scholarly journals Resonant Collisions Among Two-Dimensional Localized Waves in the Mel'nikov Equation

2021 ◽  
Author(s):  
Yinshen Xu ◽  
Dumitru Mihalache ◽  
Jingsong He
Keyword(s):  
Solitary Waves ◽  
Direct Method ◽  
Phase Shifts ◽  
Limit Case ◽  
Dark Line ◽  
Dynamical Behaviors ◽  
Different Types ◽  
Localized Waves ◽  
Special Case ◽  
Line Soliton

Abstract We study the resonant collisions among different types of localized solitary waves in the Mel'nikov equation, which are described by exact solutions constructed using Hirota's direct method. The elastic collisions among different solitary waves can be transformed into resonant collisions when the phase shifts of these solitary waves tend to infinity . First, we study the resonant collision among a breather and a dark line soliton. We obtain two collision scenarios: (i) the breather is semi-localized in space and is not localized in time when it obliquely intersects with the dark line soliton, and (ii) the breather is semi-localized in time and is not localized in space when it parallelly intersects with the dark line soliton. The resonant collision of a lump and a dark line soliton, as the limit case of resonant collision of a breather and a dark line soliton, shows the fusing process of the lump into the dark line soliton. Then we investigate the resonant collision among a breather and two dark line solitons. In this evolution process we also obtain two dynamical behaviors: (iii) when the breather and the two dark line solitons obliquely intersect each other we get that the breather is completely localized in space and is not localized in time, and (iv) when the breather and the two dark line solitons are parallel to each other, we get that the breather is completely localized in time and is not localized in space. The resonant collision of a lump and two dark line solitons is obtained as the limit case of the resonant collision among a breather and two dark line solitons. In this special case the lump first detaches from a dark line soliton and then disappears into the other dark line soliton. Eventually, we also investigate the intriguing phenomenon that when a resonant collision among a breather and four dark line solitons occurs, we get the interesting situation that two of the four dark line solitons are degenerate and the corresponding solution displays the same shape as that of the resonant collision among a breather and two dark line solitons, except for the phase shifts of the solitons, which are not only dependent of the parameters controlling the waveforms of the solitons and the breather, but also dependent of some parameters irrelevant to the waveforms.

scholarly journals Theoretical treatment of tight-binding inhibition of an enzyme. Ribonuclease inhibitor as special case

1988 ◽  
Vol 253 (2) ◽  
pp. 517-522 ◽  
Author(s):  
J M Fominaya ◽  
J M García-Segura ◽  
M Ferreras ◽  
J G Gavilanes
Keyword(s):  
Tight Binding ◽  
Theoretical Treatment ◽  
Inhibitor Protein ◽  
Ribonuclease Inhibitor ◽  
Rat Testis ◽  
Binding Inhibition ◽  
Different Types ◽  
Functional Consequences ◽  
Inhibitor System ◽  
Special Case

A general treatment of very tight-binding inhibition is described. It was applied to purified endogenous RNAase inhibitor from rat testis. This treatment discriminates among the different types of inhibition and allows for calculation of the inhibition parameters. When very tight-binding inhibitions are studied at similar molar concentrations of both enzyme and inhibitor, a further approach is required. This is also described and applied to the RNAase inhibitor. A Ki value of 3.2 x 10(-12) M was found for this inhibitor protein. On the basis of this result, it was considered inappropriate to classify this type of inhibitor in terms of competitive or non-competitive, as has been done for such inhibitors so far. Functional consequences of this analysis are discussed for the RNAase-RNAase inhibitor system.

The Unified Theory of Tubesheet Design - Part III: Comparison with ASME Method and Case Study

2021 ◽  
Author(s):  
Hong-Song Zhu ◽  
Jinguo Zhai ◽  
Guo-Yan Zhou
Keyword(s):  
Heat Exchangers ◽  
Numerical Comparison ◽  
Unified Theory ◽  
Element Analysis ◽  
Theoretical Comparison ◽  
Comparison Results ◽  
Different Types ◽  
Special Case ◽  
Simplified Mechanical Model

Abstract Based on the unified theory of tubesheet (TS) design for fixed TS heat exchangers (HEX), floating head and U-tube HEX presented in Part I and Part II, theoretical and numerical comparisons with ASME method are performed in this paper as Part III. Theoretical comparison shows that ASME method can be obtained from the special case of the simplified mechanical model of the unified theory. Numerical Comparison results indicate that predictions given by the unified theory agree well with finite element analysis (FEA), while ASME results are not accurate or not correct. Therefore, it is concluded that the unified theory deals with different types of HEX in equal detail with confidence to predict design stresses.

scholarly journals Nonlinear Analysis of Tropical Waves and Cyclogenesis Excited by Pressure Disturbance in Atmosphere

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3038
Author(s):  
Zi-Liang Li ◽  
Jin-Qing Liu
Keyword(s):  
Solitary Waves ◽  
Direct Method ◽  
Equations Of Motion ◽  
Nonlinear Process ◽  
Analytic Solutions ◽  
External Pressure ◽  
Homogeneous Fluid ◽  
Pressure Disturbance ◽  
Cyclone Genesis ◽  
Fkdv Equation

