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International audience; Graphene Nanoribbons (GN), being an important class of next-generation carbon materials, are of immense interest and find innumerable applications in diverse fields. A variation of the generalized Lambert W function, called the Offset Logarithm function, has been found to have important applications in fields such as physics, engineering and nanotechnology. We study the electronic properties of zigzag GN and use the generalized Lambert W function to study the eigenvalue equations of the massless Dirac equation applied to zigzag GN. We have studied the effects of nanoribbon width and determined the parameters that significantly affect the obtained solutions.

Jain tatvadnanapramane dnan he praman aani naya ya dohonmule hote. Paramparik jain darshanamadhe dravyarthik aani paryayik naya ase don prakarache naya sarvadnan aahet.

The degeneracy associated with dynamical symmetry of a potential can be identified in quantum mechanics, by solving the Schrödinger equation analytically, using the method of separation of variables in at least two different coordinate systems, and in classical mechanics by solving the Hamilton–Jacobi equation. In the present pedagogical review, the notion of separability and superintegrability of a potential, with profound implications, is discussed. In an earlier tutorial paper, we addressed the n2-fold degeneracy of the hydrogen atom using the Casimir operators corresponding to the SO(4) symmetry of the 1/r potential. The present paper is a sequel to that work, in which we solve the Schrödinger equation for the hydrogen atom using separation of variables in the parabolic coordinate systems. In doing so, we take the opportunity to revisit some excellent works on symmetry and degeneracy in classical and quantum physics, if only to draw attention to these insightful studies, which unfortunately miss even a mention in most undergraduate and even graduate level courses in quantum mechanics and atomic physics.

Recent development of ultrafast measurement techniques on the sub-femtosecond time scale has enabled us to see the atom–laser interaction in real time. One of the important observables to study the temporally resolved dynamics is the various time delay in the process. Time delays is an experimentally measurable quantity, where the time is not. Time delays in quantum collisions and in photoionization/photodetachment of atomic and molecular systems is reviewed. The formalisms of time delay in the context of quantum collisions by Eisenbud and Wigner that by Smith and their equivalence is discussed. The time-reversal symmetry between solutions with outgoing and ingoing wave boundary conditions allow us to interpret photoionization/photodetachment as half-scattering. Subsequently, the formalism of Eisenbud–Wigner–Smith time delay is extended in photoionization/photodetachment from collisions. We discuss that the time delay can be written as a self-adjoint quantum operator which depicts its measurability. On the experimental side, the measurement protocols are reviewed for attosecond streaking and RABBITT. Along with the EWS time delay, the measurement introduces an additional (which is negative) time delay. From the measurement of total delay and an analytical/numerical estimate of the measurement induced part, one gets the EWS time delay in the process. A few illustrative examples of studies on time delay are given to get a flavour of the outstanding advances made in this field in the last two decades.

Migration of an implanted prosthesis due to aseptic loosening is difficult to detect without regular imaging. In this paper, a low-cost, non-radiographic, robust diagnostic technique is presented, which can detect the migration of the humeral component of an elbow prosthesis. The system consists of a single magnet single sensor configuration and migration data are based on the variation in the magnetic field. The magnetic sensor was enclosed in titanium alloy and a magnet was embedded at a reference point in the humeral bone enclosed in ultra-high molecular weight polyethylene (UHMWPE). A layer of bone cement was then placed between the enclosed magnet and sensor. An algorithm linked with a Savitzky- Golay (SG) filter was developed that could decouple, convert, and filter the magnetic field signal to provide both the linear and angular displacement. The system was also designed to eliminate the cross talk and non-linearity effect of the magnet. The highest resolution the sensor achieved was 0.3 mm with a detectable linear migration range of 0.3 mm to 4 mm in the x/y axis and between 8-20 mm in the z-axis (along the humeral canal). The detectable rotational range was 0.5 to 3.0 degrees in the x/y axis. The repeatability of the calibrated sensor was analysed and showed a standard deviation of 0.05 mm over 150 cycles. The resolution was dependent upon the operating conditions and sensor positioning. There was no interference from the titanium alloy, bone cement nor the UHMWPE. This sensor system offers an alternative non-radiographic option for measuring migration of implanted prostheses.

