us to readily study anisotropy of a surface diffusion with variable grating orientation, and to investigate diffusion processes of a large dynamic range with variable grating spacings. In the second part of this work, we demonstrate that optical infrared-visible sum-frequency generation (SFG) from surfaces can be used as a viable surface vibrational spectroscopic technique. We have successfully recorded the first vibrational spectrum of a monolayer of adsorbates using optical infrared-visible SFG. The qualitative and quantitative correlation of optical SFG with infrared absorption and Raman scattering spectroscopies are examined and experimentally demonstrated. We have further investigated the possibility to use transient infrared-visible SFG to probe vibrational transients and ultrafast relaxations on surfaces. 146 refs.
International Nuclear Information System (INIS)
Dubrovsky, V. G.; Topovsky, A. V.
2013-01-01
New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u (n) , n= 1, …, N are constructed via Zakharov and Manakov ∂-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u (n) and calculated by ∂-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schrödinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u (n) . It is shown that the sums u=u (k 1 ) +...+u (k m ) , 1 ⩽k 1 2 m ⩽N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schrödinger equation and can serve as model potentials for electrons in planar structures of modern electronics.
Energy Technology Data Exchange (ETDEWEB)
Dubrovsky, V. G.; Topovsky, A. V. [Novosibirsk State Technical University, Karl Marx prosp. 20, Novosibirsk 630092 (Russian Federation)
2013-03-15
New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u{sup (n)}, n= 1, Horizontal-Ellipsis , N are constructed via Zakharov and Manakov {partial_derivative}-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u{sup (n)} and calculated by {partial_derivative}-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schroedinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u{sup (n)}. It is shown that the sums u=u{sup (k{sub 1})}+...+u{sup (k{sub m})}, 1 Less-Than-Or-Slanted-Equal-To k{sub 1} < k{sub 2} < Horizontal-Ellipsis < k{sub m} Less-Than-Or-Slanted-Equal-To N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schroedinger equation and can serve as model potentials for electrons in planar structures of modern electronics.
International Nuclear Information System (INIS)
Paris, R.B.; Wood, A.D.
1984-11-01
The asymptotic expansions of solutions of a class of linear ordinary differential equations of arbitrary order n, containing a factor zsup(m) multiplying the lower order derivatives, are investigated for large values of z in the complex plane. Four classes of solutions are considered which exhibit the following behaviour as /z/ → infinity in certain sectors: (i) solutions whose behaviour is either exponentially large or algebraic (involving p ( < n) algebraic expansions), (ii) solutions which are exponentially small (iii) solutions with a single algebraic expansion and (iv) solutions which are even and odd functions of z whenever n+m is even. The asymptotic expansions of these solutions in a full neigbourhood of the point at infinity are obtained by means of the theory of the solutions in the case m=O developed in a previous paper
Optical absorption of dilute solutions of metals in molten salts
Energy Technology Data Exchange (ETDEWEB)
Senatore, G.; Parrinello, M.; Tosi, M.P. (Trieste Univ. (Italy). Ist. di Fisica Teorica; Gruppo Nazionale di Struttura dell material del CNR, Trieste (Italy); International Centre for Theoretical Physics, Trieste (Italy))
1978-12-23
The theory of liquid structure for fluids of charged hard spheres is applied to an evaluation of the F-centre model for valence electrons in metal-molten salt solutions at high dilution. Minimization of the free energy yields the groundstate radius of the elctron bubble and hence the optical excitation energy in a Franck-Condon transition, the shift and broadening of the transition due to fluctuations in the bubble radius, the volume of mixing, and the activity of the salt in the solution.
Optical metrology for advanced process control: full module metrology solutions
Bozdog, Cornel; Turovets, Igor
2016-03-01
Optical metrology is the workhorse metrology in manufacturing and key enabler to patterning process control. Recent advances in device architecture are gradually shifting the need for process control from the lithography module to other patterning processes (etch, trim, clean, LER/LWR treatments, etc..). Complex multi-patterning integration solutions, where the final pattern is the result of multiple process steps require a step-by-step holistic process control and a uniformly accurate holistic metrology solution for pattern transfer for the entire module. For effective process control, more process "knobs" are needed, and a tighter integration of metrology with process architecture.
Optical response of the FXG solution to different phantom materials
International Nuclear Information System (INIS)
Cavinato, C.C.; Sakuraba, R.K.; Cruz, J.C.; Campos, L.L.
2011-01-01
The purpose of this work is to evaluate the performance of the Fricke xylenol gel (FXG) solution developed at IPEN, prepared with 270 Bloom gelatine (made in Brazil), for clinical electron beams to the reference depth, using different phantom materials. The colour change, optical absorption spectra, intra and inter-batches reproducibility, dose-response, lower detection limit, energy and dose rate dependent response and response uniformity were studied. The excellent results obtained indicate the viability of employing this solution in 2D spectrophotometric dosimetry (could be extended to 3D MRI dosimetry) to be applied in quality assurance for clinical radiotherapy treatment planning of superficial tumours being treated with clinical electron beams.
Linear and non-linear optical properties of amorphous Se and ...
Indian Academy of Sciences (India)
of signal transmission that requires high speeds and bit rates. [1]. Optical fibres .... mean coordination number (r) of binary glasses is the bond- .... ))(2mr)3/2) and P an integer ... that, Tauc's model that is based on the electronic transitions.
Experimental implementation of optimal linear-optical controlled-unitary gates
Czech Academy of Sciences Publication Activity Database
Lemr, K.; Bartkiewicz, K.; Černoch, Antonín; Dušek, M.; Soubusta, Jan
2015-01-01
Roč. 114, č. 15 (2015), "153602-1"-"153602-5" ISSN 0031-9007 R&D Projects: GA ČR GAP205/12/0382 Institutional support: RVO:68378271 Keywords : two-qubit gates * optimal linear-optical controlled-unitary gates * quantum computing Subject RIV: BH - Optics, Masers, Lasers Impact factor: 7.645, year: 2015
Deterministic linear-optics quantum computing based on a hybrid approach
International Nuclear Information System (INIS)
Lee, Seung-Woo; Jeong, Hyunseok
2014-01-01
We suggest a scheme for all-optical quantum computation using hybrid qubits. It enables one to efficiently perform universal linear-optical gate operations in a simple and near-deterministic way using hybrid entanglement as off-line resources
Deterministic linear-optics quantum computing based on a hybrid approach
Energy Technology Data Exchange (ETDEWEB)
Lee, Seung-Woo; Jeong, Hyunseok [Center for Macroscopic Quantum Control, Department of Physics and Astronomy, Seoul National University, Seoul, 151-742 (Korea, Republic of)
2014-12-04
We suggest a scheme for all-optical quantum computation using hybrid qubits. It enables one to efficiently perform universal linear-optical gate operations in a simple and near-deterministic way using hybrid entanglement as off-line resources.
Duan, Y.; Ju, C.G.; Yang, G.; Fron, E.; Coutino-Gonzalez, E.; Semin, S.V.; Fan, C.C.; Balok, R.S.; Cremers, J.; Tinnemans, P.T.; Feng, Y.Q.; Li, Y.L.; Hofkens, J.; Rowan, A.E.; Rasing, T.H.M.; Xu, J.L.
2016-01-01
The discovery of the phenomenon known as aggregation-induced emission (AIE) has opened the door to a variety of brilliant organic solid-state light-emitting materials. While AIE is well established in linear optics, the development of AIE luminogens (AIEgens) with highly efficient nonlinear optical
Optically-driven red blood cell rotor in linearly polarized laser tweezers
Indian Academy of Sciences (India)
We have constructed a dual trap optical tweezers set-up around an inverted microscope where both the traps can be independently controlled and manipulated in all the three dimensions. Here we report our observations on rotation of red blood cells (RBCs) in a linearly polarized optical trap. Red blood cells deform and ...
Jamison, J. W.
1994-01-01
CFORM was developed by the Kennedy Space Center Robotics Lab to assist in linear control system design and analysis using closed form and transient response mechanisms. The program computes the closed form solution and transient response of a linear (constant coefficient) differential equation. CFORM allows a choice of three input functions: the Unit Step (a unit change in displacement); the Ramp function (step velocity); and the Parabolic function (step acceleration). It is only accurate in cases where the differential equation has distinct roots, and does not handle the case for roots at the origin (s=0). Initial conditions must be zero. Differential equations may be input to CFORM in two forms - polynomial and product of factors. In some linear control analyses, it may be more appropriate to use a related program, Linear Control System Design and Analysis (KSC-11376), which uses root locus and frequency response methods. CFORM was written in VAX FORTRAN for a VAX 11/780 under VAX VMS 4.7. It has a central memory requirement of 30K. CFORM was developed in 1987.
Robust optical wireless links over turbulent media using diversity solutions
Moradi, Hassan
Free-space optic (FSO) technology, i.e., optical wireless communication (OWC), is widely recognized as superior to radio frequency (RF) in many aspects. Visible and invisible optical wireless links solve first/last mile connectivity problems and provide secure, jam-free communication. FSO is license-free and delivers high-speed data rates in the order of Gigabits. Its advantages have fostered significant research efforts aimed at utilizing optical wireless communication, e.g. visible light communication (VLC), for high-speed, secure, indoor communication under the IEEE 802.15.7 standard. However, conventional optical wireless links demand precise optical alignment and suffer from atmospheric turbulence. When compared with RF, they suffer a low degree of reliability and lack robustness. Pointing errors cause optical transceiver misalignment, adversely affecting system reliability. Furthermore, atmospheric turbulence causes irradiance fluctuations and beam broadening of transmitted light. Innovative solutions to overcome limitations on the exploitation of high-speed optical wireless links are greatly needed. Spatial diversity is known to improve RF wireless communication systems. Similar diversity approaches can be adapted for FSO systems to improve its reliability and robustness; however, careful diversity design is needed since FSO apertures typically remain unbalanced as a result of FSO system sensitivity to misalignment. Conventional diversity combining schemes require persistent aperture monitoring and repetitive switching, thus increasing FSO implementation complexities. Furthermore, current RF diversity combining schemes may not be optimized to address the issue of unbalanced FSO receiving apertures. This dissertation investigates two efficient diversity combining schemes for multi-receiving FSO systems: switched diversity combining and generalized selection combining. Both can be exploited to reduce complexity and improve combining efficiency. Unlike maximum
Measurement of picometre non-linearity in an optical grating encoder using x-ray interferometry
Yacoot, Andrew; Cross, Nigel
2003-01-01
X-ray interferometry has been used to characterize the non-linearity in an optical encoder displacement measuring system. Traceable measurements of the non-linearity have been made and an estimation of the uncertainty associated with the measurements is given. Cyclic errors with a magnitude of up to 50 pm and periodicity of the encoder system (128 nm) have been recorded.
Communication: Symmetrical quasi-classical analysis of linear optical spectroscopy
Provazza, Justin; Coker, David F.
2018-05-01
The symmetrical quasi-classical approach for propagation of a many degree of freedom density matrix is explored in the context of computing linear spectra. Calculations on a simple two state model for which exact results are available suggest that the approach gives a qualitative description of peak positions, relative amplitudes, and line broadening. Short time details in the computed dipole autocorrelation function result in exaggerated tails in the spectrum.
An investigation on the solutions for the linear inverse problem in gamma ray tomography
International Nuclear Information System (INIS)
Araujo, Bruna G.M.; Dantas, Carlos C.; Santos, Valdemir A. dos; Finkler, Christine L.L.; Oliveira, Eric F. de; Melo, Silvio B.; Santos, M. Graca dos
2009-01-01
This paper the results obtained in single beam gamma ray tomography are investigated according to direct problem formulation and the applied solution for the linear system of equations. By image reconstruction based algebraic computational algorithms are used. The sparse under and over-determined linear system of equations was analyzed. Build in functions of Matlab software were applied and optimal solutions were investigate. Experimentally a section of the tube is scanned from various positions and at different angles. The solution, to find the vector of coefficients μ, from the vector of measured p values through the W matrix inversion, constitutes an inverse problem. A industrial tomography process requires a numerical solution of the system of equations. The definition of inverse problem according to Hadmard's is considered and as well the requirement of a well posed problem to find stable solutions. The formulation of the basis function and the computational algorithm to structure the weight matrix W were analyzed. For W full rank matrix the obtained solution is unique as expected. Total Least Squares was implemented which theory and computation algorithm gives adequate treatment for the problems due to non-unique solutions of the system of equations. Stability of the solution was investigating by means of a regularization technique and the comparison shows that it improves the results. An optimal solution as a function of the image quality, computation time and minimum residuals were quantified. The corresponding reconstructed images are shown in 3D graphics in order to compare with the solution. (author)
Knotted solutions for linear and nonlinear theories: Electromagnetism and fluid dynamics
Directory of Open Access Journals (Sweden)
Daniel W.F. Alves
2017-10-01
Full Text Available We examine knotted solutions, the most simple of which is the “Hopfion”, from the point of view of relations between electromagnetism and ideal fluid dynamics. A map between fluid dynamics and electromagnetism works for initial conditions or for linear perturbations, allowing us to find new knotted fluid solutions. Knotted solutions are also found to be solutions of nonlinear generalizations of electromagnetism, and of quantum-corrected actions for electromagnetism coupled to other modes. For null configurations, electromagnetism can be described as a null pressureless fluid, for which we can find solutions from the knotted solutions of electromagnetism. We also map them to solutions of Euler's equations, obtained from a type of nonrelativistic reduction of the relativistic fluid equations.
Classical solutions of non-linear sigma-models and their quantum fluctuations
International Nuclear Information System (INIS)
Din, A.M.
1980-05-01
I study the properties of O(N) and CPsup(n-1) non-linear sigma-models in the two dimensional Euclidean space. All classical solutions of the equations of motion can be characterized and in the CPsup(n-1) model they can be expressed in a simple and explicit way in terms of holomorphic vectors. The topological winding number and the action of the general CPsup(n-1) solution can be evaluated and the latter turns out always to be a integer multiple of 2π. I further discuss the stability of the solutions and the problem of one-loop calculations of quantum fluctuations around classical solutions
Energy Technology Data Exchange (ETDEWEB)
Wei, Hai-Rui, E-mail: hrwei@ustb.edu.cn; Liu, Ji-Zhen
2017-02-15
It is very important to seek an efficient and robust quantum algorithm demanding less quantum resources. We propose one-photon three-qubit original and refined Deutsch–Jozsa algorithms with polarization and two linear momentums degrees of freedom (DOFs). Our schemes are constructed by solely using linear optics. Compared to the traditional ones with one DOF, our schemes are more economic and robust because the necessary photons are reduced from three to one. Our linear-optic schemes are working in a determinate way, and they are feasible with current experimental technology.
A solution approach for non-linear analysis of concrete members
International Nuclear Information System (INIS)
Hadi, N. M.; Das, S.
1999-01-01
Non-linear solution of reinforced concrete structural members, at and beyond its maximum strength poses complex numerical problems. This is due to the fact that concrete exhibits strain softening behaviour once it reaches its maximum strength. This paper introduces an improved non-linear solution capable to overcome the numerical problems efficiently. The paper also presents a new concept of modeling discrete cracks in concrete members by using gap elements. Gap elements are placed in between two adjacent concrete elements in tensile zone. The magnitude of elongation of gap elements, which represents the width of the crack in concrete, increases edith the increase of tensile stress in those elements. As a result, transfer of local from one concrete element to adjacent elements reduces. Results of non-linear finite element analysis of three concrete beams using this new solution strategy are compared with those obtained by other researchers, and a good agreement is achieved. (authors). 13 refs. 9 figs.,
Non-linear optics of nano-scale pentacene thin film
Yahia, I. S.; Alfaify, S.; Jilani, Asim; Abdel-wahab, M. Sh.; Al-Ghamdi, Attieh A.; Abutalib, M. M.; Al-Bassam, A.; El-Naggar, A. M.
2016-07-01
We have found the new ways to investigate the linear/non-linear optical properties of nanostructure pentacene thin film deposited by thermal evaporation technique. Pentacene is the key material in organic semiconductor technology. The existence of nano-structured thin film was confirmed by atomic force microscopy and X-ray diffraction. The wavelength-dependent transmittance and reflectance were calculated to observe the optical behavior of the pentacene thin film. It has been observed the anomalous dispersion at wavelength λ 800. The non-linear refractive index of the deposited films was investigated. The linear optical susceptibility of pentacene thin film was calculated, and we observed the non-linear optical susceptibility of pentacene thin film at about 6 × 10-13 esu. The advantage of this work is to use of spectroscopic method to calculate the liner and non-liner optical response of pentacene thin films rather than expensive Z-scan. The calculated optical behavior of the pentacene thin films could be used in the organic thin films base advanced optoelectronic devices such as telecommunications devices.
Linearization of Positional Response Curve of a Fiber-optic Displacement Sensor
Babaev, O. G.; Matyunin, S. A.; Paranin, V. D.
2018-01-01
Currently, the creation of optical measuring instruments and sensors for measuring linear displacement is one of the most relevant problems in the area of instrumentation. Fiber-optic contactless sensors based on the magneto-optical effect are of special interest. They are essentially contactless, non-electrical and have a closed optical channel not subject to contamination. The main problem of this type of sensors is the non-linearity of their positional response curve due to the hyperbolic nature of the magnetic field intensity variation induced by moving the magnetic source mounted on the controlled object relative to the sensing element. This paper discusses an algorithmic method of linearizing the positional response curve of fiber-optic displacement sensors in any selected range of the displacements to be measured. The method is divided into two stages: 1 - definition of the calibration function, 2 - measurement and linearization of the positional response curve (including its temperature stabilization). The algorithm under consideration significantly reduces the number of points of the calibration function, which is essential for the calibration of temperature dependence, due to the use of the points that randomly deviate from the grid points with uniform spacing. Subsequent interpolation of the deviating points and piecewise linear-plane approximation of the calibration function reduces the microcontroller storage capacity for storing the calibration function and the time required to process the measurement results. The paper also presents experimental results of testing real samples of fiber-optic displacement sensors.
International Nuclear Information System (INIS)
Grigoriu, Mircea; Samorodnitsky, Gennady
2004-01-01
Two methods are considered for assessing the asymptotic stability of the trivial solution of linear stochastic differential equations driven by Poisson white noise, interpreted as the formal derivative of a compound Poisson process. The first method attempts to extend a result for diffusion processes satisfying linear stochastic differential equations to the case of linear equations with Poisson white noise. The developments for the method are based on Ito's formula for semimartingales and Lyapunov exponents. The second method is based on a geometric ergodic theorem for Markov chains providing a criterion for the asymptotic stability of the solution of linear stochastic differential equations with Poisson white noise. Two examples are presented to illustrate the use and evaluate the potential of the two methods. The examples demonstrate limitations of the first method and the generality of the second method
Numerical Methods for Solution of the Extended Linear Quadratic Control Problem
DEFF Research Database (Denmark)
Jørgensen, John Bagterp; Frison, Gianluca; Gade-Nielsen, Nicolai Fog
2012-01-01
In this paper we present the extended linear quadratic control problem, its efficient solution, and a discussion of how it arises in the numerical solution of nonlinear model predictive control problems. The extended linear quadratic control problem is the optimal control problem corresponding...... to the Karush-Kuhn-Tucker system that constitute the majority of computational work in constrained nonlinear and linear model predictive control problems solved by efficient MPC-tailored interior-point and active-set algorithms. We state various methods of solving the extended linear quadratic control problem...... and discuss instances in which it arises. The methods discussed in the paper have been implemented in efficient C code for both CPUs and GPUs for a number of test examples....
Solution-mediated cladding doping of commercial polymer optical fibers
Stajanca, Pavol; Topolniak, Ievgeniia; Pötschke, Samuel; Krebber, Katerina
2018-03-01
Solution doping of commercial polymethyl methacrylate (PMMA) polymer optical fibers (POFs) is presented as a novel approach for preparation of custom cladding-doped POFs (CD-POFs). The presented method is based on a solution-mediated diffusion of dopant molecules into the fiber cladding upon soaking of POFs in a methanol-dopant solution. The method was tested on three different commercial POFs using Rhodamine B as a fluorescent dopant. The dynamics of the diffusion process was studied in order to optimize the doping procedure in terms of selection of the most suitable POF, doping time and conditions. Using the optimized procedure, longer segment of fluorescent CD-POF was prepared and its performance was characterized. Fiber's potential for sensing and illumination applications was demonstrated and discussed. The proposed method represents a simple and cheap way for fabrication of custom, short to medium length CD-POFs with various dopants.
Preprocessing in Matlab Inconsistent Linear System for a Meaningful Least Squares Solution
Sen, Symal K.; Shaykhian, Gholam Ali
2011-01-01
Mathematical models of many physical/statistical problems are systems of linear equations Due to measurement and possible human errors/mistakes in modeling/data, as well as due to certain assumptions to reduce complexity, inconsistency (contradiction) is injected into the model, viz. the linear system. While any inconsistent system irrespective of the degree of inconsistency has always a least-squares solution, one needs to check whether an equation is too much inconsistent or, equivalently too much contradictory. Such an equation will affect/distort the least-squares solution to such an extent that renders it unacceptable/unfit to be used in a real-world application. We propose an algorithm which (i) prunes numerically redundant linear equations from the system as these do not add any new information to the model, (ii) detects contradictory linear equations along with their degree of contradiction (inconsistency index), (iii) removes those equations presumed to be too contradictory, and then (iv) obtain the . minimum norm least-squares solution of the acceptably inconsistent reduced linear system. The algorithm presented in Matlab reduces the computational and storage complexities and also improves the accuracy of the solution. It also provides the necessary warning about the existence of too much contradiction in the model. In addition, we suggest a thorough relook into the mathematical modeling to determine the reason why unacceptable contradiction has occurred thus prompting us to make necessary corrections/modifications to the models - both mathematical and, if necessary, physical.
Improved harmonic balance approach to periodic solutions of non-linear jerk equations
International Nuclear Information System (INIS)
Wu, B.S.; Lim, C.W.; Sun, W.P.
2006-01-01
An analytical approximate approach for determining periodic solutions of non-linear jerk equations involving third-order time-derivative is presented. This approach incorporates salient features of both Newton's method and the method of harmonic balance. By appropriately imposing the method of harmonic balance to the linearized equation, the approach requires only one or two iterations to predict very accurate analytical approximate solutions for a large range of initial velocity amplitude. One typical example is used to verify and illustrate the usefulness and effectiveness of the proposed approach
Zeb, Salman; Yousaf, Muhammad
2017-01-01
In this article, we present a QR updating procedure as a solution approach for linear least squares problem with equality constraints. We reduce the constrained problem to unconstrained linear least squares and partition it into a small subproblem. The QR factorization of the subproblem is calculated and then we apply updating techniques to its upper triangular factor R to obtain its solution. We carry out the error analysis of the proposed algorithm to show that it is backward stable. We also illustrate the implementation and accuracy of the proposed algorithm by providing some numerical experiments with particular emphasis on dense problems.
Linear electro-optic effect in cubic silicon carbide
Tang, Xiao; Irvine, Kenneth G.; Zhang, Dongping; Spencer, Michael G.
1991-01-01
The first observation is reported of the electrooptic effect of cubic silicon carbide (beta-SiC) grown by a low-pressure chemical vapor deposition reactor using the hydrogen, silane, and propane gas system. At a wavelength of 633 nm, the value of the electrooptic coefficient r41 in beta-SiC is determined to be 2.7 +/- 0.5 x 10 (exp-12) m/V, which is 1.7 times larger than that in gallium arsenide measured at 10.6 microns. Also, a half-wave voltage of 6.4 kV for beta-SiC is obtained. Because of this favorable value of electrooptic coefficient, it is believed that silicon carbide may be a promising candidate in electrooptic applications for high optical intensity in the visible region.
No-go theorem for passive single-rail linear optical quantum computing.
Wu, Lian-Ao; Walther, Philip; Lidar, Daniel A
2013-01-01
Photonic quantum systems are among the most promising architectures for quantum computers. It is well known that for dual-rail photons effective non-linearities and near-deterministic non-trivial two-qubit gates can be achieved via the measurement process and by introducing ancillary photons. While in principle this opens a legitimate path to scalable linear optical quantum computing, the technical requirements are still very challenging and thus other optical encodings are being actively investigated. One of the alternatives is to use single-rail encoded photons, where entangled states can be deterministically generated. Here we prove that even for such systems universal optical quantum computing using only passive optical elements such as beam splitters and phase shifters is not possible. This no-go theorem proves that photon bunching cannot be passively suppressed even when extra ancilla modes and arbitrary number of photons are used. Our result provides useful guidance for the design of optical quantum computers.
International Nuclear Information System (INIS)
Reibel, R.R.; Barber, Z.W.; Fischer, J.A.; Tian, M.; Babbitt, W.R.
2004-01-01
Linear sideband chirped (LSC) programming is introduced as a means of configuring spatial-spectral holographic gratings for optical coherent transient processors. Similar to linear frequency chirped programming, LSC programming allows the use of broadband integrated electro-optic phase modulators to produce chirps instead of using elaborate broadband chirped lasers. This approach has several advantages including the ability to use a stabilized laser for the optical carrier as well as stable, reproducible chirped optical signals when the modulator is driven digitally. Using LSC programming, we experimentally demonstrate broadband true-time delay as a proof of principle for the optical control of phased array radars. Here both cw phase modulated and binary phase shift keyed probe signals are true-time delayed with bandwidths of 1 GHz and delay resolutions better than 60 ps
OPTICAL I-BAND LINEAR POLARIMETRY OF THE MAGNETAR 4U 0142+61 WITH SUBARU
Energy Technology Data Exchange (ETDEWEB)
Wang, Zhongxiang; Tziamtzis, Anestis [Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030 (China); Tanaka, Yasuyuki T.; Kawabata, Koji S. [Hiroshima Astrophysical Science Center, Hiroshima University, Higashi-Hiroshima, Hiroshima 739-8526 (Japan); Wang, Chen [National Astronomical Observatories, Chinese Academy of Sciences, A20 Datun Road, Beijing 100012 (China); Fukazawa, Yasushi; Itoh, Ryosuke [Department of Physical Sciences, Hiroshima University, Higashi-Hiroshima, Hiroshima 739-8526 (Japan)
2015-12-01
Magnetars are known to have optical and/or infrared (IR) emission, but the origin of the emission is not well understood. In order to fully study their emission properties, we have carried out for the first time optical linear polarimetry of the magnetar 4U 0142+61, which has been determined from different observations to have a complicated broadband spectrum over optical and IR wavelengths. From our I-band imaging polarimetric observation, conducted with the 8.2-m Subaru telescope, we determine the degree of linear polarization to be P = 1.0 ± 3.4%, or P ≤ 5.6% (90% confidence level). Considering models that were suggested for optical emission from magnetars, we discuss the implications of our result. The upper limit measurement indicates that, differing from radio pulsars, magnetars probably would not have strongly polarized optical emission if the emission arises from their magnetosphere as suggested.
A high-accuracy optical linear algebra processor for finite element applications
Casasent, D.; Taylor, B. K.
1984-01-01
Optical linear processors are computationally efficient computers for solving matrix-matrix and matrix-vector oriented problems. Optical system errors limit their dynamic range to 30-40 dB, which limits their accuray to 9-12 bits. Large problems, such as the finite element problem in structural mechanics (with tens or hundreds of thousands of variables) which can exploit the speed of optical processors, require the 32 bit accuracy obtainable from digital machines. To obtain this required 32 bit accuracy with an optical processor, the data can be digitally encoded, thereby reducing the dynamic range requirements of the optical system (i.e., decreasing the effect of optical errors on the data) while providing increased accuracy. This report describes a new digitally encoded optical linear algebra processor architecture for solving finite element and banded matrix-vector problems. A linear static plate bending case study is described which quantities the processor requirements. Multiplication by digital convolution is explained, and the digitally encoded optical processor architecture is advanced.
Tisdell, Christopher C.
2017-11-01
For over 50 years, the learning of teaching of a priori bounds on solutions to linear differential equations has involved a Euclidean approach to measuring the size of a solution. While the Euclidean approach to a priori bounds on solutions is somewhat manageable in the learning and teaching of the proofs involving second-order, linear problems with constant co-efficients, we believe it is not pedagogically optimal. Moreover, the Euclidean method becomes pedagogically unwieldy in the proofs involving higher-order cases. The purpose of this work is to propose a simpler pedagogical approach to establish a priori bounds on solutions by considering a different way of measuring the size of a solution to linear problems, which we refer to as the Uber size. The Uber form enables a simplification of pedagogy from the literature and the ideas are accessible to learners who have an understanding of the Fundamental Theorem of Calculus and the exponential function, both usually seen in a first course in calculus. We believe that this work will be of mathematical and pedagogical interest to those who are learning and teaching in the area of differential equations or in any of the numerous disciplines where linear differential equations are used.
Linear and quadratic exponential modulation of the solutions of the paraxial wave equation
International Nuclear Information System (INIS)
Torre, A
2010-01-01
A review of well-known transformations, which allow us to pass from one solution of the paraxial wave equation (PWE) (in one transverse space variable) to another, is presented. Such transformations are framed within the unifying context of the Lie algebra formalism, being related indeed to symmetries of the PWE. Due to the closure property of the symmetry group of the PWE we are led to consider as not trivial only the linear and the quadratic exponential modulation (accordingly, accompanied by a suitable shift or scaling of the space variables) of the original solutions of the PWE, which are seen to be just conveyed by a linear and a quadratic exponential modulation of the relevant 'source' functions. We will see that recently introduced solutions of the 1D PWE in both rectangular and polar coordinates can be deduced from already known solutions through the resulting symmetry transformation related schemes
International Nuclear Information System (INIS)
Edery, D.
1983-11-01
The reduced system of the non linear resistive MHD equations is used in the 2-D one helicity approximation in the numerical computations of stationary tearing modes. The critical magnetic Raynolds number S (S=tausub(r)/tausub(H) where tausub(R) and tausub(H) are respectively the characteristic resistive and hydro magnetic times) and the corresponding linear solution are computed as a starting approximation for the full non linear equations. These equations are then treated numerically by an iterative procedure which is shown to be rapidly convergent. A numerical application is given in the last part of this paper
Analytical solution for a linearly graded-index-profile planar waveguide.
Touam, T; Yergeau, F
1993-01-20
An analytical solution is presented for the TE modes of a planar waveguide structure comprising a high-index guiding layer and a buried layer with a profile such that the square of the index varies linearly and matches the substrate and high-index guiding layer. The electric-field profiles and the dispersion relation are obtained and discussed, and a solution by the WKB method is compared.
Asymptotic behavior of solutions of linear multi-order fractional differential equation systems
Diethelm, Kai; Siegmund, Stefan; Tuan, H. T.
2017-01-01
In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential equation systems. Next, a representation of solutions of homogeneous linear multi-order fractional differential equation systems in series form is provided. Finally, we give characteristics regarding the asymptotic behavior of solutions to some classes of line...
Fuzzy solution of the linear programming problem with interval coefficients in the constraints
Dorota Kuchta
2005-01-01
A fuzzy concept of solving the linear programming problem with interval coefficients is proposed. For each optimism level of the decision maker (where the optimism concerns the certainty that no errors have been committed in the estimation of the interval coefficients and the belief that optimistic realisations of the interval coefficients will occur) another interval solution of the problem will be generated and the decision maker will be able to choose the final solution having a complete v...
Computer programs for the solution of systems of linear algebraic equations
Sequi, W. T.
1973-01-01
FORTRAN subprograms for the solution of systems of linear algebraic equations are described, listed, and evaluated in this report. Procedures considered are direct solution, iteration, and matrix inversion. Both incore methods and those which utilize auxiliary data storage devices are considered. Some of the subroutines evaluated require the entire coefficient matrix to be in core, whereas others account for banding or sparceness of the system. General recommendations relative to equation solving are made, and on the basis of tests, specific subprograms are recommended.
Characterization of the International Linear Collider damping ring optics
Shanks, J.; Rubin, D. L.; Sagan, D.
