Abstract. This paper is concerned with the inverse scattering transform (IST) for the nonlinear derivative Schrödinger-type equation, which is an extension of the nonlinear Schrödinger (NLS) equation, under the nonzero boundary conditions (NZBCs) and scattering coefficients with double zeros based on the Riemann-Hilbert (RH) problem. On the direct scattering and the inverse scattering processes, we discuss some properties of Jost solutions, asymptotic behaviors, analyticity, symmetries of the Jost solutions and the corresponding spectral matrix, and then we give the matrix RH problem, and the reconstruction formula of potential and trace formula, correspondingly. Based on the above analysis, the explicit formula of N double-pole solutions can be obtained in the case of reflectionless potential. Moreover, we discuss an example of the double-pole soliton solution.

Abstract. In this work, we obtain new resonant lump, kinky, and periodic solutions to a combination of two Burgers' hierarchies. In particular, we study the mixed doubly nonlinear dispersive Burgers equation. The suggested model includes different types of moving unidirectional waves in the media of optical systems, nonlinear acoustics, and fluids. The resonant solitary wave-solutions can be constructed by using linear superposition principle and the Bell polynomials via the implementations of Hirota's method and the Cole-Hopf transformation. Three effective schemes are used, namely, the Kudryashov-expansion, updated rational sine-cosine functions, and Hirota's bilinear method to produce kinks, periodic, and lumps solitary wave solutions, respectively. A graphical analysis scheme is conducted to show the physical structures of the obtained solutions. Also, the impact of the model's coefficients is studied graphically as well.

Abstract. In this paper, we introduce a 2×2 matrix spectral problem with two potentials to derive a generalization of the nonlinear Schrödinger system that can be reduced to four important integrable equations: a generalization of the nonlinear Schrödinger equation, a combined nonlinear Schrödinger and derivative nonlinear Schrödinger equation, and a combined nonlinear Schrödinger and Chen-Lee-Liu equation, a combined nonlinear Schrödinger and Gerdjikov-Ivanov equation. With the help of a gauge transformation between the corresponding Lax pairs, Darboux transformations for the generalization of the nonlinear Schrödinger system and its reductions are constructed, by which explicit solutions for the generalization of the nonlinear Schrödinger system and its reduction can be engendered from their known solutions. As an application, we obtain various explicit solutions of the four integrable equations, including one-soliton, two-soliton, periodic solutions and others.

Abstract. The space-time fractional modified Benjamin-Bona-Mahony problem is reduced and analytically solved using the fractional sub-equation approach. The Riemann-Liouville derivative as modified by Jumarie is examined. Graphical representations of periodic, kink, and multi-soliton solutions are shown as examples of the obtained solutions. Using this method, researchers may create new, one-of-a-kind solutions to a wide variety of nonlinear fractional partial differential equations.

Abstract. In the present study, a one-dimensional steady-state nonlinear reactive transport model with the Michaelis-Menten term is considered, which encodes some important processes of engineering. The governing nonlinear differential equation admits multiple solutions depending on the embedding parameters in the model. Determining suitable initial guesses, an iterative discrete scheme based upon a combination of the quasilinearization method and finite difference method to approximate all branches of the solution is proposed. Furthermore, the method convergence is investigated in detail and some cases are considered to illustrate the method's accuracy.

Abstract. A numerical simulation technique for the coupled system of variable-order time fractional nonlinear Schrödinger equations is developed in this paper using the finite difference/spectral method. The finite difference method is adapted to discretize the variable-order Caputo time-fractional derivative, and the spectral technique is used for spatial approximation. The significant advantage of the proposed algorithm is that the iterative procedure is not used to implement the nonlinear term in the coupled system. In addition, numerical experiments are performed in order to verify the accuracy of the method.

Abstract. In this study, the cryptanalysis of a chaotic random number generator (RNG) based on a fractional-order exponential jerk system (FOEJS) is discussed. In order to explain the target RNG's security flaws, an attack RNG is used. It is shown that using linear continuous feedback in a drive-response arrangement, consistent synchronization between the attack and target systems can be achieved if the RNG design is known and a state variable of the fractional-order chaotic system is observable for a time interval. Once the target and attack RNGs have synced, the attack system generates the same output bit stream as the target RNG. Numerical simulations confirm the effectiveness of the attack approach. As an example demonstration, a RNG based on a fractional-order exponential jerk system is targeted in this article. Despite this specific target, the cryptanalysis method described in this paper can be applied to any RNGs based on fractional-order or integer-order chaotic systems, also based on continuous time or discrete-time chaotic systems. As a result, this study highlights the security flaws associated with RNGs based on fractional-order chaotic systems, as well as the error of treating deterministic fractional-order chaos as a single entropy source for a RNG.

