Search results for: solitary

Authors: Tadas Telksnys, Zenonas Navickas, Minvydas Ragulskis

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Necessary and sufficient conditions for the existence of second order solitary solutions to the Hodgkin-Huxley equation are derived in this paper. The generalized multiplicative operator of differentiation helps not only to construct closed-form solitary solutions but also automatically generates conditions of their existence in the space of the equation's parameters and initial conditions. It is demonstrated that bright, kink-type solitons and solitary solutions with singularities can exist in the Hodgkin-Huxley equation.

Keywords: Hodgkin-Huxley equation, solitary solution, existence condition, operator method

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Authors: Esther Baldwin

Abstract:

It is well settled that the use of solitary confinement can cause psychological and physical harm to detainees. For juveniles, who are more susceptible to irreparable harm due to their underdeveloped psyches, the risks are exacerbated. Despite these risks, across the United States juvenile detainees are regularly held in isolation for prolonged periods of time. This essay will examine the broad impact of solitary confinement on juvenile detainees while giving particular focus to the story of Kalief Browder, a juvenile awaiting trial on Rikers Island in New York for a period of three years, nearly two years of which were spent in solitary confinement. Although sadly, his story is not uncommon, Kalief’s story offers a unique perspective in that it provides first-hand insight on the effects of solitary confinement on juveniles. It is our hope that by sharing his story, we will demand better detention practices and policies for juveniles under correctional control in the United States.

Keywords: criminal justice system, juveniles, Kalief browder, solitary confinement

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Authors: Renu Tomar, Hitendra K. Malik, Raj P. Dahiya

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Similar to the sound waves in air, plasmas support the propagation of ion waves, which evolve into the solitary structures when the effect of non linearity and dispersion are balanced. The ion acoustic solitary waves have been investigated in details in homogeneous plasmas, inhomogeneous plasmas, and magnetized plasmas. The ion acoustic solitary waves are also found to reflect from a density gradient or boundary present in the plasma after propagating. Another interesting feature of the solitary waves is their collision. In the present work, we carry out analytical calculations for the head-on collision of solitary waves in a magnetized plasma which has dust grains in addition to the ions and electrons. For this, we employ Poincar´e-Lighthill-Kuo (PLK) method. To lowest nonlinear order, the problem of colliding solitary waves leads to KdV (modified KdV) equations and also yields the phase shifts that occur in the interaction. These calculations are accomplished for the uniform and nonuniform plasmas, and the results on the soliton properties are discussed in detail.

Keywords: inhomogeneous magnetized plasma, dust charging, soliton collisions, magnetized plasma

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Authors: Gerard Bray, Arya Bahadori, Sachinka Ranasinghe

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Renal cell carcinoma (RCC) is among the top 10 most common cancers worldwide, where metastatic disease carries a poor prognosis. Herein, we present a 74-year-old male presenting with asymptomatic solitary metachronous metastasis to the gall bladder 4 years following nephrectomy for clear cell RCC. Solitary RCC metastasis to the gall bladder following nephrectomy is rarely reported in the literature and brings with it a clinical conundrum of whether surgical resection or systemic therapy should be utilized. In this case, surgical excision with cholecystectomy was employed without systemic therapy. We, therefore, contribute a rare and interesting case that highlights that metastasectomy of a solitary metastasis can improve survival according to current literature.

Keywords: renal cell carcinoma, gall bladder metastasis, solitary metastasectomy, metachronous

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Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieha

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In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

Keywords: polynomial constitutive equation, solitary, stress solitary waves, nonlinear constitutive law

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Authors: Alireza Abdikian

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By assuming a quantum relativistic degenerate electron-positron (e-p) plasma media, the nonlinear acoustic solitary propagation in the presence of the stationary ions for neutralizing the plasma background of bounded cylindrical geometry was investigated. By using the standard reductive perturbation technique with cooperation the quantum hydrodynamics model for the e-p fluid, the spherical Kadomtsev-Petviashvili equation was derived for small but finite amplitude waves and was given the solitary wave solution for the parameters relevant for dense astrophysical objects such as white dwarf stars. By using a suitable coordinate transformation and using improved F-expansion technique, the SKP equation can be solved analytically. The numerical results reveal that the relativistic effects lead to propagate the electrostatic bell shape structures and by increasing the relativistic effects, the amplitude and the width of the e-p acoustic solitary wave will decrease.