2014-10-01
A method is presented for characterizing the emittance dilution and dynamic aperture for an arbitrary closed lattice that includes guide field magnet errors, multipole errors and misalignments. This method, developed and tested at the Cornell Electron Storage Ring Test Accelerator (CesrTA), has been applied to the damping ring lattice for the International Linear Collider (ILC). The effectiveness of beam based emittance tuning is limited by beam position monitor (BPM) measurement errors, number of corrector magnets and their placement, and correction algorithm. The specifications for damping ring magnet alignment, multipole errors, number of BPMs, and precision in BPM measurements are shown to be consistent with the required emittances and dynamic aperture. The methodology is then used to determine the minimum number of position monitors that is required to achieve the emittance targets, and how that minimum depends on the location of the BPMs. Similarly, the maximum tolerable multipole errors are evaluated. Finally, the robustness of each BPM configuration with respect to random failures is explored.
Solutions of First-Order Volterra Type Linear Integrodifferential Equations by Collocation Method
Directory of Open Access Journals (Sweden)
Olumuyiwa A. Agbolade
2017-01-01
Full Text Available The numerical solutions of linear integrodifferential equations of Volterra type have been considered. Power series is used as the basis polynomial to approximate the solution of the problem. Furthermore, standard and Chebyshev-Gauss-Lobatto collocation points were, respectively, chosen to collocate the approximate solution. Numerical experiments are performed on some sample problems already solved by homotopy analysis method and finite difference methods. Comparison of the absolute error is obtained from the present method and those from aforementioned methods. It is also observed that the absolute errors obtained are very low establishing convergence and computational efficiency.
Fall with linear drag and Wien's displacement law: approximate solution and Lambert function
International Nuclear Information System (INIS)
Vial, Alexandre
2012-01-01
We present an approximate solution for the downward time of travel in the case of a mass falling with a linear drag force. We show how a quasi-analytical solution implying the Lambert function can be found. We also show that solving the previous problem is equivalent to the search for Wien's displacement law. These results can be of interest for undergraduate students, as they show that some transcendental equations found in physics may be solved without purely numerical methods. Moreover, as will be seen in the case of Wien's displacement law, solutions based on series expansion can be very accurate even with few terms. (paper)
Minimization of Linear Functionals Defined on| Solutions of Large-Scale Discrete Ill-Posed Problems
DEFF Research Database (Denmark)
Elden, Lars; Hansen, Per Christian; Rojas, Marielba
2003-01-01
The minimization of linear functionals de ned on the solutions of discrete ill-posed problems arises, e.g., in the computation of con dence intervals for these solutions. In 1990, Elden proposed an algorithm for this minimization problem based on a parametric-programming reformulation involving...... the solution of a sequence of trust-region problems, and using matrix factorizations. In this paper, we describe MLFIP, a large-scale version of this algorithm where a limited-memory trust-region solver is used on the subproblems. We illustrate the use of our algorithm in connection with an inverse heat...
International Nuclear Information System (INIS)
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
International Nuclear Information System (INIS)
Li Tatsien
1994-01-01
By means of the concept of the weak linear degeneracy, one gets the global existence and the sharp estimate of the lifespan of C 1 solutions to the Cauchy problem for general first order quasilinear hyperbolic systems with small initial data with compact support. (author). 23 refs, 1 fig
Solutions of half-linear differential equations in the classes Gamma and Pi
Czech Academy of Sciences Publication Activity Database
Řehák, Pavel; Taddei, V.
2016-01-01
Roč. 29, 7-8 (2016), s. 683-714 ISSN 0893-4983 Institutional support: RVO:67985840 Keywords : half-linear differential equation * positive solution * asymptotic formula Subject RIV: BA - General Mathematics Impact factor: 0.565, year: 2016 http://projecteuclid.org/euclid.die/1462298681
Exact solutions of linearized Schwinger endash Dyson equation of fermion self-energy
International Nuclear Information System (INIS)
Zhou, B.
1997-01-01
The Schwinger endash Dyson equation of fermion self-energy in the linearization approximation is solved exactly in a theory with gauge and effective four-fermion interactions. Different expressions for the independent solutions, which, respectively, submit to irregular and regular ultraviolet boundary condition are derived and expounded. copyright 1997 American Institute of Physics
Bounded solutions of self-adjoint second order linear difference equations with periodic coeffients
Directory of Open Access Journals (Sweden)
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.
Direct interaction between linear electron transfer chains and solute transport systems in bacteria
Elferink, Marieke G.L.; Hellingwerf, Klaas J.; Belkum, Marco J. van; Poolman, Bert; Konings, Wil N.
1984-01-01
In studies on alanine and lactose transport in Rhodopseudomonas sphaeroides we have demonstrated that the rate of solute uptake in this phototrophic bacterium is regulated by the rate of light-induced cyclic electron transfer. In the present paper the interaction between linear electron transfer
Gasyna, Zbigniew L.
2008-01-01
Computational experiment is proposed in which a linear algebra method is applied to the solution of the Schrodinger equation for a diatomic oscillator. Calculations of the vibration-rotation spectrum for the HCl molecule are presented and the results show excellent agreement with experimental data. (Contains 1 table and 1 figure.)
On the solution of a class of fuzzy system of linear equations
Indian Academy of Sciences (India)
J. Mathematics and Comput. Sci. 1: 1–5. Salkuyeh D K 2011 On the solution of the fuzzy Sylvester matrix equation. Soft Computing 15: 953–961. Senthilkumar P and Rajendran G 2011 New approach to solve symmetric fully fuzzy linear systems. S¯adhan¯a 36: 933–940. Wang K and Zheng B 2007 Block iterative methods ...
Exact solution to the Coulomb wave using the linearized phase-amplitude method
Directory of Open Access Journals (Sweden)
Shuji Kiyokawa
2015-08-01
Full Text Available The author shows that the amplitude equation from the phase-amplitude method of calculating continuum wave functions can be linearized into a 3rd-order differential equation. Using this linearized equation, in the case of the Coulomb potential, the author also shows that the amplitude function has an analytically exact solution represented by means of an irregular confluent hypergeometric function. Furthermore, it is shown that the exact solution for the Coulomb potential reproduces the wave function for free space expressed by the spherical Bessel function. The amplitude equation for the large component of the Dirac spinor is also shown to be the linearized 3rd-order differential equation.
Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation
International Nuclear Information System (INIS)
Bonnet, M.; Meurant, G.
1978-01-01
Different methods of solution of linear and nonlinear algebraic systems are applied to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems, methods in general use of alternating directions type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method on nonlinear conjugate gradient is studied as also Newton's method and some of its variants. It should be noted, however that Newton's method is found to be more efficient when coupled with a good method for solution of the linear system. To conclude, such methods are used to solve a nonlinear diffusion problem and the numerical results obtained are to be compared [fr
International Nuclear Information System (INIS)
Lye, P G; Boerkamp, M; Ernest, A; Lamb, D W
2005-01-01
Polymethylmethacrylate (PMMA) optical fibres are low-cost polymer fibres that are generally more physically robust than silica fibres, are more flexible, yet like silica fibres have the potential to be used for practical evanescent field absorption sensors in aqueous solutions. However, evanescent field absorption in aqueous solutions is influenced by more than just the specific absorptivity of the solution in question. The physical configuration of the optical fibre itself, as well as surface charge interactions between the fibre and the chromophore in the solution also significantly affects the sensitivity of the fibre to evanescent field absorption. This paper reports on an investigation of numerous physical phenomena that influence evanescent field absorption for PMMA fibres using an aqueous solution of the dye Amidoblack. Parameters investigated included fibre coiling configuration and bend radius, fibre interaction length, and effect of solution pH. Coiled fibres were found to be more sensitive to evanescent field absorption than straight (uncoiled) lengths, and sensitivity was found to increase with a further reduction in bend radius. At high solution pH, the absorption versus solution concentration proved to be linear whereas at low pH the absorption versus concentration relationship exhibited a clear deviation from linearity. The observed nonlinearity at low pH points to the importance of accounting for electrostatic interactions between chromophore and fibre surface when designing a PMMA sensor for evanescent field absorption measurements in aqueous solutions
Linear-Optical Generation of Eigenstates of the Two-Site XY Model
Directory of Open Access Journals (Sweden)
Stefanie Barz
2015-04-01
Full Text Available Much of the anticipation accompanying the development of a quantum computer relates to its application to simulating dynamics of another quantum system of interest. Here, we study the building blocks for simulating quantum spin systems with linear optics. We experimentally generate the eigenstates of the XY Hamiltonian under an external magnetic field. The implemented quantum circuit consists of two cnot gates, which are realized experimentally by harnessing entanglement from a photon source and applying a cphase gate. We tune the ratio of coupling constants and the magnetic field by changing local parameters. This implementation of the XY model using linear quantum optics might open the door to future studies of quenching dynamics using linear optics.
Parallelized preconditioned BiCGStab solution of sparse linear system equations in F-COBRA-TF
International Nuclear Information System (INIS)
Geemert, Rene van; Glück, Markus; Riedmann, Michael; Gabriel, Harry
2011-01-01
Recently, the in-house development of a preconditioned and parallelized BiCGStab solver has been pursued successfully in AREVA’s advanced sub-channel code F-COBRA-TF. This solver can be run either in a sequential computation mode on a single CPU, or in a parallel computation mode on multiple parallel CPUs. The developed procedure enables the computation of several thousands of successive sparse linear system solutions in F-COBRA-TF with acceptable wall clock run times. The current paper provides general information about F-COBRA-TF in terms of modeling capabilities and application areas, and points out where the relevance arises for the efficient iterative solution of sparse linear systems. Furthermore, the preconditioning and parallelization strategies in the developed BiCGStab iterative solution approach are discussed. The paper is concluded with a number of verification examples. (author)
Accuracy requirements of optical linear algebra processors in adaptive optics imaging systems
Downie, John D.
1990-01-01
A ground-based adaptive optics imaging telescope system attempts to improve image quality by detecting and correcting for atmospherically induced wavefront aberrations. The required control computations during each cycle will take a finite amount of time. Longer time delays result in larger values of residual wavefront error variance since the atmosphere continues to change during that time. Thus an optical processor may be well-suited for this task. This paper presents a study of the accuracy requirements in a general optical processor that will make it competitive with, or superior to, a conventional digital computer for the adaptive optics application. An optimization of the adaptive optics correction algorithm with respect to an optical processor's degree of accuracy is also briefly discussed.
Non linear characterisation of optical components of a high power laser chain
International Nuclear Information System (INIS)
Santran, Stephane
2000-01-01
This work concerns the realisation of non linear properties measurement prototypes in glasses in the near infrared and in the visible range. The various devices are time resolved colinear pump probe experiments in which the non linear susceptibility is deduced by the probe beam intensity variations induced by the pump probe coupled in the material. The sensitivity of these experiments allows us to observe unexpected variations, greater than 30%, of several fused silica non linear indexes. As well, this allow us to analyse the origin of the promising oxide glasses non linearity for all optical applications and to understand an d measure non linear processes in the two photons photodiodes. Finally, an original structure for the non linear index measurement in non degenerated configuration by a probe pulse phase measurement approach with a Sagnac interferometer is demonstrated and analysed. (author) [fr
Arbitrarily complete Bell-state measurement using only linear optical elements
Energy Technology Data Exchange (ETDEWEB)
Grice, W. P. [Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Tennessee (United States)
2011-10-15
A complete Bell-state measurement is not possible using only linear-optic elements, and most schemes achieve a success rate of no more than 50%, distinguishing, for example, two of the four Bell states but returning degenerate results for the other two. It is shown here that the introduction of a pair of ancillary entangled photons improves the success rate to 75%. More generally, the addition of 2{sup N}-2 ancillary photons yields a linear-optic Bell-state measurement with a success rate of 1-1/2{sup N}.
Intelligent fiber optic sensor for solution concentration examination
Borecki, Michal; Kruszewski, Jerzy
2003-09-01
This paper presents the working principles of intelligent fiber-optic intensity sensor used for solution concentration examination. The sensor head is the ending of the large core polymer optical fiber. The head works on the reflection intensity basis. The reflected signal level depends on Fresnel reflection and reflection on suspended matter when the head is submersed in solution. The sensor head is mounted on a lift. For detection purposes the signal includes head submerging, submersion, emerging and emergence is measured. This way the viscosity turbidity and refraction coefficient has an effect on measured signal. The signal forthcoming from head is processed electrically in opto-electronic interface. Then it is feed to neural network. The novelty of presented sensor is implementation of neural network that works in generalization mode. The sensor resolution depends on opto-electronic signal conversion precision and neural network learning accuracy. Therefore, the number and quality of points used for learning process is very important. The example sensor application for examination of liquid soap concentration in water is presented in the paper.
Computational Approach for Studying Optical Properties of DNA Systems in Solution
DEFF Research Database (Denmark)
Nørby, Morten Steen; Svendsen, Casper Steinmann; Olsen, Jógvan Magnus Haugaard
2016-01-01
In this paper we present a study of the methodological aspects regarding calculations of optical properties for DNA systems in solution. Our computational approach will be built upon a fully polarizable QM/MM/Continuum model within a damped linear response theory framework. In this approach...... the environment is given a highly advanced description in terms of the electrostatic potential through the polarizable embedding model. Furthermore, bulk solvent effects are included in an efficient manner through a conductor-like screening model. With the aim of reducing the computational cost we develop a set...... of averaged partial charges and distributed isotropic dipole-dipole polarizabilities for DNA suitable for describing the classical region in ground-state and excited-state calculations. Calculations of the UV-spectrum of the 2-aminopurine optical probe embedded in a DNA double helical structure are presented...
Numerical solution of non-linear dual-phase-lag bioheat transfer equation within skin tissues.
Kumar, Dinesh; Kumar, P; Rai, K N
2017-11-01
This paper deals with numerical modeling and simulation of heat transfer in skin tissues using non-linear dual-phase-lag (DPL) bioheat transfer model under periodic heat flux boundary condition. The blood perfusion is assumed temperature-dependent which results in non-linear DPL bioheat transfer model in order to predict more accurate results. A numerical method of line which is based on finite difference and Runge-Kutta (4,5) schemes, is used to solve the present non-linear problem. Under specific case, the exact solution has been obtained and compared with the present numerical scheme, and we found that those are in good agreement. A comparison based on model selection criterion (AIC) has been made among non-linear DPL models when the variation of blood perfusion rate with temperature is of constant, linear and exponential type with the experimental data and it has been found that non-linear DPL model with exponential variation of blood perfusion rate is closest to the experimental data. In addition, it is found that due to absence of phase-lag phenomena in Pennes bioheat transfer model, it achieves steady state more quickly and always predict higher temperature than thermal and DPL non-linear models. The effect of coefficient of blood perfusion rate, dimensionless heating frequency and Kirchoff number on dimensionless temperature distribution has also been analyzed. The whole analysis is presented in dimensionless form. Copyright © 2017 Elsevier Inc. All rights reserved.
Linear and nonlinear optical properties of a hydrogenic donor in lens-shaped quantum dots
International Nuclear Information System (INIS)
Vahdani, M.R.K.; Rezaei, G.
2009-01-01
Optical transitions in a Lens-Shaped Quantum Dot (LSD) are investigated in the presence of a hydrogenic impurity. The electronic wave functions are obtained analytically and the energy eigenvalues are calculated numerically. The density matrix formulation with the intersubband relaxation are used to evaluate the (linear and third order nonlinear) absorption coefficient (AC) and the change in the refractive indices (RI) analytically. The effect of the size of the LSD and optical intensity on the AC and RI are investigated. It is found that AC and RI are strongly affected by the optical intensity and the size of the LSD.
Linear and nonlinear optical properties of a hydrogenic donor in lens-shaped quantum dots
Energy Technology Data Exchange (ETDEWEB)
Vahdani, M.R.K. [Department of Physics, College of Sciences, Shiraz University, Shiraz 71454 (Iran, Islamic Republic of); Rezaei, G., E-mail: grezaei@mail.yu.ac.i [Department of Physics, College of Sciences, Yasouj University, Yasouj 75914 (Iran, Islamic Republic of)
2009-08-17
Optical transitions in a Lens-Shaped Quantum Dot (LSD) are investigated in the presence of a hydrogenic impurity. The electronic wave functions are obtained analytically and the energy eigenvalues are calculated numerically. The density matrix formulation with the intersubband relaxation are used to evaluate the (linear and third order nonlinear) absorption coefficient (AC) and the change in the refractive indices (RI) analytically. The effect of the size of the LSD and optical intensity on the AC and RI are investigated. It is found that AC and RI are strongly affected by the optical intensity and the size of the LSD.
Iqbal, Javed; Yahia, I. S.; Zahran, H. Y.; AlFaify, S.; AlBassam, A. M.; El-Naggar, A. M.
2016-12-01
2‧,7‧ dichloro-Fluorescein (DCF) is a promising organic semiconductor material in different technological aspects such as solar cell, photodiode, Schottky diode. DCF thin film/conductive glass (FTO glass) was prepared by a low-cost spin coating technique. The spectrophotometric data such as the absorbance, reflectance and transmittance were cogitated in the 350-2500 nm wavelength range, at the normal incidence. The absorption (n) and linear refractive indices (k) were computed using the Fresnel's equations. The optical band gap was evaluated and it was found that there is two band gap described as follows: (1) It is related to the band gap of FTO/glass which is equal 3.4 eV and (2) the second one is related to the absorption edge of DCF equals 2.25 eV. The non-linear parameters such as the refractive index (n2) and optical susceptibility χ(3) were evaluated by the spectroscopic method based on the refractive index. Both (n2) and χ(3) increased rapidly on increasing the wavelength with redshift absorption. Our work represents a new idea about using FTO glass for a new generation of the optical device and technology.
Linear Scaling Solution of the Time-Dependent Self-Consistent-Field Equations
Directory of Open Access Journals (Sweden)
Matt Challacombe
2014-03-01
Full Text Available A new approach to solving the Time-Dependent Self-Consistent-Field equations is developed based on the double quotient formulation of Tsiper 2001 (J. Phys. B. Dual channel, quasi-independent non-linear optimization of these quotients is found to yield convergence rates approaching those of the best case (single channel Tamm-Dancoff approximation. This formulation is variational with respect to matrix truncation, admitting linear scaling solution of the matrix-eigenvalue problem, which is demonstrated for bulk excitons in the polyphenylene vinylene oligomer and the (4,3 carbon nanotube segment.
An efficient parallel algorithm for the solution of a tridiagonal linear system of equations
Stone, H. S.
1971-01-01
Tridiagonal linear systems of equations are solved on conventional serial machines in a time proportional to N, where N is the number of equations. The conventional algorithms do not lend themselves directly to parallel computations on computers of the ILLIAC IV class, in the sense that they appear to be inherently serial. An efficient parallel algorithm is presented in which computation time grows as log sub 2 N. The algorithm is based on recursive doubling solutions of linear recurrence relations, and can be used to solve recurrence relations of all orders.
The numerical solution of linear multi-term fractional differential equations: systems of equations
Edwards, John T.; Ford, Neville J.; Simpson, A. Charles
2002-11-01
In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.
Linear and nonlinear optical susceptibilities in a laterally coupled quantum-dot–quantum-ring system
International Nuclear Information System (INIS)
Zeng, Zaiping; Garoufalis, Christos S.; Baskoutas, Sotirios
2014-01-01
Linear and nonlinear optical susceptibilities in a laterally coupled quantum-dot–quantum-ring system have been theoretically studied. In general, we find that the structure parameters of the coupled system significantly affect the optical susceptibilities. The enhancement of the coupling effects between the dot and ring is found to increase considerably the optical susceptibilities and redshift drastically the transition energies. Comparing to the linear susceptibility, the nonlinear optical susceptibility is found to be more sensitive to the variation of the structure parameters. A comprehensive analysis of the electron probability density movement with respect to the modification of the structure parameters is provided, which offers a unique perspective of the ground-state localization. - Highlights: • Optical susceptibilities in a quantum-dot–quantum-ring system are studied. • The structure parameters significantly affect the optical susceptibilities. • The enhancement of the coupling effects increases the optical susceptibilities. • The nonlinear susceptibility is more sensitive to the change in structure parameters. • A comprehensive analysis of the electron probability density movement is provided
Non linear Euler-Poisson system. Part 1: global existence of low entropy solutions
International Nuclear Information System (INIS)
Cordier, S.
1995-05-01
In this work a 1-D model of electrons and ions plasma is considered. Electrons are supposed to be in Maxwell-Boltzmann thermodynamic equilibrium while ions are described with an isothermal flow model of charged particles submitted to a self-consistent electric field. A collision term between neutral particles and ions simulates the presence of neutral particles. This work demonstrates the existence of low entropy solutions for this simple model with arbitrary initial conditions. Most of the paper is devoted to the demonstration of this theorem and follows the successive steps: construction of a numerical scheme, recall of the classical properties of Riemann problem solutions using Glimm method, uniform estimations for the whole variation norm, and finally, convergence of the constructed solutions towards a low entropy solution for the non-linear Euler/Poisson system. Domains of application for this type of model are listed in the conclusion. (J.S.). 18 refs
Unsteady Solution of Non-Linear Differential Equations Using Walsh Function Series
Gnoffo, Peter A.
2015-01-01
Walsh functions form an orthonormal basis set consisting of square waves. The discontinuous nature of square waves make the system well suited for representing functions with discontinuities. The product of any two Walsh functions is another Walsh function - a feature that can radically change an algorithm for solving non-linear partial differential equations (PDEs). The solution algorithm of non-linear differential equations using Walsh function series is unique in that integrals and derivatives may be computed using simple matrix multiplication of series representations of functions. Solutions to PDEs are derived as functions of wave component amplitude. Three sample problems are presented to illustrate the Walsh function series approach to solving unsteady PDEs. These include an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the use of the Walsh function solution algorithms, exploiting Fast Walsh Transforms in multi-dimensions (O(Nlog(N))). Details of a Fast Walsh Reciprocal, defined here for the first time, enable inversion of aWalsh Symmetric Matrix in O(Nlog(N)) operations. Walsh functions have been derived using a fractal recursion algorithm and these fractal patterns are observed in the progression of pairs of wave number amplitudes in the solutions. These patterns are most easily observed in a remapping defined as a fractal fingerprint (FFP). A prolongation of existing solutions to the next highest order exploits these patterns. The algorithms presented here are considered a work in progress that provide new alternatives and new insights into the solution of non-linear PDEs.
Asymptotical Behavior of the Solution of a SDOF Linear Fractionally Damped Vibration System
Directory of Open Access Journals (Sweden)
Z.H. Wang
2011-01-01
Full Text Available Fractional-order derivative has been shown an adequate tool to the study of so-called "anomalous" social and physical behaviors, in reflecting their non-local, frequency- and history-dependent properties, and it has been used to model practical systems in engineering successfully, including the famous Bagley-Torvik equation modeling forced motion of a rigid plate immersed in Newtonian fluid. The solutions of the initial value problems of linear fractional differential equations are usually expressed in terms of Mittag-Leffler functions or some other kind of power series. Such forms of solutions are not good for engineers not only in understanding the solutions but also in investigation. This paper proves that for the linear SDOF oscillator with a damping described by fractional-order derivative whose order is between 1 and 2, the solution of its initial value problem free of external excitation consists of two parts, the first one is the 'eigenfunction expansion' that is similar to the case without fractional-order derivative, and the second one is a definite integral that is independent of the eigenvalues (or characteristic roots. The integral disappears in the classical linear oscillator and it can be neglected from the solution when stationary solution is addressed. Moreover, the response of the fractionally damped oscillator under harmonic excitation is calculated in a similar way, and it is found that the fractional damping with order between 1 and 2 can be used to produce oscillation with large amplitude as well as to suppress oscillation, depending on the ratio of the excitation frequency and the natural frequency.
Non-Linear Optical Studies On Sol-Gel Derived Lead Chloride Crystals Using Z-Scan Technique
Rejeena, I; Lillibai, B; Toms, Roseleena; Nampoori, VP N; Radhakrishnan, P
2014-01-01
In this paper we report the preparation, optical characterization and non linear optical behavior of pure lead chloride crystals. Lead chloride samples subjected to UV and IR irradiation and electric and magnetic fields have also been investigated Optical nonlinearity in these lead chloride samples were determined using single beam and high sensitive Z-scan technique. Non linear optical studies of these materials in single distilled water show reverse saturable absorption which makes th...
International Nuclear Information System (INIS)
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
q-analogue of summability of formal solutions of some linear q-difference-differential equations
Directory of Open Access Journals (Sweden)
Hidetoshi Tahara
2015-01-01
Full Text Available Let \\(q\\gt 1\\. The paper considers a linear \\(q\\-difference-differential equation: it is a \\(q\\-difference equation in the time variable \\(t\\, and a partial differential equation in the space variable \\(z\\. Under suitable conditions and by using \\(q\\-Borel and \\(q\\-Laplace transforms (introduced by J.-P. Ramis and C. Zhang, the authors show that if it has a formal power series solution \\(\\hat{X}(t,z\\ one can construct an actual holomorphic solution which admits \\(\\hat{X}(t,z\\ as a \\(q\\-Gevrey asymptotic expansion of order \\(1\\.
Conditional generation of arbitrary multimode entangled states of light with linear optics
International Nuclear Information System (INIS)
Fiurasek, J.; Massar, S.; Cerf, N. J.
2003-01-01
We propose a universal scheme for the probabilistic generation of an arbitrary multimode entangled state of light with finite expansion in Fock basis. The suggested setup involves passive linear optics, single-photon sources, strong coherent laser beams, and photodetectors with single-photon resolution. The efficiency of this setup may be greatly enhanced if, in addition, a quantum memory is available
Space and frequency-multiplexed optical linear algebra processor - Fabrication and initial tests
Casasent, D.; Jackson, J.
1986-01-01
A new optical linear algebra processor architecture is described. Space and frequency-multiplexing are used to accommodate bipolar and complex-valued data. A fabricated laboratory version of this processor is described, the electronic support system used is discussed, and initial test data obtained on it are presented.
Linear all-optical signal processing using silicon micro-ring resonators
DEFF Research Database (Denmark)
Ding, Yunhong; Ou, Haiyan; Xu, Jing
2016-01-01
Silicon micro-ring resonators (MRRs) are compact and versatile devices whose periodic frequency response can be exploited for a wide range of applications. In this paper, we review our recent work on linear all-optical signal processing applications using silicon MRRs as passive filters. We focus...
Ferwerda, H.A.; Hoenders, B.J.; Slump, C.H.
The fully relativistic quantum mechanical treatment of paraxial electron-optical image formation initiated in the previous paper (this issue) is worked out and leads to a rigorous foundation of the linear transfer theory. Moreover, the status of the relativistic scaling laws for mass and wavelength,
Solutions to the linearized Navier-Stokes equations for channel flow via the WKB approximation
Leonard, Anthony
2017-11-01
Progress on determining semi-analytical solutions to the linearized Navier-Stokes equations for incompressible channel flow, laminar and turbulent, is reported. Use of the WKB approximation yields, e.g., solutions to initial-value problem for the inviscid Orr-Sommerfeld equation in terms of the Bessel functions J+ 1 / 3 ,J- 1 / 3 ,J1 , and Y1 and their modified counterparts for any given wave speed c = ω /kx and k⊥ ,(k⊥2 =kx2 +kz2) . Of particular note to be discussed is a sequence i = 1 , 2 , . . . of homogeneous inviscid solutions with complex k⊥ i for each speed c, (0 < c <=Umax), in the downstream direction. These solutions for the velocity component normal to the wall v are localized in the plane parallel to the wall. In addition, for limited range of negative c, (- c * <= c <= 0) , we have found upstream-traveling homogeneous solutions with real k⊥(c) . In both cases the solutions for v serve as a source for corresponding solutions to the inviscid Squire equation for the vorticity component normal to the wall ωy.
Multiobjective Optimization of Linear Cooperative Spectrum Sensing: Pareto Solutions and Refinement.
Yuan, Wei; You, Xinge; Xu, Jing; Leung, Henry; Zhang, Tianhang; Chen, Chun Lung Philip
2016-01-01
In linear cooperative spectrum sensing, the weights of secondary users and detection threshold should be optimally chosen to minimize missed detection probability and to maximize secondary network throughput. Since these two objectives are not completely compatible, we study this problem from the viewpoint of multiple-objective optimization. We aim to obtain a set of evenly distributed Pareto solutions. To this end, here, we introduce the normal constraint (NC) method to transform the problem into a set of single-objective optimization (SOO) problems. Each SOO problem usually results in a Pareto solution. However, NC does not provide any solution method to these SOO problems, nor any indication on the optimal number of Pareto solutions. Furthermore, NC has no preference over all Pareto solutions, while a designer may be only interested in some of them. In this paper, we employ a stochastic global optimization algorithm to solve the SOO problems, and then propose a simple method to determine the optimal number of Pareto solutions under a computational complexity constraint. In addition, we extend NC to refine the Pareto solutions and select the ones of interest. Finally, we verify the effectiveness and efficiency of the proposed methods through computer simulations.
TOEPLITZ, Solution of Linear Equation System with Toeplitz or Circulant Matrix
International Nuclear Information System (INIS)
Garbow, B.
1984-01-01
Description of program or function: TOEPLITZ is a collection of FORTRAN subroutines for solving linear systems Ax=b, where A is a Toeplitz matrix, a Circulant matrix, or has one or several block structures based on Toeplitz or Circulant matrices. Such systems arise in problems of electrodynamics, acoustics, mathematical statistics, algebra, in the numerical solution of integral equations with a difference kernel, and in the theory of stationary time series and signals
Directory of Open Access Journals (Sweden)
Qiong Liu
2012-01-01
Full Text Available We study the following fourth-order elliptic equations: Δ2+Δ=(,,∈Ω,=Δ=0,∈Ω, where Ω⊂ℝ is a bounded domain with smooth boundary Ω and (, is asymptotically linear with respect to at infinity. Using an equivalent version of Cerami's condition and the symmetric mountain pass lemma, we obtain the existence of multiple solutions for the equations.
On oscillations of solutions to second-order linear delay differential equations
Czech Academy of Sciences Publication Activity Database
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
Frank, T D; Beek, P J
2001-08-01
Recently, Küchler and Mensch [Stochastics Stochastics Rep. 40, 23 (1992)] derived exact stationary probability densities for linear stochastic delay differential equations. This paper presents an alternative derivation of these solutions by means of the Fokker-Planck approach introduced by Guillouzic [Phys. Rev. E 59, 3970 (1999); 61, 4906 (2000)]. Applications of this approach, which is argued to have greater generality, are discussed in the context of stochastic models for population growth and tracking movements.
Bounds and maximum principles for the solution of the linear transport equation
International Nuclear Information System (INIS)
Larsen, E.W.
1981-01-01
Pointwise bounds are derived for the solution of time-independent linear transport problems with surface sources in convex spatial domains. Under specified conditions, upper bounds are derived which, as a function of position, decrease with distance from the boundary. Also, sufficient conditions are obtained for the existence of maximum and minimum principles, and a counterexample is given which shows that such principles do not always exist
On oscillations of solutions to second-order linear delay differential equations
Czech Academy of Sciences Publication Activity Database
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
Remark on zeros of solutions of second-order linear ordinary differential equations
Czech Academy of Sciences Publication Activity Database
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
Exact Solution of Mutator Model with Linear Fitness and Finite Genome Length
Saakian, David B.
2017-08-01
We considered the infinite population version of the mutator phenomenon in evolutionary dynamics, looking at the uni-directional mutations in the mutator-specific genes and linear selection. We solved exactly the model for the finite genome length case, looking at the quasispecies version of the phenomenon. We calculated the mutator probability both in the statics and dynamics. The exact solution is important for us because the mutator probability depends on the genome length in a highly non-trivial way.
