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At least 271 records · Page 15

Regular and chaotic dynamics of a piecewise smooth bouncer

The dynamical properties of a particle in a gravitational field colliding with a rigid wall moving with piecewise constant velocity are studied. The linear nature of the wall's motion permits further analytical investigation than is possible for the system's sinusoidal counterpart. We consider three distinct approaches to modeling collisions: (i) elastic, (ii) inelastic with constant restitution coefficient, and (iii) inelastic with a velocity-dependent restitution function. We confirm the existence of distinct unbounded orbits (Fermi acceleration) in the elastic model, and investigate regular and chaotic behavior in the inelastic cases. We also examine in the constant restitution model trajectories wherein the particle experiences an infinite number of collisions in a finite time, i.e., the phenomenon of inelastic collapse. We address these so-called “sticking solutions” and their relation to both the overall dynamics and the phenomenon of self-reanimating chaos. Additionally, we investigate the long-term behavior of the system as a function of both initial conditions and parameter values. We find the non-smooth nature of the system produces novel bifurcation phenomena not seen in the sinusoidal model, including border-collision bifurcations. The analytical and numerical investigations reveal that although our piecewise linear bouncer is a simplified version of the sinusoidal model, the former not only captures essential features of the latter but also exhibits behavior unique to the discontinuous dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Pauli-Villars regularization in nonperturbative Hamiltonian approach on the light front

The advantage of Pauli-Villars regularization in quantum field theory quantized on the light front is explained. Simple examples of scalar λφ{sup 4} field theory and Yukawa-type model are used. We give also an example of nonperturbative calculation in the theory with Pauli-Villars fields, using for that a model of anharmonic oscillator modified by inclusion of ghost variables playing the role similar to Pauli-Villars fields.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Defect reduction in overgrown semi-polar (11-22) GaN on a regularly arrayed micro-rod array template

We demonstrate a great improvement in the crystal quality of our semi-polar (11-22) GaN overgrown on regularly arrayed micro-rod templates fabricated using a combination of industry-matched photolithography and dry-etching techniques. As a result of our micro-rod configuration specially designed, an intrinsic issue on the anisotropic growth rate which is a great challenge in conventional overgrowth technique for semi-polar GaN has been resolved. Transmission electron microscopy measurements show a different mechanism of defect reduction from conventional overgrowth techniques and also demonstrate major advantages of our approach. The dislocations existing in the GaN micro-rods are effectively blocked by both a SiO{sub 2} mask on the top of each GaN micro-rod and lateral growth along the c-direction, where the growth rate along the c-direction is faster than that along any other direction. Basal stacking faults (BSFs) are also effectively impeded, leading to a distribution of BSF-free regions periodically spaced by BSF regions along the [-1-123] direction, in which high and low BSF density areas further show a periodic distribution along the [1-100] direction. Furthermore, a defect reduction model is proposed for further improvement in the crystalline quality of overgrown (11-22) GaN on sapphire.

36 MATERIALS SCIENCE↗

Toroidal regularization of the guiding center Lagrangian

In the Lagrangian theory of guiding center motion, an effective magnetic field B* = B+ (m/e)v ∥ ∇ x b appears prominently in the equations of motion. Because the parallel component of this field can vanish, there is a range of parallel velocities where the Lagrangian guiding center equations of motion are either ill-defined or very badly behaved. Moreover, the velocity dependence of B* greatly complicates the identification of canonical variables and therefore the formulation of symplectic integrators for guiding center dynamics. Here, this letter introduces a simple coordinate transformation that alleviates both these problems simultaneously. In the new coordinates, the Liouville volume element is equal to the toroidal contravariant component of the magnetic field. Consequently, the large-velocity singularity is completely eliminated. Moreover, passing from the new coordinate system to canonical coordinates is extremely simple, even if the magnetic field is devoid of flux surfaces. We demonstrate the utility of this approach in regularizing the guiding center Lagrangian by presenting a new and stable one-step variational integrator for guiding centers moving in arbitrary time-dependent electromagnetic fields.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Using Poisson-regularized inversion of Bremsstrahlung emission to extract full electron energy distribution functions from x-ray pulse-height detector data

