Orbit Length Research Articles

Relativistic artificial molecule of two coupled graphene quantum dots at tunable distances

In a molecule formed by two atoms, energy difference between bonding and antibonding orbitals depends on distance between the two atoms. However, exploring molecular orbitals of two natural atoms with tunable distance has remained an outstanding experimental challenge. Graphene quantum dots can be viewed as relativistic artificial atoms, thus offering a unique platform to study molecular physics. Here, through scanning tunneling microscope, we create and directly visualize the formation process of relativistic artificial molecules based on two coupled graphene quantum dots with tunable distance. Our study indicates that energy difference between the bonding and antibonding orbitals of the lowest quasibound state increases linearly with inverse distance between the two graphene quantum dots due to the relativistic nature of the artificial molecule. For quasibound states with higher orbital momenta, the coupling between these states leads to half-energy spacing of the confined states because the length of the molecular-like orbit is approximately twice that of the atomic-like orbit. Evolution from ring-like whispering-gallery modes in the artificial atoms to figure-eight orbitals in the artificial molecules is directly imaged. The ability to resolve the coupling and orbitals of the relativistic artificial molecule at the nanoscale level yields insights into the behavior of quantum-relativistic matter.

Description of a Remarkable New Skate Species of Leucoraja Malm, 1877 (Rajiformes, Rajidae) from the Southwestern Indian Ocean: Introducing 3D Modeling as an Innovative Tool for the Visualization of Clasper Characters.

A remarkable new deep-water skate, Leucoraja longirostris n. sp., is described based on eight specimens caught during different expeditions to the southern Madagascar Ridge in the southwestern Indian Ocean. The new species differs from all congeners by its remarkably long and acutely angled snout (horizontal preorbital length 17.2-22.6% TL vs. 8.5-11.9% TL and 4.2-6.1 vs. 1.7-3.5 times orbit length, snout angle 65-85° vs. 90-150°). Furthermore, it is apparently endemic to the Madagascar Ridge, distant from the known distribution areas of all congeners. In addition to L. fullonica and L. pristispina, L. longirostris n. sp. is also the only species with plain dorsal coloration. Furthermore, the new species is the only Leucoraja species with an external clasper component dike and, besides L. wallacei, the only one with four dorsal terminal (dt) cartilages. The shape of the accessory terminal 1 (at1) cartilage with four tips is also unique within the genus. A new approach for the visualization of the clasper characters is introduced based on 3D models of all skeletal and external features. This enables a much easier and much more precise interpretation of every single clasper component, of the entire structure, and, in particular, the relationship between external features and skeletal cartilages. A new English translation of the first diagnosis of Leucoraja is provided, along with a revised generic diagnosis and a key to the species of Leucoraja in the Indian Ocean.

Multiserver Retrial Queue with Two-Way Communication and Synchronous Working Vacation

This work investigates a two-way communication retrial queue with synchronous working vacation and a constant retrial policy. During the idle time, a server makes an outgoing call after a random length. The service time of the incoming call and outgoing call obeys exponential distribution with different rates. If the incoming call finds all servers to be unavailable, it may or may not enter orbit. All servers immediately go on vacation simultaneously as soon as they find an empty system after the service finishes. During vacation, the servers can provide a service to those incoming calls, but this is at a lower-speed rate. The stationary probability distribution and the ergodic condition are obtained utilizing the matrix geometric technique. Some system characteristics are developed. Using MATLAB software, the variation in average orbit length, idle ratio, and the average number of servers in different server states is plotted for different values of the incoming/outgoing call rate and retrial rate. We further propose a multi-objective optimization model from which the optimal rate of outgoing calls and optimal vacation rate are explicitly obtained.

Periodic orbits in chaotic systems simulated at low precision

Non-periodic solutions are an essential property of chaotic dynamical systems. Simulations with deterministic finite-precision numbers, however, always yield orbits that are eventually periodic. With 64-bit double-precision floating-point numbers such periodic orbits are typically negligible due to very long periods. The emerging trend to accelerate simulations with low-precision numbers, such as 16-bit half-precision floats, raises questions on the fidelity of such simulations of chaotic systems. Here, we revisit the 1-variable logistic map and the generalised Bernoulli map with various number formats and precisions: floats, posits and logarithmic fixed-point. Simulations are improved with higher precision but stochastic rounding prevents periodic orbits even at low precision. For larger systems the performance gain from low-precision simulations is often reinvested in higher resolution or complexity, increasing the number of variables. In the Lorenz 1996 system, the period lengths of orbits increase exponentially with the number of variables. Moreover, invariant measures are better approximated with an increased number of variables than with increased precision. Extrapolating to large simulations of natural systems, such as million-variable climate models, periodic orbit lengths are far beyond reach of present-day computers. Such orbits are therefore not expected to be problematic compared to high-precision simulations but the deviation of both from the continuum solution remains unclear.