A General Construction of Linear Differential Equations with Solutions of Prescribed Properties
Czech Academy of Sciences Publication Activity Database
Neuman, František
2004-01-01
Roč. 17, č. 1 (2004), s. 71-76 ISSN 0893-9659 R&D Projects: GA AV ČR IAA1019902; GA ČR GA201/99/0295 Institutional research plan: CEZ:AV0Z1019905 Keywords : construction of linear differential equations * prescribed qualitative properties of solutions Subject RIV: BA - General Mathematics Impact factor: 0.414, year: 2004
Remark on zeros of solutions of second-order linear ordinary differential equations
Czech Academy of Sciences Publication Activity Database
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
Solution of second order linear fuzzy difference equation by Lagrange's multiplier method
Directory of Open Access Journals (Sweden)
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.
An algorithm for computing the hull of the solution set of interval linear equations
Czech Academy of Sciences Publication Activity Database
Rohn, Jiří
2011-01-01
Roč. 435, č. 2 (2011), s. 193-201 ISSN 0024-3795 R&D Projects: GA ČR GA201/09/1957; GA ČR GC201/08/J020 Institutional research plan: CEZ:AV0Z10300504 Keywords : interval linear equations * solution set * interval hull * algorithm * absolute value inequality Subject RIV: BA - General Mathematics Impact factor: 0.974, year: 2011
A linear ion optics model for extraction from a plasma ion source
International Nuclear Information System (INIS)
Dietrich, J.
1987-01-01
A linear ion optics model for ion extraction from a plasma ion source is presented, based on the paraxial equations which account for lens effects, space charge and finite source ion temperature. This model is applied to three- and four-electrode extraction systems with circular apertures. The results are compared with experimental data and numerical calculations in the literature. It is shown that the improved calculations of space charge effects and lens effects allow better agreement to be obtained than in earlier linear optics models. A principal result is that the model presented here describes the dependence of the optimum perveance on the aspect ratio in a manner similar to the nonlinear optics theory. (orig.)
Economic planning for electric energy systems: a multi objective linearized approach for solution
International Nuclear Information System (INIS)
Mata Medeiros Branco, T. da.
1986-01-01
The economic planning problem associated to the expansion and operation of electrical power systems is considered in this study, represented for a vectorial objective function in which the minimization of resources involved and maximization of attended demand constitute goals to be satisfied. Supposing all the variables involved with linear characteristic and considering the conflict existing among the objectives to be achieved, in order to find a solution, a multi objective linearized approach is proposed. This approximation utilizes the compromise programming technique and linear programming methods. Generation and transmission are simultaneously considered into the optimization process in which associated losses and the capacity of each line are included. Illustrated examples are also presented with results discussed. (author)
Lin, Chao; Shen, Xueju; Wang, Zhisong; Zhao, Cheng
2014-06-20
We demonstrate a novel optical asymmetric cryptosystem based on the principle of elliptical polarized light linear truncation and a numerical reconstruction technique. The device of an array of linear polarizers is introduced to achieve linear truncation on the spatially resolved elliptical polarization distribution during image encryption. This encoding process can be characterized as confusion-based optical cryptography that involves no Fourier lens and diffusion operation. Based on the Jones matrix formalism, the intensity transmittance for this truncation is deduced to perform elliptical polarized light reconstruction based on two intensity measurements. Use of a quick response code makes the proposed cryptosystem practical, with versatile key sensitivity and fault tolerance. Both simulation and preliminary experimental results that support theoretical analysis are presented. An analysis of the resistance of the proposed method on a known public key attack is also provided.
On the economical solution method for a system of linear algebraic equations
Directory of Open Access Journals (Sweden)
Jan Awrejcewicz
2004-01-01
Full Text Available The present work proposes a novel optimal and exact method of solving large systems of linear algebraic equations. In the approach under consideration, the solution of a system of algebraic linear equations is found as a point of intersection of hyperplanes, which needs a minimal amount of computer operating storage. Two examples are given. In the first example, the boundary value problem for a three-dimensional stationary heat transfer equation in a parallelepiped in ℝ3 is considered, where boundary value problems of first, second, or third order, or their combinations, are taken into account. The governing differential equations are reduced to algebraic ones with the help of the finite element and boundary element methods for different meshes applied. The obtained results are compared with known analytical solutions. The second example concerns computation of a nonhomogeneous shallow physically and geometrically nonlinear shell subject to transversal uniformly distributed load. The partial differential equations are reduced to a system of nonlinear algebraic equations with the error of O(hx12+hx22. The linearization process is realized through either Newton method or differentiation with respect to a parameter. In consequence, the relations of the boundary condition variations along the shell side and the conditions for the solution matching are reported.
Impact of quadratic non-linearity on the dynamics of periodic solutions of a wave equation
International Nuclear Information System (INIS)
Kolesov, Andrei Yu; Rozov, Nikolai Kh
2002-01-01
For the non-linear telegraph equation with homogeneous Dirichlet or Neumann conditions at the end-points of a finite interval the question of the existence and the stability of time-periodic solutions bifurcating from the zero equilibrium state is considered. The dynamics of these solutions under a change of the diffusion coefficient (that is, the coefficient of the second derivative with respect to the space variable) is investigated. For the Dirichlet boundary conditions it is shown that this dynamics substantially depends on the presence - or the absence - of quadratic terms in the non-linearity. More precisely, it is shown that a quadratic non-linearity results in the occurrence, under an unbounded decrease of diffusion, of an infinite sequence of bifurcations of each periodic solution. En route, the related issue of the limits of applicability of Yu.S. Kolesov's method of quasinormal forms to the construction of self-oscillations in singularly perturbed hyperbolic boundary value problems is studied
Energy Technology Data Exchange (ETDEWEB)
Lorber, A.A.; Carey, G.F.; Bova, S.W.; Harle, C.H. [Univ. of Texas, Austin, TX (United States)
1996-12-31
The connection between the solution of linear systems of equations by iterative methods and explicit time stepping techniques is used to accelerate to steady state the solution of ODE systems arising from discretized PDEs which may involve either physical or artificial transient terms. Specifically, a class of Runge-Kutta (RK) time integration schemes with extended stability domains has been used to develop recursion formulas which lead to accelerated iterative performance. The coefficients for the RK schemes are chosen based on the theory of Chebyshev iteration polynomials in conjunction with a local linear stability analysis. We refer to these schemes as Chebyshev Parameterized Runge Kutta (CPRK) methods. CPRK methods of one to four stages are derived as functions of the parameters which describe an ellipse {Epsilon} which the stability domain of the methods is known to contain. Of particular interest are two-stage, first-order CPRK and four-stage, first-order methods. It is found that the former method can be identified with any two-stage RK method through the correct choice of parameters. The latter method is found to have a wide range of stability domains, with a maximum extension of 32 along the real axis. Recursion performance results are presented below for a model linear convection-diffusion problem as well as non-linear fluid flow problems discretized by both finite-difference and finite-element methods.
Solution-processed organic tandem solar cells with embedded optical spacers
Hadipour, Afshin; de Boer, Bert; Blom, Paul W. M.
2007-01-01
We demonstrate a solution-processed polymer tandem solar cell in which the two photoactive single cells are separated by an optical spacer. The use of an optical spacer allows for an independent optimization of both the electronic and optical properties of the tandem cell. The optical transmission
Reversible optical sensor for the analysis of actinides in solution
International Nuclear Information System (INIS)
Lesage, B.; Picard, S.; Serein-Spirau, F.; Lereporte, J.P.
2007-01-01
In this work is presented a concept of reversible optical sensor for actinides. It is composed of a p doped conducing polymer support and of an anion complexing the actinides. The chosen conducing polymer is the thiophene-2,5-di-alkoxy-benzene whose solubility and conductivity are perfectly known. The actinides selective ligand is a lacunar poly-oxo-metallate such as P 2 W 17 O 61 10- or SiW 11 O 39 8- which are strong anionic complexing agents of actinides at the oxidation state (IV) even in a very acid medium. The sensor is prepared by spin coating of the composite mixture 'polymer + ligand' on a conducing glass electrode and then tested towards its optical and electrochemical answer in presence of uranium (IV). The absorption change due to the formation of cations complexes by poly-oxo-metallate reveals the presence of uranium (IV). After the measurement, the sensor is regenerated by anodic polarization of the support and oxidation of the uranium (IV) into uranium (VI) which weakly interacts with the poly-oxo-metallate and is then released in solution. (O.M.)
On Attainability of Optimal Solutions for Linear Elliptic Equations with Unbounded Coefficients
Directory of Open Access Journals (Sweden)
P. I. Kogut
2011-12-01
Full Text Available We study an optimal boundary control problem (OCP associated to a linear elliptic equation —div (Vj/ + A(xVy = f describing diffusion in a turbulent flow. The characteristic feature of this equation is the fact that, in applications, the stream matrix A(x = [a,ij(x]i,j=i,...,N is skew-symmetric, ац(х = —a,ji(x, measurable, and belongs to L -space (rather than L°°. An optimal solution to such problem can inherit a singular character of the original stream matrix A. We show that optimal solutions can be attainable by solutions of special optimal boundary control problems.
The structure of solutions of the matrix linear unilateral polynomial equation with two variables
Directory of Open Access Journals (Sweden)
N. S. Dzhaliuk
2017-07-01
Full Text Available We investigate the structure of solutions of the matrix linear polynomial equation $A(\\lambdaX(\\lambda+B(\\lambdaY(\\lambda=C(\\lambda,$ in particular, possible degrees of the solutions. The solving of this equation is reduced to the solving of the equivalent matrix polynomial equation with matrix coefficients in triangular forms with invariant factors on the main diagonals, to which the matrices $A (\\lambda, B(\\lambda$ \\ and \\ $C(\\lambda$ are reduced by means of semiscalar equivalent transformations. On the basis of it, we have pointed out the bounds of the degrees of the matrix polynomial equation solutions. Necessary and sufficient conditions for the uniqueness of a solution with a minimal degree are established. An effective method for constructing minimal degree solutions of the equations is suggested. In this article, unlike well-known results about the estimations of the degrees of the solutions of the matrix polynomial equations in which both matrix coefficients are regular or at least one of them is regular, we have considered the case when the matrix polynomial equation has arbitrary matrix coefficients $A(\\lambda$ and $B(\\lambda.$
Spherically symmetric analysis on open FLRW solution in non-linear massive gravity
Energy Technology Data Exchange (ETDEWEB)
Chiang, Chien-I; Izumi, Keisuke; Chen, Pisin, E-mail: chienichiang@berkeley.edu, E-mail: izumi@phys.ntu.edu.tw, E-mail: chen@slac.stanford.edu [Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 10617, Taiwan (China)
2012-12-01
We study non-linear massive gravity in the spherically symmetric context. Our main motivation is to investigate the effect of helicity-0 mode which remains elusive after analysis of cosmological perturbation around an open Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. The non-linear form of the effective energy-momentum tensor stemming from the mass term is derived for the spherically symmetric case. Only in the special case where the area of the two sphere is not deviated away from the FLRW universe, the effective energy momentum tensor becomes completely the same as that of cosmological constant. This opens a window for discriminating the non-linear massive gravity from general relativity (GR). Indeed, by further solving these spherically symmetric gravitational equations of motion in vacuum to the linear order, we obtain a solution which has an arbitrary time-dependent parameter. In GR, this parameter is a constant and corresponds to the mass of a star. Our result means that Birkhoff's theorem no longer holds in the non-linear massive gravity and suggests that energy can probably be emitted superluminously (with infinite speed) on the self-accelerating background by the helicity-0 mode, which could be a potential plague of this theory.
Non linear optical investigations of silver nanoparticles synthesised by curcumin reduction
Dhanya, N. P.
2017-11-01
Metal nanoparticles have considerable applications in assorted fields like medicine, biology, photonics, metallurgy etc. Optical applications of Silver nanoparticles are of significant interest among researchers nowadays. In this paper, we report a single step chemical reduction of silver nanoparticles with Curcumin both as a reducing and stabilising agent at room temperature. Structural, plasmonic and non linear optical properties of the prepared nanoparticles are explored using Scanning Electron Microscope, Transmission Electron Microscope, UV absorption spectrometry, Spectroflurometry and Z scan. UV-Vis absorption studies affirm the Surface Plasmon Resonance (SPR) absorption and spectroflurometric studies announce the emission spectrum of the prepared silvernanoparticles at 520 nm. SEM and TEM images uphold the existence of uniform sized, spherical silvernanoparticles. Nonlinear optical studies are accomplished with the open aperture z scan technique in the nanosecond regime. The nonlinearity is in virtue of saturable absorption, two-photon absorption and excited state absorption. The marked nonlinearity and optical limiting of the Curcumin reduced silvernanoparticles enhances its photonic applications.
Directory of Open Access Journals (Sweden)
S. Maktoobi
2014-10-01
Full Text Available Switching is a principle process in digital computers and signal processing systems. The growth of optical signal processing systems, draws particular attention to design of ultra-fast optical switches. In this paper, All Optical Switches in linear state Based On photonic crystal Directional coupler is analyzed and simulated. Among different methods, the finite difference time domain method (FDTD is a preferable method and is used. We have studied the application of photonic crystal lattices, the physics of optical switching and photonic crystal Directional coupler. In this paper, Electric field intensity and the power output that are two factors to improve the switching performance and the device efficiency are investigated and simulated. All simulations are performed by COMSOL software.
Krishnan, M.
2017-05-01
We present a model for calculating the net and effective electrical charge of globular macromolecules and linear polyelectrolytes such as proteins and DNA, given the concentration of monovalent salt and pH in solution. The calculation is based on a numerical solution of the non-linear Poisson-Boltzmann equation using a finite element discretized continuum approach. The model simultaneously addresses the phenomena of charge regulation and renormalization, both of which underpin the electrostatics of biomolecules in solution. We show that while charge regulation addresses the true electrical charge of a molecule arising from the acid-base equilibria of its ionizable groups, charge renormalization finds relevance in the context of a molecule's interaction with another charged entity. Writing this electrostatic interaction free energy in terms of a local electrical potential, we obtain an "interaction charge" for the molecule which we demonstrate agrees closely with the "effective charge" discussed in charge renormalization and counterion-condensation theories. The predictions of this model agree well with direct high-precision measurements of effective electrical charge of polyelectrolytes such as nucleic acids and disordered proteins in solution, without tunable parameters. Including the effective interior dielectric constant for compactly folded molecules as a tunable parameter, the model captures measurements of effective charge as well as published trends of pKa shifts in globular proteins. Our results suggest a straightforward general framework to model electrostatics in biomolecules in solution. In offering a platform that directly links theory and experiment, these calculations could foster a systematic understanding of the interrelationship between molecular 3D structure and conformation, electrical charge and electrostatic interactions in solution. The model could find particular relevance in situations where molecular crystal structures are not available or
International Nuclear Information System (INIS)
Qin, Hong; Davidson, Ronald C.
2011-01-01
In a linear trap confining a one-component nonneutral plasma, the external focusing force is a linear function of the configuration coordinates and/or the velocity coordinates. Linear traps include the classical Paul trap and the Penning trap, as well as the newly proposed rotating-radio- frequency traps and the Mobius accelerator. This paper describes a class of self-similar nonlinear solutions of nonneutral plasma in general time-dependent linear focusing devices, with self-consistent electrostatic field. This class of nonlinear solutions includes many known solutions as special cases.
Ultrafast all-optical clock recovery based on phase-only linear optical filtering
DEFF Research Database (Denmark)
Maram, Reza; Kong, Deming; Galili, Michael
2014-01-01
We report on a novel technique for all-optical clock recovery from RZ OOK data based on phase-only filtering, significantly enhancing the recovered clock quality and energy-efficiency compared to the use of a Fabry-Perot filter....
International Nuclear Information System (INIS)
Zhu Chang-Hua; Cao Xin; Quan Dong-Xiao; Pei Chang-Xing
2014-01-01
Linear optical quantum Fredkin gate can be applied to quantum computing and quantum multi-user communication networks. In the existing linear optical scheme, two single photon detectors (SPDs) are used to herald the success of the quantum Fredkin gate while they have no photon count. But analysis results show that for non-perfect SPD, the lower the detector efficiency, the higher the heralded success rate by this scheme is. We propose an improved linear optical quantum Fredkin gate by designing a new heralding scheme with an auxiliary qubit and only one SPD, in which the higher the detection efficiency of the heralding detector, the higher the success rate of the gate is. The new heralding scheme can also work efficiently under a non-ideal single photon source. Based on this quantum Fredkin gate, large-scale quantum switching networks can be built. As an example, a quantum Beneš network is shown in which only one SPD is used. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
International Nuclear Information System (INIS)
Eckstein, U.; Harte, R.; Kraetzig, W.B.; Wittek, U.
1983-01-01
In order to describe nonlinear response and instability behaviour the paper starts with the total potential energy considering the basic kinematic equations of a consistent nonlinear shell theory for large displacements and moderate rotations. The material behaviour is assumed to be hyperelastic and isotropic. The incrementation and discretization of the total potential energy leads to the tangent stiffness relation, which is the central equation of computational algorithms based on combined incremental and iterative techniques. Here a symmetrized form of the RIKS/WEMPNER-algorithm for positive and negative load incrementation represents the basis of the nonlinear solution technique. To detect secondary equilibrium branches at points of neutral equilibrium within nonlinear primary paths a quadratic eigenvalue-problem has to be solved. In order to follow those complicated nonlinear response phenomena the RIKS/WEMPNER incrementation/iteration process is combined with a simultaneous solution of the linearized quadratic eigenvalue-problem. Additionally the essentials of a recently derived family of arbitrarily curved shell elements for linear (LACS) and geometrically nonlinear (NACS) shell problems are presented. The main advantage of these elements is the exact description of all geometric properties as well as the energy-equivalent representation of the applied loads in combination with an efficient algorithm to form the stiffness submatrices. Especially the NACS-elements are designed to improve the accuracy of the solution in the deep postbuckling range including moderate rotations. The derived finite elements and solution strategies are applied to a certain number of typical shell problems to prove the precision of the shell elements and to demonstrate the possibilities of tracing linear and nonlinear bifurcation problems as well as snap-through phenomena with and without secondary bifurcation branches. (orig.)
Improvement of PEP-II Linear Optics with a MIA-Derived Virtual Accelerator
International Nuclear Information System (INIS)
Cerio, B.; Colgate U.
2006-01-01
In several past studies, model independent analysis, in conjunction with a virtual accelerator model, has been successful in improving PEP-II linear geometric optics. In many cases, optics improvement yielded an increase in machine luminosity. In this study, an updated characterization of linear optics is presented. With the PEP-II beam position monitor (BPM) system, four independent beam centroid orbits were extracted and used to determine phase advances and linear Green's functions among BPM locations. A magnetic lattice model was then constructed with a singular value decomposition-enhanced least-square fitting of phase advances and Green's functions, which are functions of quadrupole strengths, sextupole feed-downs, as well as BPM errors, to the corresponding measured quantities. The fitting process yielded a machine model that matched the measured linear optics of the real machine and was therefore deemed the virtual accelerator. High beta beat, as well as linear coupling, was observed in both LER and HER of the virtual accelerator. Since there was higher beta beating in LER, focus was shifted to the improvement of this ring. By adjusting select quadrupoles of the virtual LER and fitting the resulting beta functions and phase advances to those of the desired lattice, the average beta beat of the virtual machine was effectively reduced. The new magnet configuration was dialed into LER on August 10, 2006, and beta beat was reduced by a factor of three. After fine tuning HER to match the improved LER for optimal collision, a record peak luminosity of 12.069 x 10 33 cm -2 s -1 was attained on August 16, 2006
One step linear reconstruction method for continuous wave diffuse optical tomography
Ukhrowiyah, N.; Yasin, M.
2017-09-01
The method one step linear reconstruction method for continuous wave diffuse optical tomography is proposed and demonstrated for polyvinyl chloride based material and breast phantom. Approximation which used in this method is selecting regulation coefficient and evaluating the difference between two states that corresponding to the data acquired without and with a change in optical properties. This method is used to recovery of optical parameters from measured boundary data of light propagation in the object. The research is demonstrated by simulation and experimental data. Numerical object is used to produce simulation data. Chloride based material and breast phantom sample is used to produce experimental data. Comparisons of results between experiment and simulation data are conducted to validate the proposed method. The results of the reconstruction image which is produced by the one step linear reconstruction method show that the image reconstruction almost same as the original object. This approach provides a means of imaging that is sensitive to changes in optical properties, which may be particularly useful for functional imaging used continuous wave diffuse optical tomography of early diagnosis of breast cancer.
International Nuclear Information System (INIS)
Lee, Hwang; Kok, Pieter; Dowling, Jonathan P.; Cerf, Nicolas J.
2002-01-01
We propose a method for preparing maximal path entanglement with a definite photon-number N, larger than two, using projective measurements. In contrast with the previously known schemes, our method uses only linear optics. Specifically, we exhibit a way of generating four-photon, path-entangled states of the form vertical bar 4,0>+ vertical bar 0,4>, using only four beam splitters and two detectors. These states are of major interest as a resource for quantum interferometric sensors as well as for optical quantum lithography and quantum holography
Structural, Linear, and Nonlinear Optical and Mechanical Properties of New Organic L-Serine Crystal
Directory of Open Access Journals (Sweden)
K. Rajesh
2014-01-01
Full Text Available Nonlinear optical single crystal of organic amino acid L-Serine (LS was grown by slow evaporation technique. Solubility study of the compound was measured and metastable zone width was found. Single crystal X-ray diffraction study was carried out for the grown crystal. The linear and nonlinear optical properties of the crystal were confirmed by UV-Vis analysis and powder SHG tester. FT-IR spectrum was recorded and functional groups were analyzed. Vickers’ microhardness studies showed the mechanical strength of the grown crystal. Laser damage threshold value of the crystal was calculated. Photoconductivity studies reveal the conductivity of the crystal.
A review of methods for experimentally determining linear optics in storage rings
International Nuclear Information System (INIS)
Safranek, J.
1995-01-01
In order to maximize the brightness and provide sufficient dynamic aperture in synchrotron radiation storage rings, one must understand and control the linear optics. Control of the horizontal beta function and dispersion is important for minimizing the horizontal beam size. Control of the skew gradient distribution is important for minimizing the vertical size. In this paper, various methods for experimentally determining the optics in a storage ring will be reviewed. Recent work at the National Synchrotron Light Source X-Ray Ring will be presented as well as work done at laboratories worldwide
Exact solutions for the higher-order nonlinear Schoerdinger equation in nonlinear optical fibres
International Nuclear Information System (INIS)
Liu Chunping
2005-01-01
First, by using the generally projective Riccati equation method, many kinds of exact solutions for the higher-order nonlinear Schoerdinger equation in nonlinear optical fibres are obtained in a unified way. Then, some relations among these solutions are revealed
Li, Yanning
2013-10-01
This article presents a new robust control framework for transportation problems in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi equation, we pose the problem of controlling the state of the system on a network link, using boundary flow control, as a Linear Program. Unlike many previously investigated transportation control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e. discontinuities in the state of the system). We also demonstrate that the same framework can handle robust control problems, in which the uncontrollable components of the initial and boundary conditions are encoded in intervals on the right hand side of inequalities in the linear program. The lower bound of the interval which defines the smallest feasible solution set is used to solve the robust LP (or MILP if the objective function depends on boolean variables). Since this framework leverages the intrinsic properties of the Hamilton-Jacobi equation used to model the state of the system, it is extremely fast. Several examples are given to demonstrate the performance of the robust control solution and the trade-off between the robustness and the optimality. © 2013 IEEE.
International Nuclear Information System (INIS)
Shimizu, Yoshiaki
1988-01-01
Due to the simplicity and effectiveness, linear program has been popular in the actual optimization in various fields. In the previous study, the uncertainty involved in the model at the different stage of optimization was dealt with by post-optimizing analysis. But it often becomes insufficient to make a decision how to deal with an uncertain system especially suffering large parameter deviation. Recently in the field of processing systems, it is desired to obtain a flexible solution which can present the counterplan to a deviating system from a practical viewpoint. The scope of this preliminary note presents how to apply a methodology development to obtain the flexible solution of a linear program. For this purpose, a simple example associated with nuclear reactor decommissioning is shown. The problem to maximize a system performance given as an objective function under the constraint of the static behavior of the system is considered, and the flexible solution is determined. In Japan, the decommissioning of commercial nuclear power plants will being in near future, and the study using the retired research reactor JPDR is in progress. The planning of decontamination and the reuse of wastes is taken as the example. (Kako, I.)
Li, Yanning; Canepa, Edward S.; Claudel, Christian G.
2013-01-01
This article presents a new robust control framework for transportation problems in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi equation, we pose the problem of controlling the state of the system on a network link, using boundary flow control, as a Linear Program. Unlike many previously investigated transportation control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e. discontinuities in the state of the system). We also demonstrate that the same framework can handle robust control problems, in which the uncontrollable components of the initial and boundary conditions are encoded in intervals on the right hand side of inequalities in the linear program. The lower bound of the interval which defines the smallest feasible solution set is used to solve the robust LP (or MILP if the objective function depends on boolean variables). Since this framework leverages the intrinsic properties of the Hamilton-Jacobi equation used to model the state of the system, it is extremely fast. Several examples are given to demonstrate the performance of the robust control solution and the trade-off between the robustness and the optimality. © 2013 IEEE.
Implementation of a controller for linear positioners applicable in optical fiber stretching
International Nuclear Information System (INIS)
Castrillo Piedra, Andres Rodolfo
2014-01-01
A low cost controller is implemented for linear positioners applicable in optic fiber stretching. The possibility of using a donated equipment is evaluated by the Escuela de Ingenieria Mecanica. The equipment is required by the non-linear photonic research laboratory (NLPR-LAB) for stretching of micro structured fiber. The process has required a slow and precise stretching, so the controllers must be precisely programmed to rotate the motors at different speeds. Donated equipment is evaluated to see if it is possible to use for fiber stretching [es
Testing the existence of optical linear polarization in young brown dwarfs
Manjavacas, E.; Miles-Páez, P. A.; Zapatero-Osorio, M. R.; Goldman, B.; Buenzli, E.; Henning, T.; Pallé, E.; Fang, M.
2017-07-01
Linear polarization can be used as a probe of the existence of atmospheric condensates in ultracool dwarfs. Models predict that the observed linear polarization increases with the degree of oblateness, which is inversely proportional to the surface gravity. We aimed to test the existence of optical linear polarization in a sample of bright young brown dwarfs, with spectral types between M6 and L2, observable from the Calar Alto Observatory, and cataloged previously as low gravity objects using spectroscopy. Linear polarimetric images were collected in I and R band using CAFOS at the 2.2-m telescope in Calar Alto Observatory (Spain). The flux ratio method was employed to determine the linear polarization degrees. With a confidence of 3σ, our data indicate that all targets have a linear polarimetry degree in average below 0.69 per cent in the I band, and below 1.0 per cent in the R band, at the time they were observed. We detected significant (I.e. P/σ ≥ 3) linear polarization for the young M6 dwarf 2MASS J04221413+1530525 in the R band, with a degree of p* = 0.81 ± 0.17 per cent.
A Fast Condensing Method for Solution of Linear-Quadratic Control Problems
DEFF Research Database (Denmark)
Frison, Gianluca; Jørgensen, John Bagterp
2013-01-01
consider a condensing (or state elimination) method to solve an extended version of the LQ control problem, and we show how to exploit the structure of this problem to both factorize the dense Hessian matrix and solve the system. Furthermore, we present two efficient implementations. The first......In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is usually the main computational effort. In this paper we...... implementation is formally identical to the Riccati recursion based solver and has a computational complexity that is linear in the control horizon length and cubic in the number of states. The second implementation has a computational complexity that is quadratic in the control horizon length as well...
Pei, Soo-Chang; Ding, Jian-Jiun
2005-03-01
Prolate spheroidal wave functions (PSWFs) are known to be useful for analyzing the properties of the finite-extension Fourier transform (fi-FT). We extend the theory of PSWFs for the finite-extension fractional Fourier transform, the finite-extension linear canonical transform, and the finite-extension offset linear canonical transform. These finite transforms are more flexible than the fi-FT and can model much more generalized optical systems. We also illustrate how to use the generalized prolate spheroidal functions we derive to analyze the energy-preservation ratio, the self-imaging phenomenon, and the resonance phenomenon of the finite-sized one-stage or multiple-stage optical systems.
Causal structure and algebraic classification of non-dissipative linear optical media
International Nuclear Information System (INIS)
Schuller, Frederic P.; Witte, Christof; Wohlfarth, Mattias N.R.
2010-01-01
In crystal optics and quantum electrodynamics in gravitational vacua, the propagation of light is not described by a metric, but an area metric geometry. In this article, this prompts us to study conditions for linear electrodynamics on area metric manifolds to be well-posed. This includes an identification of the timelike future cones and their duals associated to an area metric geometry, and thus paves the ground for a discussion of the related local and global causal structures in standard fashion. In order to provide simple algebraic criteria for an area metric manifold to present a consistent spacetime structure, we develop a complete algebraic classification of area metric tensors up to general transformations of frame. This classification, valuable in its own right, is then employed to prove a theorem excluding the majority of algebraic classes of area metrics as viable spacetimes. Physically, these results classify and drastically restrict the viable constitutive tensors of non-dissipative linear optical media.
International Nuclear Information System (INIS)
VanMeter, N. M.; Lougovski, P.; Dowling, Jonathan P.; Uskov, D. B.; Kieling, K.; Eisert, J.
2007-01-01
We introduce schemes for linear-optical quantum state generation. A quantum state generator is a device that prepares a desired quantum state using product inputs from photon sources, linear-optical networks, and postselection using photon counters. We show that this device can be concisely described in terms of polynomial equations and unitary constraints. We illustrate the power of this language by applying the Groebner-basis technique along with the notion of vacuum extensions to solve the problem of how to construct a quantum state generator analytically for any desired state, and use methods of convex optimization to identify bounds to success probabilities. In particular, we disprove a conjecture concerning the preparation of the maximally path-entangled |n,0>+|0,n> (NOON) state by providing a counterexample using these methods, and we derive a new upper bound on the resources required for NOON-state generation
Tyagi, Chetna; Yadav, Preeti; Sharma, Ambika
2018-05-01
The present work reveals the optical study of Se82Te15Bi1.0Sn2.0/polyvinylpyrrolidone (PVP) nanocomposites. Bulk glasses of chalcogenide was prepared by well-known melt quenching technique. Wet chemical technique is proposed for making the composite of Se82Te15Bi1.0Sn2.0 and PVP polymer as it is easy to handle and cost effective. The composites films were made on glass slide from the solution of Se-Te-Bi-Sn and PVP polymer using spin coating technique. The transmission as well as absorbance is recorded by using UV-Vis-NIR spectrophotometer in the spectral range 350-700 nm. The linear refractive index (n) of polymer nanocomposites are calculated by Swanepoel approach. The linear refractive index (n) PVP doped Se82Te15Bi1.0Sn2.0 chalcogenide is found to be 1.7. The optical band gap has been evaluated by means of Tauc extrapolation method. Tichy and Ticha model was utilized for the characterization of nonlinear refractive index (n2).
Hijas, K. M.; Madan Kumar, S.; Byrappa, K.; Geethakrishnan, T.; Jeyaram, S.; Nagalakshmi, R.
2018-03-01
Single crystals of 2-methoxy-4(phenyliminomethyl)phenol were grown from ethanol by slow evaporation solution growth technique. Single crystal X-ray diffraction experiment reveals the crystallization in orthorhombic system having non-centrosymmetric space group C2221. Geometrical optimization by density functional theory method was carried out using Gaussian program and compared with experimental results. Detailed experimental and theoretical vibrational analyses were carried out and the results were correlated to find close agreement. Thermal analyses show the material is thermally stable with a melting point of 159 °C. Natural bond orbital analysis was carried out to explain charge transfer interactions through hydrogen bonding. Relatively smaller HOMO-LUMO band gap favors the non linear optical activity of the molecule. Natural population analysis and molecular electrostatic potential calculations visualize the charge distribution in an isolated molecule. Calculated first-order molecular hyperpolarizability and preliminary second harmonic generation test carried out using Kurtz-Perry technique establish 2-methoxy-4(phenyliminomethyl)phenol crystal as a good non linear optical material. Z-scan proposes the material for reverse saturable absorption.