Keywords: Electron-positron plasma, Acoustic solitary wave, Relativistic plasmas, the spherical Kadomtsev-Petviashvili equation

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Authors: Mohammad R. Jalali, Mohammad M. Jalali

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The earliest theories of sloshing waves and solitary waves based on potential theory idealisations and irrotational flow have been extended to be applicable to more realistic domains. To this end, the computational fluid dynamics (CFD) methods are widely used. Three-dimensional CFD methods such as Navier-Stokes solvers with volume of fluid treatment of the free surface and Navier-Stokes solvers with mappings of the free surface inherently impose high computational expense; therefore, considerable effort has gone into developing depth-averaged approaches. Examples of such approaches include Green–Naghdi (GN) equations. In Cartesian system, GN velocity profile depends on horizontal directions, x-direction and y-direction. The effect of vertical direction (z-direction) is also taken into consideration by applying weighting function in approximation. GN theory considers the effect of vertical acceleration and the consequent non-hydrostatic pressure. Moreover, in GN theory, the flow is rotational. The present study illustrates the application of GN equations to propagation of sloshing waves and solitary waves. For this purpose, GN equations solver is verified for the benchmark tests of Gaussian hump sloshing and solitary wave propagation in shallow basins. Analysis of the free surface sloshing of even harmonic components of an initial Gaussian hump demonstrates that the GN model gives predictions in satisfactory agreement with the linear analytical solutions. Discrepancies between the GN predictions and the linear analytical solutions arise from the effect of wave nonlinearities arising from the wave amplitude itself and wave-wave interactions. Numerically predicted solitary wave propagation indicates that the GN model produces simulations in good agreement with the analytical solution of the linearised wave theory. Comparison between the GN model numerical prediction and the result from perturbation analysis confirms that nonlinear interaction between solitary wave and a solid wall is satisfactorilly modelled. Moreover, solitary wave propagation at an angle to the x-axis and the interaction of solitary waves with each other are conducted to validate the developed model.

Keywords: Green–Naghdi equations, nonlinearity, numerical prediction, sloshing waves, solitary waves

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Authors: Daniela Proca, Yuan Rong, Salvatore Luceno, Jalil Nasibli

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Introduction: Solitary Fibrous Tumors (SFT) have many histologic mimickers and the only way to diagnose it, particularly in an unusual location, such as peripheral nerve trunks, is to use a comprehensive immunohistochemical staining panel. Monoclonal STAT6 immunostain is highly sensitive and specific for SFTs and particularly useful in the diagnosis of difficult SFT cases. Methods: We describe a solitary fibrous tumor (SFT) involving the right branchial plexus in a 66 yo female with 4-year history of slowly growing chest wall mass with recent dysesthesias in fingers 4th and 5th. MRI showed a well-circumscribed heterogenous mass measuring 5.4 x 3.8 x 4.0 cm and encircling peripheral nerves of the branchial plexus; no involvement of the bone or muscle was noted. A biopsy showed a bland spindled and epithelioid proliferation with no significant mitotic activity, no necrosis, and no atypia; peripheral nerve fascicles were encircled by the lesion. The main clinical and pathologic differential diagnosis included peripheral nerve sheath tumor, particularly schwannoma; HE microscopy didn’t show the classic Antoni A and B areas but showed focal subtle nuclear palisading, as well as prominent vessels with hyalinization. Immunohistochemical stains showed focal, weak cytoplasmic S100 positivity in the lesion; CD 34 and Vimentin were strongly and diffusely positive; the neoplastic cells were negative with AE1/AE3, EMA, CD31, SMA, Desmin, Calretinin, HMB-45, Melan A, PAX-8, NSE. The immunohistochemical and histologic pattern was not typical of peripheral nerve sheath tumor. On additional stains, the tumor was positive with STAT-6 and bcl-2 and focally positive with CD99. Given this profile, the final diagnosis was that of a solitary fibrous tumor. Results: NA Conclusion: Very few SFTs involving peripheral nerves and mimicking a peripheral nerve sheath tumor are described in the literature. Although histologically benign on this biopsy, long-term follow-up is required because of the risk of recurrence of these tumors and their uncertain biological behavior.

