Electrostatic Solitary Waves in Relativistic Degenerate Electron-Positron-Ion Plasma

The linear and nonlinear properties of ion acoustic excitations propagating in warm dense electron-positron-ion plasma are investigated. Electrons and positrons are assumed relativistic and degenerate, following the Fermi-Dirac statistics, whereas the warm ions are described by a set of classical fluid equations. A linear dispersion relation is derived in the linear approximation. Adopting a reductive perturbation method, the Korteweg-de Vries equation is derived, which admits a localized wave solution in the form of a small-amplitude weakly super-acoustic pulse-shaped soliton. The analysis is extended to account for arbitrary amplitude solitary waves, by deriving a pseudoenergy-balance like equation, involving a Sagdeev-type pseudopotential. It is shown that the two approaches agree exactly in the small-amplitude weakly super-acoustic limit. The range of allowed values of the pulse soliton speed (Mach number), wherein solitary waves may exist, is determined. The effects of the key plasma configuration parameters, namely, the electron relativistic degeneracy parameter, the ion (thermal)-to-the electron (Fermi) temperature ratio, and the positron-to-electron density ratio, on the soliton characteristics and existence domain, are studied in detail. Our results aim at elucidating the characteristics of ion acoustic excitations in relativistic degenerate plasmas, e.g., in dense astrophysical objects, where degenerate electrons and positrons may occur.

Nonlinear hydrodynamic Langmuir waves in fully degenerate relativistic plasma

The combined effect of special relativity and electron degeneracy on Langmuir waves is analyzed by utilizing a rigorous fully relativistic hydrodynamic model. Assuming a traveling wave solution form, a set of conservation laws is identified, together with a pseudo-potential function depending on the relativistic parameter p<inf>F</inf>/(m c) (where p<inf>F</inf> is the Fermi momentum, m is the mass of the charge carriers and c the speed of light), as well as on the amplitude of the electrostatic energy perturbation.

Narrative Bifurcation, Cloud Computing Interfaces and Hitchcok

From a narratological perspective, this paper aims to address the theoretical issues concerning the functioning of the so called «narrative bifurcation» in data presentation and information retrieval. Its use in cyberspace calls for a reassessment as a storytelling device. Films have shown its fundamental role for the creation of suspense. Interactive fiction and games have unveiled the possibility of plots with multiple choices, giving continuity to cinema split-screen experiences. Using practical examples, this paper will show how this storytelling tool returns to its primitive form and ends up by conditioning cloud computing interface design.

Isolation of DNA sequences with homology to a degenerate FaRP oligonucleotide from the crayfish Procambarus clarkii

The neuropeptide Th1RFamide with the sequence Phe-Met-Arg-Phe-amide was originally isolated in the clam Macrocallista nimbosa (price and Greenberg, 1977). Since its discovery, a large family ofFl\1RFamide-related peptides termed FaRPs have been found to be present in all major animal phyla with functions ranging from modulation of neuronal activity to alteration of muscular contractions. However, little is known about the genetics encoding these peptides, especially in invertebrates. As FaRP-encoding genes have yet to be investigated in the invertebrate Malacostracean subphylum, the isolation and characterization ofFaRP-encoding DNA and mRNA was pursued in this project. The immediate aims of this thesis were: (1) to amplify mRNA sequences of Procambarus clarkii using a degenerate oligonucleotide primer deduced from the common amino acid sequence ofisolated Procambarus FaRPS, (2) to determine if these amplification products encode FaRP gene sequences, and (3) to create a selective cDNA library of sequences recognized by the degenerate oligonucleotide primer. The polymerase chain reaction - rapid amplification of cDNA ends (PCR-RACE) is a procedure in which a single gene-specific primer is used in conjunction with a generalized 3' or 5' primer to amplify copies ofthe region between a single point in the transcript and the 3' or 5' end of cDNA of interest (Frohman et aI., 1988). PCRRACE reactions were optimized with respect to primers used, buffer composition, cycle number, nature ofgenetic substrate to be amplified, annealing, extension and denaturation temperatures and times, and use of reamplification procedures. Amplification products were cloned into plasmid vectors and recombinant products were isolated, as were the recombinant plaques formed in the selective cDNA library. Labeled amplification products were hybridized to recombinant bacteriophage to determine ligated amplification product presence. When sequenced, the five isolated PCR-RACE amplification products were determined not to possess FaRP-encoding sequences. The 200bp, 450bp, and 1500bp sequences showed homology to the Caenorhabditis elegans cosmid K09A11, which encodes for cytochrome P450; transfer-RNA; transposase; and tRNA-Tyr, while the 500bp and 750bp sequences showed homology with the complete genome of the Vaccinia virus. Under the employed amplification conditions the degenerate oligonucleotide primer was observed to bind to and to amplify sequences with either 9 or 10bp of 17bp identity. The selective cDNA library was obselVed to be of extremely low titre. When library titre was increased, white. plaques were isolated. Amplification analysis of eight isolated Agt11 sequences from these plaques indicated an absence of an insertion sequence. The degenerate 17 base oligonucleotide primer synthesized from the common amino acid sequence ofisolated Procambarus FaRPs was thus determined to be non-specific in its binding under the conditions required for its use, and to be insufficient for the isolation and identification ofFaRP-encoding sequences. A more specific primer oflonger sequence, lower degeneracy, and higher melting temperature (TJ is recommended for further investigation into the FaRP-encoding genes of Procambarlls clarkii.