Role of statistical linearization in the solution of nonlinear stochastic equations
International Nuclear Information System (INIS)
Budgor, A.B.
1977-01-01
The solution of a generalized Langevin equation is referred to as a stochastic process. If the external forcing function is Gaussian white noise, the forward Kolmogarov equation yields the transition probability density function. Nonlinear problems must be handled by approximation procedures e.g., perturbation theories, eigenfunction expansions, and nonlinear optimization procedures. After some comments on the first two of these, attention is directed to the third, and the method of statistical linearization is used to demonstrate a relation to the former two. Nonlinear stochastic systems exhibiting sustained or forced oscillations and the centered nonlinear Schroedinger equation in the presence of Gaussian white noise excitation are considered as examples. 5 figures, 2 tables
Comparison of different methods for the solution of sets of linear equations
International Nuclear Information System (INIS)
Bilfinger, T.; Schmidt, F.
1978-06-01
The application of the conjugate-gradient methods as novel general iterative methods for the solution of sets of linear equations with symmetrical systems matrices led to this paper, where a comparison of these methods with the conventional differently accelerated Gauss-Seidel iteration was carried out. In additon, the direct Cholesky method was also included in the comparison. The studies referred mainly to memory requirement, computing time, speed of convergence, and accuracy of different conditions of the systems matrices, by which also the sensibility of the methods with respect to the influence of truncation errors may be recognized. (orig.) 891 RW [de
International Nuclear Information System (INIS)
Dehghan, Mehdi; Shakourifar, Mohammad; Hamidi, Asgar
2009-01-01
The purpose of this study is to implement Adomian-Pade (Modified Adomian-Pade) technique, which is a combination of Adomian decomposition method (Modified Adomian decomposition method) and Pade approximation, for solving linear and nonlinear systems of Volterra functional equations. The results obtained by using Adomian-Pade (Modified Adomian-Pade) technique, are compared to those obtained by using Adomian decomposition method (Modified Adomian decomposition method) alone. The numerical results, demonstrate that ADM-PADE (MADM-PADE) technique, gives the approximate solution with faster convergence rate and higher accuracy than using the standard ADM (MADM).
A comparative study of iterative solutions to linear systems arising in quantum mechanics
International Nuclear Information System (INIS)
Jing Yanfei; Huang Tingzhu; Duan Yong; Carpentieri, Bruno
2010-01-01
This study is mainly focused on iterative solutions with simple diagonal preconditioning to two complex-valued nonsymmetric systems of linear equations arising from a computational chemistry model problem proposed by Sherry Li of NERSC. Numerical experiments show the feasibility of iterative methods to some extent when applied to the problems and reveal the competitiveness of our recently proposed Lanczos biconjugate A-orthonormalization methods to other classic and popular iterative methods. By the way, experiment results also indicate that application specific preconditioners may be mandatory and required for accelerating convergence.
An overview of solution methods for multi-objective mixed integer linear programming programs
DEFF Research Database (Denmark)
Andersen, Kim Allan; Stidsen, Thomas Riis
Multiple objective mixed integer linear programming (MOMIP) problems are notoriously hard to solve to optimality, i.e. finding the complete set of non-dominated solutions. We will give an overview of existing methods. Among those are interactive methods, the two phases method and enumeration...... methods. In particular we will discuss the existing branch and bound approaches for solving multiple objective integer programming problems. Despite the fact that branch and bound methods has been applied successfully to integer programming problems with one criterion only a few attempts has been made...
On the existence of tunneling bounce solutions in piecewise linear potentials
International Nuclear Information System (INIS)
Dutta, Koushik; Hector, Cecelie; Konstandin, Thomas; Vaudrevange, Pascal M.; Westphal, Alexander
2012-02-01
Coleman tunneling in a general scalar potential with two non-degenerate minima is known to have an approximation in terms of a piecewise linear triangular-shaped potential with sharp 'kinks' at the place of the local minima. This approximate potential has a regime where the existence of the bounce solution needs the scalar field to 'wait' for some amount of Euclidean time at one of the 'kinks'. We discuss under which circumstances the correct bounce action can be consistently obtained as the limiting case of a regular scalar potential where 'kinks' are resolved as locally smooth 'cap' regions. (orig.)
International Nuclear Information System (INIS)
Barbieri, M.
2007-01-01
Bose-Einstein coalescence of independent photons at the surface of a beam splitter is the physical process that allows linear optical quantum gates to be built. When distinct parametric down-conversion events are used as an independent photon source, distinguishability arises form the energy correlation of each photon with its twin. We derive upper bound for the entanglement which can be generated under these conditions
Generation of Symmetric Dicke States of Remote Qubits with Linear Optics
International Nuclear Information System (INIS)
Thiel, C.; Zanthier, J. von; Bastin, T.; Solano, E.; Agarwal, G. S.
2007-01-01
We propose a method for generating all symmetric Dicke states, either in the long-lived internal levels of N massive particles or in the polarization degrees of freedom of photonic qubits, using linear optical tools only. By means of a suitable multiphoton detection technique, erasing Welcher-Weg information, our proposed scheme allows the generation and measurement of an important class of entangled multiqubit states
Quantum teleportation of an arbitrary two-mode coherent state using only linear optics elements
International Nuclear Information System (INIS)
Ho Ngoc Phien; Nguyen Ba An
2008-01-01
We propose a linear optics scheme to teleport an arbitrary two-mode coherent state. The devices used are beam-splitters, phase-shifters and ideal photo-detectors capable of distinguishing between even and odd photon numbers. The scheme achieves faithful teleportation with a probability of 1/4. However, with additional use of an appropriate displacement operator, the teleported state can always be made near-faithful
Growth and Zeros of Meromorphic Solutions to Second-Order Linear Differential Equations
Directory of Open Access Journals (Sweden)
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.
Phantom solution in a non-linear Israel-Stewart theory
Cruz, Miguel; Cruz, Norman; Lepe, Samuel
2017-06-01
In this paper we present a phantom solution with a big rip singularity in a non-linear regime of the Israel-Stewart formalism. In this framework it is possible to extend this causal formalism in order to describe accelerated expansion, where assumption of near equilibrium is no longer valid. We assume a flat universe filled with a single viscous fluid ruled by a barotropic EoS, p = ωρ, which can represent a late time accelerated phase of the cosmic evolution. The solution allows to cross the phantom divide without evoking an exotic matter fluid and the effective EoS parameter is always lesser than -1 and constant in time.
Optical Code-Division Multiple Access: Challenges and Solutions
Chen, Lawrence R.
2003-02-01
Optical code-division multiple-access (OCDMA) is a technique well-suited for providing the required photonic connectivity in local access networks. Although the principles of OCDMA have been known for many years, it has never delivered on its potential. In this paper, we will describe the key challenges and impediments that have prevented OCDMA from delivering on its potential, as well as discuss possible solutions. We focus on the limitations of one-dimensional codes and the benefit of exploiting the additional degrees of freedom in using multiple dimensions for defining the codes. We discuss the advantages of using differential detection in order to implement bipolar communications. We then show how two-dimensional wavelength-time codes can be appropriately combined with differential detection in order to achieve high performance OCDMA systems with a large number of users operating with good BER performance for a large aggregate capacity. We also discuss the impact of channel coding techniques, for example forward error correction or turbo coding, on BER performance.
Non-linear optical properties of SiO2 with synthesized by implantation copper nanoparticles
International Nuclear Information System (INIS)
Stepanov, A.L.; Olivares, J.; Requejo-Isidro, J.; Del Coso, R.; De Nalda, R.; Solis, J.; Afonso, C.N.; Hole, D.; Townsend, P.D.; Naudon, A.
2001-01-01
In recent years there has been a growing interest in composite dielectrics containing metal nanoparticles for their potential application in wave-guide integrated all-optical non-linear switching devices. In present work, low energy high current ion implantation (50 keV) in silica at a well controlled substrate temperature (20 0 C) at a dose of 8·10 16 ion/cm 2 has been used to produce novel composites containing a large concentration of spherical Cu clusters with an average diameter of 4 nm and a very narrow size distribution. A very large value for the third order optical susceptibility, χ (3) = 10 -7 esu, has been measured in the vicinity of the surface plasmon resonance by degenerate four wave mixing at 585 nm. This value is among the largest values ever reported for Cu nano composites. Additionally, the response time of the non-linearity has been found to be shorter than 2 ps. The superior non-linear optical response of these implants is discussed in terms of the implantation conditions
Time-Frequency (Wigner Analysis of Linear and Nonlinear Pulse Propagation in Optical Fibers
Directory of Open Access Journals (Sweden)
José Azaña
2005-06-01
Full Text Available Time-frequency analysis, and, in particular, Wigner analysis, is applied to the study of picosecond pulse propagation through optical fibers in both the linear and nonlinear regimes. The effects of first- and second-order group velocity dispersion (GVD and self-phase modulation (SPM are first analyzed separately. The phenomena resulting from the interplay between GVD and SPM in fibers (e.g., soliton formation or optical wave breaking are also investigated in detail. Wigner analysis is demonstrated to be an extremely powerful tool for investigating pulse propagation dynamics in nonlinear dispersive systems (e.g., optical fibers, providing a clearer and deeper insight into the physical phenomena that determine the behavior of these systems.
Fast spatial beam shaping by acousto-optic diffraction for 3D non-linear microscopy.
Akemann, Walther; Léger, Jean-François; Ventalon, Cathie; Mathieu, Benjamin; Dieudonné, Stéphane; Bourdieu, Laurent
2015-11-02
Acousto-optic deflection (AOD) devices offer unprecedented fast control of the entire spatial structure of light beams, most notably their phase. AOD light modulation of ultra-short laser pulses, however, is not straightforward to implement because of intrinsic chromatic dispersion and non-stationarity of acousto-optic diffraction. While schemes exist to compensate chromatic dispersion, non-stationarity remains an obstacle. In this work we demonstrate an efficient AOD light modulator for stable phase modulation using time-locked generation of frequency-modulated acoustic waves at the full repetition rate of a high power laser pulse amplifier of 80 kHz. We establish the non-local relationship between the optical phase and the generating acoustic frequency function and verify the system for temporal stability, phase accuracy and generation of non-linear two-dimensional phase functions.
Linearized Optically Phase-Modulated Fiber Optic Links for Microwave Signal Transport
2009-03-03
detectors (with internal 50- Ohm resistors) capable of 40-mA dc current per detector. With this link, the linearized SFDR would improve to 133 dB/Hz4/5...the IF) limitation on the signal. All calculations consider the 3dB power loss from the hybrid combiner and 6dB loss from parallel 50- Ohm resistors...283. [25] M. Nazarathy, J. Berger, A. Ley , I. Levi, and Y. Kagan, “Externally Modulated 80 Channel Am Catv Fiber-to-feeder Distribution System Over
Clemens, Joshua William
Game theory has application across multiple fields, spanning from economic strategy to optimal control of an aircraft and missile on an intercept trajectory. The idea of game theory is fascinating in that we can actually mathematically model real-world scenarios and determine optimal decision making. It may not always be easy to mathematically model certain real-world scenarios, nonetheless, game theory gives us an appreciation for the complexity involved in decision making. This complexity is especially apparent when the players involved have access to different information upon which to base their decision making (a nonclassical information pattern). Here we will focus on the class of adversarial two-player games (sometimes referred to as pursuit-evasion games) with nonclassical information pattern. We present a two-sided (simultaneous) optimization solution method for the two-player linear quadratic Gaussian (LQG) multistage game. This direct solution method allows for further interpretation of each player's decision making (strategy) as compared to previously used formal solution methods. In addition to the optimal control strategies, we present a saddle point proof and we derive an expression for the optimal performance index value. We provide some numerical results in order to further interpret the optimal control strategies and to highlight real-world application of this game-theoretic optimal solution.
Hanks, Brantley R.; Skelton, Robert E.
1991-01-01
Vibration in modern structural and mechanical systems can be reduced in amplitude by increasing stiffness, redistributing stiffness and mass, and/or adding damping if design techniques are available to do so. Linear Quadratic Regulator (LQR) theory in modern multivariable control design, attacks the general dissipative elastic system design problem in a global formulation. The optimal design, however, allows electronic connections and phase relations which are not physically practical or possible in passive structural-mechanical devices. The restriction of LQR solutions (to the Algebraic Riccati Equation) to design spaces which can be implemented as passive structural members and/or dampers is addressed. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical system. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist.
Linear and nonlinear optical signals in probability and phase-space representations
International Nuclear Information System (INIS)
Man'ko, Margarita A
2006-01-01
Review of different representations of signals including the phase-space representations and tomographic representations is presented. The signals under consideration are either linear or nonlinear ones. The linear signals satisfy linear quantumlike Schroedinger and von Neumann equations. Nonlinear signals satisfy nonlinear Schroedinger equations as well as Gross-Pitaevskii equation describing solitons in Bose-Einstein condensate. The Ville-Wigner distributions for solitons are considered in comparison with tomographic-probability densities describing solitons completely. different kinds of tomographies - symplectic tomography, optical tomography and Fresnel tomography are reviewed. New kind of map of the signals onto probability distributions of discrete photon number-like variable is discussed. Mutual relations between different transformations of signal functions are established in explicit form. Such characteristics of the signal-probability distribution as entropy is discussed
Transfer of optical signals around bends in two-dimensional linear photonic networks
International Nuclear Information System (INIS)
Nikolopoulos, G M
2015-01-01
The ability to navigate light signals in two-dimensional networks of waveguide arrays is a prerequisite for the development of all-optical integrated circuits for information processing and networking. In this article, we present a theoretical analysis of bending losses in linear photonic lattices with engineered couplings, and discuss possible ways for their minimization. In contrast to previous work in the field, the lattices under consideration operate in the linear regime, in the sense that discrete solitons cannot exist. The present results suggest that the functionality of linear waveguide networks can be extended to operations that go beyond the recently demonstrated point-to-point transfer of signals, such as blocking, routing, logic functions, etc. (paper)
Marazzi, Marco; Gattuso, Hugo; Monari, Antonio; Assfeld, Xavier
2018-01-01
Bio-macromolecules as DNA, lipid membranes and (poly)peptides are essential compounds at the core of biological systems. The development of techniques and methodologies for their characterization is therefore necessary and of utmost interest, even though difficulties can be experienced due to their intrinsic complex nature. Among these methods, spectroscopies, relying on optical properties are especially important to determine their macromolecular structures and behaviors, as well as the possible interactions and reactivity with external dyes-often drugs or pollutants-that can (photo)sensitize the bio-macromolecule leading to eventual chemical modifications, thus damages. In this review, we will focus on the theoretical simulation of electronic spectroscopies of bio-macromolecules, considering their secondary structure and including their interaction with different kind of (photo)sensitizers. Namely, absorption, emission and electronic circular dichroism (CD) spectra are calculated and compared with the available experimental data. Non-linear properties will be also taken into account by two-photon absorption, a highly promising technique (i) to enhance absorption in the red and infra-red windows and (ii) to enhance spatial resolution. Methodologically, the implications of using implicit and explicit solvent, coupled to quantum and thermal samplings of the phase space, will be addressed. Especially, hybrid quantum mechanics/molecular mechanics (QM/MM) methods are explored for a comparison with solely QM methods, in order to address the necessity to consider an accurate description of environmental effects on spectroscopic properties of biological systems.
Directory of Open Access Journals (Sweden)
Marco Marazzi
2018-04-01
Full Text Available Bio-macromolecules as DNA, lipid membranes and (polypeptides are essential compounds at the core of biological systems. The development of techniques and methodologies for their characterization is therefore necessary and of utmost interest, even though difficulties can be experienced due to their intrinsic complex nature. Among these methods, spectroscopies, relying on optical properties are especially important to determine their macromolecular structures and behaviors, as well as the possible interactions and reactivity with external dyes—often drugs or pollutants—that can (photosensitize the bio-macromolecule leading to eventual chemical modifications, thus damages. In this review, we will focus on the theoretical simulation of electronic spectroscopies of bio-macromolecules, considering their secondary structure and including their interaction with different kind of (photosensitizers. Namely, absorption, emission and electronic circular dichroism (CD spectra are calculated and compared with the available experimental data. Non-linear properties will be also taken into account by two-photon absorption, a highly promising technique (i to enhance absorption in the red and infra-red windows and (ii to enhance spatial resolution. Methodologically, the implications of using implicit and explicit solvent, coupled to quantum and thermal samplings of the phase space, will be addressed. Especially, hybrid quantum mechanics/molecular mechanics (QM/MM methods are explored for a comparison with solely QM methods, in order to address the necessity to consider an accurate description of environmental effects on spectroscopic properties of biological systems.
Marazzi, Marco; Gattuso, Hugo; Monari, Antonio; Assfeld, Xavier
2018-04-01
Bio-macromolecules as DNA, lipid membranes and (poly)peptides are essential compounds at the core of biological systems. The development of techniques and methodologies for their characterization is therefore necessary and of utmost interest, even though difficulties can be experienced due to their intrinsic complex nature. Among these methods, spectroscopies, relying on optical properties are especially important to determine their macromolecular structures and behaviors, as well as the possible interactions and reactivity with external dyes – often drugs or pollutants – that can (photo)sensitize the bio-macromolecule leading to eventual chemical modifications, thus damages. In this review, we will focus on the theoretical simulation of electronic spectroscopies of bio-macromolecules, considering their secondary structure and including their interaction with different kind of (photo)sensitizers. Namely, absorption, emission and electronic circular dichroism (CD) spectra are calculated and compared with the available experimental data. Non-linear properties will be also taken into account by two-photon absorption, a highly promising technique (i) to enhance absorption in the red and infra-red windows and (ii) to enhance spatial resolution. Methodologically, the implications of using implicit and explicit solvent, coupled to quantum and thermal samplings of the phase space, will be addressed. Especially, hybrid quantum mechanics/ molecular mechanics (QM/MM) methods are explored for a comparison with solely QM methods, in order to address the necessity to consider an accurate description of environmental effects on spectroscopic properties of biological systems.
Universal squash model for optical communications using linear optics and threshold detectors
International Nuclear Information System (INIS)
Fung, Chi-Hang Fred; Chau, H. F.; Lo, Hoi-Kwong
2011-01-01
Transmission of photons through open-air or optical fibers is an important primitive in quantum-information processing. Theoretical descriptions of this process often consider single photons as information carriers and thus fail to accurately describe experimental implementations where any number of photons may enter a detector. It has been a great challenge to bridge this big gap between theory and experiments. One powerful method for achieving this goal is by conceptually squashing the received multiphoton states to single-photon states. However, until now, only a few protocols admit a squash model; furthermore, a recently proven no-go theorem appears to rule out the existence of a universal squash model. Here we show that a necessary condition presumed by all existing squash models is in fact too stringent. By relaxing this condition, we find that, rather surprisingly, a universal squash model actually exists for many protocols, including quantum key distribution, quantum state tomography, Bell's inequality testing, and entanglement verification.
Fast solution of elliptic partial differential equations using linear combinations of plane waves.
Pérez-Jordá, José M
2016-02-01
Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations Ax=b, where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O(NlogN) memory and executing an iteration in O(Nlog(2)N) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.
Solution of single linear tridiagonal systems and vectorization of the ICCG algorithm on the Cray 1
International Nuclear Information System (INIS)
Kershaw, D.S.
1981-01-01
The numerical algorithms used to solve the physics equation in codes which model laser fusion are examined, it is found that a large number of subroutines require the solution of tridiagonal linear systems of equations. One dimensional radiation transport, thermal and suprathermal electron transport, ion thermal conduction, charged particle and neutron transport, all require the solution of tridiagonal systems of equations. The standard algorithm that has been used in the past on CDC 7600's will not vectorize and so cannot take advantage of the large speed increases possible on the Cray-1 through vectorization. There is however, an alternate algorithm for solving tridiagonal systems, called cyclic reduction, which allows for vectorization, and which is optimal for the Cray-1. Software based on this algorithm is now being used in LASNEX to solve tridiagonal linear systems in the subroutines mentioned above. The new algorithm runs as much as five times faster than the standard algorithm on the Cray-1. The ICCG method is being used to solve the diffusion equation with a nine-point coupling scheme on the CDC 7600. In going from the CDC 7600 to the Cray-1, a large part of the algorithm consists of solving tridiagonal linear systems on each L line of the Lagrangian mesh in a manner which is not vectorizable. An alternate ICCG algorithm for the Cray-1 was developed which utilizes a block form of the cyclic reduction algorithm. This new algorithm allows full vectorization and runs as much as five times faster than the old algorithm on the Cray-1. It is now being used in Cray LASNEX to solve the two-dimensional diffusion equation in all the physics subroutines mentioned above
Linear and nonlinear optical properties of Sb-doped GeSe2 thin films
Zhang, Zhen-Ying; Chen, Fen; Lu, Shun-Bin; Wang, Yong-Hui; Shen, Xiang; Dai, Shi-Xun; Nie, Qiu-Hua
2015-06-01
Sb-doped GeSe2 chalcogenide thin films are prepared by the magnetron co-sputtering method. The linear optical properties of as-deposited films are derived by analyzing transmission spectra. The refractive index rises and the optical band gap decreases from 2.08 eV to 1.41 eV with increasing the Sb content. X-ray photoelectron spectra further confirm the formation of a covalent Sb-Se bond. The third-order nonlinear optical properties of thin films are investigated under femtosecond laser excitation at 800 nm. The results show that the third-order nonlinear optical properties are enhanced with increasing the concentration of Sb. The nonlinear refraction indices of these thin films are measured to be on the order of 10-18 m2/W with a positive sign and the nonlinear absorption coefficients are obtained to be on the order of 10-10 m/W. These excellent properties indicate that Sb-doped Ge-Se films have a good prospect in the applications of nonlinear optical devices. Project supported by the National Key Basic Research Program of China (Grant No. 2012CB722703), the National Natural Science Foundation of China (Grant No. 61377061), the Young Leaders of Academic Climbing Project of the Education Department of Zhejiang Province, China (Grant No. pd2013092), the Program for Innovative Research Team of Ningbo City, China (Grant No. 2009B217), and the K. C. Wong Magna Fund in Ningbo University, China.
Directory of Open Access Journals (Sweden)
Reza Ezzati
2014-08-01
Full Text Available In this paper, we propose the least square method for computing the positive solution of a non-square fully fuzzy linear system. To this end, we use Kaffman' arithmetic operations on fuzzy numbers \\cite{17}. Here, considered existence of exact solution using pseudoinverse, if they are not satisfy in positive solution condition, we will compute fuzzy vector core and then we will obtain right and left spreads of positive fuzzy vector by introducing constrained least squares problem. Using our proposed method, non-square fully fuzzy linear system of equations always has a solution. Finally, we illustrate the efficiency of proposed method by solving some numerical examples.
Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation
Lin, Yu-Chu; Wang, Haitao; Wu, Kung-Chien
2018-04-01
We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad's angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543-1608, 2004), (Bull Inst Math Acad Sin 1:1-78, 2006), (Bull Inst Math Acad Sin 6:151-243, 2011) and Lee et al. (Commun Math Phys 269:17-37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.
Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation
Lin, Yu-Chu; Wang, Haitao; Wu, Kung-Chien
2018-06-01
We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad's angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543-1608, 2004), (Bull Inst Math Acad Sin 1:1-78, 2006), (Bull Inst Math Acad Sin 6:151-243, 2011) and Lee et al. (Commun Math Phys 269:17-37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.
Optically stimulated luminescence from quartz measured using the linear modulation technique
International Nuclear Information System (INIS)
Bulur, E.; Boetter-Jensen, L.; Murray, A.S.
2000-01-01
The optically stimulated luminescence (OSL) from heated natural quartz has been investigated using the linear modulation technique (LMT), in which the excitation light intensity is increased linearly during stimulation. In contrast to conventional stimulation, which usually produces a monotonically decreasing signal, linearly increasing the stimulation power gives peaks in the signal as a function of time. In cases where the OSL signal contains more than one component, the linear increase in power of the stimulation light may result in a curve containing overlapping peaks, where the most easily stimulated component occurs at a shorter time. This allows the separation of the overlapping OSL components, which are assumed to originate from different traps. The LM-OSL curve from quartz shows an initial peak followed by a broad one. Deconvolution using curve fitting has shown that the composite OSL curve from quartz can be approximated well by using a linear combination of first-order peaks. In addition to the three known components, i.e. fast, medium and slow components from continuous-wave-OSL studies, an additional slow component is also identified for the first time. The dose responses and thermal stabilities of the various components are also studied
International Nuclear Information System (INIS)
Bouaziz, M.N.; Aziz, Abdul
2010-01-01
A novel concept of double optimal linearization is introduced and used to obtain a simple and accurate solution for the temperature distribution in a straight rectangular convective-radiative fin with temperature dependent thermal conductivity. The solution is built from the classical solution for a pure convection fin of constant thermal conductivity which appears in terms of hyperbolic functions. When compared with the direct numerical solution, the double optimally linearized solution is found to be accurate within 4% for a range of radiation-conduction and thermal conductivity parameters that are likely to be encountered in practice. The present solution is simple and offers superior accuracy compared with the fairly complex approximate solutions based on the homotopy perturbation method, variational iteration method, and the double series regular perturbation method. The fin efficiency expression resembles the classical result for the constant thermal conductivity convecting fin. The present results are easily usable by the practicing engineers in their thermal design and analysis work involving fins.
International Nuclear Information System (INIS)
Belmonte-Beitia, Juan; Konotop, Vladimir V.; Perez-Garcia, Victor M.; Vekslerchik, Vadym E.
2009-01-01
Using similarity transformations we construct explicit solutions of the nonlinear Schroedinger equation with linear and nonlinear periodic potentials. We present explicit forms of spatially localized and periodic solutions, and study their properties. We put our results in the framework of the exploited perturbation techniques and discuss their implications on the properties of associated linear periodic potentials and on the possibilities of stabilization of gap solitons using polychromatic lattices.
Full-range k-domain linearization in spectral-domain optical coherence tomography.
Jeon, Mansik; Kim, Jeehyun; Jung, Unsang; Lee, Changho; Jung, Woonggyu; Boppart, Stephen A
2011-03-10
A full-bandwidth k-domain linearization method for spectral-domain optical coherence tomography (SD-OCT) is demonstrated. The method uses information of the wavenumber-pixel-position provided by a translating-slit-based wavelength filter. For calibration purposes, the filter is placed either after a broadband source or at the end of the sample path, and the filtered spectrum with a narrowed line width (∼0.5 nm) is incident on a line-scan camera in the detection path. The wavelength-swept spectra are co-registered with the pixel positions according to their central wavelengths, which can be automatically measured with an optical spectrum analyzer. For imaging, the method does not require a filter or a software recalibration algorithm; it simply resamples the OCT signal from the detector array without employing rescaling or interpolation methods. The accuracy of k-linearization is maximized by increasing the k-linearization order, which is known to be a crucial parameter for maintaining a narrow point-spread function (PSF) width at increasing depths. The broadening effect is studied by changing the k-linearization order by undersampling to search for the optimal value. The system provides more position information, surpassing the optimum without compromising the imaging speed. The proposed full-range k-domain linearization method can be applied to SD-OCT systems to simplify their hardware/software, increase their speed, and improve the axial image resolution. The experimentally measured width of PSF in air has an FWHM of 8 μm at the edge of the axial measurement range. At an imaging depth of 2.5 mm, the sensitivity of the full-range calibration case drops less than 10 dB compared with the uncompensated case.
Rajagopal, Vaishnavi; Stokes, Chris; Ferzoco, Alessandra
2018-02-01
We report a custom-geometry linear ion trap designed for fluorescence spectroscopy of gas-phase ions at ambient to cryogenic temperatures. Laser-induced fluorescence from trapped ions is collected from between the trapping rods, orthogonal to the excitation laser that runs along the axis of the linear ion trap. To increase optical access to the ion cloud, the diameter of the round trapping rods is 80% of the inscribed diameter, rather than the roughly 110% used to approximate purely quadrupolar electric fields. To encompass as much of the ion cloud as possible, the first collection optic has a 25.4 mm diameter and a numerical aperture of 0.6. The choice of geometry and collection optics yields 107 detected photons/s from trapped rhodamine 6G ions. The trap is coupled to a closed-cycle helium refrigerator, which in combination with two 50 Ohm heaters enables temperature control to below 25 K on the rod electrodes. The purpose of the instrument is to broaden the applicability of fluorescence spectroscopy of gas-phase ions to cases where photon emission is a minority relaxation pathway. Such studies are important to understand how the microenvironment of a chromophore influences excited state charge transfer processes.
Growth of KNN thin films for non-linear optical applications
International Nuclear Information System (INIS)
Sharma, Shweta; Gupta, Reema; Gupta, Vinay; Tomar, Monika
2018-01-01
Two-wave mixing is a remarkable area of research in the field of non-linear optics, finding various applications in the development of opto-electronic devices, photorefractive waveguides, real time holography, etc. Non-linear optical properties of ferroelectric potassium sodium niobate (KNN) thin films have been interrogated using two-wave mixing phenomenon. Regarding this, a-axis oriented K 0.35 Na (1-0.35) NbO 3 thin films were successfully grown on epitaxial matched (100) SrTiO 3 substrate using pulsed laser deposition (PLD) technique. The uniformly distributed Au micro-discs of 200 μm diameter were integrated with KNN/STO thin film to study the plasmonic enhancement in the optical response. Beam amplification has been observed as a result of the two-wave mixing. This is due to the alignment of ferroelectric domains in KNN films and the excitement of plasmons at the metal-dielectric (Au-KNN) interface. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Growth of KNN thin films for non-linear optical applications
Energy Technology Data Exchange (ETDEWEB)
Sharma, Shweta; Gupta, Reema; Gupta, Vinay [Department of Physics and Astrophysics, University of Delhi (India); Tomar, Monika [Department of Physics, Miranda House University of Delhi (India)
2018-02-15
Two-wave mixing is a remarkable area of research in the field of non-linear optics, finding various applications in the development of opto-electronic devices, photorefractive waveguides, real time holography, etc. Non-linear optical properties of ferroelectric potassium sodium niobate (KNN) thin films have been interrogated using two-wave mixing phenomenon. Regarding this, a-axis oriented K{sub 0.35}Na{sub (1-0.35)}NbO{sub 3} thin films were successfully grown on epitaxial matched (100) SrTiO{sub 3} substrate using pulsed laser deposition (PLD) technique. The uniformly distributed Au micro-discs of 200 μm diameter were integrated with KNN/STO thin film to study the plasmonic enhancement in the optical response. Beam amplification has been observed as a result of the two-wave mixing. This is due to the alignment of ferroelectric domains in KNN films and the excitement of plasmons at the metal-dielectric (Au-KNN) interface. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
FINAL REPORT "Extreme non-linear optics of plasmas" Pierre Michel (16-LW-022)
Energy Technology Data Exchange (ETDEWEB)
Michel, Pierre [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2017-11-03
Large laser facilities such as the National Ignition Facility (NIF) are typically limited in performance and physical scale (and thus cost) by optics damage. In this LDRD, we investigated a radically new way to manipulate light at extreme powers and energies, where “traditional” (crystal-based) optical elements are replaced by a medium that is already “broken” and thus does not suffer from optics damage: a plasma. Our method consisted in applying multiple lasers into plasmas to imprint refractive micro-structures with optical properties designed to be similar to those of crystals or dielectric structures used in optics. In particular, we focused our efforts on two elements used to manipulate the polarization of lasers (i.e. the orientation of the light’s electric field vector): i) a polarizer, which only lets a given polarization direction pass and blocks the others, and ii) a “Pockels cell”, which can “rotate” the polarization direction or convert it from linear to elliptical or circular. These two elements are essential building blocks in almost all laser systems – for example, they can be combined to design optical gates. Here, we introduced the new concepts of a “plasma polarizer” and a “plasma Pockels cell”. Both concepts were demonstrated in proof-of-principle laboratory experiments in this LDRD. We also demonstrated that such laser-plasma systems could be used to provide full control of the refractive index of plasmas as well as their dispersion (variation of the index vs. the light wavelength), which constituted the basis for a final experiment aimed at demonstrating the feasibility of “slow light” in plasmas, i.e. the capability to slow down a light pulse almost to a full stop.
