Time-Dependent Cylindrical and Spherical Solitary Structures and Double Layers of Dust Ion-Acoustic Waves in Ultra-Relativistic Dense Plasma

Cylindrical and spherical (nonplanar) solitary waves (SWs) and double layers (DLs) in a multi-ion plasma system (containing inertial positively as well as negatively charged ions, non-inertial degenerate electrons, and negatively charged static dust) are studied by employing the standard reductive perturbation method. The modified Gardner (MG) equation describing the nonlinear propagation of the dust ion-acoustic (DIA) waves is derived, and its nonplanar SWs and DLs solutions are numerically analyzed. The parametric regimes for the existence of SWs, which are associated with both positive and negative potential, and DLs which are associated with negative potential, are obtained. The basic features of nonplanar DIA SWs, and DLs, which are found to be different from planar ones, are also identified.     

Nonplanar Electron - Acoustic Shock Waves with Superthermal Hot Electrons

Nonplanar electron-acoustic shock waves having superthermal hot electrons are investigated with two temperature electrons model in unmagnetized plasma. Using reductive perturbation method, Korteweg-de Vries-Burgers (KdVB) equation is obtained in the cylindrical/spherical coordinates. Dissipation effect is introduced in the model by means of kinematic viscosity term. On the basis of the solutions of KdVB equation, variation of shock waves features (amplitude, velocity and width) with different plasma parameters are analysed. KdV-Burgers equation always leads to monotonic solitons and no oscillatory peak may appear. The combined effect of particle density (α), superthermal parameter (κ), electron temperature ratio (??) and kinetic viscosity (η₀) is numerically studied, and it is observed that these parameters significantly change the properties of the shock waves in nonplanar geometry especially in spherical coordinates. Results could be helpful to analyse the soliton features in laboratory as well as in the space environments.     

Spherical Kadomtsev-Petviashvili Solitons in a Suprathermal Complex Plasma

The nonlinear aspects of nonplanar dust acoustic (DA) solitary waves are investigated in an unmagnetized complex plasma comprising of cold dust grains, kappa-distributed ions as well as electrons. The nonplanar DA solitons are studied based on the reductive perturbation technique. It is shown that the evolution of DA solitons is governed by a spherical Kadomtsev-Petviashvili (sKP) equation and then the impact of suprathermality on the spatial structure as well as the nature of DA soliton is studied. It seems that the properties of DA solitons in nonplanar geometry are quite different from that of the planar solitons.     

Spherical Kadomtsev-Petviashvili Solitons in a Suprathermal Complex Plasma

The nonlinear aspects of nonplanar dust acoustic (DA) solitary waves are investigated in an unmagnetized complex plasma comprising of cold dust grains,kappa-distributed ions as well as electrons.The nonplanar DA solitons are studied based on the reductive perturbation technique.It is shown that the evolution of DA solitons is governed by a spherical Kadomtsev-Petviashvili (sKP) equation and then the impact of suprathermality on the spatial structure as well as the nature of DA soliton is studied.It seems that the properties of DA solitons in nonplanar geometry are quite different from that of the planar solitons.     

Dual resonance theory

It is suggested that a dual model could provide a Born approximation to a complete theory of hadrons. After reviewing various properties of Veneziano model amplitudes, including their underlying algebraic structure, more recent developments are discussed. The spectrum generating algebra is constructed and used to prove the no-ghost theorem for space-time dimension d ? 26. A modification of the Veneziano model incorporating SU(N) symmetry in a dynamical fashion is shown to have critical dimension 26?N. A detailed discussion of the dual pion model and its extension to fermions is presented. It is proved that both the meson and fermion sectors are ghost free for d ? 10. Finally, there is a discussion of nonplanar models and their possible connection with the pomeron singularities arising from nonplanar loop diagrams.     

Reanalysis of optical-axis perturbation in nonplanar ring resonators in ray matrix approach with appropriate coordinate systems

Ray matrix approach with appropriate coordinate systems has been proposed in this paper. It is employed to analyze the optical-axis perturbation in nonplanar ring resonators. The sensitivities of optical-axis decentration (SD) and optical-axis tilt (ST) in nonplanar resonators with 90° and 270° image rotation are discussed in detail in the region of 0 < K < 8, where K is the ratio of the total cavity length to the radius of the curvature mirrors. There are both four singular points in the whole region of 0 < K < 8. On the left of the first singularity, it is found that the longer the mirror radius, the less the optical-axis decentration sensitivity. This is opposite the behavior of planar ring resonators, but the behaviors of optical-axis tilt sensitivity in planar and nonplanar ring resonators are similar. It is worth to note that SD and ST in the nonplanar resonator with certain parameters have the similar singularities. The analysis in this paper is important for the cavity design and alignment of nonplanar ring resonators.     