Automaticité dans le coeur ischémique : analyse de bifurcation d’un modèle mathématique de cellule ventriculaire humaine

L’ischémie aigüe (restriction de la perfusion suite à l’infarctus du myocarde) induit des changements majeurs des propriétés électrophysiologique du tissu ventriculaire. Dans la zone ischémique, on observe une augmentation du potassium extracellulaire qui provoque l’élévation du potentiel membranaire et induit un "courant de lésion" circulant entre la zone affectée et saine. Le manque d’oxygène modifie le métabolisme des cellules et diminue la production d’ATP, ce qui entraîne l’ouverture de canaux potassique ATP-dépendant. La tachycardie, la fibrillation ventriculaire et la mort subite sont des conséquences possibles de l’ischémie. Cependant les mécanismes responsables de ces complications ne sont pas clairement établis. La création de foyer ectopique (automaticité), constitue une hypothèse intéressante expliquant la création de ses arythmies. Nous étudions l’effet de l’ischémie sur l’automaticité à l’aide d’un modèle mathématique de la cellule ventriculaire humaine (Ten Tusscher, 2006) et d’une analyse exhaustive des bifurcations en fonction de trois paramètres : la concentration de potassium extracellulaire, le "courant de lésion" et l’ouverture de canaux potassiques ATP-dépendant. Dans ce modèle, nous trouvons que seule la présence du courant de lésion peut entrainer une activité automatique. Les changements de potassium extracellulaire et du courant potassique ATP-dépendant altèrent toutefois la structure de bifurcation.

Investigations on the Dynamics of Combination Maps and the Analysis of Bifurcation in a Discontinuous Logistic Map

This thesis is a study of discrete nonlinear systems represented by one dimensional mappings.As one dimensional interative maps represent Poincarre sections of higher dimensional flows,they offer a convenient means to understand the dynamical evolution of many physical systems.It highlighting the basic ideas of deterministic chaos.Qualitative and quantitative measures for the detection and characterization of chaos in nonlinear systems are discussed.Some simple mathematical models exhibiting chaos are presented.The bifurcation scenario and the possible routes to chaos are explained.It present the results of the numerical computational of the Lyapunov exponents (λ) of one dimensional maps.This thesis focuses on the results obtained by our investigations on combinations maps,scaling behaviour of the Lyapunov characteristic exponents of one dimensional maps and the nature of bifurcations in a discontinous logistic map.It gives a review of the major routes to chaos in dissipative systems,namely, Period-doubling ,Intermittency and Crises.This study gives a theoretical understanding of the route to chaos in discontinous systems.A detailed analysis of the dynamics of a discontinous logistic map is carried out, both analytically and numerically ,to understand the route it follows to chaos.The present analysis deals only with the case of the discontinuity parameter applied to the right half of the interval of mapping.A detailed analysis for the n –furcations of various periodicities can be made and a more general theory for the map with discontinuities applied at different positions can be on a similar footing