On the existence of tunneling bounce solutions in piecewise linear potentials
Energy Technology Data Exchange (ETDEWEB)
Dutta, Koushik; Hector, Cecelie; Konstandin, Thomas; Vaudrevange, Pascal M.; Westphal, Alexander
2012-02-15
Coleman tunneling in a general scalar potential with two non-degenerate minima is known to have an approximation in terms of a piecewise linear triangular-shaped potential with sharp 'kinks' at the place of the local minima. This approximate potential has a regime where the existence of the bounce solution needs the scalar field to 'wait' for some amount of Euclidean time at one of the 'kinks'. We discuss under which circumstances the correct bounce action can be consistently obtained as the limiting case of a regular scalar potential where 'kinks' are resolved as locally smooth 'cap' regions. (orig.)
Non-linear dynamics of the passivity breakdown of iron in acidic solutions
Sazou, D
2003-01-01
Breakdown of the iron passivity in acid solutions accompanied by current oscillations was investigated by using electrochemical techniques, which reveal the non-linear dynamical response of the system in the current-potential (I-E) and current-time (I-t) planes. Current oscillations of the Fe-electrolyte electrochemical system were studied in the (a) absence and (b) presence of chlorides. In case (a) two oscillatory regions were distinguished; one at low potentials associated with the formation-dissolution of a ferrous salt and another at higher potentials associated with the formation-breakdown of the oxide film. Chaotic oscillations appear in the former region whereas periodic oscillations of a relaxation type appear in the latter region. In case (b), complex periodic and aperiodic oscillations are induced by small amounts of chlorides due to pitting corrosion. Pitting corrosion is a multistage localized process of a great technological importance. It consists of a local breakdown of the passive oxide film ...
Directory of Open Access Journals (Sweden)
T. H. S. Abdelaziz
2005-01-01
Full Text Available In this paper we introduce a complete parametric approach for solving the problem of eigenstructure assignment via state-derivative feedback for linear systems. This problem is always solvable for any controllable systems iff the open-loop system matrix is nonsingular. In this work, two parametric solutions to the feedback gain matrix are introduced that describe the available degrees of freedom offered by the state-derivative feedback in selecting the associated eigenvectors from an admissible class. These freedoms can be utilized to improve robustness of the closed-loop system. Accordingly, the sensitivity of the assigned eigenvalues to perturbations in the system and gain matrix is minimized. Numerical examples are included to show the effectiveness of the proposed approach.
DEFF Research Database (Denmark)
Köyluoglu, H.U.; Nielsen, Søren R.K.; Cakmak, A.S.
1994-01-01
perturbation method using stochastic differential equations. The joint statistical moments entering the perturbation solution are determined by considering an augmented dynamic system with state variables made up of the displacement and velocity vector and their first and second derivatives with respect......The paper deals with the first and second order statistical moments of the response of linear systems with random parameters subject to random excitation modelled as white-noise multiplied by an envelope function with random parameters. The method of analysis is basically a second order...... to the random parameters of the problem. Equations for partial derivatives are obtained from the partial differentiation of the equations of motion. The zero time-lag joint statistical moment equations for the augmented state vector are derived from the Itô differential formula. General formulation is given...
An algebraic approach to linear-optical schemes for deterministic quantum computing
International Nuclear Information System (INIS)
Aniello, Paolo; Cagli, Ruben Coen
2005-01-01
Linear-optical passive (LOP) devices and photon counters are sufficient to implement universal quantum computation with single photons, and particular schemes have already been proposed. In this paper we discuss the link between the algebraic structure of LOP transformations and quantum computing. We first show how to decompose the Fock space of N optical modes in finite-dimensional subspaces that are suitable for encoding strings of qubits and invariant under LOP transformations (these subspaces are related to the spaces of irreducible unitary representations of U (N). Next we show how to design in algorithmic fashion LOP circuits which implement any quantum circuit deterministically. We also present some simple examples, such as the circuits implementing a cNOT gate and a Bell state generator/analyser
Linear Optical and SERS Study on Metallic Membranes with Subwavelength Complementary Patterns
Hao, Qingzhen; Zeng, Yong; Jensen, Lasse; Werner, Douglas; Crespi, Vincent; Huang, Tony Jun; Interdepartmental Collaboration
2011-03-01
An efficient technique is developed to fabricate optically thin metallic films with subwavelength patterns and their complements simultaneously. By comparing the spectra of the complementary films, we show that Babinet's principle nearly holds in the optical domain. A discrete-dipole approximation can qualitatively describe their spectral dependence on the geometry of the constituent particles and the illuminating polarization. Using pyridine as probe molecules, we studied surface-enhanced Raman spectroscopy (SERS) from the complementary structure. Although the complementary structure posses closely related linear spectra, they have quite different near-field behaviors. For hole arrays, their averaged local field gains as well as the SERS enhancements are strongly correlated to their transmission spectra. We therefore can use cos 4 θ to approximately describe the dependence of the Raman intensity on the excitation polarization angle θ , while the complementary particle arrays present maximal local field gains at wavelengths generally much bigger than their localized surface plasmonic resonant wavelengths.
Quantum Optical Realization of Arbitrary Linear Transformations Allowing for Loss and Gain
Tischler, N.; Rockstuhl, C.; Słowik, K.
2018-04-01
Unitary transformations are routinely modeled and implemented in the field of quantum optics. In contrast, nonunitary transformations, which can involve loss and gain, require a different approach. In this work, we present a universal method to deal with nonunitary networks. An input to the method is an arbitrary linear transformation matrix of optical modes that does not need to adhere to bosonic commutation relations. The method constructs a transformation that includes the network of interest and accounts for full quantum optical effects related to loss and gain. Furthermore, through a decomposition in terms of simple building blocks, it provides a step-by-step implementation recipe, in a manner similar to the decomposition by Reck et al. [Experimental Realization of Any Discrete Unitary Operator, Phys. Rev. Lett. 73, 58 (1994), 10.1103/PhysRevLett.73.58] but applicable to nonunitary transformations. Applications of the method include the implementation of positive-operator-valued measures and the design of probabilistic optical quantum information protocols.
Optical tuning in the arcs and final focus sections of the Stanford Linear Collider
International Nuclear Information System (INIS)
Bambade, P.S.
1989-03-01
In this thesis, we present the experimental tuning procedures developed for the Arcs and for the Final Focus Section of the Stanford Linear Collider (SLC). Such tuning is necessary to maximize the luminosity, by minimizing the beam size at the interaction point, and to reduce backgrounds in the experiment. In the final Focus Section, the correction strategy must result from the principles of the optical design, which is based on cancellations between second order aberrations, and on the ability to measure micron-size beams typical of the SLC. In the Arcs, the corrections were designed after the initial commissioning, to make the system more error-tolerant, through a modification in the optical design, and to enable adjustments of the beam phase-space a the injection to the Final Focus System, through a harmonic perturbation technique inspired from circular accelerators. Although the overall optimization of the SLC is not entirely finished, an almost optimal set-up has been achieved for the optics of the Arcs and of the Final Focus Section. Beams with transverse sizes close to the nominal ones, of a few microns, have been obtained at the interaction point. We present and discuss our results and the optical limits to the present performance. 24 refs., 25 figs., 2 tabs
Optical tuning in the arcs and final focus sections of the Stanford Linear Collider
Energy Technology Data Exchange (ETDEWEB)
Bambade, P.S.
1989-03-01
In this thesis, we present the experimental tuning procedures developed for the Arcs and for the Final Focus Section of the Stanford Linear Collider (SLC). Such tuning is necessary to maximize the luminosity, by minimizing the beam size at the interaction point, and to reduce backgrounds in the experiment. In the final Focus Section, the correction strategy must result from the principles of the optical design, which is based on cancellations between second order aberrations, and on the ability to measure micron-size beams typical of the SLC. In the Arcs, the corrections were designed after the initial commissioning, to make the system more error-tolerant, through a modification in the optical design, and to enable adjustments of the beam phase-space a the injection to the Final Focus System, through a harmonic perturbation technique inspired from circular accelerators. Although the overall optimization of the SLC is not entirely finished, an almost optimal set-up has been achieved for the optics of the Arcs and of the Final Focus Section. Beams with transverse sizes close to the nominal ones, of a few microns, have been obtained at the interaction point. We present and discuss our results and the optical limits to the present performance. 24 refs., 25 figs., 2 tabs.
Counter-propagating dual-trap optical tweezers based on linear momentum conservation
International Nuclear Information System (INIS)
Ribezzi-Crivellari, M.; Huguet, J. M.; Ritort, F.
2013-01-01
We present a dual-trap optical tweezers setup which directly measures forces using linear momentum conservation. The setup uses a counter-propagating geometry, which allows momentum measurement on each beam separately. The experimental advantages of this setup include low drift due to all-optical manipulation, and a robust calibration (independent of the features of the trapped object or buffer medium) due to the force measurement method. Although this design does not attain the high-resolution of some co-propagating setups, we show that it can be used to perform different single molecule measurements: fluctuation-based molecular stiffness characterization at different forces and hopping experiments on molecular hairpins. Remarkably, in our setup it is possible to manipulate very short tethers (such as molecular hairpins with short handles) down to the limit where beads are almost in contact. The setup is used to illustrate a novel method for measuring the stiffness of optical traps and tethers on the basis of equilibrium force fluctuations, i.e., without the need of measuring the force vs molecular extension curve. This method is of general interest for dual trap optical tweezers setups and can be extended to setups which do not directly measure forces.
Optical tuning of arcs and final focus section of the Standard Linear Collider (SLC)
International Nuclear Information System (INIS)
Bambade, P.
1989-03-01
In this thesis, we present the experimental tuning procedures developed for the Arcs and for the Final Focus Section of the Stanford Linear Collider (SLC). Such tuning is necessary to maximize the luminosity, by minimizing the beam size at the interaction point, and to reduce backgrounds in the experiment. In the final Focus Section, the correction strategy must result from the principles of the optical design, which is based on cancellations between second order aberrations, and on the ability to measure micron-size beams typical of the SLC. In the Arcs, the corrections were designed after the initial commissioning, to make the system more error-tolerant, through a modification in the optical design, and to enable adjustements of the beam phase-space at the injection to the Final Focus System, through a harmonic perturbation technique inspired from circular accelerators. Although the overall optimization of the SLC is not entirely finished, an almost optimal set-up has been achieved for the optics of the Arcs and of the Final Focus Section. Beams with transverse sizes close to the nominal ones, of a few microns, have been obtained at the interaction point. We present and discuss our results and the optical limits to the present performance [fr
Counter-propagating dual-trap optical tweezers based on linear momentum conservation
Energy Technology Data Exchange (ETDEWEB)
Ribezzi-Crivellari, M.; Huguet, J. M. [Small Biosystems Lab, Dept. de Fisica Fonamental, Universitat de Barcelona, Avda. Diagonal 647, 08028 Barcelona (Spain); Ritort, F. [Small Biosystems Lab, Dept. de Fisica Fonamental, Universitat de Barcelona, Avda. Diagonal 647, 08028 Barcelona (Spain); Ciber-BBN de Bioingenieria, Biomateriales y Nanomedicina, Instituto de Salud Carlos III, Madrid (Spain)
2013-04-15
We present a dual-trap optical tweezers setup which directly measures forces using linear momentum conservation. The setup uses a counter-propagating geometry, which allows momentum measurement on each beam separately. The experimental advantages of this setup include low drift due to all-optical manipulation, and a robust calibration (independent of the features of the trapped object or buffer medium) due to the force measurement method. Although this design does not attain the high-resolution of some co-propagating setups, we show that it can be used to perform different single molecule measurements: fluctuation-based molecular stiffness characterization at different forces and hopping experiments on molecular hairpins. Remarkably, in our setup it is possible to manipulate very short tethers (such as molecular hairpins with short handles) down to the limit where beads are almost in contact. The setup is used to illustrate a novel method for measuring the stiffness of optical traps and tethers on the basis of equilibrium force fluctuations, i.e., without the need of measuring the force vs molecular extension curve. This method is of general interest for dual trap optical tweezers setups and can be extended to setups which do not directly measure forces.
A linear complementarity method for the solution of vertical vehicle-track interaction
Zhang, Jian; Gao, Qiang; Wu, Feng; Zhong, Wan-Xie
2018-02-01
A new method is proposed for the solution of the vertical vehicle-track interaction including a separation between wheel and rail. The vehicle is modelled as a multi-body system using rigid bodies, and the track is treated as a three-layer beam model in which the rail is considered as an Euler-Bernoulli beam and both the sleepers and the ballast are represented by lumped masses. A linear complementarity formulation is directly established using a combination of the wheel-rail normal contact condition and the generalised-α method. This linear complementarity problem is solved using the Lemke algorithm, and the wheel-rail contact force can be obtained. Then the dynamic responses of the vehicle and the track are solved without iteration based on the generalised-α method. The same equations of motion for the vehicle and track are adopted at the different wheel-rail contact situations. This method can remove some restrictions, that is, time-dependent mass, damping and stiffness matrices of the coupled system, multiple equations of motion for the different contact situations and the effect of the contact stiffness. Numerical results demonstrate that the proposed method is effective for simulating the vehicle-track interaction including a separation between wheel and rail.
International Nuclear Information System (INIS)
Li Yong; Lu Jing; Cui Xiaobing; Xu Jiqing; Li Kechang; Sun Huaying; Li Guanghua; Pan Lingyun; Yang Qingxin
2005-01-01
Both the homometal cluster [P(ph 4 )] 2 [Mo 2 O 2 (μ-S) 2 (S 2 ) 2 ] (1) and [Mo 2 O 2 (μ-S) 2 (Et 2 dtc) 2 ] (2) (Et 2 dtc=diethyl-dithiocarbamate) were successfully synthesized by low-temperature solid-state reactions. X-ray single-crystal diffraction studies suggest that compound (1) is a dinuclear anion cluster, and compound (2) is a dinuclear neutral cluster. The two compounds were characterized by elemental analyses, IR spectra and UV-Vis spectra. The third-order non-linear optical (NLO) properties of the clusters were also investigated and all exhibited nice non-linear absorption and self-defocusing performance with moduli of the hyperpolarizabilities 5.145x10 -30 esu for (1) and 5.428x10 -30 esu for (2)
Linearly interpolated sub-symbol optical phase noise suppression in CO-OFDM system.
Hong, Xuezhi; Hong, Xiaojian; He, Sailing
2015-02-23
An optical phase noise suppression algorithm, LI-SCPEC, based on phase linear interpolation and sub-symbol processing is proposed for CO-OFDM system. By increasing the temporal resolution of carrier phase tracking through dividing one symbol into several sub-blocks, i.e., sub-symbols, inter-carrier-interference (ICI) mitigation is achieved in the proposed algorithm. Linear interpolation is employed to obtain a reliable temporal reference for sub-symbol phase estimation. The new algorithm, with only a few number of sub-symbols (N(B) = 4), can provide a considerably larger laser linewidth tolerance than several other ICI mitigation algorithms as demonstrated by Monte-Carlo simulations. Numerical analysis verifies that the best performance is achieved with an optimal and moderate number of sub-symbols. Complexity analysis shows that the required number of complex-valued multiplications is independent of the number of sub-symbols used in the proposed algorithm.
Splitting of quantum information in travelling wave fields using only linear optical elements
Energy Technology Data Exchange (ETDEWEB)
Cardoso, W B; De Almeida, N G; Avelar, A T; Baseia, B [Instituto de Fisica, Universidade Federal de Goias, 74.001-970, Goiania-GO (Brazil)
2011-02-28
In this paper we present a feasible post-selection scheme to split quantum information in the realm of travelling waves with success probability of 50%. Taking advantage of this scheme we have also proposed the generation of a class of W states useful for perfect teleportation and superdense coding. The scheme employs only linear optical elements as beam splitters (BS) and phase shifters, plus two photon counters and a source of two spontaneous parametric down-conversion photons. It is shown that splitting of quantum information with high fidelity is possible, even when using inefficient detectors and photoabsorption BS.
Superconducting resonators as beam splitters for linear-optics quantum computation.
Chirolli, Luca; Burkard, Guido; Kumar, Shwetank; Divincenzo, David P
2010-06-11
We propose and analyze a technique for producing a beam-splitting quantum gate between two modes of a ring-resonator superconducting cavity. The cavity has two integrated superconducting quantum interference devices (SQUIDs) that are modulated by applying an external magnetic field. The gate is accomplished by applying a radio frequency pulse to one of the SQUIDs at the difference of the two mode frequencies. Departures from perfect beam splitting only arise from corrections to the rotating wave approximation; an exact calculation gives a fidelity of >0.9992. Our construction completes the toolkit for linear-optics quantum computing in circuit quantum electrodynamics.
Deconfinement and Phase Diagram of Bosons in a Linear Optical Lattice with a Particle Reservoir
International Nuclear Information System (INIS)
Majumdar, Kingshuk; Fertig, H.A.
2005-01-01
We investigate the zero-temperature phases of bosons in a one-dimensional optical lattice with an explicit tunnel coupling to a Bose-condensed particle reservoir. Renormalization group analysis of this system is shown to reveal three phases: one in which the linear system is fully phase locked to the reservoir; one in which Josephson vortices between the one-dimensional system and the particle reservoir deconfine due to quantum fluctuations, leading to a decoupled state in which the one-dimensional system is metallic; and one in which the one-dimensional system is in a Mott insulating state
Guo, Rui; Zhou, Lan; Gu, Shi-Pu; Wang, Xing-Fu; Sheng, Yu-Bo
2017-03-01
The concatenated Greenberger-Horne-Zeilinger (C-GHZ) state is a new type of multipartite entangled state, which has potential application in future quantum information. In this paper, we propose a protocol of constructing arbitrary C-GHZ entangled state approximatively. Different from previous protocols, each logic qubit is encoded in the coherent state. This protocol is based on the linear optics, which is feasible in experimental technology. This protocol may be useful in quantum information based on the C-GHZ state.
Barnett, Alex H.; Nelson, Bradley J.; Mahoney, J. Matthew
2015-09-01
We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve, the square of the wavenumber (refractive index) varies linearly in one coordinate, i.e. (Δ + E +x2) u (x1 ,x2) = 0 where E is a constant; this models quantum particles of fixed energy in a uniform gravitational field, and has broader applications to stratified media in acoustics, optics and seismology. We evaluate the fundamental solution efficiently with exponential accuracy via numerical saddle-point integration, using the truncated trapezoid rule with typically 102 nodes, with an effort that is independent of the frequency parameter E. By combining with a high-order Nyström quadrature, we are able to solve the scattering from obstacles 50 wavelengths across to 11 digits of accuracy in under a minute on a desktop or laptop.
Interpolation problem for the solutions of linear elasticity equations based on monogenic functions
Grigor'ev, Yuri; Gürlebeck, Klaus; Legatiuk, Dmitrii
2017-11-01
Interpolation is an important tool for many practical applications, and very often it is beneficial to interpolate not only with a simple basis system, but rather with solutions of a certain differential equation, e.g. elasticity equation. A typical example for such type of interpolation are collocation methods widely used in practice. It is known, that interpolation theory is fully developed in the framework of the classical complex analysis. However, in quaternionic analysis, which shows a lot of analogies to complex analysis, the situation is more complicated due to the non-commutative multiplication. Thus, a fundamental theorem of algebra is not available, and standard tools from linear algebra cannot be applied in the usual way. To overcome these problems, a special system of monogenic polynomials the so-called Pseudo Complex Polynomials, sharing some properties of complex powers, is used. In this paper, we present an approach to deal with the interpolation problem, where solutions of elasticity equations in three dimensions are used as an interpolation basis.
Solution to the Diffusion equation for multi groups in X Y geometry using Linear Perturbation theory
International Nuclear Information System (INIS)
Mugica R, C.A.
2004-01-01
Diverse methods exist to solve numerically the neutron diffusion equation for several energy groups in stationary state among those that highlight those of finite elements. In this work the numerical solution of this equation is presented using Raviart-Thomas nodal methods type finite element, the RT0 and RT1, in combination with iterative techniques that allow to obtain the approached solution in a quick form. Nevertheless the above mentioned, the precision of a method is intimately bound to the dimension of the approach space by cell, 5 for the case RT0 and 12 for the RT1, and/or to the mesh refinement, that makes the order of the problem of own value to solve to grow considerably. By this way if it wants to know an acceptable approach to the value of the effective multiplication factor of the system when this it has experimented a small perturbation it was appeal to the Linear perturbation theory with which is possible to determine it starting from the neutron flow and of the effective multiplication factor of the not perturbed case. Results are presented for a reference problem in which a perturbation is introduced in an assemble that simulates changes in the control bar. (Author)
Ladiges, Daniel R.; Sader, John E.
2018-05-01
Nanomechanical resonators and sensors, operated in ambient conditions, often generate low-Mach-number oscillating rarefied gas flows. Cercignani [C. Cercignani, J. Stat. Phys. 1, 297 (1969), 10.1007/BF01007482] proposed a variational principle for the linearized Boltzmann equation, which can be used to derive approximate analytical solutions of steady (time-independent) flows. Here we extend and generalize this principle to unsteady oscillatory rarefied flows and thus accommodate resonating nanomechanical devices. This includes a mathematical approach that facilitates its general use and allows for systematic improvements in accuracy. This formulation is demonstrated for two canonical flow problems: oscillatory Couette flow and Stokes' second problem. Approximate analytical formulas giving the bulk velocity and shear stress, valid for arbitrary oscillation frequency, are obtained for Couette flow. For Stokes' second problem, a simple system of ordinary differential equations is derived which may be solved to obtain the desired flow fields. Using this framework, a simple and accurate formula is provided for the shear stress at the oscillating boundary, again for arbitrary frequency, which may prove useful in application. These solutions are easily implemented on any symbolic or numerical package, such as Mathematica or matlab, facilitating the characterization of flows produced by nanomechanical devices and providing insight into the underlying flow physics.
Directory of Open Access Journals (Sweden)
Luo Li-Qin
2016-01-01
Full Text Available In this paper, we investigate the value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations, and obtain the results on the relations between the order of the solutions and the convergence exponents of the zeros, poles, a-points and small function value points of the solutions, which show the relations in the case of non-homogeneous equations are sharper than the ones in the case of homogeneous equations.
International Nuclear Information System (INIS)
Solaimani, M.; Morteza, Izadifard; Arabshahi, H.; Reza, Sarkardehi Mohammad
2013-01-01
In this work, we have studied the effect of the number of the wells, in a multiple quantum wells structure with constant total effective length, on the optical properties of multiple quantum wells like the absorption coefficient and the refractive index by means of compact density matrix approach. GaAs/Al x Ga (1−x) As multiple quantum wells systems was selected as an example. Besides, the effect of varying number of wells on the subband energies, wave functions, number of bound states, and the Fermi energy have been also investigated. Our calculation revealed that the number of wells in a multiple quantum well is a criterion with which we can control the amount of nonlinearity. This study showed that for the third order refractive index change there is two regimes of variations and the critical well number was six. In our calculations, we have used the same wells and barrier thicknesses to construct the multiple quantum wells system. - Highlights: ► OptiOptical Non-Linear. ► Total Effective Length. ► Multiple Quantum Wells System - genetic algorithm ► Schrödinger equation solution. ► Nanostructure.
Silicon Photonics: All-Optical Devices for Linear and Nonlinear Applications
Driscoll, Jeffrey B.
Silicon photonics has grown rapidly since the first Si electro-optic switch was demonstrated in 1987, and the field has never grown more quickly than it has over the past decade, fueled by milestone achievements in semiconductor processing technologies for low loss waveguides, high-speed Si modulators, Si lasers, Si detectors, and an enormous toolbox of passive and active integrated devices. Silicon photonics is now on the verge of major commercialization breakthroughs, and optical communication links remain the force driving integrated and Si photonics towards the first commercial telecom and datacom transceivers; however other potential and future applications are becoming uncovered and refined as researchers reveal the benefits of manipulating photons on the nanoscale. This thesis documents an exploration into the unique guided-wave and nonlinear properties of deeply-scaled high-index-contrast sub-wavelength Si waveguides. It is found that the tight confinement inherent to single-mode channel waveguides on the silicon-on-insulator platform lead to a rich physics, which can be leveraged for new devices extending well beyond simple passive interconnects and electro-optic devices. The following chapters will concentrate, in detail, on a number of unique physical features of Si waveguides and extend these attributes towards new and interesting devices. Linear optical properties and nonlinear optical properties are investigated, both of which are strongly affected by tight optical confinement of the guided waveguide modes. As will be shown, tight optical confinement directly results in strongly vectoral modal components, where the electric and magnetic fields of the guided modes extend into all spatial dimensions, even along the axis of propagation. In fact, the longitudinal electric and magnetic field components can be just as strong as the transverse fields, directly affecting the modal group velocity and energy transport properties since the longitudinal fields
Liu, Ying; Song, Huadong; Zhu, Panpan; Lu, Hao; Tang, Qi
2017-08-01
The elasticity of erythrocytes is an important criterion to evaluate the quality of blood. This paper presents a novel research on erythrocytes' elasticity with the application of optical tweezers and the finite element method (FEM) during blood storage. In this work, the erythrocytes with different in vitro times were linearly stretched by trapping force using optical tweezers and the time dependent elasticity of erythrocytes was investigated. The experimental results indicate that the membrane shear moduli of erythrocytes increased with the increasing in vitro time, namely the elasticity was decreasing. Simultaneously, an erythrocyte shell model with two parameters (membrane thickness h and membrane shear modulus H) was built to simulate the linear stretching states of erythrocytes by the FEM, and the simulations conform to the results obtained in the experiment. The evolution process was found that the erythrocytes membrane thicknesses were decreasing. The analysis assumes that the partial proteins and lipid bilayer of erythrocyte membrane were decomposed during the in vitro preservation of blood, which results in thin thickness, weak bending resistance, and losing elasticity of erythrocyte membrane. This study implies that the FEM can be employed to investigate the inward mechanical property changes of erythrocyte in different environments, which also can be a guideline for studying the erythrocyte mechanical state suffered from different diseases.
Structural, electronic, linear, and nonlinear optical properties of ZnCdTe{sub 2} chalcopyrite
Energy Technology Data Exchange (ETDEWEB)
Ouahrani, Tarik [Laboratoire de Physique Theorique, Universite de Tlemcen, B.P. 230, Tlemcen 13000 (Algeria); Reshak, Ali H. [Institute of Physical Biology, South Bohemia University, Nove Hrady 37333 (Czech Republic); School of Microelectronic Engineering, University of Malaysia Perlis (UniMAP), Block A, Kompleks Pusat Pengajian, 02600 Arau Jejawi, Perlis (Malaysia); Khenata, R. [Laboratoire de Physique Quantique et de Modelisation Mathematique, Universite de Mascara, Mascara 29000 (Algeria); Department of Physics and Astronomy, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451 (Saudi Arabia); Baltache, H.; Amrani, B. [Laboratoire de Physique Quantique et de Modelisation Mathematique, Universite de Mascara, Mascara 29000 (Algeria); Bouhemadou, A. [Department of Physics and Astronomy, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451 (Saudi Arabia); Faculty of Sciences, Department of Physics, University of Setif, Setif 19000 (Algeria)
2011-03-15
We report results of first-principles density functional calculations using the full-potential linearized augmented plane wave method. The generalized gradient approximation (GGA) and the Engel-Vosko-GGA (EV-GGA) formalism were used for the exchange-correlation energy to calculate the structural, electronic, linear, and nonlinear optical properties of the chalcopyrite ZnCdTe{sub 2} compound. The valence band maximum and the conduction band minimum are located at the {gamma}-point, resulting in a direct band gap of about 0.71 eV for GGA and 1.29 eV for EV-GGA. The results of bulk properties, such as lattice parameters (a, c, and u), bulk modulus B, and its pressure derivative B' are evaluated. The optical properties of this compound, namely the real and the imaginary parts of the dielectric function, reflectivity, and refractive index, show a considerable anisotropy as a consequence ZnCdTe{sub 2} posseses a strong birefringence. In addition, the extinction coefficient, the electron energy loss function, and the nonlinear susceptibility are calculated and their spectra are analyzed. (Copyright copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Mancosu, Pietro; Fogliata, Antonella; Stravato, Antonella; Tomatis, Stefano; Cozzi, Luca; Scorsetti, Marta
2016-01-01
Frameless stereotactic radiosurgery (SRS) requires dedicated systems to monitor the patient position during the treatment to avoid target underdosage due to involuntary shift. The optical surface monitoring system (OSMS) is here evaluated in a phantom-based study. The new EDGE linear accelerator from Varian (Varian, Palo Alto, CA) integrates, for cranial lesions, the common cone beam computed tomography (CBCT) and kV-MV portal images to the optical surface monitoring system (OSMS), a device able to detect real-time patient׳s face movements in all 6 couch axes (vertical, longitudinal, lateral, rotation along the vertical axis, pitch, and roll). We have evaluated the OSMS imaging capability in checking the phantoms׳ position and monitoring its motion. With this aim, a home-made cranial phantom was developed to evaluate the OSMS accuracy in 4 different experiments: (1) comparison with CBCT in isocenter location, (2) capability to recognize predefined shifts up to 2° or 3cm, (3) evaluation at different couch angles, (4) ability to properly reconstruct the surface when the linac gantry visually block one of the cameras. The OSMS system showed, with a phantom, to be accurate for positioning in respect to the CBCT imaging system with differences of 0.6 ± 0.3mm for linear vector displacement, with a maximum rotational inaccuracy of 0.3°. OSMS presented an accuracy of 0.3mm for displacement up to 1cm and 1°, and 0.5mm for larger displacements. Different couch angles (45° and 90°) induced a mean vector uncertainty < 0.4mm. Coverage of 1 camera produced an uncertainty < 0.5mm. Translations and rotations of a phantom can be accurately detect with the optical surface detector system. Copyright © 2016 American Association of Medical Dosimetrists. Published by Elsevier Inc. All rights reserved.
Heralded creation of photonic qudits from parametric down-conversion using linear optics
Yoshikawa, Jun-ichi; Bergmann, Marcel; van Loock, Peter; Fuwa, Maria; Okada, Masanori; Takase, Kan; Toyama, Takeshi; Makino, Kenzo; Takeda, Shuntaro; Furusawa, Akira
2018-05-01
We propose an experimental scheme to generate, in a heralded fashion, arbitrary quantum superpositions of two-mode optical states with a fixed total photon number n based on weakly squeezed two-mode squeezed state resources (obtained via weak parametric down-conversion), linear optics, and photon detection. Arbitrary d -level (qudit) states can be created this way where d =n +1 . Furthermore, we experimentally demonstrate our scheme for n =2 . The resulting qutrit states are characterized via optical homodyne tomography. We also discuss possible extensions to more than two modes concluding that, in general, our approach ceases to work in this case. For illustration and with regards to possible applications, we explicitly calculate a few examples such as NOON states and logical qubit states for quantum error correction. In particular, our approach enables one to construct bosonic qubit error-correction codes against amplitude damping (photon loss) with a typical suppression of √{n }-1 losses and spanned by two logical codewords that each correspond to an n -photon superposition for two bosonic modes.
Circularly polarized light to study linear magneto-optics for ferrofluids: θ-scan technique
Meng, Xiangshen; Huang, Yan; He, Zhenghong; Lin, Yueqiang; Liu, Xiaodong; Li, Decai; Li, Jian; Qiu, Xiaoyan
2018-06-01
Circularly polarized light can be divided into two vertically linearly polarized light beams with ±π/2 phase differences. In the presence of an external magnetic field, when circularly polarized light travels through a ferrofluid film, whose thickness is no more than that of λ/4 plate, magneto-optical, magnetic birefringence and dichroism effects cause the transmitted light to behave as elliptically polarized light. Using angular scan by a continuously rotating polarizer as analyzer, the angular (θ) distribution curve of relative intensity (T) corresponding to elliptically polarized light can be measured. From the T ‑ θ curve having ellipsometry, the parameters such as the ratio of short to long axis, and angular orientation of the long axis to the vertical field direction can be obtained. Thus, magnetic birefringence and dichroism can be probed simultaneously by measuring magneto-optical, positive or negative birefringence and dichroism features from the transmission mode. The proposed method is called θ-scan technique, and can accurately determine sample stability, magnetic field direction, and cancel intrinsic light source ellipticity. This study may be helpful to further research done to ferrofluids and other similar colloidal samples with anisotropic optics.