Keywords: solitary fibrous tumor, pathology, diagnosis, immunohistochemistry

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Authors: Rafat Alshorman, Fadi Awawdeh

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By employing a simplified bilinear method, a class of generalized fifth-order KdV (gfKdV) equations which arise in nonlinear lattice, plasma physics and ocean dynamics are investigated. With the aid of symbolic computation, both solitary wave solutions and multiple-soliton solutions are obtained. These new exact solutions will extend previous results and help us explain the properties of nonlinear solitary waves in many physical models in shallow water. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by the coefficient parameters in the equation.

Keywords: multiple soliton solutions, fifth-order evolution equations, Cole-Hopf transformation, Hirota bilinear method

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Authors: Mezghiche Kamel

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We present solitary wave solutions for the perturbed nonlinear Schrodinger (PNLS) equation describing propagation of femtosecond light pulses through the fiber Bragg grating structure where the pulse dynamics is governed by the nonlinear-coupled mode (NLCM) equations. Using the multiple scale analysis, we reduce the NLCM equations into the perturbed nonlinear Schrodinger (PNLS) type equation. Unlike the reported solitary wave solutions of the PNLS equation, the novel ones can describe W shaped of solitons and their properties.

Keywords: fiber bragg grating, nonlinear-coupled mode equations, w shaped of solitons, PNLS

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Authors: Naila Nasreen, Dianchen Lu

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This paper explores the dynamical behavior of the (2+1)-dimensional Boussinesq equation, which is a nonlinear water wave equation and is used to model wave packets in dispersive media with weak nonlinearity. This equation depicts how long wave made in shallow water propagates due to the influence of gravity. The (2+1)- dimensional Boussinesq equation combines the two-way propagation of the classical Boussinesq equation with the dependence on a second spatial variable, as that occurs in the two-dimensional Kadomstev- Petviashvili equation. This equation provides a description of head- on collision of oblique waves and it possesses some interesting properties. The governing model is discussed by the assistance of Ricatti equation mapping method, a relatively integration tool. The solutions have been extracted in different forms the solitary wave solutions as well as hyperbolic and periodic solutions. Moreover, the sensitivity analysis is demonstrated for the designed dynamical structural system’s wave profiles, where the soliton wave velocity and wave number parameters regulate the water wave singularity. In addition to being helpful for elucidating nonlinear partial differential equations, the method in use gives previously extracted solutions and extracts fresh exact solutions. Assuming the right values for the parameters, various graph in different shapes are sketched to provide information about the visual format of the earned results. This paper’s findings support the efficacy of the approach taken in enhancing nonlinear dynamical behavior. We believe this research will be of interest to a wide variety of engineers that work with engineering models. Findings show the effectiveness simplicity, and generalizability of the chosen computational approach, even when applied to complicated systems in a variety of fields, especially in ocean engineering.

Keywords: (2+1)-dimensional Boussinesq equation, solitary wave solutions, Ricatti equation mapping approach, nonlinear phenomena

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Authors: Hurtado Zuñiga Yonel Marcos, Ferreira Joao Tiago

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Introduction: Leiomyoma is a benign smooth muscle tumor. It is predominantly found between 40-49 years with a small prevalence in men. It is commonly found in the uterus, stomach, and in areas with smooth muscle. It presents as nodular, solitary, variable size, slow growing, and asymptomatic. It is classified into solid, vascular, and epithelioid leiomyoma. Vascular leiomyoma is the most common in the oral cavity. Oral leiomyomas are very rare because a smooth muscle in the oral cavity isn’t common. The most frequent areas of this pathologyaretongue, lip, buccal mucosa, and palate. It may be derived from the vascular walls or excretory ducts of the salivary glands. The diagnosis is made by histologically analysis. The treatment of choice is complete excision. Recurrence is rare. Objective: To report the case of a solid leiomyoma on the dorsum of the tongue and review the literature. Case description: A 78-year-old female patient presented a nodular (ovoid) elevation of 8x6mm, brownish color, with irregular limits and firm consistency located in the dorsal part of the tongue with slight symptoms. An excisional biopsy was performed, photographic record, and 3 weeks post-surgical follow-up. Result: The surgical specimen was submitted to an anatomopathological analysis, resulting in a benign nodule with defined limits compatible with solid leiomyoma of the tongue. Discussion: It is a pathology that presents in a solitary, nodular, well-defined, asymptomatic form; in the oral cavity, leiomyomas are found in the tongue, lip, buccal mucosa, and palate; as in our patient, it was nodular and, in the tongue, with a difference only in the symptomatology. The most prevalent age is 40-49 years and with small predominance in men, unlike our female patient with 78 years. Conclusions: Oral leiomyoma is a rare benign lesion that presents as a solitary nodular nodule; for its diagnosis, an anatomopathological analysis should be performed, and the treatment of choice is total excision with little recurrence.