Enhanced S-boxes for the Advanced Encryption Standard with maximal periodicity and better avalanche property

This paper investigates a particular family of enhanced substitution boxes for the Advanced Encryption Standard. In contrast to the original substitution box design where each input has relatively short orbit lengths, the modified S-boxes proposed here have the maximal periodicity property. In the family of enhanced substitution boxes, every S-box input has the maximum orbit length, which is 256. We determine completely all the parameters for the S-box to have this maximal periodicity property. We also show that our new enhanced S-boxes have better bit avalanche property.

Distinguishing between regular and chaotic orbits of flows by the weighted Birkhoff average

This paper investigates the utility of the weighted Birkhoff average (WBA) for distinguishing between regular and chaotic orbits of flows, extending previous results that applied the WBA to maps. It is shown that the WBA can be super-convergent for flows when the dynamics and phase space function are smooth, and the dynamics is conjugate to a rigid rotation with Diophantine rotation vector. The dependence of the accuracy of the average on orbit length and width of the weight function width are investigated. In practice, the average achieves machine precision of the rotation frequency of quasiperiodic orbits for an integration time of O(103) periods. The contrasting, relatively slow convergence for chaotic trajectories allows an efficient discrimination criterion. Three example systems are studied: a two-wave Hamiltonian system, a quasiperiodically forced, dissipative system that has a strange attractor with no positive Lyapunov exponents, and a model for magnetic field line flow.

A Computed Tomographic Investigation of the Ophthalmic Artery Volume and Its Relevance to Soft Tissue Filler Injections.

The measured intraarterial volume of cadaveric ophthalmic arteries was utilized for safety recommendations during facial soft tissue filler injections. However, its clinical practicability and model applicability have become questionable. To measure the volume of the ophthalmic artery in living individuals by utilizing computed tomography (CT) imaging technology. A total of 40 Chinese patients (23 males, 17 females) were included in this study with a mean age of 61.0 (14.2) years and a mean body mass index of 23.7 (3.3) kg/m2. Patients were investigated with CT imaging technology to evaluate the length, diameter, and volume of the bilateral ophthalmic arteries as well as the length of the bony orbits, resulting in a total of 80 investigated ophthalmic arteries and orbits. Independent of gender, the average length of the ophthalmic artery was 80.6 (18.7) mm, the calculated volume of the ophthalmic artery was 0.16 (0.05) mL and the minimal and maximal internal diameter of the ophthalmic artery were 0.50 (0.05) mm and 1.06 (0.1) mm, respectively. Based on the results obtained from the investigation of 80 ophthalmic arteries it must be concluded that current safety recommendations should be reevaluated. The volume of the ophthalmic artery appears to be 0.2 mL rather than 0.1 mL as previously reported. In addition, it appears impractical to limit the volume of soft tissue filler bolus injections to 0.1 mL due to the aesthetic requirements of each individual patient and treatment plan.

Brho -defined isochronous mass spectrometry and mass measurements of ^{58}Ni fragments

A novel isochronous mass spectrometry, termed as Brho -defined IMS, has been established at the experimental cooler-storage ring CSRe in Lanzhou. Its potential has been studied through high precision mass measurements of ^{58}Ni projectile fragments. Two time-of-flight detectors were installed in one of the straight sections of CSRe, thus enabling simultaneous measurements of the velocity and the revolution time of each stored short-lived ion. This allows for calculating the magnetic rigidity Brho and the orbit length C of each ion. The accurate Brho (C) function has been constructed, which is a universal calibration curve used to deduce the masses of the stored nuclides. The sensitivity to single stored ions, fast measurement time, and background-free characteristics of the method are ideally suited to address nuclides with very short lifetimes and smallest production yields. In the limiting case of just a single particle, the achieved mass resolving power allows one to determine its mass-over-charge ratio m/q with a remarkable precision of merely sim 5 keV. Masses of T_z=-3/2fp-shell nuclides are re-determined with high accuracy, and the validity of the isospin multiplet mass equation is tested up to the heaviest isospin quartet with A=55. The new masses are also used to investigate the mirror symmetry of empirical residual proton-neutron interactions.

