scholarly journals RESONANCES ON HEDGEHOG MANIFOLDS

2013 ◽  
Vol 53 (5) ◽  
pp. 416-426 ◽  
Author(s):  
Pavel Exner ◽  
Jiří Lipovský
Keyword(s):  
Real Axis ◽  
Quantum Particle ◽  
Single Point ◽  
Three Dimensional ◽  
High Energy ◽  
Quantum Graphs ◽  
The Real ◽  
Momentum Plane ◽  
Embedded Eigenvalues ◽  
Aharonov Bohm

We discuss resonances for a nonrelativistic and spinless quantum particle confined to a two- or three-dimensional Riemannian manifold to which a finite number of semiinfinite leads is attached. Resolvent and scattering resonances are shown to coincide in this situation. Next we consider the resonances together with embedded eigenvalues and ask about the high-energy asymptotics of such a family. For the case when all the halflines are attached at a single point we prove that all resonances are in the momentum plane confined to a strip parallel to the real axis, in contrast to the analogous asymptotics in some metric quantum graphs; we illustrate this on several simple examples. On the other hand, the resonance behaviour can be influenced by a magnetic field. We provide an example of such a ‘hedgehog’ manifold at which a suitable Aharonov-Bohm flux leads to absence of any true resonance, i.e. that corresponding to a pole outside the real axis.

FRACTALS WITH HYPERBOLIC SCATORS IN 1 + 2 DIMENSIONS

Fractals ◽  
2015 ◽  
Vol 23 (02) ◽  
pp. 1550004
Author(s):  
M. FERNÁNDEZ-GUASTI
Keyword(s):  
Real Axis ◽  
Three Dimensional ◽  
Basins Of Attraction ◽  
Mandelbrot Set ◽  
Hyperbolic Numbers ◽  
The Real ◽  
Real Roots ◽  
3D Objects ◽  
3D Space ◽  
Self Similar

A nondistributive scator algebra in 1 + 2 dimensions is used to map the quadratic iteration. The hyperbolic numbers square bound set reveals a rich structure when taken into the three-dimensional (3D) hyperbolic scator space. Self-similar small copies of the larger set are obtained along the real axis. These self-similar sets are located at the same positions and have equivalent relative sizes as the small M-set copies found between the Myrberg-Feigenbaum (MF) point and -2 in the complex Mandelbrot set. Furthermore, these small copies are self similar 3D copies of the larger 3D bound set. The real roots of the respective polynomials exhibit basins of attraction in a 3D space. Slices of the 3D confined scator set, labeled [Formula: see text](s;x,y), are shown at different planes to give an approximate idea of the 3D objects highly complicated boundary.

scholarly journals POSSIBILITY OF FORMING A LARGE DCC IN ULTRA-RELATIVISTIC HEAVY-ION COLLISIONS

2000 ◽  
Vol 15 (15) ◽  
pp. 2269-2288
Author(s):  
SANATAN DIGAL ◽  
RAJARSHI RAY ◽  
SUPRATIM SENGUPTA ◽  
AJIT M. SRIVASTAVA
Keyword(s):  
Three Dimensional ◽  
Thermal Fluctuations ◽  
Heavy Ion ◽  
High Energy ◽  
Chiral Condensate ◽  
Relativistic Heavy Ion Collisions ◽  
Maximum Temperature ◽  
Chiral Field ◽  
Heavy Nuclei ◽  
True Vacuum

We demonstrate the possibility of forming a single, large domain of disoriented chiral condensate (DCC) in a heavy-ion collision. In our scenario, rapid initial heating of the parton system provides a driving force for the chiral field, moving it away from the true vacuum and forcing it to go to the opposite point on the vacuum manifold. This converts the entire hot region into a single DCC domain. Subsequent rolling down of the chiral field to its true vacuum will then lead to emission of a large number of (approximately) coherent pions. The requirement of suppression of thermal fluctuations to maintain the (approximate) coherence of such a large DCC domain, favors three-dimensional expansion of the plasma over the longitudinal expansion even at very early stages of evolution. This also constrains the maximum temperature of the system to lie within a window. We roughly estimate this window to be about 200–400 MeV. These results lead us to predict that extremely high energy collisions of very small nuclei (possibly hadrons) are better suited for observing signatures of a large DCC. Another possibility is to focus on peripheral collisions of heavy nuclei.