It is remarkable that time delay is an experimentally measurable quantity, but time itself is not. Time delay in quantum collisions and in photoionisation/photodetachment of atomic and molecular sy...

This work reports an effort to introduce a few advanced concepts in quantum physics to undergraduate students who have only a minimal familiarity with wave mechanics. The geometric phase is not introduced in most introductory courses on quantum mechanics. It is of pivotal significance for the understanding of topological phase transitions which are becoming increasingly important in a large number of physical phenomena, including those that involve platforms for robust quantum computing. This article would provide a gentle introduction to the geometric phase. Toward this goal, Feynman’s path integral approach to quantum mechanics and its application in the interpretation of the wondrous Aharonov–Bohm effect is introduced in a gentle manner. A computer simulation of this interesting phenomenology is presented to help gain an early insight into some advanced concepts.

A theoretical study of the dipole photoelectron angular distribution asymmetry parameter, β, of the 6s, 5s and 4s subshells has been conducted for a range of closed-shell heavy, Hg (Z = 80), Rn (Z = 86), Ra (Z = 88) and superheavy, No (Z = 102), Cn (Z = 112), Og (Z = 118), Ubn (Z = 120) elements to understand the deviation of β from the nonrelativistic value of 2 owing to relativistic effects. It was found that the deviation, strongest in Cooper minimum regions, persists over all energy for all ns subshells, and the deviations increase with Z. Three levels of relativistic calculations were performed in order to pinpoint the particular interactions responsible for the details of the behavior of the ns β’s as functions of energy, n, and Z and, in addition to the effects of the (relativistic) spin–orbit interaction, interchannel coupling was found to be of crucial importance in the determination of the β parameter in most of the situations studied.

Purpose In this paper, a solid circular cylinder of finite length occupying the space 0⩽r⩽1, 0⩽z⩽h is considered. The purpose of this paper is to adopt a linear hygrothermal effect to analyze the unsteady state responses in a finite long solid cylinder subjected to axisymmetric hygrothermal loading T=TR and C=CR at the surface. The analytical solution of temperature, moisture and thermal stresses is obtained by using the integral transform technique. The coupling and uncoupling effects of temperature, moisture and thermal stresses are discussed for a graphite fiber-reinforced epoxy matrix composite material (T300/5208). The numerical results of transient response hygrothermoelastic field are presented graphically. Design/methodology/approach In the present problem, hygrothermoelastic response of a finite solid circular cylinder has been investigated by integral transform technique consisting of Laplace transform, Hankel transform and Fourier-cosine transform. The problem is investigated subjected to prescribed sources. Numerical algorithm has been developed for numerical computation. Findings The analytical solution of temperature, moisture and thermal stresses is obtained by using the integral transform technique. The coupling and uncoupling effects of temperature, moisture and thermal stresses are discussed for a graphite fiber-reinforced epoxy matrix composite material (T300/5208). The numerical results of transient response hygrothermoelastic field are presented graphically. Research limitations/implications The work presented here is mostly hypothetical in nature and totally mathematical. Practical implications It may be useful for composite materials, composite laminated plates in hygrothermal environment. Also it is having the applications in hygrothermal field where porous media exposed to heat and moisture. The problem investigated will be beneficial for the researcher working in the field thermoelastic diffusion and hygrothermoelastic materials. Originality/value Till date, the other authors did the research work on hygrothermal effect of an infinitely long cylinder without thickness. In this paper, the authors consider finite solid cylinder with finite length and discuss the hygrothermal effect within a small range. Second, the material properties are both homogenous and isotropic and are independent of both temperature and moisture.

Accounting for temporal changes in carbon dioxide (CO2) emissions from freshwaters remains a challenge for global and regional carbon budgets. Here, we synthesize 171 site-months of e...

