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Applied Mathematics

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Selected Works

2006

Articles 1 - 14 of 14

Full-Text Articles in Physical Sciences and Mathematics

Guiding Of Laser Beams In Plasmas By Radiation Cascade Compression, Serguei Y. Kalmykov, Gennady Shvets Nov 2006

Guiding Of Laser Beams In Plasmas By Radiation Cascade Compression, Serguei Y. Kalmykov, Gennady Shvets

Serge Youri Kalmykov

The near-resonant beatwave excitation of an electron plasma wave (EPW) can be employed for generating trains of few-fs electromagnetic pulses in rarefied plasmas. The EPW produces a co-moving index grating that induces a laser phase modulation at the beat frequency. Consequently, the cascade of sidebands red- and blue-shifted from the fundamental by integer multiples of the beat frequency is generated in the laser spectrum. When the beat frequency is lower than the electron plasma frequency, the phase chirp enables laser beatnote compression by the group velocity dispersion [S. Kalmykov and G. Shvets, Phys. Rev. E 73, 46403 (2006)]. In the …

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Injection, Trapping, And Acceleration Of Electrons In A Three-Dimensional Nonlinear Laser Wakefield, Serguei Y. Kalmykov, Leonid M. Gorbunov, Patrick Mora, Gennady Shvets Oct 2006

Injection, Trapping, And Acceleration Of Electrons In A Three-Dimensional Nonlinear Laser Wakefield, Serguei Y. Kalmykov, Leonid M. Gorbunov, Patrick Mora, Gennady Shvets

Serge Youri Kalmykov

It is demonstrated that the accelerating and focusing phases of the nonlinear three-dimensional axisymmetric laser wake can almost entirely overlap starting from a certain distance behind the laser pulse in homogeneous plasma. Such field structure results from the curvature of phase fronts due to the radially inhomogeneous relativistic shift of plasma frequency. Consequently, the number of trapped low-energy electrons can be much greater than that predicted by the linear wake theory. This effect is favorable for quasi-monoenergetic acceleration of a considerable charge (several hundreds of pC) to about 1 GeV per electron in the plasma wakefield driven by an ultrashort …

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Snapshots Of Laser Wakefields, Nicholas H. Matlis, Steven A. Reed, Stepan S. Bulanov, Vladimir Chvykov, Galina Kalintchenko, Takeshi Matsuoka, Pascal Rousseau, Victor Yanovsky, Anatoly Maksimchuk, Serguei Y. Kalmykov, Gennady Shvets, Michael C. Downer Oct 2006

Snapshots Of Laser Wakefields, Nicholas H. Matlis, Steven A. Reed, Stepan S. Bulanov, Vladimir Chvykov, Galina Kalintchenko, Takeshi Matsuoka, Pascal Rousseau, Victor Yanovsky, Anatoly Maksimchuk, Serguei Y. Kalmykov, Gennady Shvets, Michael C. Downer

Serge Youri Kalmykov

Tabletop plasma accelerators can now produce GeV-range electron beams and femtosecond X-ray pulses, providing compact radiation sources for medicine, nuclear engineering, materials science and high-energy physics. In these accelerators, electrons surf on electric fields exceeding 100 GeV m^{−1}, which is more than 1,000 times stronger than achievable in conventional accelerators. These fields are generated within plasma structures (such as Langmuir waves or electron density ‘bubbles’) propagating near light speed behind laser or charged-particle driving pulses. Here, we demonstrate single-shot visualization of laser-wakefield accelerator structures for the first time. Our ‘snapshots’ capture the evolution of multiple wake periods, detect structure variations …

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The Localized Dynamics Of A Ca2+Channel (30-Minute Talk), Borbala Mazzag, Christoper Tignanelli, Gregory D. Smith Aug 2006

The Localized Dynamics Of A Ca2+Channel (30-Minute Talk), Borbala Mazzag, Christoper Tignanelli, Gregory D. Smith

Borbala Mazzag

No abstract provided.

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Compression Of Laser Radiation In Plasmas Via Electromagnetic Cascading, Serguei Y. Kalmykov, Gennady Shvets Apr 2006

Compression Of Laser Radiation In Plasmas Via Electromagnetic Cascading, Serguei Y. Kalmykov, Gennady Shvets

Serge Youri Kalmykov

A train of few-laser-cycle relativistically intense radiation spikes with a terahertz repetition rate can be organized self-consistently in plasma from two frequency detuned co-propagating laser beams of low intensity. Large frequency bandwidth for the compression of spikes is produced via laser-induced periodic modulation of the plasma refractive index. The beat-wave-driven electron plasma wave downshifted from the plasma frequency creates a moving index grating thus inducing a periodic phase modulation of the driving laser (in spectral terms, electromagnetic cascading). The group velocity dispersion compresses the chirped laser beat notes to a few-cycle duration and relativistic intensity either concurrently in the same, …

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Nonlinear Evolution Of The Plasma Beat Wave: Compressing The Laser Beat Notes Via Electromagnetic Cascading, Serguei Y. Kalmykov, Gennady Shvets Mar 2006