Unreliable retrial queueing system with working vacation

<abstract><p>This paper investigates an unreliable $ M/G(P_{1}, P_{2})/1 $ retrial queueing system with a woking vacation. An arriving customer successfully starts the first phase service with the probability $ \alpha $ or the server fails with the probability $ \bar{\alpha} $. Once failure happens, the serving customer is taken to the orbit. The failed server is taken for repair with some delay. Once the repair is comleted, the server is ready to provide service once again. In this background, we implemented the working vacation scenario. During working vacation, the service will be provided at a slower rate, rather than entirely stopping the service. The supplementary variable method was adopted to find the orbit and system lengths. Additionally, some unique results and numerical evaluations have been presented.</p></abstract>

One can hear the shape of ellipses of small eccentricity

We show that if the eccentricity of an ellipse is sufficiently small, then up to isometries it is spectrally unique among all smooth domains. We do not assume any symmetry, convexity, or closeness to the ellipse, on the class of domains. In the course of the proof we also show that for nearly circular domains, the lengths of periodic orbits that are shorter than the perimeter of the domain must belong to the singular support of the wave trace. As a result we also obtain a Laplace spectral rigidity result for the class of axially symmetric nearly circular domains using a similar result of De Simoi, Kaloshin, and Wei concerning the length spectrum of such domains.

Quantum signatures of chaos in relativistic quantum billiards with shapes of circle- and ellipse-sectors* *Dedicated to the memory of Fritz Haake. Fritz introduced me (Barbara) into the field of quantum chaos. He supervised my diploma and doctoral thesis and since then has been a mentor, friend and helpful advisor during all the stages of my scientific career. I take his

According to the Berry–Tabor conjecture, the spectral properties of typical nonrelativistic quantum systems with an integrable classical counterpart agree with those of Poissonian random numbers. We investigate to what extend it applies to relativistic neutrino billiards (NBs) consisting of a spin-1/2 particle confined to a bounded planar domain by imposing suitable boundary conditions (BCs). In distinction to nonrelativistic quantum billiards (QBs), NBs do not have a well-defined classical counterpart. However, the peaks in the length spectra, that is, the modulus of the Fourier transform of the spectral density from wave number to length, of NBs are just like for QBs at the lengths of periodic orbits of the classical billiard (CB). This implies that there must be a connection between NBs and the dynamic of the CB. We demonstrate that NBs with shapes of circle- and ellipse-sectors with an integrable classical dynamic, obtained by cutting the circle and ellipse NB along symmetry lines, have no common eigenstates with the latter and that, indeed, their spectral properties can be similar to those of classically chaotic QBs. These features orginate from the intermingling of symmetries of the spinor components and the discontinuity in the BCs leading to contradictory conditional equations at corners connecting curved and straight boundary parts. To corroborate the necessity of the curved boundary part in order to generate GOE-like behavior, we furthermore consider the right-angled triangle NB constructed by halving the equilateral-triangle NB along a symmetry axis. For an understanding of these findings in terms of purely classical quantities we use the semiclassical approach recently developed for massive NBs, and Poincaré–Husimi distributions of the eigenstates in classical phase space. The results indicate, that in the ultrarelativistic limit these NBs do not show the behavior expected for classically chaotic QBs.

CROSS-SECTIONAL ASSESSMENT OF THE NON-TRAUMATIC ABNORMAL SHAPE OF POSTERIOR EYE GLOBE IN PATIENTS UNDERGOING BRAIN IMAGING.