We measured Electron Energy Distribution Functions (EEDFs) from below 200 eV to over 8 keV and spanning five orders-of-magnitude in intensity, produced in a low-power, RF-heated, tandem mirror discharge in the PFRC-II apparatus. The EEDF was obtained from the x-ray energy distribution function (XEDF) using a novel Poisson-regularized spectrum inversion algorithm applied to pulse-height spectra that included both Bremsstrahlung and line emissions. The XEDF was measured using a specially calibrated Amptek Silicon Drift Detector (SDD) pulse-height system with 125 eV FWHM at 5.9 keV. Finally, the algorithm is found to out-perform current leading x-ray inversion algorithms when the error due to counting statistics is high.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Design of semiconductor surface pits for fabrication of regular arrays of quantum dots and nanorings

We report a systematic computational study on the formation of complex nanostructures consisting of quantum dots and nanorings on surfaces of coherently strained thin films grown epitaxially on pit-patterned substrates. The analysis is based on self-consistent dynamical simulations according to a film surface evolution model that has been validated experimentally by comparison of its predictions with experimental observations on Ge films grown on Si pit-patterned substrates and is supported by linear stability theory that explains the film surface nanopattern formation as the outcome of a Stranski-Krastanow instability. Emphasis is placed on the design of conical pit patterns and the effects on the resulting film surface nanopattern of varying geometrical design parameters including film thickness, pit-pattern period, pit depth, pit opening diameter, and pit wall inclination. We demonstrate that varying the pit opening diameter and the pit wall slope leads to formation of complex nanostructures inside the pits of a regular pit pattern on the film surface, which include quantum dots, as well as single nanorings and multiple concentric nanorings that may or may not surround a central quantum dot inside each pit. Our simulation predictions demonstrate that the ordered nanostructure patterns forming on the film surface can be controlled precisely by tuning the geometrical parameters of the pits on the pit-patterned substrate. Our findings have important implications for designing optimal semiconductor surface patterns toward enabling future nanofabrication technologies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Two single-reference approaches to singlet biradicaloid problems: Complex, restricted orbitals and approximate spin-projection combined with regularized orbital-optimized Møller-Plesset perturbation theory

We present a comprehensive study of two single-reference approaches to singlet biradicaloids. These two approaches are based on the recently developed regularized orbital-optimized Møller-Plesset method (κ-OOMP2). The first approach is to combine Yamaguchi's approximate projection (AP) scheme and κ-OOMP2 with unrestricted (U) orbitals (κ-UOOMP2). By capturing only essential symmetry breaking, κ-UOOMP2 can serve as a suitable basis for AP. The second approach is κ-OOMP2 with complex, restricted (cR) orbitals (κ-cROOMP2). Although its applicability is more limited due to the comparative rarity of cR solutions, κ-cROOMP2 offers a simple framework for describing singlet biradicaloids with complex polarization while removing artificial spatial symmetry breaking. We compare the scope of these two methods with numerical studies. We show that AP+κ-UOOMP2 and κ-cROOMP2 can perform similarly well in the TS12 set, a dataset that includes 12 data points for triplet-singlet gaps of several atoms and diatomic molecules with a triplet ground state. This was also found to be true for the barrier height of a reaction involving attack on a cysteine ion by a singlet oxygen molecule. However, we also demonstrate that in highly symmetric systems like C 30 (D 5h ), κ-cROOMP2 is more suitable as it conserves spatial symmetry. Finally, we present an organic biradicaloid that does not have a κ-cROOMP2 solution in which case only AP+κ-UOOMP2 is applicable. Here, we recommend κ-cROOMP2 whenever complex polarization is essential and AP+κ-UOOMP2 for biradicaloids without essential complex polarization but with essential spin-polarization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Xanthophyll-cycle based model of the rapid photoprotection of Nannochloropsis in response to regular and irregular light/dark sequences