The horizontal equations of motion for an inviscid homogeneous fluid under the influence of pressure disturbance and waves are applied to investigate the nonlinear process of solitary waves and cyclone genesis forced by a moving pressure disturbance in atmosphere. Based on the reductive perturbation analysis, it is shown that the nonlinear evolution equation for the wave amplitude satisfies the Korteweg–de Vries equation with a forcing term (fKdV equation for short), which describes the physics of a shallow layer of fluid subject to external pressure forcing. Then, with the help of Hirota’s direct method, the analytic solutions of the fKdV equation are studied and some exact vortex solutions are given as examples, from which one can see that the solitary waves and vortex multi-pole structures can be excited by external pressure forcing in atmosphere, such as pressure perturbation and waves. It is worthy to point out that cyclone and waves can be excited by different type of moving atmospheric pressure forcing source.

scholarly journals A Bayesian Approach for Estimating Parameter of Rayleigh Distribution

2019 ◽  
Vol 11 (1) ◽  
pp. 23-39
Author(s):  
J. Mahanta ◽  
M. B. A. Talukdar
Keyword(s):  
Weibull Distribution ◽  
Loss Function ◽  
Bayesian Approach ◽  
Rayleigh Distribution ◽  
Loss Functions ◽  
Bayes Risk ◽  
Squared Error ◽  
Different Types ◽  
Two Parameters ◽  
Special Case

This paper is concerned with estimating the parameter of Rayleigh distribution (special case of two parameters Weibull distribution) by adopting Bayesian approach under squared error (SE), LINEX, MLINEX loss function. The performances of the obtained estimators for different types of loss functions are then compared. Better result is found in Bayesian approach under MLINEX loss function. Bayes risk of the estimators are also computed and presented in graphs.

scholarly journals Abundant distinct types of solutions for the nervous biological fractional FitzHugh–Nagumo equation via three different sorts of schemes

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Abdel-Haleem Abdel-Aty ◽  
Mostafa M. A. Khater ◽  
Dumitru Baleanu ◽  
E. M. Khalil ◽  
Jamel Bouslimi ◽  
...  
Keyword(s):  
Nervous System ◽  
Expansion Method ◽  
B Spline ◽  
Stability Behavior ◽  
Nerve Impulses ◽  
Dynamical Behaviors ◽  
Different Types ◽  
Nagumo Equation ◽  
The Stability

Abstract The dynamical attitude of the transmission for the nerve impulses of a nervous system, which is mathematically formulated by the Atangana–Baleanu (AB) time-fractional FitzHugh–Nagumo (FN) equation, is computationally and numerically investigated via two distinct schemes. These schemes are the improved Riccati expansion method and B-spline schemes. Additionally, the stability behavior of the analytical evaluated solutions is illustrated based on the characteristics of the Hamiltonian to explain the applicability of them in the model’s applications. Also, the physical and dynamical behaviors of the gained solutions are clarified by sketching them in three different types of plots. The practical side and power of applied methods are shown to explain their ability to use on many other nonlinear evaluation equations.

Nonlocal Symmetry and its Applications in Perturbed mKdV Equation

2016 ◽  
Vol 71 (6) ◽  
pp. 557-564 ◽  
Author(s):  
Bo Ren ◽  
Ji Lin
Keyword(s):  
Constant Coefficient ◽  
Direct Method ◽  
Symmetry Transformation ◽  
Mkdv Equation ◽  
Nonlocal Symmetry ◽  
Rational Solutions ◽  
Initial Value ◽  
Interaction Solutions ◽  
Different Types ◽  
Painlevé Ii

AbstractBased on the modified direct method, the variable-coefficient perturbed mKdV equation is changed to the constant-coefficient perturbed mKdV equation. The truncated Painlevé method is applied to obtain the nonlocal symmetry of the constant-coefficient perturbed mKdV equation. By introducing one new dependent variable, the nonlocal symmetry can be localized to the Lie point symmetry. Thanks to the localization procedure, the finite symmetry transformation is presented by solving the initial value problem of the prolonged systems. Furthermore, many explicit interaction solutions among different types of solutions such as solitary waves, rational solutions, and Painlevé II solutions are obtained using the symmetry reduction method to the enlarged systems. Two special concrete soliton-cnoidal interaction solutions are studied in both analytical and graphical ways.

scholarly journals On the number of excursion sets of planar Gaussian fields

2020 ◽  
Vol 178 (3-4) ◽  
pp. 655-698
Author(s):  
Dmitry Beliaev ◽  
Michael McAuley ◽  
Stephen Muirhead
Keyword(s):  
Plane Wave ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Gaussian Fields ◽  
Important Special Case ◽  
Level Densities ◽  
Excursion Sets ◽  
Nodal Set ◽  
Different Types ◽  
Special Case

Abstract The Nazarov–Sodin constant describes the average number of nodal set components of smooth Gaussian fields on large scales. We generalise this to a functional describing the corresponding number of level set components for arbitrary levels. Using results from Morse theory, we express this functional as an integral over the level densities of different types of critical points, and as a result deduce the absolute continuity of the functional as the level varies. We further give upper and lower bounds showing that the functional is at least bimodal for certain isotropic fields, including the important special case of the random plane wave.