Nonlinear Evolution Of The Plasma Beat Wave: Compressing The Laser Beat Notes Via Electromagnetic Cascading, Serguei Y. Kalmykov, Gennady Shvets

Serge Youri Kalmykov

The near-resonant beat wave excitation of an electron plasma wave (EPW) can be employed for generating the trains of few-femtosecond electromagnetic (EM) pulses in rarefied plasmas. The EPW produces a comoving index grating that induces a laser phase modulation at the difference frequency. As a result, the cascade of sidebands red and blue shifted by integer multiples of the beat frequency is generated in the laser spectrum. The bandwidth of the phase-modulated laser is proportional to the product of the plasma length, laser wavelength, and amplitude of the electron density perturbation. When the beat frequency is lower than the electron …

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Fun With Fractals, Borbala Mazzag Feb 2006

Fun With Fractals, Borbala Mazzag

Borbala Mazzag

No abstract provided.

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Multivariate Expansion Associated With Sheffer-Type Polynomials And Operators, Tian-Xiao He, Leetsch Hsu, Peter Shiue Dec 2005

Multivariate Expansion Associated With Sheffer-Type Polynomials And Operators, Tian-Xiao He, Leetsch Hsu, Peter Shiue

Tian-Xiao He

With the aid of multivariate Sheffer-type polynomials and differential operators, this paper provides two kinds of general expansion formulas, called respectively the first expansion formula and the second expansion formula, that yield a constructive solution to the problem of the expansion of A(ˆt)f([g(t)) (a composition of any given formal power series) and the expansion of the multivariate entire functions in terms of multivariate Sheffer-type polynomials, which may be considered an application of the first expansion formula and the Sheffer-type operators. The results are applicable to combinatorics and special function theory.

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On The Convergence Of The Summation Formulas Constructed By Using A Symbolic Operator Approach, Tian-Xiao He, Leetsch C. Hsu, Peter J.-S. Shiue Dec 2005

On The Convergence Of The Summation Formulas Constructed By Using A Symbolic Operator Approach, Tian-Xiao He, Leetsch C. Hsu, Peter J.-S. Shiue

Tian-Xiao He

This paper deals with the convergence of the summation of power series of the form Σa ≤ k ≤ bf(k)xk, where 0 ≤ a ≤ b < ∞, and {f(k)} is a given sequence of numbers with k ∈ [a, b) or f(t) a differentiable function defined on [a, b). Here, the summation is found by using the symbolic operator approach shown in [1]. We will give a different type of the remainder of the summation formulas. The convergence of the corresponding power series will be determined consequently. Several examples such as the generalized Euler's transformation series will also be given. In addition, we will compare the convergence of the given series transforms.

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Numerical Approximation To Ζ(2n+1), Tian-Xiao He, Michael J. Dancs Dec 2005

Numerical Approximation To Ζ(2n+1), Tian-Xiao He, Michael J. Dancs

Tian-Xiao He

In this short paper, we establish a family of rapidly converging series expansions ζ(2n +1) by discretizing an integral representation given by Cvijovic and Klinowski [3] in Integral representations of the Riemann zeta function for odd-integer arguments, J. Comput. Appl. Math. 142 (2002) 435–439. The proofs are elementary, using basic properties of the Bernoulli polynomials.

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On The Generalized Möbius Inversion Formulas, Tian-Xiao He, Peter J. S. Shiue3, Leetsch C. Hsu Dec 2005

On The Generalized Möbius Inversion Formulas, Tian-Xiao He, Peter J. S. Shiue3, Leetsch C. Hsu

Tian-Xiao He

We provide a wide class of M¨obius inversion formulas in terms of the generalized M¨obius functions and its application to the setting of the Selberg multiplicative functions.

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An Euler-Type Formula For Ζ(2k +1), Tian-Xiao He, Michael J. Dancs Dec 2005

An Euler-Type Formula For Ζ(2k +1), Tian-Xiao He, Michael J. Dancs

Tian-Xiao He

In this short paper, we give several new formulas for ζ(n) when n is an odd positive integer. The method is based on a recent proof, due to H. Tsumura, of Euler’s classical result for even n. Our results illuminate the similarities between the even and odd cases, and may give some insight into why the odd case is much more difficult.

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Exp-Function Method For Nonlinear Wave Equations, Ji-Huan He, Xu-Hong Wu Dec 2005

Exp-Function Method For Nonlinear Wave Equations, Ji-Huan He, Xu-Hong Wu

Ji-Huan He

In this paper, a new method, called Exp-function method, is proposed to seek solitary solutions, periodic solutions and compacton-like solutions of nonlinear differential equations. The modified KdV equation and Dodd–Bullough–Mikhailov equation are chosen to illustrate the effectiveness and convenience of the suggested method.

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Crisp Solution Of A General Fuzzy Linear System, S. Abbasbandy, R. Ezzati Dec 2005

Crisp Solution Of A General Fuzzy Linear System, S. Abbasbandy, R. Ezzati

Saeid Abbasbandy

In this paper a method for solving a general fuzzy linear system with crisp solution is considered. We consider the method in special case when the elements of the coefficient matrix and the right hand side are trapezoidal fuzzy numbers. The method in detail is discussed and followed by theorem and illustrated by solving some examples.

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