Nonlinear Dynamics of Nd:YAG lasers: Hopf bifurcation, Multistability and Chaotic Synchronization

In this thesis we have presented some aspects of the nonlinear dynamics of Nd:YAG lasers including synchronization, Hopf bifurcation, chaos control and delay induced multistability.We have chosen diode pumped Nd:YAG laser with intracavity KTP crystal operating with two mode and three mode output as our model system.Different types of orientation for the laser cavity modes were considered to carry out the studies. For laser operating with two mode output we have chosen the modes as having parallel polarization and perpendicular polarization. For laser having three mode output, we have chosen them as two modes polarized parallel to each other while the third mode polarized orthogonal to them.

Z-scan and Degenerate Four Wave Mixing Studies in Certain Photonic Materials

International School of Photonics, Cochin University of Science & Technology

Degenerate four wave mixing in some metal phthalocyanines and naphthalocyanines

Here we report measurements of third-order susceptibility χ(3), figure of merit F defined as χ(3)/α (where α is the absorption coefficient) and second hyperpolarizability 〈γ〉 of some metal substituted phthalocyanines and a naphthalocyanine in solutions of dimethyl formamide using degenerate four wave mixing at 532 nm under nanosecond excitation. It was found that among samples investigated, bis-naphthalocyanine possessed the highest value of 〈γ〉 followed by the bis-phthalocyanine. This observation is explained on the basis that bis-naphthalocyanine followed by bis-phthalocyanine has higher degree of π electron conjugation.

Third order nonlinear optical studies in europium naphthalocyanine using degenerate four wave mixing and Z-scan

Third order nonlinear susceptibility χ(3) and second hyperpolarizability (γ) of a bis-naphthalocyanine viz. europium naphthalocyanines, Eu(Nc)2, were measured in dimethyl formamide solution using degenerate four wave mixing at 532 nm under nanosecond pulse excitation. Effective nonlinear absorption coefficient, βeff and imaginary part of nonlinear susceptibility, Im(χ(3)) were obtained using open aperture /Z-scan technique at the same wavelength. Optical limiting property of the sample was also investigated. The role of excited state absorption in deciding the nonlinear properties of this material is discussed.

Hopf bifurcation in parallel polarized Nd:YAG laser

Dynamics of Nd:YAG laser with intracavity KTP crystal operating in two parallel polarized modes is investigated analytically and numerically. System equilibrium points were found out and the stability of each of them was checked using Routh–Hurwitz criteria and also by calculating the eigen values of the Jacobian. It is found that the system possesses three equilibrium points for (Ij, Gj), where j = 1, 2. One of these equilibrium points undergoes Hopf bifurcation in output dynamics as the control parameter is increased. The other two remain unstable throughout the entire region of the parameter space. Our numerical analysis of the Hopf bifurcation phenomena is found to be in good agreement with the analytical results. Nature of energy transfer between the two modes is also studied numerically.

Bifurcation structure and Lyapunov exponents of a modulated logistic map

We have studied the bifurcation structure of the logistic map with a time dependant control parameter. By introducing a specific nonlinear variation for the parameter, we show that the bifurcation structure is modified qualitatively as well as quantitatively from the first bifurcation onwards. We have also computed the two Lyapunov exponents of the system and find that the modulated logistic map is less chaotic compared to the logistic map.

Subcritical Hopf bifurcation in Ne-Nd hollow cathode discharge

We report the experimental observation of subcritical Hopf bifurcation and the existence of non-oscillating “windows” in the dynamics of a Ne-Nd hollow cathode discharge current as the control parameter.

The role of energy correlations on Coulomb suppression in ballistic conductors contacted to degenerate reservoirs

Coulomb suppression of shot noise in a ballistic diode connected to degenerate ideal contacts is analyzed in terms of the correlations taking place between current fluctuations due to carriers injected with different energies. By using Monte Carlo simulations we show that at low frequencies the origin of Coulomb suppression can be traced back to the negative correlations existing between electrons injected with an energy close to that of the potential barrier present in the diode active region and all other carriers injected with higher energies. Correlations between electrons with energy above the potential barrier with the rest of electrons are found to influence significantly the spectra at high frequency in the cutoff region.