Analogy between optically driven injection-locked laser diodes and driven damped linear oscillators
International Nuclear Information System (INIS)
Murakami, Atsushi; Shore, K. Alan
2006-01-01
An analytical study of optically driven laser diodes (LDs) has been undertaken to meet the requirement for a theoretical treatment for chaotic drive and synchronization occurring in the injection-locked LDs with strong injection. A small-signal analysis is performed for the sets of rate equations for the injection-locked LDs driven by a sinusoidal optical signal. In particular, as a model of chaotic driving signals from LD dynamics, an optical signal caused by direct modulation to the master LD is assumed, oscillating both in field amplitude and phase as is the case with chaotic driving signals. Consequently, we find conditions that allow reduction in the degrees of freedom of the driven LD. Under these conditions, the driven response is approximated to a simple form which is found to be equivalent to driven damped linear oscillators. The validity of the application of this theory to previous work on the synchronization of chaos and related phenomena occurring in the injection-locked LDs is demonstrated
Side Effect of Good's Buffers on Optical Properties of Gold Nanoparticle Solutions
DEFF Research Database (Denmark)
Engelbrekt, Christian; Wagner, Michal; Undall-Behrend Christiansen, Mikkel
2016-01-01
spectroscopy. Distinct absorption features at ca. 290 and 360 nm and fluorescence emission in the 408-484 nm range are observed in filtered AuNP-free solutions. Electrochemical oxidation of these buffers generates similar optical properties, suggesting that the degradation products of the buffers contribute...... to the optical properties of AuNP solutions. This work indicates deeper evaluation of fluorescence signals based on metal NPs or NCs is needed....
A linear laser-driver array for optical transmission in the LHC experiments
Cervelli, G; Moreira, P; Vasey, F
2000-01-01
A 4-way linear laser driver has been designed and implemented in a commercial 0.25 mu m CMOS technology. The full-custom IC is intended for analogue and digital data transmission as part of the 50 000 optical fibre links of the CMS particle tracking system. Intrinsic radiation tolerance and specific design methodologies enable the device to operate over 10 years in the harsh radiation environment of the innermost LHC detectors. Although optimised for analogue operation the driver is compatible with LVDS digital signalling. A combination of linearization methods achieves good analogue performance (8-bit equivalent dynamic range with a bandwidth of 100 MHz), while maintaining wide input common-mode range (+or-350 mV) and limited power dissipation. The linearly amplified signal is added to a DC current, which can be set over a wide range (-60 mA to +60 mA). The latter capability allows tracking of changes in laser threshold due to ageing or radiation damage. The driver gain and bias current are set via a serial ...
International Nuclear Information System (INIS)
Karimi, M.J.; Rezaei, G.; Nazari, M.
2014-01-01
Based on the effective mass and parabolic one band approximations, simultaneous effects of the geometrical size, hydrogenic impurity, hydrostatic pressure, and temperature on the intersubband optical absorption coefficients and refractive index changes in multilayered spherical quantum dots are studied. Energy eigenvalues and eigenvectors are calculated using the fourth-order Runge–Kutta method and optical properties are obtained using the compact density matrix approach. The results indicate that the hydrogenic impurity, hydrostatic pressure, temperature and geometrical parameters such as the well and barrier widths have a great influence on the linear, the third-order nonlinear and the total optical absorption coefficients and refractive index changes. -- Highlights: • Hydrogenic impurity effects on the optical properties of a MSQD are investigated. • Hydrostatic pressure and temperature effects are also studied. • Hydrogenic impurity has a great influence on the linear and nonlinear ACs and RICs. • Hydrostatic pressure and temperature change the linear and nonlinear ACs and RICs
Energy Technology Data Exchange (ETDEWEB)
Fuentes, Carlos [Instituto Mexicano de Tecnologia del Agua, Jiutepec, Morelos (Mexico); Parlangue, Jean-Yves [Departamento de Agricultura e Ingenieria Biologica (United States); Haverkamp, Randel; Vauclin, Michael [Laboratorio de Estudio de las Transferencias en Hidrologia y Medio ambiente (France)
2001-12-01
The exact solution of the one-dimensional vertical infiltration equation is deducted, when the hydraulic diffusivity is considered constant and the hydraulic conductivity is a combination of both a linear and quadratic functions of the soil water content. This quasi-linear solution includes as particular cases, both the classical solution known as linear soil and the Knight solution. The cumulative infiltrated water as a function of time provided by the quasi-linear solution has been compared with the cumulative infiltrated water obtained from the numerical solution of the Richards equation on three different soils of contrasting hydrodynamic properties. The good agreement between the two solutions has shown that the quasi-linear solution can be used on soils where the accepted hypothesis, on hydraulic diffusivity and hydraulic conductivity, for its deduction is not satisfied. [Spanish] Se deduce la solucion exacta de la ecuacion de la infiltracion unidimensional vertical cuando la difusividad hidraulica es considerada constante y la conductividad hidraulica es una combinacion de una funcion lineal y una cuadratica del contenido volumetrico de agua. Esta solucion cuasi-lineal de la infiltracion contiene, como casos particulares, la solucion clasica conocida como suelo lineal y la solucion de Knight. La lamina infiltrada acumulada en funcion del tiempo proporcionada por la solucion cuasi-lineal se ha comparado con la lamina infiltrada proporcionada por la solucion numerica de la ecuacion de Richards en tres suelos de propiedades hidrodinamicas contrastantes. El buen acuerdo entre las laminas infiltradas ha mostrado que la solucion cuasi-lineal puede utilizarse en suelos donde la difusividad y la conductividad hidraulicas no satisfacen los supuestos de la deduccion.
Buret, Thomas; Ramecourt, David; Napolitano, Fabien
2017-11-01
The aim of this article is to present how the qualification of the Fiber Optic Gyroscope technology from IXSEA has been achieved through the qualification of a large range of optical devices and related manufacturing processes. These qualified optical devices and processes, that are now fully mastered by IXSEA through vertical integration of the technology, can be used for other space optical sensors. The example of the SWARM project will be discussed.
Yahia, I. S.; Ganesh, V.; Shkir, M.; AlFaify, S.; Zahran, H. Y.; Algarni, H.; Abutalib, M. M.; Al-Ghamdi, Attieh A.; El-Naggar, A. M.; AlBassam, A. M.
2016-09-01
In the current work, the authors present the systematic study on linear and nonlinear optical properties of Copper-phathalocyanine thin film deposited by thermal evaporation system for the first time. The thickness of the prepared thin film was measured and found to be ~300 nm. X-ray diffraction and AFM study confirms that the prepared thin film possess good quality. The orientation of the grown thin film is found to be along (100). UV-vis-NIR study shows that the deposited thin film is highly transparent (>80%) in the wavelength range of 700-2500 nm. Further, the recorded optical data was used to determine the various linear and nonlinear optical parameters. The calculated value of refractive index is found to be in the range of 0.4-1.0. The direct and indirect band gap value is found to be 2.9 and 3.25 eV, respectively. The value of linear and nonlinear susceptibilities is found to be in order of 10-12. The higher value of linear and nonlinear parameters makes it suitable for optoelectronic applications.
Energy Technology Data Exchange (ETDEWEB)
Yahia, I.S. [Nano-Science & Semiconductor Labs, Metallurgical Lab., Department of Physics, Faculty of Education, Ain Shams University, Roxy, Cairo (Egypt); Advanced Functional Materials & Optoelectronic Laboratory (AFMOL), Department of Physics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha (Saudi Arabia); Ganesh, V. [Advanced Functional Materials & Optoelectronic Laboratory (AFMOL), Department of Physics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha (Saudi Arabia); Shkir, M., E-mail: shkirphysics@gmail.com [Advanced Functional Materials & Optoelectronic Laboratory (AFMOL), Department of Physics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha (Saudi Arabia); AlFaify, S. [Advanced Functional Materials & Optoelectronic Laboratory (AFMOL), Department of Physics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha (Saudi Arabia); Zahran, H.Y. [Nano-Science & Semiconductor Labs, Metallurgical Lab., Department of Physics, Faculty of Education, Ain Shams University, Roxy, Cairo (Egypt); Advanced Functional Materials & Optoelectronic Laboratory (AFMOL), Department of Physics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha (Saudi Arabia); Algarni, H. [Advanced Functional Materials & Optoelectronic Laboratory (AFMOL), Department of Physics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha (Saudi Arabia); Abutalib, M.M.; Al-Ghamdi, Attieh A. [Centre of Nanotechnology, Physics Department-Faculty of Science-AL Faisaliah Campus, King Abdulaziz University, Jeddah (Saudi Arabia); El-Naggar, A.M.; AlBassam, A.M. [Research Chair of Exploitation of Renewable Energy Applications in Saudi Arabia, Physics & Astronomy Dept., College of Science, King Saud University, P.O. Box 2455, Riyadh 11451 (Saudi Arabia)
2016-09-01
In the current work, the authors present the systematic study on linear and nonlinear optical properties of Copper-phathalocyanine thin film deposited by thermal evaporation system for the first time. The thickness of the prepared thin film was measured and found to be ~300 nm. X-ray diffraction and AFM study confirms that the prepared thin film possess good quality. The orientation of the grown thin film is found to be along (100). UV–vis-NIR study shows that the deposited thin film is highly transparent (>80%) in the wavelength range of 700–2500 nm. Further, the recorded optical data was used to determine the various linear and nonlinear optical parameters. The calculated value of refractive index is found to be in the range of 0.4–1.0. The direct and indirect band gap value is found to be 2.9 and 3.25 eV, respectively. The value of linear and nonlinear susceptibilities is found to be in order of 10{sup −12}. The higher value of linear and nonlinear parameters makes it suitable for optoelectronic applications.
Falvo, Cyril
2018-02-01
The theory of linear and non-linear infrared response of vibrational Holstein polarons in one-dimensional lattices is presented in order to identify the spectral signatures of self-trapping phenomena. Using a canonical transformation, the optical response is computed from the small polaron point of view which is valid in the anti-adiabatic limit. Two types of phonon baths are considered: optical phonons and acoustical phonons, and simple expressions are derived for the infrared response. It is shown that for the case of optical phonons, the linear response can directly probe the polaron density of states. The model is used to interpret the experimental spectrum of crystalline acetanilide in the C=O range. For the case of acoustical phonons, it is shown that two bound states can be observed in the two-dimensional infrared spectrum at low temperature. At high temperature, analysis of the time-dependence of the two-dimensional infrared spectrum indicates that bath mediated correlations slow down spectral diffusion. The model is used to interpret the experimental linear-spectroscopy of model α-helix and β-sheet polypeptides. This work shows that the Davydov Hamiltonian cannot explain the observations in the NH stretching range.
Microrheology of concentrated DNA solutions using optical tweezers
Indian Academy of Sciences (India)
. In this work, we report the determination of microrheological properties of concentrated, double-stranded calf thymus DNA (CT-DNA) solutions using passive, laser-scattering based particle-tracking methodology. From power spectral analysis, ...
Directory of Open Access Journals (Sweden)
Chun-Fu Chen
2014-03-01
Full Text Available Linear analytical study on the mechanical sensitivity in large deflection of unsymmetrically layered and laterally loaded piezoelectric plate under pretension is conducted. von Karman plate theory for large deflection is utilized but extended to the case of an unsymmetrically layered plate embedded with a piezoelectric layer. The governing equations thus obtained are simplified by omitting the arising nonlinear terms, yielding a Bessel or modified Bessel equation for the lateral slope. Depending on the relative magnitude of the piezoelectric effect, for both cases, analytical solutions of various geometrical responses are developed and formulated via Bessel and modified Bessel functions. The associated ultimate radial stresses are further derived following lamina constitutive law to evaluate the mechanical sensitivity of the considered plate. For a nearly monolithic plate under a very low applied voltage, the results are in good agreement with those for a single-layered case due to pure mechanical load available in literature, and thus the present approach is checked. For a two-layered unsymmetric plate made of typical silicon-based materials, a sound piezoelectric effect is illustrated particularly in a low pretension condition.
Lattice cluster theory of associating polymers. I. Solutions of linear telechelic polymer chains.
Dudowicz, Jacek; Freed, Karl F
2012-02-14
The lattice cluster theory (LCT) for the thermodynamics of a wide array of polymer systems has been developed by using an analogy to Mayer's virial expansions for non-ideal gases. However, the high-temperature expansion inherent to the LCT has heretofore precluded its application to systems exhibiting strong, specific "sticky" interactions. The present paper describes a reformulation of the LCT necessary to treat systems with both weak and strong, "sticky" interactions. This initial study concerns solutions of linear telechelic chains (with stickers at the chain ends) as the self-assembling system. The main idea behind this extension of the LCT lies in the extraction of terms associated with the strong interactions from the cluster expansion. The generalized LCT for sticky systems reduces to the quasi-chemical theory of hydrogen bonding of Panyioutou and Sanchez when correlation corrections are neglected in the LCT. A diagrammatic representation is employed to facilitate the evaluation of the corrections to the zeroth-order approximation from short range correlations. © 2012 American Institute of Physics
Adding salt to a surfactant solution: Linear rheological response of the resulting morphologies
Energy Technology Data Exchange (ETDEWEB)
Gaudino, Danila; Pasquino, Rossana, E-mail: r.pasquino@unina.it; Grizzuti, Nino [DICMaPI, Università degli Studi di Napoli Federico II, P.le Tecchio 80, 80125 Napoli (Italy)
2015-11-15
The micellar system composed of Cetylpyridinium Chloride-Sodium Salicylate (CPyCl-NaSal) in brine aqueous solutions has been studied by systematically changing the salt concentration, in order to investigate the rheology of the arising morphologies. In particular, the zero-shear viscosity and the linear viscoelastic response have been measured as a function of the NaSal concentration (with [CPyCl] = 100 mM). The Newtonian viscosity shows a nonmonotonic dependence upon concentration, passing through a maximum at NaSal/CPyCl ≈ 0.6, and eventually dropping at higher salt concentrations. The progressive addition of salt determines first a transition from a Newtonian to a purely Maxwell-like behavior as the length of the micelles significantly increases. Beyond the peak viscosity, the viscoelastic data show two distinct features. On the one hand, the main relaxation time of the system strongly decreases, while the plateau modulus remains essentially constant. Calculations based on the rheological data show that, as the binding salt concentration increases, there is a decrease in micelles breaking rate and a decrease in their average length. On the other hand, in the same concentration region, a low-frequency elastic plateau is measured. Such a plateau is considered as the signature of a tenuous, but persistent branched network, whose existence is confirmed by cryo-transmission electron microscopy images.
Experimental investigation of a four-qubit linear-optical quantum logic circuit.
Stárek, R; Mičuda, M; Miková, M; Straka, I; Dušek, M; Ježek, M; Fiurášek, J
2016-09-20
We experimentally demonstrate and characterize a four-qubit linear-optical quantum logic circuit. Our robust and versatile scheme exploits encoding of two qubits into polarization and path degrees of single photons and involves two crossed inherently stable interferometers. This approach allows us to design a complex quantum logic circuit that combines a genuine four-qubit C(3)Z gate and several two-qubit and single-qubit gates. The C(3)Z gate introduces a sign flip if and only if all four qubits are in the computational state |1〉. We verify high-fidelity performance of this central four-qubit gate using Hofmann bounds on quantum gate fidelity and Monte Carlo fidelity sampling. We also experimentally demonstrate that the quantum logic circuit can generate genuine multipartite entanglement and we certify the entanglement with the use of suitably tailored entanglement witnesses.
Cosine bend-linear waveguide digital optical switch with parabolic heater
Yulianti, Ian; Supa'at, Abu Sahmah Mohd.; Idrus, Sevia M.; Al-hetar, Abdulaziz M.
2010-02-01
A new digital optical switch (DOS) with large branching angle and short device length that exhibits low crosstalk and low power consumption is demonstrated. The Y-branch shape was optimized by introducing constant effective refractive index difference between branches (Δ N eff) along the propagation direction through beam propagation method (BPM) scheme. To provide decreasing local branching angle that results in the improvement of the crosstalk, two modified cosine bend was introduced to form the Y-branch. The modified cosine branch was then connected to a linear branch. The heater electrode was optimized so that the temperature fields induce a constant Δ N eff to satisfy initial assumption in designing the Y-branch shape. With branching angle of 0.299° and device length of only 5 mm, the simulation shows that the device could exhibits crosstalk of -33 dB at calculated required power of only 26 mW.
Post-processing with linear optics for improving the quality of single-photon sources
International Nuclear Information System (INIS)
Berry, Dominic W; Scheel, Stefan; Myers, Casey R; Sanders, Barry C; Knight, Peter L; Laflamme, Raymond
2004-01-01
Triggered single-photon sources produce the vacuum state with non-negligible probability, but produce a much smaller multiphoton component. It is therefore reasonable to approximate the output of these photon sources as a mixture of the vacuum and single-photon states. We show that it is impossible to increase the probability for a single photon using linear optics and photodetection on fewer than four modes. This impossibility is due to the incoherence of the inputs; if the inputs were pure-state superpositions, it would be possible to obtain a perfect single-photon output. In the more general case, a chain of beam splitters can be used to increase the probability for a single photon, but at the expense of adding an additional multiphoton component. This improvement is robust against detector inefficiencies, but is degraded by distinguishable photons, dark counts or multiphoton components in the input
Spatiotemporal dynamics of Bose-Einstein condensates in linear- and circular-chain optical lattices
International Nuclear Information System (INIS)
Tsukada, N.
2002-01-01
We investigate the spatiotemporal dynamics of Bose-Einstein condensates in optical lattices that have a linear-or a circular-chain configuration with the tunneling couplings between nearest-neighbor lattice sites. A discrete nonlinear Schroedinger equation has been solved for various initial conditions and for a definite range of repulsive and attractive interatomic interactions. It is shown that the diversity of the spatiotemporal dynamics of the atomic population distribution such as a macroscopic self-trapping, bright and dark solitons, and symmetry breaking is derived from the positive and negative interatomic interactions. For the circular-chain configuration, two types of rotational modes are obtained as we introduce a definite relation for the initial phase conditions
Jiang, YuXiao; Guo, PengLiang; Gao, ChengYan; Wang, HaiBo; Alzahrani, Faris; Hobiny, Aatef; Deng, FuGuo
2017-12-01
We present an original self-error-rejecting photonic qubit transmission scheme for both the polarization and spatial states of photon systems transmitted over collective noise channels. In our scheme, we use simple linear-optical elements, including half-wave plates, 50:50 beam splitters, and polarization beam splitters, to convert spatial-polarization modes into different time bins. By using postselection in different time bins, the success probability of obtaining the uncorrupted states approaches 1/4 for single-photon transmission, which is not influenced by the coefficients of noisy channels. Our self-error-rejecting transmission scheme can be generalized to hyperentangled n-photon systems and is useful in practical high-capacity quantum communications with photon systems in two degrees of freedom.
Wang, Hong; Ren, Bao-Cang; Alzahrani, Faris; Hobiny, Aatef; Deng, Fu-Guo
2017-10-01
Hyperentanglement has significant applications in quantum information processing. Here we present an efficient hyperentanglement concentration protocol (hyper-ECP) for partially hyperentangled Bell states simultaneously entangled in polarization, spatial-mode and time-bin degrees of freedom (DOFs) with the parameter-splitting method, where the parameters of the partially hyperentangled Bell states are known to the remote parties. In this hyper-ECP, only one remote party is required to perform some local operations on the three DOFs of a photon, only the linear optical elements are considered, and the success probability can achieve the maximal value. Our hyper-ECP can be easily generalized to concentrate the N-photon partially hyperentangled Greenberger-Horne-Zeilinger states with known parameters, where the multiple DOFs have largely improved the channel capacity of long-distance quantum communication. All of these make our hyper-ECP more practical and useful in high-capacity long-distance quantum communication.
Optical fibres sensor based in the intensity switch of a linear laser with two Bragg gratings
International Nuclear Information System (INIS)
Basurto P, M.A.; Kuzin, E.A.; Archundia B, C.; Marroquin, E.; May A, M.; Cerecedo N, H.H.; Sanchez M, J.J.; Tentori S, D.; Marquez B, I.; Shliagin, M.; Miridonov, S.
2000-01-01
In this work we propose a new configuration for an optical fiber temperature sensor, based on a linear type Er-doped fiber laser. The laser cavity consists of an Er-doped fiber and two identical Bragg gratings at the fiber ends (working as reflectors). Temperature changes are detected by measuring, through one of the gratings, the intensity variations at the system's output. When the temperature of one of the Bragg gratings is modified, a wavelength shift of its spectral reflectivity is observed. Hence, the laser emission intensity of the system is modified. We present experimental results of the intensity switch observed when the temperature difference between the gratings detunes their spectral reflectance. Making use of this effect it is possible to develop limit comparators to bound the temperature range for the object under supervision. This limiting work can be performed with a high sensitivity using a very simple interrogation procedure. (Author)
Directory of Open Access Journals (Sweden)
Sukhpreet Kaur Sidhu
2014-01-01
Full Text Available The drawbacks of the existing methods to obtain the fuzzy optimal solution of such linear programming problems, in which coefficients of the constraints are represented by real numbers and all the other parameters as well as variables are represented by symmetric trapezoidal fuzzy numbers, are pointed out, and to resolve these drawbacks, a new method (named as Mehar method is proposed for the same linear programming problems. Also, with the help of proposed Mehar method, a new method, much easy as compared to the existing methods, is proposed to deal with the sensitivity analysis of the same type of linear programming problems.
Significant and variable linear polarization during the prompt optical flash of GRB 160625B.
Troja, E.; Lipunov, V. M.; Mundell, C. G.; Butler, N. R.; Watson, A. M.; Kobayashi, S.; Cenko, S. B.; Marshall, F. E.; Ricci, R.; Fruchter, A.; Wieringa, M. H.; Gorbovskoy, E. S.; Kornilov, V.; Kutyrev, A.; Lee, W. H.; Toy, V.; Tyurina, N. V.; Budnev, N. M.; Buckley, D. A. H.; González, J.; Gress, O.; Horesh, A.; Panasyuk, M. I.; Prochaska, J. X.; Ramirez-Ruiz, E.; Rebolo Lopez, R.; Richer, M. G.; Roman-Zuniga, C.; Serra-Ricart, M.; Yurkov, V.; Gehrels, N.
2017-07-01
Newly formed black holes of stellar mass launch collimated outflows (jets) of ionized matter that approach the speed of light. These outflows power prompt, brief and intense flashes of γ-rays known as γ-ray bursts (GRBs), followed by longer-lived afterglow radiation that is detected across the electromagnetic spectrum. Measuring the polarization of the observed GRB radiation provides a direct probe of the magnetic fields in the collimated jets. Rapid-response polarimetric observations of newly discovered bursts have probed the initial afterglow phase, and show that, minutes after the prompt emission has ended, the degree of linear polarization can be as high as 30 per cent - consistent with the idea that a stable, globally ordered magnetic field permeates the jet at large distances from the central source. By contrast, optical and γ-ray observations during the prompt phase have led to discordant and often controversial results, and no definitive conclusions have been reached regarding the origin of the prompt radiation or the configuration of the magnetic field. Here we report the detection of substantial (8.3 ± 0.8 per cent from our most conservative simulation), variable linear polarization of a prompt optical flash that accompanied the extremely energetic and long-lived prompt γ-ray emission from GRB 160625B. Our measurements probe the structure of the magnetic field at an early stage of the jet, closer to its central black hole, and show that the prompt phase is produced via fast-cooling synchrotron radiation in a large-scale magnetic field that is advected from the black hole and distorted by dissipation processes within the jet.
International Nuclear Information System (INIS)
Fernandes, L.; Friedlander, A.; Guedes, M.; Judice, J.
2001-01-01
This paper addresses a General Linear Complementarity Problem (GLCP) that has found applications in global optimization. It is shown that a solution of the GLCP can be computed by finding a stationary point of a differentiable function over a set defined by simple bounds on the variables. The application of this result to the solution of bilinear programs and LCPs is discussed. Some computational evidence of its usefulness is included in the last part of the paper
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.
International Nuclear Information System (INIS)
Anastassi, Z. A.; Simos, T. E.
2010-01-01
We develop a new family of explicit symmetric linear multistep methods for the efficient numerical solution of the Schroedinger equation and related problems with oscillatory solution. The new methods are trigonometrically fitted and have improved intervals of periodicity as compared to the corresponding classical method with constant coefficients and other methods from the literature. We also apply the methods along with other known methods to real periodic problems, in order to measure their efficiency.
Investigation of the in-solution relaxation of polymer optical fibre Bragg gratings
DEFF Research Database (Denmark)
Fasano, Andrea; Woyessa, Getinet; Janting, Jakob
2016-01-01
We investigate the response of PMMA microstructured polymer optical fibre Bragg gratings whenimmersed in methanol/water solutions. Overall we observe a permanent blue-shift in Bragg gratingwavelength after solvent evaporation. The main contribution in the resonance wavelength shift probably...... arisesfrom a permanent change in the size of the fibre, as already reported for high-temperature annealing ofpolymer optical fibres. As a consequence of the solution concentration dependence of the glass transitiontemperature of polymers, different methanol/water solutions lead to various degrees of frozen...
LINPACK, Subroutine Library for Linear Equation System Solution and Matrix Calculation
International Nuclear Information System (INIS)
Dongarra, J.J.
1979-01-01
: CO, SL; SGT: SL; SPT: SL; SCH: DC, UD, DD, EX; SQR: SL, DC; SSV: DC. The LINPACK package also includes a set of routines to perform basic vector operations called the Basic Linear Algebra Subprograms (BLAS). 2 - Method of solution: Gaussian elimination, Cholesky decomposition, QR, and singular value decomposition methods are used. 3 - Restrictions on the complexity of the problem: There are no subroutines for general sparse matrices or for iterative methods for very large problems
Demonstration of feed-forward control for linear optics quantum computation
International Nuclear Information System (INIS)
Pittman, T.B.; Jacobs, B.C.; Franson, J.D.
2002-01-01
One of the main requirements in linear optics quantum computing is the ability to perform single-qubit operations that are controlled by classical information fed forward from the output of single-photon detectors. These operations correspond to predetermined combinations of phase corrections and bit flips that are applied to the postselected output modes of nondeterministic quantum logic devices. Corrections of this kind are required in order to obtain the correct logical output for certain detection events, and their use can increase the overall success probability of the devices. In this paper, we report on the experimental demonstration of the use of this type of feed-forward system to increase the probability of success of a simple nondeterministic quantum logic operation from approximately (1/4) to (1/2). This logic operation involves the use of one target qubit and one ancilla qubit which, in this experiment, are derived from a parametric down-conversion photon pair. Classical information describing the detection of the ancilla photon is fed forward in real time and used to alter the quantum state of the output photon. A fiber-optic delay line is used to store the output photon until a polarization-dependent phase shift can be applied using a high-speed Pockels cell
X-ray topographic studies of organic and non-linear optical materials
International Nuclear Information System (INIS)
Halfpenny, P. J.; Sherwood, J. N.; Simpson, G. S.
1997-01-01
The flexible and non-destructive nature of X-ray topography is ideally suited to the study of large single crystals for both fundamental research and technological applications as well as the optimisation of crystal growth processes. Three examples are discussed, illustrating the application of X-ray topographic methods to non-linear optical (NLO) crystals. Synchrotron radiation section topography has been applied to the examination of large organic crystals. X-ray topography has been used to examine growth defects and the quality of crystals of m-nitroaniline (mNA) grown by the Bridgeman method. These studies allow evaluation of growth parameters together with their influence on defect density and show that in the case of mNA, remarkably low defect densities can be achieved under optimum growth conditions. Double-crystal reflection topography, with synchrotron radiation has been used to image defects intersecting the (011) faces of the inorganic NLO material potassium titanyl phosphate (KTP). X-ray images have been combined with optical microscopy and interferometry to provide valuable information on the crystal growth process
International Nuclear Information System (INIS)
Martínez-Orozco, J.C.; Mora-Ramos, M.E.; Duque, C.A.
2014-01-01
The conduction band states of GaAs-based vertically coupled double triangular quantum dots in two dimensions are investigated within the effective mass and parabolic approximation, using a diagonalization procedure to solve the corresponding Schrödinger-like equation. The effect of an externally applied static electric field is included in the calculation, and the variation of the lowest confined energy levels as a result of the change of the field strength is reported for different geometrical setups. The linear and nonlinear optical absorptions and the relative change of the refractive index, associated with the energy transition between the ground and the first excited state in the system, are studied as a function of the incident light frequency for distinct configurations of inter-dot distance and electric field intensities. The blueshift of the resonant absorption peaks is detected as a consequence of the increment in the field intensity, whereas the opposite effect is obtained from the increase of inter-dot vertical distance. It is also shown that for large enough values of the electric field there is a quenching of the optical absorption due to field-induced change of symmetry of the first excited state wavefunction, in the case of triangular dots of equal shape and size
Structural, linear and nonlinear optical properties of co-doped ZnO thin films
Shaaban, E. R.; El-Hagary, M.; Moustafa, El Sayed; Hassan, H. Shokry; Ismail, Yasser A. M.; Emam-Ismail, M.; Ali, A. S.
2016-01-01
Different compositions of Co-doped zinc oxide [(Zn(1- x)Co x O) ( x = 0, 0.02, 0.04, 0.06, 0.08 and 0.10)] thin films were evaporated onto highly clean glass substrates by thermal evaporation technique using a modified source. The structural properties investigated by X-ray diffraction revealed hexagonal wurtzite ZnO-type structure. The crystallite size of the films was found to decrease with increasing Co content. The optical characterization of the films has been carried out using spectral transmittance and reflectance obtained in the wavelength range from 300 to 2500 nm. The refractive index has been found to increase with increasing Co content. It was further found that optical energy gap decreases from 3.28 to 3.03 eV with increasing Co content from x = 0 to x = 0.10, respectively. The dispersion of refractive index has been analyzed in terms of Wemple-DiDomenico (WDD) single-oscillator model. The oscillator parameters, the single-oscillator energy ( E o), the dispersion energy ( E d), and the static refractive index ( n 0), were determined. The nonlinear refractive index of the Zn(1- x)Co x O thin films was calculated and revealed well correlation with the linear refractive index and WDD parameters which in turn depend on the density and molar volume of the system.
Energy Technology Data Exchange (ETDEWEB)
Martínez-Orozco, J.C. [Unidad Académica de Física. Universidad Autónoma de Zacatecas, Calzada Solidaridad esquina con Paseo la Bufa S/N, C.P. 98060. Zacatecas, Zac. (Mexico); Grupo de Materia Condensada-UdeA, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA, Calle 70 No. 52-21, Medellín (Colombia); Mora-Ramos, M.E. [Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Ave. Universidad 1001, CP 62209, Cuernavaca, Morelos (Mexico); Duque, C.A., E-mail: cduque@fisica.udea.edu.co [Grupo de Materia Condensada-UdeA, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA, Calle 70 No. 52-21, Medellín (Colombia)
2014-11-01
The conduction band states of GaAs-based vertically coupled double triangular quantum dots in two dimensions are investigated within the effective mass and parabolic approximation, using a diagonalization procedure to solve the corresponding Schrödinger-like equation. The effect of an externally applied static electric field is included in the calculation, and the variation of the lowest confined energy levels as a result of the change of the field strength is reported for different geometrical setups. The linear and nonlinear optical absorptions and the relative change of the refractive index, associated with the energy transition between the ground and the first excited state in the system, are studied as a function of the incident light frequency for distinct configurations of inter-dot distance and electric field intensities. The blueshift of the resonant absorption peaks is detected as a consequence of the increment in the field intensity, whereas the opposite effect is obtained from the increase of inter-dot vertical distance. It is also shown that for large enough values of the electric field there is a quenching of the optical absorption due to field-induced change of symmetry of the first excited state wavefunction, in the case of triangular dots of equal shape and size.