Abstract. Under investigations in this paper are the bright solitons on the zero and periodic wave background in the space-shifted PT-symmetric nonlocal nonlinear Schrödinger equation. These soliton solutions are constructed through the bilinear KP-hierarchy reduction method, and are given in terms of determinants. The collision dynamics of bright two-soliton solutions on the zero background are studied based on their asymptotic expressions. The bright four-soliton solutions can form bound state two-soliton pairs. The bright two-soliton solutions on the periodic wave background are also studied. Compared with the case of solitons on the zero background, the bright two-soliton solutions on the periodic wave background have completely different dynamics, even though the periodic waves vanish into the background.

Abstract. Superheavy nuclei of interest for the forthcoming synthesis of the isotopes with Z = 119,120 are investigated. One of the very interesting experiment was performed at the velocity filter SHIP (GSI Darmstadt) trying to produce ²⁹⁹120 in a fusion reaction ²⁵⁸Cm(⁵⁴Cr,3n)²⁹⁹120. We report calculations of α decay halflives using four models: AKRA (Akrawy), ASAF (Analytical Super-Asymmetric Fission), UNIV (Universal Formula), and semFIS (Semi-empirical formula based on Fission Theory). The released energy, Q, is calculated using the theoretical model of atomic masses WS4, see Phys. Rev. C 84 (2011) 014333 and Phys. Lett. B 734 (2014) 215. For ^92,94Sr cluster radioactivity of ^300,302120 we predict a branching ratio relative to α decay of −0.10 and 0.49, respectively, which is expected to be measured in a forthcoming experiment.

Abstract. The angular distributions of prompt-fission γ-rays with respect to the direction of fission fragments in the monochromatic “warm” neutron induced fission of ²³⁵U have been studied. The fragments were detected with low-pressure position sensitive multi-wire proportional counter and the gamma-rays with a plastic scintillators. The time-of-flight method is used to discriminate prompt neutrons and prompt γ-rays of fission. From the measured angular distributions with respect to the direction of the selected fragments, the value of the laboratory anisotropy has been found to be 15 % in comparison to the value obtained in the perpendicular direction. The measurements indicate the existence of a significant anisotropy of emission of the γ-rays in the emitting-fragment system, suggesting the presence of significant angular momenta of the fragments correlated with the fission axis, which also lead to an enhanced emission of the γ-rays. Moreover, the article includes a new technique for measuring and correcting the obtained angular distribution, in the case of when plastic scintillators have different threshold levels for detection of γ-rays.

Abstract. The method for the determination of the absolute distance from the excess ratios of multiwavelength interferometry, invented by Benoît in 1898, was confronted from its inception with the problem of ambiguity and the lack of an analytical formula for calculations. I offer here a solution for the elimination of the ambiguities at the ends of the period within assumed measurement errors, a true analytical recurrent formula for the determination of the absolute distance, and other improvements. My method is proven rigorously to be well-defined and optimized for precision. It is shown here that my method is the boundary between ambiguity and precision.

Abstract. Measurements of ultra-low absorption ≈7 × 10⁻⁸ cm⁻¹ in synthetic crystalline quartz shielded by absorption in the ambient air are demonstrated using a time-resolved photothermal common-path interferometry scheme. A modified optical part of the scheme that provides a Gaussian-like shape of laser beams in the volume of measured samples is presented. The absorption coefficient is calculated by processing the signal waveforms obtained in this optical scheme in different crystal volumes. A theoretically determined thermo-optical parameter is used for calculations. The characteristic heat diffusion times in the ambient air and crystalline quartz are measured.

Abstract. We theoretically investigated the interaction of an asymmetric double quantum well with an intense non-resonant laser radiation and its effects on energy spectrum, wavelength of the emitted radiation, threshold current density and characteristic temperature if this structure becomes the active medium of a laser. The results reveal an increase/decrease in the energy of the conduction/valence subbands of the double well leading to an increase in the effective width of the band-gap with the augment of the laser intensity. We found a larger variation of the emitted wavelength, lower threshold currents and a higher characteristic temperature than conventional quantum well lasers.