We explore the photoprotection dynamics of Nannochloropsis oceanica using time-correlated single photon counting under regular and irregular actinic light sequences. The varying light sequences mimic natural conditions, allowing us to probe the real-time response of non-photochemical quenching (NPQ) pathways. Durations of fluctuating light exposure during a fixed total experimental time and prior light exposure of the algae are both found to have a profound effect on NPQ. These observations are rationalized with a quantitative model based on the xanthophyll cycle and the protonation of LHCX1. The model is able to accurately describe the dynamics of non-photochemical quenching across a variety of light sequences. The combined model and observations suggest that the accumulation of a quenching complex, likely zeaxanthin bound to a protonated LHCX1, is responsible for the gradual rise in NPQ. Additionally, the model makes specific predictions for the light sequence dependence of xanthophyll concentrations that are in reasonable agreement with independent chromatography measurements taken during a specific light/dark sequence.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Laser field control of subradiant states of a system of several atoms in a configuration close to a regular polygon

Some collective excitations of an ensemble of closely spaced (two-level) atoms can be characterised by extremely low rates of radiation decay, which is of considerable interest for storing quantum information. Such (dark) states are realised, for example, in planar geometry when atoms are located at the nodes of a regular polygon. However, the decay rate of such excitations increases markedly when the geometry deviates from ideal. Using the example of small deformation of a square in a rhombus, we show that an increase in the decay rate of the dark state due to symmetry breaking can be compensated for by adjusting the transition frequency of some atoms exposed to external laser radiation. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Regularizations of time-crystal dynamics

We demonstrate herein that nonconvex Lagrangians, as contemplated in the theory of time crystals, can arise in the effective description of conventional, physically realizable systems. Such embeddings resolve dynamical singularities which arise in the reduced description. Microstructure featuring intervals of fixed velocity interrupted by quick resets—“Sisyphus dynamics”—is a generic consequence. In quantum mechanics, this microstructure can be blurred, leaving entirely regular behavior.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Crystal Structure of Clustered Regularly Interspaced Short Palindromic Repeats (CRISPR)-associated Csn2 Protein Revealed Ca[superscript 2+]-dependent Double-stranded DNA Binding Activity

Clustered regularly interspaced short palindromic repeats (CRISPR) and their associated protein genes (cas genes) are widespread in bacteria and archaea. They form a line of RNA-based immunity to eradicate invading bacteriophages and malicious plasmids. A key molecular event during this process is the acquisition of new spacers into the CRISPR loci to guide the selective degradation of the matching foreign genetic elements. Csn2 is a Nmeni subtype-specific cas gene required for new spacer acquisition. Here we characterize the Enterococcus faecalis Csn2 protein as a double-stranded (ds-) DNA-binding protein and report its 2.7 {angstrom} tetrameric ring structure. The inner circle of the Csn2 tetrameric ring is {approx}26 {angstrom} wide and populated with conserved lysine residues poised for nonspecific interactions with ds-DNA. Each Csn2 protomer contains an {alpha}/{beta} domain and an {alpha}-helical domain; significant hinge motion was observed between these two domains. Ca{sup 2+} was located at strategic positions in the oligomerization interface. We further showed that removal of Ca{sup 2+} ions altered the oligomerization state of Csn2, which in turn severely decreased its affinity for ds-DNA. In summary, our results provided the first insight into the function of the Csn2 protein in CRISPR adaptation by revealing that it is a ds-DNA-binding protein functioning at the quaternary structure level and regulated by Ca{sup 2+} ions.

59 BASIC BIOLOGICAL SCIENCES↗

Relation between the standard perturbation theory and regularized multi-point propagator method

We investigate the relation between the regularized multi-propagator method, called 'Reg PT', and the standard perturbation theory. Reg PT is one of the most successful models to describe nonlinear evolution of dark matter fluctuations. However, Reg PT is a mathematically unproven interpolation formula between the large-scale solution calculated by the standard perturbation theory and the limiting solution in the small scale calculated by the multi-point propagator method. In this paper, we give an alternative explanation for Reg PT in the context of the standard perturbation theory, showing that Reg PT does not ever have more effective information on nonlinear matter evolution than the standard perturbation theory. In other words, the solutions of the standard perturbation theory reproduce the results of N-body simulations better than those of Reg PT, especially at the high-k region. This fact means that the standard perturbation theory at the two-loop level is still one of the best predictions of the nonlinear power spectrum to date. Nevertheless, the standard perturbation theory has not been preferred because of the divergent behavior of the solution at small scales. To solve this problem, we also propose a modified standard perturbation theory which avoids the divergence.