Keywords: tongue, bening tumor, oral leiomyoma, leiomyoma

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Authors: Sharmin Sultana, Reinhard Schlickeiser

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A degenerate relativistic quantum plasma (DRQP) system (containing relativistically degenerate electrons, degenerate/non-degenerate light nuclei, and non-degenerate heavy nuclei) is considered to investigate the propagation characteristics of electrostatic solitary waves (in the ionic scale length) theoretically and numerically. The ion-acoustic solitons are found to be associated with the modified ion-acoustic waves (MIAWs) in which inertia (restoring force) is provided by mass density of the light or heavy nuclei (degenerate pressure of the cold electrons). A mechanical-motion analog (Sagdeev-type) pseudo-potential approach is adopted to study the properties of large amplitude solitary waves. The basic properties of the large amplitude MIAWs and their existence domain in terms of soliton speed (Mach number) are examined. On the other hand, a multi-scale perturbation approach, leading to an evolution equation for the envelope dynamics, is adopted to derive the cubic nonlinear Schrödinger equation (NLSE). The criteria for the occurrence of modulational instability (MI) of the MIAWs are analyzed via the nonlinear dispersion relation of the NLSE. The possibility for the formation of highly energetic localized modes (e.g. peregrine solitons, rogue waves, etc.) is predicted in such DRQP medium. Peregrine solitons or rogue waves with amplitudes of several times of the background are observed to form in DRQP. The basic features of these modulated waves (e.g. envelope solitons, peregrine solitons, and rogue waves), which are found to form in DRQP, and their MI criteria (on the basis of different intrinsic plasma parameters), are investigated. It is emphasized that our results should be useful in understanding the propagation characteristics of localized disturbances and the modulation dynamics of envelope solitons, and their instability criteria in astrophysical DRQP system (e.g. white dwarfs, neutron stars, etc., where matters under extreme conditions are assumed to exist) and also in ultra-high density experimental plasmas.

Keywords: degenerate plasma, envelope solitons, modified ion-acoustic waves, modulational instability, rogue waves

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Authors: Edamana Krishnan, Khalil Al-Ghafri

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In this paper, modified K(n,n) and K(n+1,n+1) equations have been solved using mapping methods which give a variety of solutions in terms of Jacobi elliptic functions. The solutions when m approaches 0 and 1, with m as the modulus of the JEFs have also been deduced. The role of constraint conditions has been discussed.

Keywords: travelling wave solutions, solitary wave solutions, compactons, Jacobi elliptic functions, mapping methods

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Authors: L. A. Ostrovsky, Yu. A. Stepanyants