Abstract. Inaugural studies of medicine-supporting research foreseen to be implemented at the High-Power Laser Systems (HPLS) at ELI-NP will benefit substantially from achieving a fast and localized delivery of radiological substances. Microbubbles driven by an ultrasonic transducer have been used successfully as delivery agents for pharmaceuticals for several decades. They can support future oncology programs facilitating high-dose rate therapies (e.g., flash therapy) at ELI-NP, since a very localized and swift delivery of drugs and nanoparticles is achievable using the bubbles. We herein depict a theoretical evaluation to control the critical microbubble explosion that creates the high-pressure gradients of need for in-vitro and in-vivo sonoporation of drugs and nanoparticles based on the Rayleigh-Plesset equation. Suitable bubble sizes R₀ and corresponding resonance frequencies f_res are derived for which an ultrasonic-driven explosion can be achieved assuming an externally applied pressure P_∞(t) of sinusoidal nature. With R₀ in the μm and f_res in the MHz regime, the crucial explosion times T_expl can be short (<2 μs) allowing the sought-after fast delivery of the pharmaceutical payload.

Abstract. The reconstructed phase images (PIs) from digital holographic microscopy contain in each pixel values of the phase shift introduced by the sample in optical path, which allow to segment cells in the most important compartments: nucleus and cytoplasm. Based on PIs, we computed optical properties of cells from two sublines with different malignancy levels and propose a three-layers numerical model to analyze the response under the stress of a high frequency continuous wave electric field. The induced transmembrane voltage is compared for different values of dielectric properties assigned to the cell compartments. Considering the nucleus as a distinct domain with specific electrical properties, brings the model closer to realistic cases; the importance of its presence in simulation models was also investigated.

Abstract. Two Monte Carlo simulations were used to determine the optimal amount and shape of cultural heritage cellulose-based materials for decontamination with an industrial e-beam accelerator of an in-house design. The findings are encouraging for the large volume treatment of historic book collections and archives at iradiation facilities around the world.

Abstract. Spheres or cylinders rolling on horizontal surfaces or inclined planes are relatively common in the physics education literature but rolling on concave tracks are rarely reported. In this work we report the Tracker video analysis and modeling of a small rubber sphere rolling along a cycloidal track. Ansatz type solutions to the differential equation of motion were built based on the video-data graph shapes, a procedure that can be applied to differential equations whose analytical solutions are very hard to obtain or non-existent. Very close agreement between experiment and model was found. We have taken into account that the deformation of objects in contact is inherent to rolling motion. The distinction between sliding friction and rolling friction is discussed. Our main results are: i) the x(t) and y(t) coordinates show exponential decay in amplitude due to the combined action of velocity-dependent rolling friction and air damping forces, ii) the upward and downward rolling motions are not symmetric, iii) at every quarter-cycle of oscillation the maxima in the kinetic energy are shifted to the right and to the left from the equilibrium position. This low-cost experiment provides a pedagogical demonstration of the asymmetry between the upward and downward motion.

Abstract. This paper reports the effect of gamifying an Introductory Physics Course at the Universidad Politécnica de Madrid on the motivation of students and understanding of basic physics concepts in a playful way. For that purpose, the Physics Course was designed to include some elements of gamification as digital Escape Rooms using Genially, a web-based platform. To escape from the laboratory, students must solve challenges to exit, and when they escape, in a given time, they must answer some questions for feedback statistical analysis. From the results of this study the gamified instruction increased the student's motivation as well as a positive effect on their learning process. The authors also compared the answers provided by students attending two different university degrees.

Abstract. The use of digital tools in physics education increases the students' digital competencies, their motivation and highly contributes to develop cognitive learning processes during their interaction with software simulations. In this paper, we present how to employ GeoGebra software for teaching geometrical optics phenomena. The proposed approach started with the study of spherical diopter, since optical systems, such as mirrors and lenses, are set of surfaces that reflect or refract light rays and the mathematical relations that describe these systems are obtained from the diopter formulas. Another system that combines light reflection and refraction, for which we created a dynamical model, is the optical prism. Dynamic simulations for these systems offer the possibility to examine, by geometrical tools, the involved physics laws. Moreover, one can identify various attributes or properties that are changing and their effects, leading to processes of reflection and to knowledge construction. We also explored the possibility to take the advantage of GeoGebra software in solving problems, by creating an attractive environment that promotes better comprehension of the concepts and of the involved optical phenomena. The use of images, instead of the commonly employed symbolic representations, can greatly support students having a lower capacity for abstraction and facilitates their understanding of physics problems.