Cylindrical and Spherical Electron-Acoustic Shock Waves in Electron-Positron-Ion Plasmas with Nonextensive Electrons and Positrons

Electron-acoustic shock waves (EASWs) in an unmagnetized four-component plasma (containing hot electrons and positrons following the q-nonextensive distribution, cold mobile viscous electron fluid, and immobile positive ions) are studied in nonplanar (cylindrical and spherical) geometry. With the help of the reductive perturbation method, the modified Burgers equation is derived. Analytically, the effects of nonplanar geometry, nonextensivity, relative number density and temperature ratios, and cold electron kinematic viscosity on the basic properties (viz. amplitude, width, speed, etc.) of EASWs are discussed. It is examined that the EASWs in nonplanar geometry significantly differ from those in planar geometry. The results of this investigation can be helpful in understanding the nonlinear features of EASWs in various astrophysical plasmas.     

Nonplanar contribution to the four-loop universal anomalous dimension of the twist-2 Wilson operators in the $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory

The result of the direct component calculation of the nonplanar contribution to the four-loop anomalous dimension of the Konishi operator in the \(\mathcal{N}\) = 4 supersymmetric Yang-Mills theory is reported. The result contains only the ζ(5) term proportional to the ζ(5) contribution in the planar case, which comes only from wrapping corrections. The previous calculations of the leading transcendent contribution to the anomalous dimension of the twist-2 operators for first three even moments are also expanded to the nonplanar case and the same results as in the planar case are obtained up to a general factor. These two results imply that the nonplanar contribution of the four-loop universal anomalous dimension of the twist-2 Wilson operators with an arbitrary Lorentz spin j is proportional to S ₁ ² (j)ζ(5). This result provides a nonstandard square logarithmic asymptotic behavior ln² j for large Lorentz spins j of the operators.     

Planar and Nonplanar Shock Waves in a Degenerate Quantum Plasma

The nonlinear propagation of modified electron‐acoustic (mEA) shock waves in an unmagnetized, collisionless, relativistic, degenerate quantum plasma (containing non‐relativistic degenerate inertial cold electrons, both nonrelativistic and ultra‐relativistic degenerate hot electron and inertial positron fluids, and positively charged static ions) has been investigated theoretically. The well‐known Burgers type equation has been derived for both planar and nonplanar geometry by employing the reductive perturbation method. The shock wave solution has also been obtained and numerically analyzed. It has been observed that the mEA shock waves are significantly modified due to the effects of degenerate pressure and other plasma parameters arised in this investigation. The properties of planar Burgers shocks are quite different from those of nonplanar Burgers shocks. The basic features and the underlying physics of shock waves, which are relevant to some astrophysical compact objects (viz. non‐rotating white dwarfs, neutron stars, etc.), are briefly discussed. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optical-axis perturbation in nonplanar ring resonators

Several findings on the optical-axis perturbation of nonplanar ring resonators have been obtained identical by utilizing the augmented 5 × 5 matrix formulation and augmented 6 × 6 matrix formulation, respectively. It has been found out that in the whole region of 0 < L/R < 2, the longer the mirror radius, the higher the sensitivity of optical-axis decentration, while the total cavity length is L and the radius of the curvature mirrors is R. The sensitivity of optical-axis tilt in the region of 0 < L/R < 2 has been carried out too. The optical-axis decentration and optical-axis tilt inside the region of L/R > 2 have been discussed. The differences of the optical-axis perturbation between planar and nonplanar ring resonators have also been analyzed. These interesting findings are important to the cavity design of nonplanar ring resonators.     

Nonplanar Ion-Acoustic Solitons in Electron-Positron-Ion Quantum Plasmas

The propagation of nonplanar quantum ion-acoustic solitary waves in a dense, unmagnetized electron-positronion （e-p-i） plasma are studied by using the Korteweg-de Vries （KdV） model. The quantum hydrodynamic （QHD） equations are used taking into account the quantum diffraction and quantum statistics corrections. The analytical and numerical solutions of KdV equation reveal that the nonplanar ion-acoustic solitons arc modified significantly with quantum corrections and positron concentration, and behave differently in different geometries.     

Particle diffraction by a thin rigid crystal lattice: A formal approach

The diffraction process of a particle by a thin rigid crystal is considered. An integral equation is derived for the particle wave function φ which is quite suitable to obtain physical and mathematical properties. A class of potentials is presented for which the integral equation can be solved by means of the Fredholm theory. The convergence of the Born series for φ is studied, as well as the existence and convergence properties of the transmission and reflection amplitudes T^±. Results are given about φ and T^±: (i) at high energies, (ii) at those special energies such that new diffracted beams appear, and (iii) at glancing incidence on the crystal. Analyticity properties of T^± as functions of the energy are derived and analytic representations for them are presented. The diffraction process when the particle is being simultaneously accelerated by a uniform electric field is also considered. Finally, the generalization to the case of an imperfect thin crystal is treated.     

