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Bashar MH, Mawa H, Biswas A, Rahman M, Roshid MM, Islam J. The modified extended tanh technique ruled to exploration of soliton solutions and fractional effects to the time fractional couple Drinfel'd-Sokolov-Wilson equation. Heliyon 2023; 9:e15662. [PMID: 37215912 PMCID: PMC10192409 DOI: 10.1016/j.heliyon.2023.e15662] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2023] [Revised: 04/15/2023] [Accepted: 04/18/2023] [Indexed: 05/24/2023] Open
Abstract
The modified extended tanh technique is used to investigate the conformable time fractional Drinfel'd-Sokolov-Wilson (DSW) equation and integrate some precise and explicit solutions in this survey. The DSW equation was invented in fluid dynamics. The modified extended tanh technique executes to integrate the nonlinear DSW equation for achieve diverse solitonic and traveling wave envelops. Because of this, trigonometric, hyperbolic and rational solutions have been found with a few acceptable parameters. The dynamical behaviors of the obtained solutions in the pattern of the kink, bell, multi-wave, kinky lump, periodic lump, interaction lump, and kink wave types have been illustrated with 3D and density plots for arbitrary chose of the permitted parameters. By characterizing the particular benefits of the exemplified boundaries by the portrayal of sketches and by deciphering the actual events, we have laid out acceptable soliton plans and managed the actual significance of the acquired courses of action. New precise voyaging wave arrangements are unambiguously gained with the aid of symbolic computation using the procedures that have been announced. Therefore, the obtained outcomes expose that the projected schemes are very operative, easier and efficient on realizing natures of waves and also introducing new wave strategies to a diversity of NLEEs that occur within the engineering sector.
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Affiliation(s)
- Md Habibul Bashar
- Department of Mathematics, European University of Bangladesh, Dhaka 1216, Bangladesh
- Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh
| | - H.Z. Mawa
- Department of Civil Engineering, Presidency University Dhaka 1212, Bangladesh
| | - Anita Biswas
- Department of Mathematics, European University of Bangladesh, Dhaka 1216, Bangladesh
| | - M.M. Rahman
- Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh
| | - Md Mamunur Roshid
- Department of Mathematics, Hamdard University Bangladesh, Munshiganj 1510, Bangladesh
| | - Jahedul Islam
- Department of Civil Engineering, Presidency University Dhaka 1212, Bangladesh
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Ozdemir N, Secer A, Ozisik M, Bayram M. Obtaining the soliton solutions of local M-fractional magneto-electro-elastic media. Heliyon 2023; 9:e13015. [PMID: 36711318 PMCID: PMC9876988 DOI: 10.1016/j.heliyon.2023.e13015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2022] [Revised: 12/10/2022] [Accepted: 01/13/2023] [Indexed: 01/21/2023] Open
Abstract
In this research paper, the generalized projective Riccati equations method (GPREM) is applied successfully to procure the soliton solutions of the local M-fractional longitudinal wave equation (LWE) arising in mathematical physics with dispersion caused by the transverse Poisson's effect in a magneto-electro-elastic circular rod (MEECR). Applying a wave transformation to the local M-fractional LWE, the equation can be turned into a set of algebraic equations. Solving the algebraic equation system, we procure the soliton solutions of the local M-fractional LWE. Both the obtained solution functions in the study and the graphical simulations depicted for these functions. It will assist researchers working in this field in the physical interpretation of this equation. Moreover, the reported solutions propose a rich platform to examine the local M-fractional LWE.
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Affiliation(s)
- Neslihan Ozdemir
- Istanbul Gelisim University, Department of Software Engineering, Istanbul, Turkey
| | - Aydin Secer
- Biruni University, Department of Computer Engineering, Istanbul, Turkey,Yildiz Technical University, Department of Mathematical Engineering, Istanbul, Turkey
| | - Muslum Ozisik
- Yildiz Technical University, Department of Mathematical Engineering, Istanbul, Turkey
| | - Mustafa Bayram
- Biruni University, Department of Computer Engineering, Istanbul, Turkey,Corresponding author.