Confined atomic systems are of great importance owing a multitude of possible applications in various areas of science and technology. Of particular interest are atoms encaged in the $$\hbox {C}_{{60}}$$ molecule, $$\hbox {A}@\hbox {C}_{{60}}$$ , since the near-spherical symmetry of $$\hbox {C}_{{60}}$$ simplifies theoretical studies, and the stability of $$\hbox {C}_{{60}}$$ renders it amenable to experimental examination. A review of investigations of the electronic structure and dynamics of $$\hbox {A}@\hbox {C}_{{60}}$$ is presented in this manuscript focusing on developments in the last decade. Addressed mainly are how the confinement affects electronic structure properties such as ionization potentials, localization of atomic electrons, Shannon entropy, correlation effects, relativistic interactions, and others. In the area of dynamics, photoionization and e- $$\hbox {A}@\hbox {C}_{{60}}$$ scattering are reviewed and summarized, and the major effects of confinement on the dynamical properties, e.g., confinement resonances, hybridization, Wigner time delay, are delineated.

The photoionization branching ratios of spin–orbit doublets are studied both experimentally and theoretically at energies several keV above threshold. The results show significant relativistic effects for Ar 2p in the autoionizing region below the 1s threshold, and large many-body effects for Xe 3d and 4d in the vicinity of the L-shell thresholds. The branching ratios in Xe are also found to vary significantly over very broad multi-keV energy regions both above and below the inner-shell thresholds. In addition, the Ar 2p study confirms experimentally the decades-old theoretical prediction that the nonresonant branching ratio does not approach the statistical (nonrelativistic) value, and, in fact, progressively diverges from statistical with increasing photon energy.

Enlightened by the Coronavirus, the present paper deals with a mathematical model of COVID-19 to investigate the impact of S-I-R-M model on the pregnant women and the newly borns due to the influence of availability of suitable conditions. The rates of infection, rate of recovery, rate of mortality for pregnant women before and after delivery and for newly born babies due to the transmission rate have been discussed for the present observed data. The numerical illustrations have been carried out for the parameters, functions and represented graphically by MATHEMATICA Software. Moreover some comparisons have been shown in the figure to estimate the impact of susceptible conditions and represent the particular cases of S-I-R-M model.

In the present scenario, the whole world struggling with COVID-19 which affects highly transmittable and pathogenic viral infection that rose by a newly discovered coronavirus and believed to be or...

Palmar midcarpal instability is an uncommon condition diagnosed clinically with a painful pathognomonic clunk on terminal ulnar deviation of the wrist. Various causes have been described, but congenital laxity of the carpal ligaments is thought to be a key contributor. Treatment commences with conservative measures. This includes proprioceptive training based on more recent concepts on the sensorimotor function of the wrist. When these measures plateau, surgery is considered. The lack of high-level evidence and consensus on its cause continue to hamper our understanding and knowledge of this condition. The purpose of this review is to examine the current evidence to conceptualize this mysterious, yet infrequent phenomenon, and to provide an algorithm on its management.

High-$Z$ atoms are excellent laboratories to study the combination of relativistic and many-electron correlation effects in electronic structure and dynamics. In the present work, the relativistic-random-phase approximation at different levels of truncation is employed to explore the final-state correlation effects in the photoelectron dynamics of the heaviest known element in the Periodic Table: oganesson (Og) with $Z=118$. The focus of this work is to illustrate the relativistic effects resulting from coupling different photoionization channels arising from spin-orbit split subshells, termed the spin-orbit-interaction-activated interchannel coupling effect. Comparison with the photoelectron dynamics of Rn on a qualitative level is also carried out, since Og is a homologue of Rn. The photoelectron dynamics of $7p,7s$, and $6d$ subshells are investigated and differences between Og and Rn, due to enhanced relativistic effects, are investigated.

Data for the poster presented in the conferenceQuantum simulation and computation, Spain, 14-18/10/2019 https://zenodo.org/record/3733498#.XoSaAy-w3PA &nbsp