Mathieu-Gauss beams: A thermal consideration

The generation of Helmholtz-Gauss beam families such as Mathieu-Gauss (MG) and Bessel-Gauss (BG) beams can be dramatically suffered from heat-induced thermal effects. This work is devoted to the generation of MG beams under severe induced thermal loads. The output MG beams of a solid-state laser were assumed to pass through an ABCD system matrix. The simulated results which were achieved by characterization of the transfer matrix of the thermally affected inhomogeneous medium report systematic variations of the intensity profile of MG beams from pump power of 1-5 W. It is shown that for high values of pump power, the thermal effects are so influential and the beam intensity profile is so changed that the identification of MG beams is not easily possible at first hand. The results can facilitate this identification and can be utilized for deeper understanding of thermal effects phenomena.     

On the numerical solution of nonplanar dust-acoustic super rogue waves in a strongly coupled dusty plasma

The occurrence of cylindrical and spherical low-frequency dust-acoustic freak waves (DAFWs) in a strongly coupled dusty plasma is numerically investigated in the framework of the phenomenological generalized hydrodynamic model. The basic equations are reduced to a modified/nonplanar nonlinear Schrödinger equation (mNLSE) using a reductive perturbation method. The existing regions of instability structures have been carefully identified. For studying the propagation of rogue waves in case of nonplanar (cylindrical and spherical coordinates), the mNLSE has been solved numerically. The effects of nonplanar geometries on the basic features of the DAFWs for the first- and second-orders rogue waves are discussed. Finally, our results are of relevance in ultradense situations where nonplaner geometrical effects are significant. In particular, we expect for our findings to be important to understand the DA breathers experimentally in a strongly coupled dusty plasma.     

Nonlinear Dynamics in a Nonextensive Complex Plasma with Viscous Electron Fluids

Cylindrical and spherical dust-electron-acoustic(DEA) shock waves and double layers in an unmagnetized,collisionless,complex or dusty plasma system are carried out.The plasma system is assumed to be composed of inertial and viscous cold electron fluids,nonextensive distributed hot electrons,Maxwellian ions,and negatively charged stationary dust grains.The standard reductive perturbation technique is used to derive the nonlinear dynamical equations,that is,the nonplanar Burgers equation and the nonplanar further Burgers equation.They are also numerically analyzed to investigate the basic features of shock waves and double layers(DLs).It is observed that the roles of the viscous cold electron fluids,nonextensivity of hot electrons,and other plasma parameters in this investigation have significantly modified the basic features(such as,polarity,amplitude and width) of the nonplanar DEA shock waves and DLs.It is also observed that the strength of the shock is maximal for the spherical geometry,intermediate for cylindrical geometry,while it is minimal for the planar geometry.The findings of our results obtained from this theoretical investigation may be useful in understanding the nonlinear phenomena associated with the nonplanar DEA waves in both space and laboratory plasmas.     

The Bethe-Goldstone equation with singular interactions: A fully off-shell solution for the boundary condition model

The mutual interaction of a pair of fermions imbedded in a many-body system of identical particles when they are excited out of the filled Fermi sea, is studied via the T-matrix or transition amplitude specified by the Bethe-Goldstone (BG) equation. The role of the bare two-body interaction is emphasised, and in particular the consequences are elucidated of whether the potential is “well-behaved” (nonsingular) or not. The properties of the BG T-matrix, including generalized orthonormality and completeness relations, are derived both for nonsingular potentials and for singular potentials containing an infinite hard core. General analytic properties are exploited to derive relations that express the fully off-shell BG T-matrix purely in terms of the half-shell amplitude (and the properties of any possible bound states in the medium). The general formalism is illustrated by deriving exact analytic expressions for the fully off-shell BG T-matrices for a pair of particles with equal and opposite momenta interacting via either of two singular model interactions; namely, the pure hard-core interaction and the boundary condition model. Results for both models are expressed in terms of the solution to a simple one-dimensional Fredholm integral equation. The analytic properties of the solutions are discussed and exploited to prove both their uniqueness and that they satisfy the various general relations derived. To our knowledge, these results represent the first exact nontrivial solution to the fully off-shell BG equation for any local potential, or singular limiting case thereof.     