79 ASTRONOMY AND ASTROPHYSICS↗

Lens statistics with gravitationally lensed yet morphologically regular images

GRAMORs are GRAvitationally highly magnified yet MORphologically regular images. An example of this phenomenon was discovered in the cluster MACS J1149.5+2223 in 2009. We investigate the lens statistics of GRAMORs in detail. Assuming a NFW profile for a sample of clusters, we calculate the expected number and redshift distribution of GRAMORs using parameters from COSMOS data for the number density of the background galaxy. A model with a cluster placed at z = 0.544 based on WMAP5 cosmology predicts the redshift of a GRAMOR at z≃1.49 which is close to the observed z = 1.4906. These results show that the expected number of GRAMORs is about two per cluster in the most likely case, and thus a large number of GRAMORs would be observed in a systematic survey. The probability distribution function of source redshift for GRAMORs depends strongly on dark energy and may be useful for constraining the nature of dark energy.

79 ASTRONOMY AND ASTROPHYSICS↗

One-dimensional phase retrieval: Regularization, box relaxation and uniqueness

Recovering a signal from its Fourier magnitude is referred to as phase retrieval, which occurs in different fields of engineering and applied physics. This paper gives a new characterization of the phase retrieval problem. Particularly useful is the analysis revealing that the common gradient-based regularization does not restrict the set of solutions to a smaller set. Specifically focusing on binary signals, we show that a box relaxation is equivalent to the binary constraint for Fourier-types of phase retrieval. Here, we further prove that binary signals can be recovered uniquely up to trivial ambiguities under certain conditions. Finally, we use the characterization theorem to develop an efficient denoising algorithm.

97 MATHEMATICS AND COMPUTING↗

Chaos and regularity of radionuclides with maximum likelihood estimation method

Abstract In this study, we considered the fluctuation properties of some energy levels of even and odd mass radionuclides, which are used in complex phenomena. Different sequences are prepared by using all the available experimental data and analyzed by using the maximum likelihood estimation technique to get the chaoticity parameter of Abul-magd distribution. The dependence of chaoticity degrees of different radionuclides to their mass regions, their decay modes, and also their physical half-lives are studied. Our results show more chaotic behavior of odd-mass radionuclides in comparison with even–even mass and also the most Poisson-like behavior for even–even mass in the A > 150 mass region. The results offer the most regular behavior for long-lived, even mass radionuclides in comparison to other categories of half-lives. Also, we got an obvious difference between the chaoticity degrees for nuclei which undergo β + decay in comparison with radionuclides which show electron capture mode.

Physics↗

Regularizing cosmological singularities by varying physical constants

Varying physical constant cosmologies were claimed to solve standard cosmological problems such as the horizon, the flatness and the Λ-problem. In this paper, we suggest yet another possible application of these theories: solving the singularity problem. By specifying some examples we show that various cosmological singularities may be regularized provided the physical constants evolve in time in an appropriate way.

79 ASTRONOMY AND ASTROPHYSICS↗

Measuring the Kerr spin parameter of regular black holes from their shadow

In a previous paper, one of us has showed that, at least in some cases, the Kerr-nature of astrophysical black hole candidates is extremely difficult to test and current techniques, even in presence of excellent data not available today, cannot distinguish a Kerr black hole from a Bardeen one, despite the substantial difference of the two backgrounds. In this paper, we investigate if the detection of the ''shadow'' of nearby super-massive black hole candidates by near future mm/sub-mm very long baseline interferometry experiments can do the job. More specifically, we consider the measurement of the Kerr spin parameter of the Bardeen and Hayward regular black holes from their shadow, and we then compare the result with the estimate inferred from the Kα iron line and from the frequency of the innermost stable circular orbit. For non-rotating black holes, the shadow approach provides different values, and therefore the Kerr black hole hypothesis can potentially be tested. For near extremal objects, all the approaches give quite similar results, and therefore it is not possible to constrain deviations from the Kerr solution. The present work confirms that it is definitively challenging to test this kind of metrics, even with future facilities. However, the detection of a source that looks like a fast-rotating Kerr black hole can put meaningful constraints on the nature of the compact object.

79 ASTRONOMY AND ASTROPHYSICS↗