Introduction: Causes of abnormal shape of eye globe are axial myopia, staphyloma, coloboma, apparent enlargement of eye. The presence and types of staphyloma are determined by the entire eye shape in CT/MRI scans. To look for the shape of posterior eyeball in patients who come for brain imaging CT/MRI is useful in preventing the vision. Aim & Objectives: To study various types of posterior eye globe shapes using cross-sectional imaging (CT/MRI).Role of cross-sectional imaging (CT/MRI) in the prevention of vision loss. Material And Method: This is a cross-sectional observational study done in the department of radio-diagnosis, Pacic Institute of Medical Sciences, Udaipur from June 2021 to January 2022 (over the period of 6 months). This study included 2000 patients (age above 40 years) referred for cross-sectional brain imaging (CT/MRI) for various symptoms/abnormalities. In 50 patients, assessment for the posterior eye globe shape was performed. Axial lengths of orbits were also measured in all 50 patients. Results: Out of 50 patients, 23 patients had axial myopia, 15 patients had staphyloma,4 patients had coloboma,3 patients had apparent enlargement of eye ball ,3 patients had enlargement of eyeball due to glaucoma and 2 patients had irregularity in shape of eye globe due to secondary involvement by mucormycosis. Conclusion: Posterior enlargement of the eye globe is common in old age patient, and CT & MRI are useful modalities to diagnose various types of enlargement. In MRI, the sagittal and axial plane of T2WI are very useful for checking for eyeball size, shape, and pathology.

Type-II polyadic constacyclic codes over finite fields

Polyadic constacyclic codes over finite fields have been of interest due to their nice algebraic structures, good parameters, and wide applications. Recently, the study of Type-I m-adic constacyclic codes over finite fields has been established. In this paper, a family of Type-II m-adic constacyclic codes is investigated. The existence of such codes is determined using the length of orbits in a suitable group action. A necessary condition and a sufficient condition for a positive integer s to be a multiplier of a Type-II m-adic constacyclic code are determined. Subsequently, for a given positive integer m, a necessary condition and a sufficient condition for the existence of Type-II m-adic constacyclic codes are derived. In many cases, these conditions become both necessary and sufficient. For the other cases, determining necessary and sufficient conditions is equivalent to the discrete logarithm problem which is considered to be computationally intractable. Some special cases are investigated together with examples of Type-II polyadic constacyclic codes with good parameters.

Precision measurement of the transition energy [formula omitted] versus magnetic rigidity for storage-ring isochronous mass spectrometry

The transition energy, γt, of a heavy-ion storage ring is an important machine parameter. The variation of γt versus the magnetic rigidity, Bρ, over the acceptance of the ring directly affects the mass resolving power achievable in the high-precision isochronous mass spectrometry (IMS). With two time-of-flight (TOF) detectors installed in a straight section of the ring, revolution frequency (revolution time) and velocity of each stored ion can simultaneously be measured. By using these quantities, a method for fast and precise γt determinations has been developed. The dependence of γt on the orbit length (or Bρ) has been obtained. The newly developed method does not require particle identification and is thus suitable for real-time monitoring of the ion optical setting during experiment.

Maximal escape rate for shifts

<p style='text-indent:20px;'>We consider the shift transformation on the space of infinite sequences over a finite alphabet endowed with the invariant product measure, and examine the presence of a <i>hole</i> on the space. The holes we study are specified by the sequences that do not contain a given finite word as initial sub-string. The measure of the set of sequences that do not fall into the hole in the first <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula> iterates of the shift is known to decay exponentially with <inline-formula><tex-math id="M2">\begin{document}$ n $\end{document}</tex-math></inline-formula>, and its exponential rate is called <i>escape rate</i>. In this paper we provide a complete characterization of the holes with maximal escape rate. In particular we show that, contrary to the case of equiprobable symbols, ordering the holes by their escape rate corresponds to neither the order by their measure nor by the length of the shortest periodic orbit they contain. Finally, we adapt our technique to the case of shifts endowed with Markov measures, where preliminary results show that a more intricate situation is to be expected.</p>

Classical Fuzzy Retrial Queue with Working Vacation using Hexagonal Fuzzy Numbers

Using fuzzy techniques “Classical Fuzzy Retrial Queue with Working Vacation(WV) using Hexagonal Fuzzy Numbers” is discussed in this paper. We acquire model in fuzzy environment as the average orbit length, Probability(Pr) that the server busy, and Pr(the server is in a WV period), the sojourn time of a customer in the queue. Finally numerical results are presented.

A descriptive and comparative neurocranium morphology of Anguilliformes fishes in Taiwan waters.