Propagation of cosmic rays and their secondaries in the intracluster medium

2020 ◽  
Vol 15 (S359) ◽  
pp. 178-179
Author(s):  
Saqib Hussain ◽  
Rafael Alves Batista ◽  
Elisabete Maria de Gouveia Dal Pino ◽  
Klaus Dolag
Keyword(s):  
Cosmic Rays ◽  
Gamma Rays ◽  
Intergalactic Medium ◽  
Three Dimensional ◽  
High Energy ◽  
Intracluster Medium ◽  
High Energy Cosmic Rays ◽  
Test Particles

AbstractWe present results of the propagation of high-energy cosmic rays (CRs) and their secondaries in the intracluster medium (ICM). To this end, we employ three-dimensional cosmological magnetohydrodynamical simulations of the turbulent intergalactic medium to explore the propagation of CRs with energies between 1014 and 1019 eV. We study the interaction of test particles with this environment considering all relevant electromagnetic, photohadronic, photonuclear, and hadronuclear processes. Finally, we discuss the consequences of the confinement of high-energy CRs in clusters for the production of gamma rays and neutrinos.

scholarly journals Spatially Resolved Forming Mechanisms Detection in Single Point Incremental Forming Using Synchrotron Based Texture Analysis

2021 ◽  
Author(s):  
Mateus Dobecki ◽  
Alexander Poeche ◽  
Walter Reimers
Keyword(s):  
Texture Analysis ◽  
Incremental Forming ◽  
Single Point ◽  
High Energy ◽  
X Ray Diffraction ◽  
X Ray ◽  
Forming Mechanism ◽  
Spatially Resolved ◽  
Step Down ◽  
Stress States

AbstractDespite the ongoing success of understanding the deformation states in sheets manufactured by single-point incremental forming (SPIF), the unawareness of the spatially resolved influence of the forming mechanisms on the residual stress states of incrementally formed sheet metal parts impedes their application-optimized use. In this study, a well-founded experimental proof of the occurring forming mechanisms shear, bending and stretching is presented using spatially resolved, high-energy synchrotron x-ray diffraction-based texture analysis in transmission mode. The measuring method allows even near-surface areas to be examined without any impairment of microstructural influences due to tribological reactions. The depth-resolved texture evolution for different sets of forming parameters offers insights into the forming mechanisms acting in SPIF. Therefore, the forming mechanisms are triggered explicitly by adjusting the vertical step-down increment Δz for groove, plate and truncated cone geometries. The texture analysis reveals that the process parameters and the specimen geometries used lead to characteristic changes in the crystallites’ orientation distribution in the formed parts due to plastic deformation. These forming-induced reorientations of the crystallites could be assigned to the forming mechanisms by means of defined reference states. It was found that for groove, plate and truncated cone geometries, a decreasing magnitude of step-down increments leads to a more pronounced shear deformation, which causes an increasing work hardening especially at the tool contact area of the formed parts. Larger step-down increments, on the other hand, induce a greater bending deformation. The plastic deformation by bending leads to a complex stress field that involves alternating residual tensile stresses on the tool and residual compressive stresses on the tool-averted side incrementally formed sheets. The present study demonstrates the potential of high-energy synchrotron x-ray diffraction for the spatially resolved forming mechanism research in SPIF. Controlling the residual stress states by optimizing the process parameters necessitates knowledge of the fundamental forming mechanism action.

On Graeffe's Method for Complex Roots of Algebraic Equations

1924 ◽  
Vol 22 (2) ◽  
pp. 83-87 ◽  
Author(s):  
S. Brodetsky ◽  
G. Smeal
Keyword(s):  
Nineteenth Century ◽  
Real Axis ◽  
Practical Method ◽  
Algebraic Equations ◽  
Argand Diagram ◽  
Considerable Difficulty ◽  
The Real ◽  
Real Roots ◽  
Bipolar Coordinates ◽  
Complex Roots