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Effect of Earth rotation on nonlinear waves is a practically important and theoretically challenging problem of fluid mechanics and geophysics. Whereas the large-scale, geostrophic processes such as Rossby waves are a classical object of oceanic and atmospheric physics, rotation effects on mesoscale waves are not well studied. In particular, the Coriolis force can radically modify the behavior of nonlinear internal gravity waves in the ocean having spatial scales of 1-10 kilometers and time durations of few hours. In the last decade, such a non-trivial behavior was observed more than once. Similar effects are possible for magnetic sound in the ionosphere. Here we outline the main physical peculiarities in the behavior of nonlinear internal waves due to the rotation effect and present some results of our recent studies. The consideration is based on the fourth-order equation derived by one of the authors as a rotation-modified Korteweg–de Vries (rKdV) equation which includes two types of dispersion: one is responsible for the finiteness of depth as in the classical KdV equation; another is due to the Coriolis effect. This equation is, in general, non-integrable; moreover, under the conditions typical of oceanic waves (positive dispersion parameter), it does not allow solitary solutions at all. In the opposite case (negative dispersion) which is possible for, e.g., magnetic sound, solitary solutions do exist and can form complex bound states (multisoliton). Another non-trivial properties of nonlinear internal waves with rotation include, to name a few, the ‘terminal’ damping of the initial KdV soliton disappearing in a finite time due to radiation losses caused by Earth’s rotation, and eventual transformation of a KdV soliton into a wave packet (an envelope soliton). The new results to be discussed refer to the interaction of a soliton with a long background wave. It is shown, in particular, that in this case internal solitons can exist since the radiation losses are compensated by energy pumping from the background wave. Finally, the relevant oceanic observations of rotation effect on internal waves are briefly described.

Keywords: Earth rotation, internal waves, nonlinear waves, solitons

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Authors: Wendy Carolina Gomez Ramirez, Rodulfo Ospina Torres

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Thygater aethiops is a species of solitary bee with a neotropical distribution that has been adapted to live in urban environments. This species of bee presents a marked sexual dimorphism since the males have antenna almost as long as their body different from the females that present antenna with smaller size. In this work, placoid sensilla were studied, which are structures that appear in the antenna and are involved in the detection of substances both, for reproduction and for the search of food. The aim of this study was to evaluate the differences between these sensory structures in the different sexes, for which males and females were captured. Later some body measures were taken such as fresh weight with abdomen and without it, since the weight could be modified by the stomach content; other measures were taken as the total antenna length and length of the flagellum and flagelomere. After negative imprints of the antenna were made using nail polish, the imprint was cut with a microblade and mounted onto a microscope slide. The placoid sensilla were visible on the imprint, so they were counted manually on the 100x objective lens of the optical microscope. Initially, the males presented a specific distribution pattern in two types of sensilla: trichoid and placoid, the trichoid were found aligned in the dorsal face of the antenna and the placoid were distributed along the entire antenna; that was different to the females since they did not present a distribution pattern the sensilla were randomly organized. It was obtained that the males, because they have a longer antenna, have a greater number of sensilla in relation to the females. Additionally, it was found that there was no relationship between the weight and the number of sensilla, but there was a positive relationship between the length of the antenna, the length of the flagellum and the number of sensilla. The relationship between the number of sensilla per unit area in each of the sexes was also calculated, which showed that, on average, males have 4.2 ± 0.38 sensilla per unit area and females present 2.2 ± 0.20 and likewise a significant difference between sexes. This dimorphism found may be related to the sexual behavior of the species, since it has been demonstrated that males are more adapted to the perception of substances related to reproduction than to the search of food.

Keywords: antenna, olfactory organ, sensilla, sexual dimorphism, solitary bees

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Authors: Muhammad Younis

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In this article, the novel (G′/G)-expansion method is successfully applied to construct the abundant travelling wave solutions to the modified Burgers’ equation with the aid of computation. The method is reliable and useful, which gives more general exact travelling wave solutions than the existing methods. These obtained solutions are in the form of hyperbolic, trigonometric and rational functions including solitary, singular and periodic solutions which have many potential applications in physical science and engineering. Some of these solutions are new and some have already been constructed. Additionally, the constraint conditions, for the existence of the solutions are also listed.

Keywords: traveling wave solutions, NLPDE, computation, integrability

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Authors: A. A. Soliman

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The Modified Regularized Long Wave (MRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. The temporal evaluation of a Maxwellian initial pulse is then studied.

Keywords: collocation method, MRLW equation, Quartic B-splines, solitons

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Authors: Khulood Miliany

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This study examines the media habits of young people in Saudi Arabia, in particular their use of the Internet and television in the domestic sphere, and how use of the Internet impacts upon other activities. In order to address the research questions, focus group interviews were conducted with Saudi university students. The study found that television has become a central part of social life within the household where television represents a main source for family time, particularly in Ramadan while the Internet is a solitary activity where it is used in more private spaces. Furthermore, Saudi females were also more likely to have their Internet access monitored and circumscribed by family members, with parents controlling the location and the amount of time spent using the Internet.