Spectral manifestations of nonplanarity effects in Pd complexes of porphyrins

It is found on the basis of kinetic spectral studies in nonane, dodecane, and vitreous solutions at 77 K (phosphorescence spectra, polarized phosphorescence, decay kinetics, and phosphorescence excitation spectra) that symmetric and nonsymmetric Pd-porphyrins are characterized by the presence of two noninteracting spectrally different long-and short-wavelength forms in the ground state. The existence of the long-wavelength form is associated with the displacement of the central Pd ion from the macrocycle plane, which leads to the formation of the nonplanar “dome” conformation of the porphyrin ligand. In the case of a nonsymmetrically substituted Pd-tetramethyl-diethylporphyrin molecule, the nonplanar conformation of the π-conjugated macrocycle is characterized by the splitting of the triplet state into two components (T ₁ and T ₂, Δν=90 cm^?1 at 77 K). Both narrow components, which have the same decay, form a dual phosphorescence of the long-wavelength form of this compound, which is caused by efficient thermal exchange between T ₁ and T ₂ levels in the course of deactivation to the ground state.     

Manifestation of nonplanarity effects and charge-transfer interactions in spectral and kinetic properties of triplet states of sterically strained octaethylporphyrins

Properties of the triplet states of octaethylporphyrins with the steric hindrance (free bases and Pd complexes) are studied by the methods of stationary and kinetic spectroscopy in the temperature range from 77 to 293 K. The mono-mesophenyl substitution results in a decrease in the quantum yield and shortening of the phosphorescence lifetime of Pd complexes by 250–3500 times in degassed toluene at 293 K. The phosphorescence quenching is caused by nonplanar dynamic conformations of the porphyrin macrocycle in the T ₁ state, which also lead to the appearance of new bands at λ～1000 nm in the T-T absorption spectra. As the number of meso-phenyls (Pd-octaetyltetraphenylporphyrin) increases, the quantum yield of phosphorescence further decreases (<10^?5) at 293 K, the lifetime of the T ₁ state shortens (<50 ns), and the efficiency of the singlet oxygen generation abruptly decreases (<0.01). The intense bathochromic emission of this compound at 705 nm with a lifetime of 1 ms at 77 K is assigned to the phosphorescence of a nonplanar conformation. Upon meso-orthonitrophenyl substitution, the quenching of phosphorescence of Pd complexes (by more than 10⁴ times at 293 K) is caused by direct nonadiabatic photoinduced electron transfer from the T ₁ state to the nearest charge-transfer state with the probability k _et ^T =(1.5–4.0)×10⁶ s^?1. The induced absorption of ortho-nitro derivatives in the region between 110 and 1400 nm is caused by mixing of pure ππ* states with charge-transfer states.     

Absorption and fluorescent properties of pyrylium compounds: I. The nature of electronic transitions and structural rearrangement in the excited state

The localization of molecular orbitals in 2,4,6-substituted derivatives of pyrylium is studied. The conformation of three asymmetrical molecules with oxyethyl substituents in positions 2 and 4 and different substituents in position 6 of the pyrylium ring is calculated by the AM1 method. The localization of the four upper occupied and two lower unoccupied MOs is determined, the fragment localization numbers are found, and the energies of five optical transitions, localization numbers, and the numbers of charge transfer between fragments are calculated. The conformation analysis of molecules in the S ₀ and S ₁ states is performed. Solid and liquid pyrylium solutions of different viscosity and polarity are experimentally investigated. The absorption spectra are recorded and absorption cross sections are measured, as well as fluorescence spectra and fluorescence anisotropy spectra. The following conclusions are made. In nonplanar molecules of pyrylium salts, four absorption transitions are localized at different parts of the molecule containing the pyrylium ring and one of the substituents. Upon excitation of molecules with complex substituents in position 6, the molecular fragment in position 2 turns around. This results in a flattening of the molecular fragment containing the pyrylium ring and substituents 2 and 6 on which the fluorescence transition is localized. The rearrangement involves the lowamplitude motion; it occurs almost without a loss of the excitation energy and only slightly affects the localization of molecular orbitals. As a result, two excited conformers are formed that possess close absorption and fluorescence properties. The radiative transitions in these conformers completely determine fluorescence of liquid solutions of any viscosity, including glycerol solutions. Strong solvatochromism is related to the nonplanar structure of stable pyrylium molecules, whereas the weak solvatochromism of liquid solutions is caused by localization of radiative transitions on a planar fragment of unstable fluorescing conformers.     

Spinor with Schrödinger symmetry and non-relativistic supersymmetry

We construct the d-dimensional “half” Schrödinger equation, which is a kind of the root of the Schrödinger equation, from the (d+1)-dimensional free Dirac equation. The solution of the “half” Schrödinger equation also satisfies the usual free Schrödinger equation. We also find that the explicit transformation laws of the Schrödinger and the half Schrödinger fields under the Schrödinger symmetry transformation are derived by starting from the Klein-Gordon equation and the Dirac equation in d+1 dimensions. We derive the 3- and 4-dimensional super-Schrödinger algebra from the superconformal algebra in 4 and 5 dimensions. The algebra is realized by introducing two complex scalar and one (complex) spinor fields and the explicit transformation properties have been found.