The only really useful practical method for solving numerical algebraic equations of higher orders, possessing complex roots, is that devised by C. H. Graeffe early in the nineteenth century. When an equation with real coefficients has only one or two pairs of complex roots, the Graeffe process leads to the evaluation of these roots without great labour. If, however, the equation has a number of pairs of complex roots there is considerable difficulty in completing the solution: the moduli of the roots are found easily, but the evaluation of the arguments often leads to long and wearisome calculations. The best method that has yet been suggested for overcoming this difficulty is that by C. Runge (Praxis der Gleichungen, Sammlung Schubert). It consists in making a change in the origin of the Argand diagram by shifting it to some other point on the real axis of the original Argand plane. The new moduli and the old moduli of the complex roots can then be used as bipolar coordinates for deducing the complex roots completely: this also checks the real roots.

Interaction between a nanocrack with surface elasticity and a screw dislocation

2016 ◽  
Vol 22 (2) ◽  
pp. 131-143 ◽  
Author(s):  
Xu Wang ◽  
Hui Fan
Keyword(s):  
Screw Dislocation ◽  
Real Axis ◽  
Analytical Study ◽  
Logarithmic Singularity ◽  
Surface Elasticity ◽  
Spontaneous Generation ◽  
The Real ◽  
Crack Tips ◽  
Interaction Problem ◽  
The Continuum

In the present analytical study, we consider the problem of a nanocrack with surface elasticity interacting with a screw dislocation. The surface elasticity is incorporated by using the continuum-based surface/interface model of Gurtin and Murdoch. By considering both distributed screw dislocations and line forces on the crack, we reduce the interaction problem to two decoupled first-order Cauchy singular integro-differential equations which can be numerically solved by the collocation method. The analysis indicates that if the dislocation is on the real axis where the crack is located, the stresses at the crack tips only exhibit the weak logarithmic singularity; if the dislocation is not on the real axis, however, the stresses exhibit both the weak logarithmic and the strong square-root singularities. Our result suggests that the surface effects of the crack will make the fracture more ductile. The criterion for the spontaneous generation of dislocations at the crack tip is proposed.

scholarly journals SPECTRAL CORRELATIONS IN DISORDERED MESOSCOPIC METALS AND THEIR RELEVANCE FOR PERSISTENT CURRENTS

1996 ◽  
Vol 10 (28) ◽  
pp. 1397-1406 ◽  
Author(s):  
AXEL VÖLKER ◽  
PETER KOPIETZ
Keyword(s):  
Energy Levels ◽  
Three Dimensional ◽  
Average Density ◽  
Electron Interaction ◽  
Energy Window ◽  
Persistent Currents ◽  
Dependent Part ◽  
The Difference ◽  
Aharonov Bohm ◽  
Grand Canonical

We use the Lanczos method to calculate the variance σ2(E, ϕ) of the number of energy levels in an energy window of width E below the Fermi energy for noninteracting disordered electrons on a thin three-dimensional ring threaded by an Aharonov–Bohm flux ϕ. We confirm numerically that for small E the flux-dependent part of σ2(E, ϕ) is well described by the Altshuler–Shklovskii-diagram involving two Cooperons. However, in the absence of electron–electron interactions this result cannot be extrapolated to energies E where the energy-dependence of the average density of states becomes significant. We discuss consequences for persistent currents and argue that for the calculation of the difference between the canonical- and grand canonical current it is crucial to take the electron–electron interaction into account.

Successive coefficients of close-to-convex functions

2020 ◽  
Vol 32 (5) ◽  
pp. 1131-1141 ◽  
Author(s):  
Paweł Zaprawa
Keyword(s):  
Real Axis ◽  
Convex Functions ◽  
Positive Direction ◽  
The Real ◽  
Coefficient Problems ◽  
The Difference

AbstractIn this paper we discuss coefficient problems for functions in the class {{\mathcal{C}}_{0}(k)}. This family is a subset of {{\mathcal{C}}}, the class of close-to-convex functions, consisting of functions which are convex in the positive direction of the real axis. Our main aim is to find some bounds of the difference of successive coefficients depending on the fixed second coefficient. Under this assumption we also estimate {|a_{n+1}|-|a_{n}|} and {|a_{n}|}. Moreover, it is proved that {\operatorname{Re}\{a_{n}\}\geq 0} for all {f\in{\mathcal{C}}_{0}(k)}.

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