Taiwan is one of the richest in the world in terms of eel fauna. In this study, we examined the osteological and morphological characteristics of eels under order Anguilliformes. Furthermore, we focused on the neurocranium of total of 30 Anguilliformes fishes under family Congridae (10), Muraenesocidae (1), Muraenidae (7), Nemichthyidae (1), Nettastomatidae (2), Ophichthidae (5), Synaphobranchidae (4), which are caught in Taiwanese waters. This paper shows the results of a comparative study on osteological characters of the neurocranium including the ratio of seven length characters using its NCL (neurocranium length), NCW (neurocranium width), OBL (orbit length), MFW (maximum frontal width), NCDB (neurocranium depth at basisphenoid), PEVW (premaxilla-ethmovomer width) and mPOBL (mid pre-orbital length), and 20 morphological diagnostic characters for 30 eel species. Results shows that species under family Nemichthyidae and Nettastomatidae have the highest values on the ratio of NCL/MFW, NCL/NCDB, and NCW/mPOBD. In morphological characters, it shows that species of the same family mostly share similar formation of the PEV plate and frontal structure. The usage of the length measurements and morphological diagnostic characters of neurocranium allowed for a more in depth understanding of how similar or different these eels can be. The neurocranial description and morphological characters may prove valuable for identification purposes and might be necessary tool for further studies on the status of order Anguilliformes.

Evolution of orbit size in toothed whales (Artiodactyla: Odontoceti).

For many marine tetrapods, vision is important for finding food and navigating underwater, and eye size has increased to improve the capture of light in dim ocean depths. Odontocete whales, in contrast, rely instead on echolocation for navigation and prey capture. We tested whether the evolution of echolocation has influenced the orbit size, a proxy for eye size, and examined how orbit size evolved over time. We also assessed variation in orbit size amongst whales and tested how body size, diving ability, sound production, foraging habitat, and prey capture strategy influenced the orbit size using phylogenetic independent contrasts and phylogenetic ANOVAs. Using measurements of orbit length and bizygomatic width, we calculated proportional orbit size for 70 extant and 29 extinct whale taxa, with an emphasis on Odontoceti. We then performed ancestral character state reconstruction on a time-calibrated composite phylogeny. Our analysis revealed that there was no shift in proportional orbit size from archaeocetes through stem odontocetes, indicating that the evolution of echolocation did not influence the orbit size. Proportional orbit size increased in Ziphiidae, Phocoenidae, and Cephalorhynchus. Proportional orbit size decreased in Balaenidae, Physeteridae, Platanistidae, and Lipotidae. Body size, diving ability, foraging environment, and prey capture strategy had a significant influence on orbit size, but only without phylogenetic correction. An increase in orbit size is associated with deep diving behavior in beaked whales, while progenesis and retention of juvenile features into adulthood explain the pattern observed in Phocoenidae and Cephalorhynchus. Decrease in proportional orbit size is associated with adaptation toward murky freshwater environments in odontocetes and skim feeding in balaenids. Our study reveals that the evolution of echolocation had little effect on orbit size, which is variable in whales, and that adaptation for different feeding modes and habitat explains some of this variance.

Symmetric 1-designs from PGL2(q), for q an odd prime power

All non-trivial point and block-primitive 1-(v, k, k) designs 𝓓 that admit the group G = PGL2(q), where q is a power of an odd prime, as a permutation group of automorphisms are determined. These self-dual and symmetric 1-designs are constructed by defining { |M|/|M ∩ Mg|: g ∈ G } to be the set of orbit lengths of the primitive action of G on the conjugates of M.

Probing hole spin transport of disorder quantum dots via Pauli spin-blockade in standard silicon transistors

Single hole transport and spin detection is achievable in standard p-type silicon transistors owing to the strong orbital quantization of disorder based quantum dots. Through the use of the well acting as a pseudo-gate, we discover the formation of a double-quantum dot system exhibiting Pauli spin-blockade and investigate the magnetic field dependence of the leakage current. This enables attributes that are key to hole spin state control to be determined, where we calculate a tunnel coupling t c of 57 μeV and a short spin−orbit length l SO of 250 nm. The demonstrated strong spin−orbit interaction at the interface when using disorder based quantum dots supports electric-field mediated control. These results provide further motivation that a readily scalable platform such as industry standard silicon technology can be used to investigate interactions which are useful for quantum information processing.