Keywords: domestication of technology, internet, social context, television, young people

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Authors: Geliashvili T. M., Tyulyandina A. S., Valiev A. K., Kononets P. V., Kharatishvili T. K., Salkov A. G., Pronin A. I., Gadzhieva E. H., Parnas A. V., Ilyakov V. S.

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Aim/Introduction: Metastasis (Mts) to the sternum, while extremely rare in differentiated thyroid cancer (DTC) (1), requires a personalized, multidisciplinary treatment approach. In aggressively growing Mts to the sternum, which rapidly become unresectable, a comprehensive therapeutic and diagnostic approach is particularly important. Materials and methods: We present a clinical case of solitary Mts to the sternum as first manifestation of a papillary thyroid microcarcinoma in a 55-year-old man. Results: 18F-FDG PET/CT after thyroidectomy confirmed the solitary Mts to the sternum with extremely high FDG uptake (SUVmax=71,1), which predicted its radioiodine-refractory (RIR). Due to close attachment to the mediastinum and rapid growth, Mts was considered unresectable. During the next three months, the patient received targeted therapy with the tyrosine kinase inhibitor (TKI) Lenvatinib 24 mg per day. 1st course of radioiodine therapy (RIT) 6 GBq was also performed, the results of which confirmed the RIR of the tumor process. As a result of systemic therapy (targeted therapy combined with RIT and suppressive hormone therapy with L-thyroxine), there was a significant biochemical response (decrease of serum thyroglobulin level from 50,000 ng/ml to 550 ng/ml) and a partial response with decrease of tumor size (from 80x69x123 mm to 65x50x112 mm) and decrease of FDG accumulation (SUVmax from 71.1 to 63). All of this made possible to perform surgical treatment of Mts - sternal extirpation with its replacement by an individual titanium implant. At the control examination, the stimulated thyroglobulin level was only 134 ng/ml, and PET/CT revealed postoperative areas of 18F-FDG metabolism in the removed sternal Mts. Also, 18F-FDG PET/CT in the early (metabolic) stage revealed two new bone Mts (in the area of L3 SUVmax=17,32 and right iliac bone SUVmax=13,73), which, as well as the removed sternal Mts, appeared to be RIRs at the 2nd course of RIT 6 GBq. Subsequently, on 02.2022, external beam radiation therapy (EBRT) was performed on the newly identified oligometastatic bone foci. At present, the patient is under dynamic monitoring and in the process of suppressive hormone therapy with L-thyroxine. Conclusion: Thus, only due to the early prescription of targeted TKI therapy was it possible to perform surgical resection of Mts to the sternum, thereby improve the patient's quality of life and preserve the possibility of radical treatment in case of oligometastatic disease progression.

Keywords: differentiated thyroid cancer, metastasis to the sternum, radioiodine therapy, radioiodine-refractory cancer, targeted therapy, lenvatinib

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Authors: E. V. Krishnan

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In this paper, we employ mapping methods to construct exact travelling wave solutions for a modified Korteweg-de Vries equation. We have derived periodic wave solutions in terms of Jacobi elliptic functions, kink solutions and singular wave solutions in terms of hyperbolic functions.

Keywords: travelling wave solutions, Jacobi elliptic functions, solitary wave solutions, Korteweg-de Vries equation

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Authors: Abdel-Maksoud Abdel-Kader Soliman

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The General Regularized Long Wave (GRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the Fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm.

Keywords: generalized RLW equation, solitons, quartic b-spline, nonlinear partial differential equations, difference equations

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Authors: H. Triki, Y. Hamaizi, A. El-Akrmi

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We consider the higher order nonlinear Schrödinger equation model with fourth-order dispersion, cubic-quintic terms, and self-steepening. This equation governs the propagation of fem to second pulses in optical fibers. We present new bright and dark solitary wave type solutions for such a model under certain parametric conditions. This kind of solution may be useful to explain some physical phenomena related to wave propagation in a nonlinear optical fiber systems supporting high-order nonlinear and dispersive effects.