Sukarno; Law, Cheryl Suwen; Santos, Abel
2017-06-08
We present the first realisation of linear variable bandpass filters in nanoporous anodic alumina (NAA-LVBPFs) photonic crystal structures. NAA gradient-index filters (NAA-GIFs) are produced by sinusoidal pulse anodisation and used as photonic crystal platforms to generate NAA-LVBPFs. The anodisation period of NAA-GIFs is modified from 650 to 850 s to systematically tune the characteristic photonic stopband of these photonic crystals across the UV-visible-NIR spectrum. Then, the nanoporous structure of NAA-GIFs is gradually widened along the surface under controlled conditions by wet chemical etching using a dip coating approach aiming to create NAA-LVBPFs with finely engineered optical properties. We demonstrate that the characteristic photonic stopband and the iridescent interferometric colour displayed by these photonic crystals can be tuned with precision across the surface of NAA-LVBPFs by adjusting the fabrication and etching conditions. Here, we envisage for the first time the combination of the anodisation period and etching conditions as a cost-competitive, facile, and versatile nanofabrication approach that enables the generation of a broad range of unique LVBPFs covering the spectral regions. These photonic crystal structures open new opportunities for multiple applications, including adaptive optics, hyperspectral imaging, fluorescence diagnostics, spectroscopy, and sensing.
Su, Yonggang; Tang, Chen; Li, Biyuan; Lei, Zhenkun
2018-05-01
This paper presents a novel optical colour image watermarking scheme based on phase-truncated linear canonical transform (PT-LCT) and image decomposition (ID). In this proposed scheme, a PT-LCT-based asymmetric cryptography is designed to encode the colour watermark into a noise-like pattern, and an ID-based multilevel embedding method is constructed to embed the encoded colour watermark into a colour host image. The PT-LCT-based asymmetric cryptography, which can be optically implemented by double random phase encoding with a quadratic phase system, can provide a higher security to resist various common cryptographic attacks. And the ID-based multilevel embedding method, which can be digitally implemented by a computer, can make the information of the colour watermark disperse better in the colour host image. The proposed colour image watermarking scheme possesses high security and can achieve a higher robustness while preserving the watermark’s invisibility. The good performance of the proposed scheme has been demonstrated by extensive experiments and comparison with other relevant schemes.
Giacometti, Paolo; Diamond, Solomon G.
Diffuse optical tomography (DOT) is a functional brain imaging technique that measures cerebral blood oxygenation and blood volume changes. This technique is particularly useful in human neuroimaging measurements because of the coupling between neural and hemodynamic activity in the brain. DOT is a multichannel imaging extension of near-infrared spectroscopy (NIRS). NIRS uses laser sources and light detectors on the scalp to obtain noninvasive hemodynamic measurements from spectroscopic analysis of the remitted light. This review explains how NIRS data analysis is performed using a combination of the modified Beer-Lambert law (MBLL) and the diffusion approximation to the radiative transport equation (RTE). Laser diodes, photodiode detectors, and optical terminals that contact the scalp are the main components in most NIRS systems. Placing multiple sources and detectors over the surface of the scalp allows for tomographic reconstructions that extend the individual measurements of NIRS into DOT. Mathematically arranging the DOT measurements into a linear system of equations that can be inverted provides a way to obtain tomographic reconstructions of hemodynamics in the brain.
Directory of Open Access Journals (Sweden)
Yonghua Qu
2014-05-01
Full Text Available The canopy foliage clumping effect is primarily caused by the non-random distribution of canopy foliage. Currently, measurements of clumping index (CI by handheld instruments is typically time- and labor-intensive. We propose a low-cost and low-power automatic measurement system called Multi-point Linear Array of Optical Sensors (MLAOS, which consists of three above-canopy and nine below-canopy optical sensors that capture plant transmittance at different times of the day. Data communication between the MLAOS node is facilitated by using a ZigBee network, and the data are transmitted from the field MLAOS to a remote data server using the Internet. The choice of the electronic element and design of the MLAOS software is aimed at reducing costs and power consumption. A power consumption test showed that, when a 4000 mAH Li-ion battery is used, a maximum of 8–10 months of work can be achieved. A field experiment on a coniferous forest revealed that the CI of MLAOS may reveal a clumping effect that occurs within the canopy. In further work, measurement of the multi-scale clumping effect can be achieved by utilizing a greater number of MLAOS devices to capture the heterogeneity of the plant canopy.
X-band rf driven free electron laser driver with optics linearization
Directory of Open Access Journals (Sweden)
Yipeng Sun (孙一鹏
2014-11-01
Full Text Available In this paper, a compact hard X-ray free electron lasers (FEL design is proposed with all X-band rf acceleration and two stage bunch compression. It eliminates the need of a harmonic rf linearization section by employing optics linearization in its first stage bunch compression. Quadrupoles and sextupoles are employed in a bunch compressor one (BC1 design, in such a way that second order longitudinal dispersion of BC1 cancels the second order energy correlation in the electron beam. Start-to-end 6-D simulations are performed with all the collective effects included. Emittance growth in the horizontal plane due to coherent synchrotron radiation is investigated and minimized, to be on a similar level with the successfully operating Linac coherent light source (LCLS. At a FEL radiation wavelength of 0.15 nm, a saturation length of 40 meters can be achieved by employing an undulator with a period of 1.5 cm. Without tapering, a FEL radiation power above 10 GW is achieved with a photon pulse length of 50 fs, which is LCLS-like performance. The overall length of the accelerator plus undulator is around 250 meters which is much shorter than the LCLS length of 1230 meters. That makes it possible to build hard X-ray FEL in a laboratory with limited size.
Bounds on achievable accuracy in analog optical linear-algebra processors
Batsell, Stephen G.; Walkup, John F.; Krile, Thomas F.
1990-07-01
Upper arid lower bounds on the number of bits of accuracy achievable are determined by applying a seconth-ortler statistical model to the linear algebra processor. The use of bounds was found necessary due to the strong signal-dependence of the noise at the output of the optical linear algebra processor (OLAP). 1 1. ACCURACY BOUNDS One of the limiting factors in applying OLAPs to real world problems has been the poor achievable accuracy of these processors. Little previous research has been done on determining noise sources from a systems perspective which would include noise generated in the multiplication ard addition operations spatial variations across arrays and crosstalk. We have previously examined these noise sources and determined a general model for the output noise mean and variance. The model demonstrates a strony signaldependency in the noise at the output of the processor which has been confirmed by our experiments. 1 We define accuracy similar to its definition for an analog signal input to an analog-to-digital (ND) converter. The number of bits of accuracy achievable is related to the log (base 2) of the number of separable levels at the P/D converter output. The number of separable levels is fouri by dividing the dynamic range by m times the standard deviation of the signal a. 2 Here m determines the error rate in the P/D conversion. The dynamic range can be expressed as the
Fast-steering solutions for cubesat-scale optical communications
Kingsbury, R. W.; Nguyen, T.; Riesing, K.; Cahoy, K.
2017-11-01
We describe the design of a compact free-space optical communications module for use on a nanosatellite and present results from a detailed trade study to select an optical fine steering mechanism compatible with our stringent size, weight and power (SWaP) constraints. This mechanism is an integral component of the compact free-space optical communications system that is under development at the MIT Space Systems Laboratory [1]. The overall goal of this project is to develop a laser communications (lasercom) payload that fits within the SWaP constraints of a typical ``3U'' CubeSat. The SWaP constraints for the entire lasercom payload are 5 cm × 10 cm × 10 cm, 600 g and 10W. Although other efforts are underway to qualify MEMS deformable mirrors for use in CubeSats [2], there has been very little work towards qualifying tip-tilt MEMS mirrors [3]. Sec. II provides additional information on how the fast steering mechanism is used in our lasercom system. Performance requirements and desirable traits of the mechanism are given. In Sec. III we describe the various types of compact tip-tilt mirrors that are commercially available as well as the justification for selecting a MEMS-based device for our application. Sec. IV presents an analysis of the device's transfer function characteristics and ways of predicting this behavior that are suitable for use in the control processor. This analysis is based upon manufacturer-provided test data which was collected at standard room conditions. In the final section, we describe on-going work to build a testbed that will be used to measure device performance in a thermal chamber.
Refraction at a curved dielectric interface - Geometrical optics solution
Lee, S.-W.; Sheshadri, M. S.; Mittra, R.; Jamnejad, V.
1982-01-01
The transmission of a spherical or plane wave through an arbitrarily curved dielectric interface is solved by the geometrical optics theory. The transmitted field is proportional to the product of the conventional Fresnel's transmission coefficient and a divergence factor (DF), which describes the cross-sectional variation (convergence or divergence) of a ray pencil as the latter propagates in the transmitted region. The factor DF depends on the incident wavefront, the curvatures of the interface, and the relative indices of the two media. Explicit matrix formulas for calculating DF are given, and its physical significance is illustrated via examples.
Naganthran, Kohilavani; Nazar, Roslinda; Pop, Ioan
2018-05-01
This study investigated the influence of the non-linearly stretching/shrinking sheet on the boundary layer flow and heat transfer. A proper similarity transformation simplified the system of partial differential equations into a system of ordinary differential equations. This system of similarity equations is then solved numerically by using the bvp4c function in the MATLAB software. The generated numerical results presented graphically and discussed in the relevance of the governing parameters. Dual solutions found as the sheet stretched and shrunk in the horizontal direction. Stability analysis showed that the first solution is physically realizable whereas the second solution is not practicable.
Energy Technology Data Exchange (ETDEWEB)
Nygaard, K
1967-12-15
The numerical deconvolution of spectra is equivalent to the solution of a (large) system of linear equations with a matrix which is not necessarily a square matrix. The demand that the square sum of the residual errors shall be minimum is not in general sufficient to ensure a unique or 'sound' solution. Therefore other demands which may include the demand for minimum square errors are introduced which lead to 'sound' and 'non-oscillatory' solutions irrespective of the shape of the original matrix and of the determinant of the matrix of the normal equations.
Ryo, Ikehata
Uniform energy and L2 decay of solutions for linear wave equations with localized dissipation will be given. In order to derive the L2-decay property of the solution, a useful device whose idea comes from Ikehata-Matsuyama (Sci. Math. Japon. 55 (2002) 33) is used. In fact, we shall show that the L2-norm and the total energy of solutions, respectively, decay like O(1/ t) and O(1/ t2) as t→+∞ for a kind of the weighted initial data.
Directory of Open Access Journals (Sweden)
Dauda GuliburYAKUBU
2012-12-01
Full Text Available Accurate solutions to initial value systems of ordinary differential equations may be approximated efficiently by Runge-Kutta methods or linear multistep methods. Each of these has limitations of one sort or another. In this paper we consider, as a middle ground, the derivation of continuous general linear methods for solution of stiff systems of initial value problems in ordinary differential equations. These methods are designed to combine the advantages of both Runge-Kutta and linear multistep methods. Particularly, methods possessing the property of A-stability are identified as promising methods within this large class of general linear methods. We show that the continuous general linear methods are self-starting and have more ability to solve the stiff systems of ordinary differential equations, than the discrete ones. The initial value systems of ordinary differential equations are solved, for instance, without looking for any other method to start the integration process. This desirable feature of the proposed approach leads to obtaining very high accuracy of the solution of the given problem. Illustrative examples are given to demonstrate the novelty and reliability of the methods.
International Nuclear Information System (INIS)
Phan Thanh An; Phan Le Na; Ngo Quoc Chung
2004-05-01
We describe a practical implementation for finding parametric domain for asymptotic stability with probability one of zero solution of linear Ito stochastic differential equations based on Korenevskij and Mitropolskij's sufficient condition and our sufficient conditions. Numerical results show that all of these sufficient conditions are crucial in the implementation. (author)
International Nuclear Information System (INIS)
Chen, Haixia; Zhang, Jing
2007-01-01
We propose a scheme for continuous-variable quantum cloning of coherent states with phase-conjugate input modes using linear optics. The quantum cloning machine yields M identical optimal clones from N replicas of a coherent state and N replicas of its phase conjugate. This scheme can be straightforwardly implemented with the setups accessible at present since its optical implementation only employs simple linear optical elements and homodyne detection. Compared with the original scheme for continuous-variable quantum cloning with phase-conjugate input modes proposed by Cerf and Iblisdir [Phys. Rev. Lett. 87, 247903 (2001)], which utilized a nondegenerate optical parametric amplifier, our scheme loses the output of phase-conjugate clones and is regarded as irreversible quantum cloning
Thach, Trung Thanh; Shin, Donghyuk; Han, Seungsu; Lee, Sangho
2016-04-01
The conformational flexibility of linkage-specific polyubiquitin chains enables ubiquitylated proteins and their receptors to be involved in a variety of cellular processes. Linear or Met1-linked polyubiquitin chains, associated with nondegradational cellular signalling pathways, have been known to adopt multiple conformations from compact to extended conformations. However, the extent of such conformational flexibility remains open. Here, the crystal structure of linear Ub2 was determined in a more compact conformation than that of the previously known structure (PDB entry 3axc). The two structures differ significantly from each other, as shown by an r.m.s.d. between C(α) atoms of 3.1 Å. The compactness of the linear Ub2 structure in comparison with PDB entry 3axc is supported by smaller values of the radius of gyration (Rg; 18 versus 18.9 Å) and the maximum interatomic distance (Dmax; 55.5 versus 57.8 Å). Extra intramolecular hydrogen bonds formed among polar residues between the distal and proximal ubiquitin moieties seem to contribute to stabilization of the compact conformation of linear Ub2. An ensemble of three semi-extended and extended conformations of linear Ub2 was also observed by small-angle X-ray scattering (SAXS) analysis in solution. In addition, the conformational heterogeneity in linear polyubiquitin chains is clearly manifested by SAXS analyses of linear Ub3 and Ub4: at least three distinct solution conformations are observed in each chain, with the linear Ub3 conformations being compact. The results expand the extent of conformational space of linear polyubiquitin chains and suggest that changes in the conformational ensemble may be pivotal in mediating multiple signalling pathways.
International Nuclear Information System (INIS)
Theodorakis, Stavros
2003-01-01
We emulate the cubic term Ψ 3 in the nonlinear Schroedinger equation by a piecewise linear term, thus reducing the problem to a set of uncoupled linear inhomogeneous differential equations. The resulting analytic expressions constitute an excellent approximation to the exact solutions, as is explicitly shown in the case of the kink, the vortex, and a δ function trap. Such a piecewise linear emulation can be used for any differential equation where the only nonlinearity is a Ψ 3 one. In particular, it can be used for the nonlinear Schroedinger equation in the presence of harmonic traps, giving analytic Bose-Einstein condensate solutions that reproduce very accurately the numerically calculated ones in one, two, and three dimensions
International Nuclear Information System (INIS)
Goncalves, Glenio A.; Bodmann, Bardo; Bogado, Sergio; Vilhena, Marco T.
2008-01-01
Analytical solutions for neutron transport in cylindrical geometry is available for isotropic problems, but to the best of our knowledge for anisotropic problems are not available, yet. In this work, an analytical solution for the neutron transport equation in an infinite cylinder assuming anisotropic scattering is reported. Here we specialize the solution, without loss of generality, for the linearly anisotropic problem using the combined decomposition and HTS N methods. The key feature of this method consists in the application of the decomposition method to the anisotropic problem by virtue of the fact that the inverse of the operator associated to isotropic problem is well know and determined by the HTS N approach. So far, following the idea of the decomposition method, we apply this operator to the integral term, assuming that the angular flux appearing in the integrand is considered to be equal to the HTS N solution interpolated by polynomial considering only even powers. This leads to the first approximation for an anisotropic solution. Proceeding further, we replace this solution for the angular flux in the integral and apply again the inverse operator for the isotropic problem in the integral term and obtain a new approximation for the angular flux. This iterative procedure yields a closed form solution for the angular flux. This methodology can be generalized, in a straightforward manner, for transport problems with any degree of anisotropy. For the sake of illustration, we report numerical simulations for linearly anisotropic transport problems. (author)
Corsetti, James A; Green, William E; Ellis, Jonathan D; Schmidt, Greg R; Moore, Duncan T
2016-10-10
Characterizing the thermal properties of optical materials is necessary for understanding how to design an optical system for changing environmental conditions. A method is presented for simultaneously measuring both the linear coefficient of thermal expansion and the temperature-dependent refractive index coefficient of a sample interferometrically in air. Both the design and fabrication of the interferometer is presented as well as a discussion of the results of measuring both a steel and a CaF2 sample.
International Nuclear Information System (INIS)
Chao, A.W.; Lee, M.J.
1975-09-01
Effects upon longitudinal bunch shape in a storage ring due to linear and nonlinear potential can be calculated by finding the stationary solution to the Fokker-Planck equation for the particle distribution. Effects upon transverse bunch shape of a stored electron beam due to photon emissions and damping can be calculated by this method. It has been found that this method can also be used for a case in which the transverse modes of oscillation are coupled to the energy deviation δ. Examples of lattice elements which produce linear coupling between these oscillations are skew quadrupole magnets and solenoid magnets. For the linearly coupled case the stationary solution has been found to be given by exp (ΣΣA/sub ij/ x/sub i/x/sub j/) with x/sub i/ the canonical variables (x,p/sub x/, y, p/sub y/, δ, p/sub δ/) and A /sub ij/ some constants. The solution for the values of A /sub ij/'s will be described in this report. It will be shown that this solution can be expressed in a compact form. For simple cases, this form of solution leads directly to analytic expressions for the values of A /sub ij/'s and the bunch shape can be calculated by integrating the distribution function over some of the coordinates; for the more complex cases, it can be conveniently adapted as an algorithm for numerical evaluation. 16 refs
International Nuclear Information System (INIS)
Pouyat, D.; Couston, L.; Noire, M.H.; Davin, T.; Delage, J.; Bouzon, C.; Goutier, J.; Marty, P.
1998-01-01
In nuclear fuel reprocessing factories, an in line determination of actinides and acidity is useful to control the efficiency of the liquid-liquid extraction steps. Although molecular absorptiometric methods are very efficient at the laboratory scale, in-line analysis require to develop passive optical fibre sensor, spectral treatment, and optical fibre active sensors for ions or molecule without optical property such H + . In the first case, a specific optical fibre sensor has been developed to reduce radiological or optical contamination, and to remove the hydraulic perturbations of an intrusive technology. The optical spectrum is directly measured- through a Teflon-PFA tube. Five determination (U IV , U VI , Pu III , Pu IV and HNO 2 ) on eight different process point are achieved every 3 seconds, by using Partial Least Square (PLS) multivariate treatment based on a standards data base. For non linear interference, such as matrix effects on U VI spectrum in nitric acid media, PLS is not very efficient. A physical-chemical model is then required to get a linear relationship. For acidity measurements, an acid-sensitive dye is coated on the core of an optical fiber by the Sol-Gel process. The sensor response, proportional to the indicator protonation, is based on the evanescent wave absorption. This system is free from spectral interference, the response time is fast and measurements are reversible, even with Pu IV at 4 g/l. (author)
International Nuclear Information System (INIS)
Jia, Jingfei; Kim, Hyun K.; Hielscher, Andreas H.
2015-01-01
It is well known that radiative transfer equation (RTE) provides more accurate tomographic results than its diffusion approximation (DA). However, RTE-based tomographic reconstruction codes have limited applicability in practice due to their high computational cost. In this article, we propose a new efficient method for solving the RTE forward problem with multiple light sources in an all-at-once manner instead of solving it for each source separately. To this end, we introduce here a novel linear solver called block biconjugate gradient stabilized method (block BiCGStab) that makes full use of the shared information between different right hand sides to accelerate solution convergence. Two parallelized block BiCGStab methods are proposed for additional acceleration under limited threads situation. We evaluate the performance of this algorithm with numerical simulation studies involving the Delta–Eddington approximation to the scattering phase function. The results show that the single threading block RTE solver proposed here reduces computation time by a factor of 1.5–3 as compared to the traditional sequential solution method and the parallel block solver by a factor of 1.5 as compared to the traditional parallel sequential method. This block linear solver is, moreover, independent of discretization schemes and preconditioners used; thus further acceleration and higher accuracy can be expected when combined with other existing discretization schemes or preconditioners. - Highlights: • We solve the multiple-right-hand-side problem in DOT with a block BiCGStab method. • We examine the CPU times of the block solver and the traditional sequential solver. • The block solver is faster than the sequential solver by a factor of 1.5–3.0. • Multi-threading block solvers give additional speedup under limited threads situation.
Iterative solution of linear systems in the 20th century
Saad, Y.; Vorst, H.A. van der
2000-01-01
This paper sketches the main research developments in the area of iterative methods for solving linear systems during the 20th century. Although iterative methods for solving linear systems find their origin in the early nineteenth century (work by Gauss), the field has seen an explosion of
THE HIERARCHY OF COMPONENT FOR TASKS SOLUTION IN THE COURSE OF “LINEAR ALGEBRA”.
Directory of Open Access Journals (Sweden)
V. S. Kruglyk
2009-06-01
Full Text Available In the present article the case in point is an application of new informational technologies in the process of teaching Linear Algebra in Kherson State University. The component-oriented approach to the teaching Linear Algebra is examined as well as hierarchy of components which is used in the system and advantages of such approach in comparison with traditional approach.
Optical soliton solutions for two coupled nonlinear Schroedinger systems via Darboux transformation
International Nuclear Information System (INIS)
Zhang Haiqiang; Li Juan; Xu Tao; Zhang Yaxing; Hu Wei; Tian Bo
2007-01-01
In nonlinear optical fibers, the vector solitons can be governed by the systems of coupled nonlinear Schroedinger from polarized optical waves in an isotropic medium. Based on the Ablowitz-Kaup-Newell-Segur technology, the Darboux transformation method is successfully applied to two coupled nonlinear Schroedinger systems. With the help of symbolic computation, the bright vector one- and two-soliton solutions including one-peak and two-peak solitons are further constructed via the iterative algorithm of Darboux transformation. Through the figures for several sample solutions, the stable propagation and elastic collisions for these kinds of bright vector solitons are discussed and the possible applications are pointed out in optical communications and relevant optical experiments.In addition, the conserved quantities of such two systems, i.e., the energy, momentum and Hamiltonian, are also presented
The nonlinear Schrödinger equation singular solutions and optical collapse
Fibich, Gadi
2015-01-01
This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) solutions of the nonlinear Schrödinger equation. With great care and detail, it develops the subject including the mathematical and physical background and the history of the subject. It combines rigorous analysis, asymptotic analysis, informal arguments, numerical simulations, physical modelling, and physical experiments. It repeatedly emphasizes the relations between these approaches, and the intuition behind the results. The Nonlinear Schrödinger Equation will be useful to graduate students and researchers in applied mathematics who are interested in singular solutions of partial differential equations, nonlinear optics and nonlinear waves, and to graduate students and researchers in physics and engineering who are interested in nonlinear optics and Bose-Einstein condensates. It can be used for courses on partial differential equations, nonlinear waves, and nonlinear optics. Gadi Fib...
Lifetime of digital media: is optics the solution?
Spitz, Erich; Hourcade, Jean-Charles; Lalo", Franck
2010-01-01
While the short term and mid-term archiving of digital data and information can be handled reasonably well with modern techniques, the long term aspects of the problem (several decades or even centuries) are much more difficult to manage. The heart of the problem is the longevity of storage media, which presently does not go beyond a few years, maybe one or two decades in the best cases. In this article, we review the various strategies for long term archiving, with two main categories: active and passive. We evaluate the various recording media in terms of their longevity. We then discuss the recordable optical digital disks (RODDs) and the state of the art in this domain; the present situation is that, with the techniques that are implemented commercially, good prospects for long term archiving are not available. Nevertheless, the conceptual simplicity of RODDs could be exploited to create new recordable digital media; the improvements that are needed seem to be reachable with reasonable development effort. Since RODDs are now in strong competition with other systems (hard disks or flash memory for instance) that constantly make enormous progress, there seems to be little hope to see RODDs win the race of capacity; nevertheless, longevity could provide them with a new market, since the need for long term archiving is so pressing everywhere in the world.
Non destructive testing of uranium in solution using a portable optical fiber photometer
International Nuclear Information System (INIS)
Boisde, Gilbert; Guillot, Philippe; Monier, Jean; Perez, J.J.
1983-01-01
The portable instrument, called TELEPHOT 3 N, has be following main characteristics: - regulated light source, - optical fibers used as a light vector, - an optical probe fitted with a mirror immersed in the solution, - optical system with interference filters to balance the three measurement channels, - analog and digital absorbance measurement electronic, - associated microcomputer for automatic data acquisition and processing. The parameters and computer programs were determined by a series of measurements taken on reference solutions covering the target ranges. A mathematical model showing uranium complexes in solution leads to the solution of second degree equation. A first degree equation is sufficient for low acidities. This unit -hardware and programs- has been qualified on different uranyl nitrate solutions subject to nuclear materials control. The small minimum quantities of product required, about 25 ml, and the short response time of around 1 minute, wake at a highly practical instrument for check measurements during inspection proceedings. Similar remote measurements is planned during inspection for the glove box control of plutonium solutions. This spectrophotometry technique can be adapted for the process control of industrial solutions [fr
International Nuclear Information System (INIS)
Medeiros, Adriana S.
2009-01-01
Poly(vinylidene fluoride) [PVDF] is a semicrystalline linear homopolymer composed by the repetition of CH 2 - CF 2 monomers. The Poly(vinylidene fluoride-trifluoroethylene) [P(VDF-TrFE)] is a copolymer which is obtained with the random introduction of fluorinated CHF-CF 2 monomers in the PVDF main chain. PVDF, and also its copolymers with TrFE contents ranging from 18 to 63 wt. %, have long been studied for their striking ferroelectric properties and their applications in actuators, transducers and ferroelectric memory. Recent research work around the world have demonstrated that, for TrFE contents ranging from with 30 to 50 wt. %, the copolymer can have its ferroelectric properties modified by high doses of ionizing radiation, with the appearing of radio-induced relaxor ferroelectric features. These studies have lead us to investigate the possible use of these copolymers as high dose dosemeters, once the reported amount of induced C=C conjugated bonds after X-ray, UV and gamma irradiation seems to be a function of the delivered radiation dose. In a first investigation for doses ranging from 0.1 to 100 kGy we found out a linear relation between the gamma radiation dose and the absorption peak intensities in the UV region of the spectrum, i.e., at 223 and 274 nm. The absorption peak at 223 nm is the most sensitive to gamma rays and can be used for detecting gamma doses ranging from 0.3 to 75 kGy. Simultaneously, the absorption peak at 274 nm can be used for doses ranging from 1 to 100 kGy. Now, in the present work, we extended the investigation to gamma doses up to 3 MGy. Particularly, this study is focused in the optical absorption peak at 274 nm, corresponding to the radio-induction of triplets of conjugated C=C double bonds. The investigation revealed a linear correlation between the gamma dose and peak intensity at 274 nm for gamma doses ranging from 0.1 to more than 750 KGy, with a huge extension of the original usable dose range. Calorimetric data revealed a
Thomas, Michael E
2006-01-01
PART I: Background Theory and Measurement. 1. Optical Electromagnetics I. 2. Optical Electromagnetics II. 3. Spectroscopy of Matter. 4. Electrodynamics I: Macroscopic Interaction of Light and Matter. 5. Electrodynamics II: Microscopic Interaction of Light and Matter. 6. Experimental Techniques. PART II: Practical Models for Various Media. 7. Optical Propagation in Gases and the Atmosphere of the Earth. 8. Optical Propagation in Solids. 9. Optical Propagation in Liquids. 10. Particle Absorption and Scatter. 11. Propagation Background and Noise
Solution of linear transport equation using Chebyshev polynomials and Laplace transform
International Nuclear Information System (INIS)
Cardona, A.V.; Vilhena, M.T.M.B. de
1994-01-01
The Chebyshev polynomials and the Laplace transform are combined to solve, analytically, the linear transport equation in planar geometry, considering isotropic scattering and the one-group model. Numerical simulation is presented. (author)
International Nuclear Information System (INIS)
Zou, X B; Pahlke, K; Mathis, W
2005-01-01
We present a scheme to generate a multi-photon Greenberger-Horne-Zeilinger (GHZ) state by using single-photon sources, linear optical elements and photon detectors. Such a maximum entanglement has wide applications in the demonstration of quantum nonlocality and quantum information processing
Manafian, Jalil; Foroutan, Mohammadreza; Guzali, Aref
2017-11-01
This paper examines the effectiveness of an integration scheme which is called the extended trial equation method (ETEM) for solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the Lakshmanan-Porsezian-Daniel (LPD) equation with Kerr and power laws of nonlinearity which describes higher-order dispersion, full nonlinearity and spatiotemporal dispersion is considered, and as an achievement, a series of exact travelling-wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of LPD equation. The movement of obtained solutions is shown graphically, which helps to understand the physical phenomena of this optical soliton equation. Many other such types of nonlinear equations arising in basic fabric of communications network technology and nonlinear optics can also be solved by this method.
Growth of meromorphic solutions of higher-order linear differential equations
Directory of Open Access Journals (Sweden)
Wenjuan Chen
2009-01-01
Full Text Available In this paper, we investigate the higher-order linear differential equations with meromorphic coefficients. We improve and extend a result of M.S. Liu and C.L. Yuan, by using the estimates for the logarithmic derivative of a transcendental meromorphic function due to Gundersen, and the extended Winman-Valiron theory which proved by J. Wang and H.X. Yi. In addition, we also consider the nonhomogeneous linear differential equations.
Energy Technology Data Exchange (ETDEWEB)
Palma, Daniel A.P. [CEFET QUIMICA de Nilopolis/RJ, 21941-914 Rio de Janeiro (Brazil)], E-mail: agoncalves@con.ufrj.br; Martinez, Aquilino S.; Goncalves, Alessandro C. [COPPE/UFRJ - Programa de Engenharia Nuclear, Rio de Janeiro (Brazil)
2009-09-15
The analytical solution of point kinetics equations with a group of delayed neutrons is useful in predicting the variation of neutron density during the start-up of a nuclear reactor. In the practical case of an increase of nuclear reactor power resulting from the linear insertion of reactivity, the exact analytical solution cannot be obtained. Approximate solutions have been obtained in previous articles, based on considerations that need to be verifiable in practice. In the present article, an alternative analytic solution is presented for point kinetics equations in which the only approximation consists of disregarding the term of the second derivative for neutron density in relation to time. The results proved satisfactory when applied to practical situations in the start-up of a nuclear reactor through the control rods withdraw.
International Nuclear Information System (INIS)
Palma, Daniel A.P.; Martinez, Aquilino S.; Goncalves, Alessandro C.
2009-01-01
The analytical solution of point kinetics equations with a group of delayed neutrons is useful in predicting the variation of neutron density during the start-up of a nuclear reactor. In the practical case of an increase of nuclear reactor power resulting from the linear insertion of reactivity, the exact analytical solution cannot be obtained. Approximate solutions have been obtained in previous articles, based on considerations that need to be verifiable in practice. In the present article, an alternative analytic solution is presented for point kinetics equations in which the only approximation consists of disregarding the term of the second derivative for neutron density in relation to time. The results proved satisfactory when applied to practical situations in the start-up of a nuclear reactor through the control rods withdraw.
Hanks, Brantley R.; Skelton, Robert E.
1991-01-01
This paper addresses the restriction of Linear Quadratic Regulator (LQR) solutions to the algebraic Riccati Equation to design spaces which can be implemented as passive structural members and/or dampers. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical systems. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist. Some examples of simple spring mass systems are shown to illustrate key points.