A general time-dependent invariant for and integrability of the quadratic system

1994 ◽  
Vol 444 (1922) ◽  
pp. 643-650 ◽  
Keyword(s):  
Direct Method ◽  
First Integral ◽  
Quadratic System ◽  
Time Dependent ◽  
Polynomial Invariant ◽  
Polynomial Invariants ◽  
Linear Polynomial ◽  
A Direct Method ◽  
Special Case ◽  
General Time

We derive a general time-dependent invariant (first integral) for the quadratic system (QS) that requires only one condition on the coefficients of the QS. The general invariant could yield asymptotic behaviour of phase-space trajectories. With more conditions imposed on the coefficients, the general invariant reduces to polynomial form and is equivalent to polynomial invariants found using a direct method. For the special case of a linear polynomial invariant where one of the variables is analytically invertible, the solution of the QS is reduced to a quadrature.

Between Story and Narrated World: Reflections on the Difference between Homo- and Heterodiegesis

2014 ◽  
Vol 8 (2) ◽  
Author(s):  
Simone Elisabeth Lang
Keyword(s):  
Present Article ◽  
Literary Studies ◽  
Textual Interpretation ◽  
Different Types ◽  
The Difference ◽  
The One ◽  
The Relationship ◽  
Special Case ◽  
Shed Light ◽  
Theoretical Standpoint

AbstractIn describing the position of the narrator, research in literary studies generally follows Gérard Genette’s pioneering theory of narrative in distinguishing between the homo- and heterodiegetic type of narrator. This categorization is not sufficient to allow the position of the narrator to be described properly. The different ways in which the terms are used in literary studies reveal a shortcoming in the distinction behind them. Even in Genette’s work, there is a contradiction between the definition and the names of the two categories: Genette defines homo- and heterodiegesis with reference to the narrator’s presence in the narrated story, whereas he elsewhere states that the diegesis (in the sense of FrenchThe present article aims to do just that, starting from a theoretical standpoint. Thus, the different types of narrator that are possible are sketched in outline, and then explained with the help of examples.I begin by exposing the problems that result from using the terms in Genette’s manner (1), in order then to develop a list of possible narratorial standpoints based on the one hand on the involvement of the narratorial instance in the narrated world and on the other on its involvement in the story. By establishing separation of the two aspects as a ground rule in this way, a number of misunderstandings that are due to the varied ways in which the terminology has been used to date can be overcome.There follows a description of those cases that are unambiguously hetero- and homodiegetic (2), after which the problematic cases are considered (3), yielding the different types of homodiegetic narration that are possible. This latter set of distinctions will, like the others, shed light on the contours of the different narratorial positions and thus be capable of being put profitably into practice in textual interpretation. Accordingly, what is suggested is a way of using the terms that is first unambiguous and second beneficial to the interpretation of works, thus doing justice to the heuristic importance of narratology (see Kindt/Müller 2003; Stanzel 2002, 19).Thus, whereas the concept of diegesis provides the foundation for a distinction based on an ontological criterion that divides homo- and heterodiegesis from each other, the relationship between story and narrator is used to describe various types of homodiegetic narration. In the process, there come to light two types that are distinguished from each other by involvement in events (›homodiegetic, in the story‹ and ›homodiegetic, not in the story‹ narrators). If the narrator is not involved in events, the question arises of whether it would in principle have been possible for him to be involved in events, which is the norm with ›homodiegetic, not in the story‹ narrators, or whether a physical impossibility is the reason for his lack of involvement in the story. A special case of the ›homodiegetic, not in the story‹ narrator can be derived from this: peridiegetic narration: whereas narratorial instances of the ›homodiegetic, in the story‹ and ›homodiegetic, not in the story‹ types could in principle have been involved in the action and those of the ›homodiegetic, in the story‹ type actually were, peridiegetic narrators are marked by the fact that they cannot have been involved in the events.In summary, it will be shown that the concept of homodiegesis – in particular in the form in which it has previously been used, where links with the action and appearance in the story were not kept distinct – is in effect an umbrella term that brings together a number of possible forms. There is a prominent distinction between the ›homodiegetic, in the story‹ and the ›homodiegetic, not in the story‹ types of narrator (these types are represented in the present article by the old lawyer in Leo Perutz’s »The Beaming Moon« and the narrator who is a friend of Nathanael in E. T. A. Hoffmann’s »Sandman« respectively). The different degrees of homodiegetic narrator, which have often been mentioned in previous research and are defined by the strength of the character’s presence in the narrated world (from an uninvolved witness to an autodiegetic protagonist), are also to be situated between these two poles.It will also be shown in the process that the case of the narrator who is, for reasons of physical difference, not involved in events (the peridiegetic narrator) should be treated as a form of homodiegesis (for instance the schoolmaster in Theodor Storm’s

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