Keywords: nonlinear Schrödinger equation, high-order effects, soliton solution

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Authors: Ritu Shitak

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Humans are social mammals, of the primate order. Our biology, behaviour, and pathologies are unique to us. In our desire to understand, reduce solitary confinement one source of information is the many reports of social isolation of other social mammals, especially primates. A behavioural study was conducted in the department of pharmacology at Indira Gandhi Medical College, Shimla in Himachal Pradesh province in India using white albino mice. Different behavioural parameters were observed by using open field, tail suspension, tests for aggressive behaviour and social interactions and the effect of isolation was studied. The results were evaluated and the standard statistics were applied. The said study was done to establish facts that isolation itself impairs social behaviour and can lead to alcohol dependence as well as related drug dependence.

Keywords: social isolation, albino mice, drug dependence, isolation on social behaviour

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Authors: Jian-Jun Shu

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It is common knowledge that many physical problems (such as non-linear shallow-water waves and wave motion in plasmas) can be described by the Korteweg-de Vries (KdV) equation, which possesses certain special solutions, known as solitary waves or solitons. As a marriage of the KdV equation and the classical Burgers (KdVB) equation, the Korteweg-de Vries-Burgers (KdVB) equation is a mathematical model of waves on shallow water surfaces in the presence of viscous dissipation. Asymptotic analysis is a method of describing limiting behavior and is a key tool for exploring the differential equations which arise in the mathematical modeling of real-world phenomena. By using variable transformations, the asymptotic expansion of the KdVB equation is presented in this paper. The asymptotic expansion may provide a good gauge on the validation of the corresponding numerical scheme.

Keywords: asymptotic expansion, differential equation, Korteweg-de Vries-Burgers (KdVB) equation, soliton

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Authors: Christy M. Moen, Richard B. Townsley

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Introduction: Metastasis to the frontal bone in thyroid cancer is extremely rare. A literature review found only six cases of thyroid cancer that metastasised to the frontal bone, with two of those involving further bone sites. Case Report: The patient was originally referred to the Oral and Maxillofacial Surgery team with an isolated mass on her forehead. Biopsies were performed, which showed this was likely a metastatic deposit from thyroid cancer. CT-PET scan showed this was an isolated lesion. The patient had a total thyroidectomy, and the forehead lesion was managed with radiotherapy. On interval scanning, the patient’s bony lesion had increased in size and had new lung nodules, which likely represented further metastasis. Conclusion: Isolated bony metastases to the frontal bone are rare. An important clinical principle to remember is that a bony metastasis from an unknown primary is more likely than primary bone cancer.

Keywords: cancer, thyroid, head and neck, surgery

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Authors: Mohammed Daher Albalwi

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The transcritical flow of a stratified fluid over an obstacle for negative forcing amplitude (hole) that generation upstream and downstream, connected by an unsteady solution, is examined. In the weakly nonlinear, weakly dispersive regime, the problem is formulated in the forced Korteweg-de Vries–Burgers framework. This is done by including the influence of the viscosity of the fluid beyond the Korteweg–de Vries approximation. The results show that the influence of viscosity is crucial in determining various wave properties, including the amplitudes of solitary waves in the upstream and downstream directions, as well as the widths of the bores. We focused here on weak damping, and the results are presented for transcritical, supercritical, and subcritical flows. In general, the outcomes are not qualitatively similar to those from the forced Korteweg-de–Vries equation when the value of the viscous is small, interesting differences emerge as the magnitude of the value of viscous increases.

Keywords: Korteweg–de Vries–Burgers equation, soliton, transcritical flow, viscous flow

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Authors: Moustafa Ahmed, Ahmed Bakry, Fumio Koyama

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We report on the use of strong external optical feedback to enhance the modulation response of semiconductor lasers over a frequency passband around modulation frequencies higher than 60 GHz. We show that this modulation enhancement is a type of photon-photon resonance (PPR) of oscillating modes in the external cavity formed between the laser and the external reflector. The study is based on a time-delay rate equation model that takes into account both the strong feedback and multiple reflections in the external cavity. We examine the harmonic and intermodulation distortions associated with single and two-tone modulations in the mm-wave band of the resonant modulation. We show that compared with solitary lasers modulated around the carrier-photon resonance frequency, the present mm-wave modulated signal has lower distortions.