Physical origin of third order non-linear optical response of porphyrin nanorods
International Nuclear Information System (INIS)
Mongwaketsi, N.; Khamlich, S.; Pranaitis, M.; Sahraoui, B.; Khammar, F.; Garab, G.; Sparrow, R.; Maaza, M.
2012-01-01
The non-linear optical properties of porphyrin nanorods were studied using Z-scan, Second and Third harmonic generation techniques. We investigated in details the heteroaggregate behaviour formation of [H 4 TPPS 4 ] 2- and [SnTPyP] 2+ mixture by means of the UV-VIS spectroscopy and aggregates structure and morphology by transmission electron microscopy. The porphyrin nanorods under investigation were synthesized by self assembly and molecular recognition method. They have been optimized in view of future application in the construction of the light harvesting system. The focus of this study was geared towards understanding the influence of the type of solvent used on these porphyrins nanorods using spectroscopic and microscopic techniques. Highlights: ► We synthesized porphyrin nanorods by self assembly and molecular recognition method. ► TEM images confirmed solid cylindrical shapes. ► UV-VIS spectroscopy showed the decrease in the absorbance peaks of the precursors. ► The enhanced third-order nonlinearities were observed.
Linear and nonlinear optics, dynamics, and lasing in ZnO bulk and nanostructures
International Nuclear Information System (INIS)
Klingshirn, C.; Fallert, J.; Gogolin, O.; Wissinger, M.; Hauschild, R.; Hauser, M.; Kalt, H.; Zhou, H.
2008-01-01
In linear optics, we report on measurements of the absolute external quantum efficiency of bulk ZnO and powders using an integrating sphere. At low temperature the near band edge emission efficiency can reach 0.15 in the best samples. For deep center luminescence this value may be even higher. When going to room temperature (RT) the quantum efficiency drops by about one order of magnitude. From time resolved luminescence measurements we deduce the lifetime of the free and bound excitons to be in the sub ns regime and find for the latter a systematic increase with increasing binding energy. Concerning lasing, we discuss the role of excitonic processes and the recombination in an inverted electron-hole plasma (EHP). While excitonic processes seem well justified at lower temperatures and densities, doubts arise concerning the concept of excitonic lasing at RT in ZnO. The densities at laser threshold at RT are frequently close to the Mott density or above but below the density at which population inversion in an EHP is reached. We suggest alternative processes which can explain stimulated emission in this density regime in an EHP at RT
Effect of weak nonsphericity on linear and nonlinear optical properties of small particle composites
International Nuclear Information System (INIS)
Goncharenko, A.V.; Popelnukh, V.V.; Venger, E.F.
2002-01-01
A small particle composite in which the inclusions are slightly nonspherical and distributed in shape is considered. Within the framework of the mean-field approximation, the functions of linear and nonlinear optical responses are calculated in terms of a nonsphericity parameter specifying the width of the distribution function in shape. To estimate the effect of weak nonsphericity on the functions, their second derivatives with respect to the nonsphericity parameter are computed. The derivatives are shown to be complexly structured surfaces in the coordinates (Re(ε i /ε m ), Im(ε i /ε m )), where ε i and ε m are the inclusion and matrix permittivity, respectively. Based on the results obtained, applicability area of the classical Maxwell Garnett theory is discussed. The main conclusion is that weak nonsphericity is significant only in the close vicinity of a dipole resonance of a single ball made of inclusion material. At the same time, the role of nonsphericity increases with decreasing the imaginary part of inclusion permittivity. (author)
Active liquid/liquid interfaces: contributions of non linear optics and tensiometry
International Nuclear Information System (INIS)
Gassin, P.M.
2013-01-01
Liquid-liquid extraction processes are widely used in the industrial fields of selective separation. Despite its numerous applications, the microscopic mechanisms which occur during a liquid-liquid extraction processes are really unknown specially at the liquid/liquid interface. Thus, this work deals on the understanding of the phenomena which drive the mass transfer across a liquid/liquid interface. Two experimental techniques were used in this work: dynamic interfacial tension measurement and non-linear optical experiments. Along with the use of this experimental approach, a numerical model describing the mass transfer dynamic has been developed. This model works under the assumption that both diffusion and a chemical step describing adsorption and desorption processes contribute to the global transfer kinetics. Model systems of surfactant molecules, chromophore molecules and complexing molecule were investigated at liquid/liquid and air/liquid interface. Interfacial phenomena like adsorption, surface aggregation and ion complexing were studied. Finally, the methodology developed in this work was applied to studied an extractant molecule with potential industrial application. (author) [fr
Two-Hierarchy Entanglement Swapping for a Linear Optical Quantum Repeater.
Xu, Ping; Yong, Hai-Lin; Chen, Luo-Kan; Liu, Chang; Xiang, Tong; Yao, Xing-Can; Lu, He; Li, Zheng-Da; Liu, Nai-Le; Li, Li; Yang, Tao; Peng, Cheng-Zhi; Zhao, Bo; Chen, Yu-Ao; Pan, Jian-Wei
2017-10-27
Quantum repeaters play a significant role in achieving long-distance quantum communication. In the past decades, tremendous effort has been devoted towards constructing a quantum repeater. As one of the crucial elements, entanglement has been created in different memory systems via entanglement swapping. The realization of j-hierarchy entanglement swapping, i.e., connecting quantum memory and further extending the communication distance, is important for implementing a practical quantum repeater. Here, we report the first demonstration of a fault-tolerant two-hierarchy entanglement swapping with linear optics using parametric down-conversion sources. In the experiment, the dominant or most probable noise terms in the one-hierarchy entanglement swapping, which is on the same order of magnitude as the desired state and prevents further entanglement connections, are automatically washed out by a proper design of the detection setting, and the communication distance can be extended. Given suitable quantum memory, our techniques can be directly applied to implementing an atomic ensemble based quantum repeater, and are of significant importance in the scalable quantum information processing.
Two-Hierarchy Entanglement Swapping for a Linear Optical Quantum Repeater
Xu, Ping; Yong, Hai-Lin; Chen, Luo-Kan; Liu, Chang; Xiang, Tong; Yao, Xing-Can; Lu, He; Li, Zheng-Da; Liu, Nai-Le; Li, Li; Yang, Tao; Peng, Cheng-Zhi; Zhao, Bo; Chen, Yu-Ao; Pan, Jian-Wei
2017-10-01
Quantum repeaters play a significant role in achieving long-distance quantum communication. In the past decades, tremendous effort has been devoted towards constructing a quantum repeater. As one of the crucial elements, entanglement has been created in different memory systems via entanglement swapping. The realization of j -hierarchy entanglement swapping, i.e., connecting quantum memory and further extending the communication distance, is important for implementing a practical quantum repeater. Here, we report the first demonstration of a fault-tolerant two-hierarchy entanglement swapping with linear optics using parametric down-conversion sources. In the experiment, the dominant or most probable noise terms in the one-hierarchy entanglement swapping, which is on the same order of magnitude as the desired state and prevents further entanglement connections, are automatically washed out by a proper design of the detection setting, and the communication distance can be extended. Given suitable quantum memory, our techniques can be directly applied to implementing an atomic ensemble based quantum repeater, and are of significant importance in the scalable quantum information processing.
Mechanism of linear and nonlinear optical properties of bis-thiourea cadmium chloride single crystal
International Nuclear Information System (INIS)
Yang, J.T.; Luo, S.J.; Yi, L.; Laref, A.
2013-01-01
Within the generalized gradient approximation (GGA), a calculation of the electronic structure of a semiorganic crystal named bis-thiourea cadmium chloride (BTCC) was performed, then the linear and nonlinear optical responses were obtained over a wide energy range, using a scissor energy of 1.30 eV, and our results are in good agreement with the experiments. The accurate full-potential projected augmented wave (FP-PAW) method was used. The prominent spectrum of the second harmonic generation (SHG) was successfully correlated with the dielectric function in terms of single- and double-photon resonances. Both the virtual electron (VE) and virtual hole (VH) processes make contributions to the SHG of BTCC crystal, and the VH process is enhanced by the Cd-centered tetrahedron. The SHG effect of the semiorganic material is attributed to the charge transfer (CT). The CT model for the semiorganic crystal is named as “M-Π O ⋯X”. “M” is a metal atom providing electrons, “Π O ” is a π-conjugated covalent of an organic molecule, and “X” is a high electronegativity atom. The CT across the BTCC molecule is along a π-electron conjugation covalence bond, and the delocalized electrons of sulfur provide an excellent bridge. The strong “pull” effect for the CT is due to the intramolecular hydrogen bonds provided by the chlorine with the high electron affinity.
Operational method of solution of linear non-integer ordinary and partial differential equations.
Zhukovsky, K V
2016-01-01
We propose operational method with recourse to generalized forms of orthogonal polynomials for solution of a variety of differential equations of mathematical physics. Operational definitions of generalized families of orthogonal polynomials are used in this context. Integral transforms and the operational exponent together with some special functions are also employed in the solutions. The examples of solution of physical problems, related to such problems as the heat propagation in various models, evolutional processes, Black-Scholes-like equations etc. are demonstrated by the operational technique.
ZHU, C. S.; ROBB, D. A.; EWINS, D. J.
2002-05-01
The multiple-solution response of rotors supported on squeeze film dampers is a typical non-linear phenomenon. The behaviour of the multiple-solution response in a flexible rotor supported on two identical squeeze film dampers with centralizing springs is studied by three methods: synchronous circular centred-orbit motion solution, numerical integration method and slow acceleration method using the assumption of a short bearing and cavitated oil film; the differences of computational results obtained by the three different methods are compared in this paper. It is shown that there are three basic forms for the multiple-solution response in the flexible rotor system supported on the squeeze film dampers, which are the resonant, isolated bifurcation and swallowtail bifurcation multiple solutions. In the multiple-solution speed regions, the rotor motion may be subsynchronous, super-subsynchronous, almost-periodic and even chaotic, besides synchronous circular centred, even if the gravity effect is not considered. The assumption of synchronous circular centred-orbit motion for the journal and rotor around the static deflection line can be used only in some special cases; the steady state numerical integration method is very useful, but time consuming. Using the slow acceleration method, not only can the multiple-solution speed regions be detected, but also the non-synchronous response regions.
Chen, Y.-M.; Koniges, A. E.; Anderson, D. V.
1989-10-01
The biconjugate gradient method (BCG) provides an attractive alternative to the usual conjugate gradient algorithms for the solution of sparse systems of linear equations with nonsymmetric and indefinite matrix operators. A preconditioned algorithm is given, whose form resembles the incomplete L-U conjugate gradient scheme (ILUCG2) previously presented. Although the BCG scheme requires the storage of two additional vectors, it converges in a significantly lesser number of iterations (often half), while the number of calculations per iteration remains essentially the same.
Czech Academy of Sciences Publication Activity Database
Farwig, R.; Guenther, R.; Thomann, E.; Nečasová, Šárka
2014-01-01
Roč. 34, č. 2 (2014), s. 511-529 ISSN 1078-0947 R&D Projects: GA ČR(CZ) GAP201/11/1304; GA MŠk LC06052 Institutional support: RVO:67985840 Keywords : fundamental solution * linearized problem * Navier-Stokes problem Subject RIV: BA - General Mathematics Impact factor: 0.826, year: 2014 http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=8831
Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation
International Nuclear Information System (INIS)
Bonnet, M.; Meurant, G.
1978-01-01
The object of this study is to compare different methods of solving linear and nonlinear algebraic systems and to apply them to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems the conventional methods of alternating direction type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method of nonlinear conjugate gradient is studied together with Newton's method and some of its variants. It should be noted, however, that Newton's method is found to be more efficient when coupled with a good method for solving the linear system. As a conclusion, these methods are used to solve a nonlinear diffusion problem and the numerical results obtained are compared [fr
An implicit meshless scheme for the solution of transient non-linear Poisson-type equations
Bourantas, Georgios
2013-07-01
A meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. © 2013 Elsevier Ltd.
An implicit meshless scheme for the solution of transient non-linear Poisson-type equations
Bourantas, Georgios; Burganos, Vasilis N.
2013-01-01
A meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. © 2013 Elsevier Ltd.
High-speed linear optics quantum computing using active feed-forward.
Prevedel, Robert; Walther, Philip; Tiefenbacher, Felix; Böhi, Pascal; Kaltenbaek, Rainer; Jennewein, Thomas; Zeilinger, Anton
2007-01-04
As information carriers in quantum computing, photonic qubits have the advantage of undergoing negligible decoherence. However, the absence of any significant photon-photon interaction is problematic for the realization of non-trivial two-qubit gates. One solution is to introduce an effective nonlinearity by measurements resulting in probabilistic gate operations. In one-way quantum computation, the random quantum measurement error can be overcome by applying a feed-forward technique, such that the future measurement basis depends on earlier measurement results. This technique is crucial for achieving deterministic quantum computation once a cluster state (the highly entangled multiparticle state on which one-way quantum computation is based) is prepared. Here we realize a concatenated scheme of measurement and active feed-forward in a one-way quantum computing experiment. We demonstrate that, for a perfect cluster state and no photon loss, our quantum computation scheme would operate with good fidelity and that our feed-forward components function with very high speed and low error for detected photons. With present technology, the individual computational step (in our case the individual feed-forward cycle) can be operated in less than 150 ns using electro-optical modulators. This is an important result for the future development of one-way quantum computers, whose large-scale implementation will depend on advances in the production and detection of the required highly entangled cluster states.
ON THE BOUNDEDNESS AND THE STABILITY OF SOLUTION TO THIRD ORDER NON-LINEAR DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In this paper we investigate the global asymptotic stability,boundedness as well as the ultimate boundedness of solutions to a general third order nonlinear differential equation,using complete Lyapunov function.
On symmetry reduction and exact solutions of the linear one-dimensional Schroedinger equation
International Nuclear Information System (INIS)
Barannik, L.L.
1996-01-01
Symmetry reduction of the Schroedinger equation with potential is carried out on subalgebras of the Lie algebra which is the direct sum of the special Galilei algebra and one-dimensional algebra. Some new exact solutions are obtained
Nemeth, Michael P.; Schultz, Marc R.
2012-01-01
A detailed exact solution is presented for laminated-composite circular cylinders with general wall construction and that undergo axisymmetric deformations. The overall solution is formulated in a general, systematic way and is based on the solution of a single fourth-order, nonhomogeneous ordinary differential equation with constant coefficients in which the radial displacement is the dependent variable. Moreover, the effects of general anisotropy are included and positive-definiteness of the strain energy is used to define uniquely the form of the basis functions spanning the solution space of the ordinary differential equation. Loading conditions are considered that include axisymmetric edge loads, surface tractions, and temperature fields. Likewise, all possible axisymmetric boundary conditions are considered. Results are presented for five examples that demonstrate a wide range of behavior for specially orthotropic and fully anisotropic cylinders.
Solutions for ultra-high speed optical wavelength conversion and clock recovery
DEFF Research Database (Denmark)
Oxenløwe, Leif Katsuo; Galili, Michael; Mulvad, Hans Christian Hansen
2006-01-01
This paper reports on our recent advances in ultra-fast optical communications relying on ultra-short pulses densely stacked in ultra-high bit rate serial data signals at a single wavelength. The paper describes details in solutions for the network functionalities of wavelength conversion and clock...... recovery at bit rates up to 320 Gb/s...
International Nuclear Information System (INIS)
Russo, R.E.; Robouch, P.B.; Silva, R.J.
1990-01-01
A photoacoustic spectrometer, equipped with an 85 meter optical fiber, was used to perform absorption measurements of lanthanide and actinide samples, located in a glovebox. The spectrometer was tested using aqueous solutions of praseodymium and americium ions; the sensitivity for remote measurements was found to be similar to that achieved in the laboratory without the fiber. 14 refs., 3 figs
Analytical vs. Simulation Solution Techniques for Pulse Problems in Non-linear Stochastic Dynamics
DEFF Research Database (Denmark)
Iwankiewicz, R.; Nielsen, Søren R. K.
Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically-numerical tec......Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically...
A solution to the varying response of the linear power monitor induced by xenon poisoning
Energy Technology Data Exchange (ETDEWEB)
Godsey, T A; Randall, J D [Texas A and M University (United States)
1974-07-01
After conversion to FLIP fuel at Texas A and M, the fuel temperatures were examined very carefully. It was observed that the fuel temperature at 1 Mw varied over a wide range during the week. This variation was shown to be due to the variation in response of the linear CIC which was used to establish reactor power level. A modification of the linear power monitor was designed and installed. The response of this system was verified by using cobalt wires, fuel temperature, and a fission chamber located at 6 feet from the reactor core. The system has proven to be operationally satisfactory. (author)
International Nuclear Information System (INIS)
Bykova, L.N.; Chesnokova, O.Ya.; Orlova, M.V.
1995-01-01
The method for linearizing the potentiometric curves of precipitation titration is studied for its application in the determination of halide ions (Cl - , Br - , I - ) in dimethylacetamide, dimethylformamide, in which titration is complicated by additional equilibrium processes. It is found that the method of linearization permits the determination of the titrant volume at the end point of titration to high accuracy in the case of titration curves without a potential jump in the proximity of the equivalent point (5 x 10 -5 M). 3 refs., 2 figs., 3 tabs
Fast Combinatorial Algorithm for the Solution of Linearly Constrained Least Squares Problems
Van Benthem, Mark H.; Keenan, Michael R.
2008-11-11
A fast combinatorial algorithm can significantly reduce the computational burden when solving general equality and inequality constrained least squares problems with large numbers of observation vectors. The combinatorial algorithm provides a mathematically rigorous solution and operates at great speed by reorganizing the calculations to take advantage of the combinatorial nature of the problems to be solved. The combinatorial algorithm exploits the structure that exists in large-scale problems in order to minimize the number of arithmetic operations required to obtain a solution.
Heinkenschloss, Matthias
2005-01-01
We study a class of time-domain decomposition-based methods for the numerical solution of large-scale linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete-time optimal control (DTOC) problem. The optimality conditions for this DTOC problem lead to a linear block tridiagonal system. The diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time-subintervals. This motivates the application of block Gauss-Seidel (GS)-type methods for the solution of the block tridiagonal systems. Numerical experiments show that the spectral radii of the block GS iteration matrices are larger than one for typical applications, but that the eigenvalues of the iteration matrices decay to zero fast. Hence, while the GS method is not expected to convergence for typical applications, it can be effective as a preconditioner for Krylov-subspace methods. This is confirmed by our numerical tests.A byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block GS method applied to the DTOC optimality system.
Chen, Haoyao; Wang, Can; Lou, Yunjiang
2013-06-01
This paper presents an efficient approach to achieve microparticles flocking with robotics and optical tweezers technologies. All particles trapped by optical tweezers can be automatically moved toward a predefined region without collision. The main contribution of this paper lies in the proposal of several solutions to the flocking manipulation of microparticles in microenvironments. First, a simple flocking controller is proposed to generate the desired positions and velocities for particles' movement. Second, a velocity saturation method is implemented to prevent the desired velocities from exceeding a safe limit. Third, a two-layer control architecture is proposed for the motion control of optical tweezers. This architecture can help make many robotic manipulations achievable under microenvironments. The proposed approach with these solutions can be applied to many bioapplications especially in cell engineering and biomedicine. Experiments on yeast cells with a robot-tweezers system are finally performed to verify the effectiveness of the proposed approach.
An Explicit Enclosure of the Solution Set of Overdetermined Interval Linear Equations
Czech Academy of Sciences Publication Activity Database
Rohn, Jiří
2017-01-01
Roč. 24, February (2017), s. 1-10 ISSN 1573-1340 Institutional support: RVO:67985807 Keywords : interval linear equations * interval hull * unit midpoint * enclosure Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics http://interval.louisiana.edu/ reliable -computing-journal/volume-24/ reliable -computing-24-pp-001-010.pdf
Variations in the Solution of Linear First-Order Differential Equations. Classroom Notes
Seaman, Brian; Osler, Thomas J.
2004-01-01
A special project which can be given to students of ordinary differential equations is described in detail. Students create new differential equations by changing the dependent variable in the familiar linear first-order equation (dv/dx)+p(x)v=q(x) by means of a substitution v=f(y). The student then creates a table of the new equations and…
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
A Fifth Order Hybrid Linear Multistep method For the Direct Solution ...
African Journals Online (AJOL)
A linear multistep hybrid method (LMHM)with continuous coefficients isconsidered and directly applied to solve third order initial and boundary value problems (IBVPs). The continuous method is used to obtain Multiple Finite Difference Methods (MFDMs) (each of order 5) which are combined as simultaneous numerical ...
Torre, Amalia
2005-01-01
Ray, wave and quantum concepts are central to diverse and seemingly incompatible models of light. Each model particularizes a specific ''manifestation'' of light, and then corresponds to adequate physical assumptions and formal approximations, whose domains of applicability are well-established. Accordingly each model comprises its own set of geometric and dynamic postulates with the pertinent mathematical means.At a basic level, the book is a complete introduction to the Wigner optics, which bridges between ray and wave optics, offering the optical phase space as the ambience and the Wigner f
Non-linear dynamics and alternating 'flip' solutions in ferrofluidic Taylor-Couette flow
Altmeyer, Sebastian
2018-04-01
This study treats with the influence of a symmetry-breaking transversal magnetic field on the nonlinear dynamics of ferrofluidic Taylor-Couette flow - flow confined between two concentric independently rotating cylinders. We detected alternating 'flip' solutions which are flow states featuring typical characteristics of slow-fast-dynamics in dynamical systems. The flip corresponds to a temporal change in the axial wavenumber and we find them to appear either as pure 2-fold axisymmetric (due to the symmetry-breaking nature of the applied transversal magnetic field) or involving non-axisymmetric, helical modes in its interim solution. The latter ones show features of typical ribbon solutions. In any case the flip solutions have a preferential first axial wavenumber which corresponds to the more stable state (slow dynamics) and second axial wavenumber, corresponding to the short appearing more unstable state (fast dynamics). However, in both cases the flip time grows exponential with increasing the magnetic field strength before the flip solutions, living on 2-tori invariant manifolds, cease to exist, with lifetime going to infinity. Further we show that ferrofluidic flow turbulence differ from the classical, ordinary (usually at high Reynolds number) turbulence. The applied magnetic field hinders the free motion of ferrofluid partials and therefore smoothen typical turbulent quantities and features so that speaking of mildly chaotic dynamics seems to be a more appropriate expression for the observed motion.
International Nuclear Information System (INIS)
Silva, Cleber F.
2011-01-01
The DL-Alanine (C 3 H 7 NO 2 ) is an amino acid tissue equivalent traditionally used as standard dosimetric material in EPR dosimetry. Recently, it has been studied to be applied in gel dosimetry, considering that the addition of Alanine in the Fricke gel solution improves the production of ferric ions radiation induced. The spectrophotometric evaluation technique can be used comparing the two spectrum wavelengths bands: 457 nm band that corresponds to ferrous ions and 588 nm band that corresponds to ferric ions concentration to evaluate the dosimetric properties of this material. The performance of the Alanine gel solution developed at IPEN has been firstly studied using the spectrophotometric technique aiming to apply this material to 3D clinical doses evaluations using MRI technique. In this work, the optical and the energy dependent response of this solution submitted to clinical photons and electrons beams were studied. Different batches of gel solutions were prepared and maintained at low temperature during 12 h to solidification. Before irradiation, the samples were maintained during 1 h at room temperature. The photons and electrons irradiations were carried out using a Varian 2100C Medical Linear Accelerator of the Radiotherapy Department of the Hospital das Clinicas of the University of Sao Paulo with absorbed doses between 1 and 40 Gy; radiation field of 10 x 10 cm 2 ; photon energies of 6 MeV and 15 MeV; and electron with energies between 6 and 15 MeV. The obtained results indicate that signal response dependence for clinical photons and electrons beams, to the same doses, for Alanine gel dosimeter is better than 3.6 % (1σ), and the energy dependence response, to the same doses, is better 3% (1σ) for both beams. These results indicate that the same calibration factor can be used and the optical response is energy independent in the studied dose range and clinical photons and electrons beams energies. (author)
Energy Technology Data Exchange (ETDEWEB)
Nageshwari, M.; Jayaprakash, P.; Kumari, C. Rathika Thaya [PG & Research Department of Physics, Arignar Anna Govt. Arts College, Cheyyar 604407, Tamil Nadu (India); Vinitha, G. [Department of Physics, School of Advanced Sciences, VIT Chennai, 600127 Tamil Nadu (India); Caroline, M. Lydia, E-mail: lydiacaroline2006@yahoo.co.in [PG & Research Department of Physics, Arignar Anna Govt. Arts College, Cheyyar 604407, Tamil Nadu (India)
2017-04-15
An efficient nonlinear optical semiorganic material L-valinium L-valine chloride (LVVCl) was synthesized and grown-up by means of slow evaporation process. Single crystal XRD evince that LVVCl corresponds to monoclinic system having acentric space group P2{sub 1}. The diverse functional groups existing in LVVCl were discovered with FTIR spectral investigation. The UV-Visible and photoluminescence spectrum discloses the optical and electronic properties respectively for the grown crystal. Several optical properties specifically extinction coefficient, reflectance, linear refractive index, electrical and optical conductivity were also determined. The SEM analysis was also carried out and it portrayed the surface morphology of LVVCl. The calculated value of laser damage threshold was 2.59 GW/cm{sup 2}. The mechanical and dielectric property of LVVCl was investigated employing microhardness and dielectric studies. The second and third order nonlinear optical characteristics of LVVCl was characterized utilizing Kurtz Perry and Z scan technique respectively clearly suggest its suitability in the domain of optics and photonics. - Graphical abstract: Good quality transparent single crystals of L-valinium L-valine chloride single crystal was grown by slow evaporation technique. The grown crystals were analyzed using different instrumentation methods to check its usefulness for the device fabrication. The determination of nonlinear refractive index (n{sub 2}), absorption coefficient (β) and third order nonlinear susceptibility was determined by Z scan technique, highlighted that LVVCl can serve as a promising candidate for opto electronic and nonlinear optical applications.
International Nuclear Information System (INIS)
Ungan, F.; Yesilgul, U.; Kasapoglu, E.; Sari, H.; Sökmen, I.
2012-01-01
In this present work, we have investigated theoretically the effects of applied electric and magnetic fields on the linear and nonlinear optical properties in a GaAs/Al x Ga 1−x As inverse parabolic quantum well for different Al concentrations at the well center. The Al concentration at the barriers was always x max =0.3. The energy levels and wave functions are calculated within the effective mass approximation and the envelope function approach. The analytical expressions of optical properties are obtained by using the compact density-matrix approach. The linear, third-order nonlinear and total absorption and refractive index changes depending on the Al concentration at the well center are investigated as a function of the incident photon energy for the different values of the applied electric and magnetic fields. The results show that the applied electric and magnetic fields have a great effect on these optical quantities. - Highlights: ► The x c concentration has a great effect on the optical characteristics of these structures. ► The EM fields have a great effect on the optical properties of these structures. ► The total absorption coefficients increased as the electric and magnetic field increases. ► The RICs reduced as the electric and magnetic field increases.
Existence of entire solutions of some non-linear differential-difference equations.
Chen, Minfeng; Gao, Zongsheng; Du, Yunfei
2017-01-01
In this paper, we investigate the admissible entire solutions of finite order of the differential-difference equations [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] are two non-zero polynomials, [Formula: see text] is a polynomial and [Formula: see text]. In addition, we investigate the non-existence of entire solutions of finite order of the differential-difference equation [Formula: see text], where [Formula: see text], [Formula: see text] are two non-constant polynomials, [Formula: see text], m , n are positive integers and satisfy [Formula: see text] except for [Formula: see text], [Formula: see text].
Scott, James R.; Atassi, Hafiz M.
1990-01-01
A linearized unsteady aerodynamic analysis is presented for unsteady, subsonic vortical flows around lifting airfoils. The analysis fully accounts for the distortion effects of the nonuniform mean flow on the imposed vortical disturbances. A frequency domain numerical scheme which implements this linearized approach is described, and numerical results are presented for a large variety of flow configurations. The results demonstrate the effects of airfoil thickness, angle of attack, camber, and Mach number on the unsteady lift and moment of airfoils subjected to periodic vortical gusts. The results show that mean flow distortion can have a very strong effect on the airfoil unsteady response, and that the effect depends strongly upon the reduced frequency, Mach number, and gust wave numbers.
Solutions to estimation problems for scalar hamilton-jacobi equations using linear programming
Claudel, Christian G.; Chamoin, Timothee; Bayen, Alexandre M.
2014-01-01
This brief presents new convex formulations for solving estimation problems in systems modeled by scalar Hamilton-Jacobi (HJ) equations. Using a semi-analytic formula, we show that the constraints resulting from a HJ equation are convex, and can be written as a set of linear inequalities. We use this fact to pose various (and seemingly unrelated) estimation problems related to traffic flow-engineering as a set of linear programs. In particular, we solve data assimilation and data reconciliation problems for estimating the state of a system when the model and measurement constraints are incompatible. We also solve traffic estimation problems, such as travel time estimation or density estimation. For all these problems, a numerical implementation is performed using experimental data from the Mobile Century experiment. In the context of reproducible research, the code and data used to compute the results presented in this brief have been posted online and are accessible to regenerate the results. © 2013 IEEE.
Non-linear partial differential equations an algebraic view of generalized solutions
Rosinger, Elemer E
1990-01-01
A massive transition of interest from solving linear partial differential equations to solving nonlinear ones has taken place during the last two or three decades. The availability of better computers has often made numerical experimentations progress faster than the theoretical understanding of nonlinear partial differential equations. The three most important nonlinear phenomena observed so far both experimentally and numerically, and studied theoretically in connection with such equations have been the solitons, shock waves and turbulence or chaotical processes. In many ways, these phenomen
International Nuclear Information System (INIS)
Kalmykov, Mikhail Yu.; Kniehl, Bernd A.
2012-05-01
We argue that the Mellin-Barnes representations of Feynman diagrams can be used for obtaining linear systems of homogeneous differential equations for the original Feynman diagrams with arbitrary powers of propagators without recourse to the integration-by-parts technique. These systems of differential equation can be used (i) for the differential reductions to sets of basic functions and (ii) for counting the numbers of master-integrals.
Freeman, Jason L; Zhao, Qun; Zhang, Yuanli; Wang, Jianwei; Lawson, Christopher M; Gray, Gary M
2013-10-21
Two new series of phosphonato-substituted bithiophenes, BpP(X)(C4H2S)2H and BpP(X)(C4H2S)2P(X)Bp (Bp = 2,2'-C12H8O2, X = O, S, Se), have been synthesized and characterized using linear absorption and emission spectra, and third-order nonlinear absorption measurements at 430 nm with 27 ps laser pulses. The compounds were synthesized in three steps: (1) reacting lithiated bithiophene with (Et2N)2PCl; (2) reacting the product from the first step with biphenol; and (3) reacting the product from the second step with the appropriate chalcogen. The X-ray crystal structures of two of the compounds, BpP(O)(C4H2S)2P(O)Bp and BpP(Se)(C4H2S)2P(Se)Bp, are reported and show a number of intermolecular π-π interactions. The linear absorption spectra, emission spectra, and emission quantum yields show distinct trends with respect to the chalcogen and the number of phosphorus substituents attached to the 2,2'-bithiophene ring. The compounds show emission maxima at wavelengths ranging from 380-400 nm and, BpP(S)(C4H2S)2H shows a 23-fold increase in fluorescence quantum yield relative to that of 2,2'-bithiophene. Fluorescence lifetimes and radiative and non-radiative decay rate constants for the first singlet excited state have been extracted from the quantum yields using time-dependent DFT calculations. Nonlinear transmission measurements indicate that all of the compounds show nonlinear absorption at 430 nm with 27 ps laser pulses in spite of their low solubilities. Notably, the nonlinear absorption threshold of a 0.16 mol L(-1) CH2Cl2 solution of BpP(Se)(C4H2S)2H is 0.9 J cm(-2). The excellent emission quantum yields and good nonlinear absorptions make these compounds promising candidates for optical power limiting applications and as host materials for violet-blue organic light emitting diodes.