Purpose The present work is concerned with the solution of a fractional-order thermoelastic problem of a two-dimensional infinite half space under axisymmetric distributions in which lower surface is traction free and subjected to a periodically varying heat source. The thermoelastic displacement, stresses and temperature are determined within the context of fractional-order thermoelastic theory. To observe the variations of displacement, temperature and stress inside the half space, the authors compute the numerical values of the field variables for copper material by utilizing Gaver-Stehfast algorithm for numerical inversion of Laplace transform. The effects of fractional-order parameter on the variations of field variables inside the medium are analyzed graphically. The paper aims to discuss these issues. Design/methodology/approach Integral transform technique and Gaver-Stehfast algorithm are applied to prepare the mathematical model by considering the periodically varying heat source in cylindrical co-ordinates. Findings This paper studies a problem on thermoelastic interactions in an isotropic and homogeneous elastic medium under fractional-order theory of thermoelasticity proposed by Sherief (Ezzat and El-Karamany, 2011b). The analytic solutions are found in Laplace transform domain. Gaver-Stehfast algorithm (Ezzat and El-Karamany, 2011d; Ezzat, 2012; Ezzat, El Karamany, Ezzat, 2012) is used for numerical inversion of the Laplace transform. All the integrals were evaluated using Romberg’s integration technique (El-Karamany et al., 2011) with variable step size. A mathematical model is prepared for copper material and the results are presented graphically with the discussion on the effects of fractional-order parameter. Research limitations/implications Constructed purely on theoretical mathematical model by considering different parameters and the functions. Practical implications The system of equations in this paper may prove to be useful in studying the thermal characteristics of various bodies in real-life engineering problems by considering the time fractional derivative in the field equations. Originality/value In this problem, the authors have used the time fractional-order theory of thermoelasticity to solve the problem for a half space with a periodically varying heat source to control the speed of wave propagation in terms of heat and elastic waves for different conductivity like weak conductivity, moderate conductivity and super conductivity which is a new and novel contribution.

The time nonlocal generalization of the classical Fourier law with the “Long-tail” power kernel can be interpreted in terms of fractional calculus and leads to the time fractional heat conduction e...

Even as the theory of relativity is more than a hundred years old, it is not within easy reach of undergraduate students. These students have an insatiable urge to learn more about it even if the full machinery of the tools required to study the same is not within their comfortable reach. The recent detection of gravitational waves has only augmented their enthusiasm about the General Theory of Relativity (GTR), developed just over a hundred years now, encapsulated in Einstein’s Field Equations. The GTR provided a consistent formulation of the theory of gravity, removed the anomalies in the Newtonian model, and predicted spectacular natural phenomena which eventual experiments have testified to. This pedagogical article retraces some of the major milestones that led to the GTR and presents a simple numerical simulation of the GTR advance of the perihelion of planetary motion about the sun.

If at first the idea is not absurd, then there is no hope for it. —Albert Einstein GEOMETRY OF THE SPACE–TIME CONTINUUM The gravitational interaction is the earliest physical interaction that humans have registered. The earliest speculations about just what is the nature of gravity were not merely wrong, but absurdly far-fetched. Ancient philosophers even conjectured that the earth is the natural abode of things, and objects fall down when they are dropped just as horses return to their stables. Various theories of gravity were proposed, and the one that lasted much is that developed by Isaac Newton in the seventeenth century. Newton's work on gravity integrated the dynamics of astronomical objects with that of falling apples or coconuts, determined by one common principle (Chapter 8). We celebrate this principle as Newton's one-over-distance-square law of gravity. An amazing consequence of the constancy of the speed of light in all inertial frames of reference that we studied in the previous chapter is the time-dilation and Lorentz contraction (also called the length contraction ). The phenomenon that is responsible for the traveling twin to age slower than the home-bound twin holds for any and every object in motion. We have already noted that this happens to decaying muons. Essentially, the faster you move through space, the slower you move through time, in the spacetime continuum. We all enjoy raising our speed, covering more distance in lesser, and lesser, time. Let us therefore ask, to what extent can we speed up an object? We ask if there is a natural limit for this. If you look back into the relations for time-dilation and the length contraction in the previous chapter, you will recognize that if v = c , the effect of time-dilation would be such that the traveling twin will simply stop ageing. Time would stop for her; time freezes. The effect of Lorentz contraction would also be total; she would think that the rest of the universe has spatially contracted to a point. She is therefore already everywhere (along the line of motion). All of these dramatic aftermaths are because of a simple fundamental property that the speed of the headlight of a car coming toward you at a velocity v is no different from that of the tail light of another that is receding away from you.