Keywords: semiconductor laser, optical feedback, modulation, harmonic distortion

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Authors: Eugene Kogan

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We analytically study the localized running waves in the discrete Josephson transmission lines (JTL), constructed from Josephson junctions (JJ) and capacitors. The quasi-continuum approximation reduces the calculation of the running wave properties to the problem of equilibrium of an elastic rod in the potential field. Making additional approximations, we reduce the problem to the motion of the fictitious Newtonian particle in the potential well. We show that there exist running waves in the form of supersonic kinks and solitons and calculate their velocities and profiles. We show that the nonstationary smooth waves, which are small perturbations on the homogeneous non-zero background, are described by Korteweg-de Vries equation, and those on zero background -by the modified Korteweg-de Vries equation. We also study the effect of dissipation on the running waves in JTL and find that in the presence of the resistors, shunting the JJ and/or in series with the ground capacitors, the only possible stationary running waves are the shock waves, whose profiles are also found.

Keywords: Josephson transmission line, shocks, solitary waves, nonlinear waves

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Authors: Kunal Garg, Louise Theusen Hermansan, Kanoktip Puttaraska, Oliver Hendricks, Heidi Pirttinen, Leona Gilbert

Abstract:

The Germ Theory (one infectious determinant is equal to one disease) has unarguably evolved our capability to diagnose and treat infectious diseases over the years. Nevertheless, the advent of technology, climate change, and volatile human behavior has brought about drastic changes in our environment, leading us to question the relevance of the Germ Theory in our day, i.e. will vector-borne disease (VBD) sufferers produce multiple immune responses when tested for multiple microbes? Vector diseased patients producing multiple immune responses to different microbes would evidently suggest human polymicrobial infections (HPI). Ongoing diagnostic tools are exceedingly unequipped with the current research findings that would aid in diagnosing patients for polymicrobial infections. This shortcoming has caused misdiagnosis at very high rates, consequently diminishing the patient’s quality of life due to inadequate treatment. Equipped with the state-of-art scientific knowledge, PolyScan intends to address the pitfalls in current VBD diagnostics. PolyScan is a multiplex and multifunctional enzyme linked Immunosorbent assay (ELISA) platform that can test for numerous VBD microbes and allow simultaneous screening for multiple types of antibodies. To validate PolyScan, Lyme Borreliosis (LB) and spondyloarthritis (SpA) patient groups (n = 54 each) were tested for Borrelia burgdorferi, Borrelia burgdorferi Round Body (RB), Borrelia afzelii, Borrelia garinii, and Ehrlichia chaffeensis against IgM and IgG antibodies. LB serum samples were obtained from Germany and SpA serum samples were obtained from Denmark under relevant ethical approvals. The SpA group represented chronic LB stage because reactive arthritis (SpA subtype) in the form of Lyme arthritis links to LB. It was hypothesized that patients from both the groups will produce multiple immune responses that as a consequence would evidently suggest HPI. It was also hypothesized that the multiple immune response proportion in SpA patient group would be significantly larger when compared to the LB patient group across both antibodies. It was observed that 26% LB patients and 57% SpA patients produced multiple immune responses in contrast to 33% LB patients and 30% SpA patients that produced solitary immune responses when tested against IgM. Similarly, 52% LB patients and an astounding 73% SpA patients produced multiple immune responses in contrast to 30% LB patients and 8% SpA patients that produced solitary immune responses when tested against IgG. Interestingly, IgM immune dysfunction in both the patient groups was also recorded. Atypically, 6% of the unresponsive 18% LB with IgG antibody was recorded producing multiple immune responses with the IgM antibody. Similarly, 12% of the unresponsive 19% SpA with IgG antibody was recorded producing multiple immune responses with the IgM antibody. Thus, results not only supported hypothesis but also suggested that IgM may atypically prevail longer than IgG. The PolyScan concept will aid clinicians to detect patients for early, persistent, late, polymicrobial, & immune dysfunction conditions linked to different VBD. PolyScan provides a paradigm shift for the VBD diagnostic industry to follow that will drastically shorten patient’s time to receive adequate treatment.

Keywords: diagnostics, immune dysfunction, polymicrobial, TICK-TAG

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