European Physical Journal Plus 

About: European Physical Journal Plus is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Physics & Nonlinear system. It has an ISSN identifier of 2190-5444. Over the lifetime, 7180 publications have been published receiving 80213 citations. The journal is also known as: EPJ plus.

DarkSide-20k: A 20 tonne two-phase LAr TPC for direct dark matter detection at LNGS

Abstract: Building on the successful experience in operating the DarkSide-50 detector, the DarkSide Collaboration is going to construct DarkSide-20k, a direct WIMP search detector using a two-phase Liquid Argon Time Projection Chamber (LAr TPC) with an active (fiducial) mass of 23 t (20 t). This paper describes a preliminary design for the experiment, in which the DarkSide-20k LAr TPC is deployed within a shield/veto with a spherical Liquid Scintillator Veto (LSV) inside a cylindrical Water Cherenkov Veto (WCV). This preliminary design provides a baseline for the experiment to achieve its physics goals, while further development work will lead to the final optimization of the detector parameters and an eventual technical design. Operation of DarkSide-50 demonstrated a major reduction in the dominant 39Ar background when using argon extracted from an underground source, before applying pulse shape analysis. Data from DarkSide-50, in combination with MC simulation and analytical modeling, shows that a rejection factor for discrimination between electron and nuclear recoils of $>3 \times 10^{9}$ is achievable. This, along with the use of the veto system and utilizing silicon photomultipliers in the LAr TPC, are the keys to unlocking the path to large LAr TPC detector masses, while maintaining an experiment in which less than $< 0.1$ events (other than $ u$ -induced nuclear recoils) is expected to occur within the WIMP search region during the planned exposure. DarkSide-20k will have ultra-low backgrounds than can be measured in situ, giving sensitivity to WIMP-nucleon cross sections of $1.2 \times 10^{-47}$ cm2 ( $1.1 \times 10^{-46}$ cm2) for WIMPs of 1 TeV/c2 (10 TeV/c2) mass, to be achieved during a 5 yr run producing an exposure of 100 t yr free from any instrumental background.

Nonlinear intersubband absorption and refractive index change in n-type δ -doped GaAs for different donor distributions

Abstract: In this study, both the linear and nonlinear intersubband optical absorption coefficients and the refractive index changes are calculated for the uniform, triangular and Gaussian-like donor distribution. The Gaussian-like distribution differs from the Gaussian distribution other authors use. The electronic structure of n-type Si δ-doped GaAs has been theoretically calculated by solving the Schrodinger and Poisson equations self-consistently. Our results show that the location and the size of the linear and total absorption coefficients and refractive index changes depend on the donor distribution type. The shape of δ-effective potential profile and the subband properties are changed as dependent on the donor distribution model. Therefore, the variation of the absorption coefficients and refraction index changes, which can be appropriate for various optical modulators and infrared optical device applications can be smooth obtained by the alteration donor distribution model.

Decolonisation of fractional calculus rules: Breaking commutativity and associativity to capture more natural phenomena

Abstract: To answer some issues raised about the concept of fractional differentiation and integration based on the exponential and Mittag-Leffler laws, we present, in this paper, fundamental differences between the power law, exponential decay, Mittag-Leffler law and their possible applications in nature. We demonstrate the failure of the semi-group principle in modeling real-world problems. We use natural phenomena to illustrate the importance of non-commutative and non-associative operators under which the Caputo-Fabrizio and Atangana-Baleanu fractional operators fall. We present statistical properties of generator for each fractional derivative, including Riemann-Liouville, Caputo-Fabrizio and Atangana-Baleanu ones. The Atangana-Baleanu and Caputo-Fabrizio fractional derivatives show crossover properties for the mean-square displacement, while the Riemann-Liouville is scale invariant. Their probability distributions are also a Gaussian to non-Gaussian crossover, with the difference that the Caputo Fabrizio kernel has a steady state between the transition. Only the Atangana-Baleanu kernel is a crossover for the waiting time distribution from stretched exponential to power law. A new criterion was suggested, namely the Atangana-Gomez fractional bracket, that helps describe the energy needed by a fractional derivative to characterize a 2-pletic manifold. Based on these properties, we classified fractional derivatives in three categories: weak, mild and strong fractional differential and integral operators. We presented some applications of fractional differential operators to describe real-world problems and we proved, with numerical simulations, that the Riemann-Liouville power-law derivative provides a description of real-world problems with much additional information, that can be seen as noise or error due to specific memory properties of its power-law kernel. The Caputo-Fabrizio derivative is less noisy while the Atangana-Baleanu fractional derivative provides an excellent description, due to its Mittag-Leffler memory, able to distinguish between dynamical systems taking place at different scales without steady state. The study suggests that the properties of associativity and commutativity or the semi-group principle are just irrelevant in fractional calculus. Properties of classical derivatives were established for the ordinary calculus with no memory effect and it is a failure of mathematical investigation to attempt to describe more complex natural phenomena using the same notions.

New numerical approximation of fractional derivative with non-local and non-singular kernel: Application to chaotic models

Abstract: Recently a new concept of fractional differentiation with non-local and non-singular kernel was introduced in order to extend the limitations of the conventional Riemann-Liouville and Caputo fractional derivatives. A new numerical scheme has been developed, in this paper, for the newly established fractional differentiation. We present in general the error analysis. The new numerical scheme was applied to solve linear and non-linear fractional differential equations. We do not need a predictor-corrector to have an efficient algorithm, in this method. The comparison of approximate and exact solutions leaves no doubt believing that, the new numerical scheme is very efficient and converges toward exact solution very rapidly.

Bound states of spatially dependent mass Dirac equation with the Eckart potential including Coulomb tensor interaction

Abstract: We investigate the approximate solutions of the Dirac equation with the position-dependent mass particle in the Eckart potential field including the Coulomb tensor interaction by using the parametric Nikiforov-Uvarov method. Taking an appropriate approximation to deal with the centrifugal term, the Dirac energy states and the corresponding normalized two-spinor components of the wave function are obtained in closed form. Some special cases of our solution are investigated. Furthermore, we present the correct solutions obtained via the asymptotic iteration method which are in agreement with the parametric Nikiforov-Uvarov method results.