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Abstract
BACKGROUND From the laboratory at Scripps Institution of Oceanography, it is common to see the brown pelican (Pelecanus occidentalis) traveling along the crests of ocean waves just offshore of the surf-zone. When flying in this manner, the birds can travel long distances without flapping, centimeters above the ocean's surface. Here we derive a theoretical framework for assessing the energetic savings related to this behavior, 'wave-slope soaring,' in which an organism in flight takes advantage of localized updrafts caused by traveling ocean surface gravity waves. METHODS The energy cost of steady, constant altitude flight in and out of ground effect are analyzed as controls. Potential flow theory is used to quantify the ocean wave-induced wind associated with near-shoaling, weakly nonlinear, shallow water ocean surface gravity waves moving through an atmosphere initially at rest. Using perturbation theory and the Green's function for Laplace's equation in 2D with Dirichlet boundary conditions, we obtain integrals for the horizontal and vertical components of the wave-induced wind in a frame of reference moving with the wave. Wave-slope soaring flight is then analyzed using an energetics-based approach for waves under a range of ocean conditions and the body plan of P. occidentalis. RESULTS For ground effect flight, we calculate a ∼15 - 25% reduction in cost of transport as compared with steady, level flight out of ground effect. When wave-slope soaring is employed at flight heights ∼2m in typical ocean conditions (2m wave height, 15s period), we calculate 60-70% reduction in cost of transport as compared with flight in ground effect. A relatively small increase in swell amplitude or decrease in flight height allows up to 100% of the cost of transport to be offset by wave-slope soaring behavior. CONCLUSIONS The theoretical development presented here suggests there are energy savings associated with wave-slope soaring. Individual brown pelicans may significantly decrease their cost of transport utilizing this mode of flight under typical ocean conditions. Thus wave-slope soaring may provide fitness benefit to these highly mobile organisms that depend on patchy prey distribution over large home ranges.
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Affiliation(s)
- Ian A. Stokes
- Dept. of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92037, USA
- Scripps Institution of Oceanography, University of California, San Diego, 8622 Kennel Way, La Jolla, CA 92037, USA
| | - Andrew J. Lucas
- Dept. of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92037, USA
- Scripps Institution of Oceanography, University of California, San Diego, 8622 Kennel Way, La Jolla, CA 92037, USA
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Takembo CN, Ekonde Sone M. Pattern selection in coupled neurons under high-low frequency electric field. Heliyon 2021; 7:e06132. [PMID: 33553767 PMCID: PMC7848657 DOI: 10.1016/j.heliyon.2021.e06132] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2020] [Revised: 11/23/2020] [Accepted: 01/25/2021] [Indexed: 10/25/2022] Open
Abstract
Biological neurons exposed to an external electric field can induce polarization and charge fluctuation. Indeed, the exchange of calcium, sodium and potassium ions across the cell membrane can induce an electric field as a result of a time-varying electromagnetic field set up. This field could further modulate the cell electrical activity by inducing multiple firing modes. Based on the physical law of electric field, an improved model which includes an additive electrical field variable is constructed for a network of neurons to study wave propagation and mode transition by exploring the longtime dynamics of slightly perturbed plane waves in the network. Wave pattern and mode transition dependence on the different parameters of external electric field are discussed. It is found that the plane wave propagating in the coupled system breaks down to localized structures under the activation of modulational instability. The network under high-low external electric field supports bursting synchronization. This could be a fruitful avenue to discern the occurrence of paroxysmal epilepsy.
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Affiliation(s)
- Clovis Ntahkie Takembo
- Department of Electrical and Electronic Engineering, College of Technology, University of Buéa, P.O. Box 63, Buéa, Cameroon
| | - Michael Ekonde Sone
- Department of Electrical and Electronic Engineering, College of Technology, University of Buéa, P.O. Box 63, Buéa, Cameroon
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Islam KA, Deeba F, Kamal-Al-Hassan M. Dust ion acoustic solitons in a complex dusty plasma system with an adiabatic state. Heliyon 2020; 6:e05373. [PMID: 33163659 PMCID: PMC7610275 DOI: 10.1016/j.heliyon.2020.e05373] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2020] [Revised: 08/17/2020] [Accepted: 10/26/2020] [Indexed: 10/27/2022] Open
Abstract
In this theoretical work nonlinear behavior of dust ion acoustic solitary waves (SWs) has been investigated, and then the effect of the adiabatic change on them has been observed. The complex plasma system consists of inertial positive and negative ions, Maxwell's electrons, and positively and negatively charged stationary dust particles. The effects of dust polarity on the dust ion acoustic SWs have also been observed. Using the reductive perturbation method, we first derive K-dV equation which lets to analyze both the positive (bright) and negative (dark) solitons in a very limited region. After that mK-dV equation has been derived, and this let to analyze positive soliton for a large region, but cannot show the negative soliton. Finally, the Gardner equation has been derived employing the same method, through which we were able to analyze both the positive and negative solitons for a large region. It has been found that both the positive and negative solitons significantly depend on the mass number density, ion number density, and dust polarity in the adiabatic and isothermal system.
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Affiliation(s)
| | - F Deeba
- Department of Physics, Dhaka University of Engineering & Technology, Gazipur, Bangladesh
| | - Md Kamal-Al-Hassan
- Department of Physics, Dhaka University of Engineering & Technology, Gazipur, Bangladesh
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Bernstein OM, McGee TE, Silzel LE, Silzel JW. Fluorescent pseudorotaxanes of a quinodicarbocyanine dye with gamma cyclodextrin. Spectrochim Acta A Mol Biomol Spectrosc 2018; 189:202-214. [PMID: 28820972 DOI: 10.1016/j.saa.2017.07.060] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2017] [Revised: 07/26/2017] [Accepted: 07/30/2017] [Indexed: 06/07/2023]
Abstract
Spectrophotometric titration of buffered solutions of gamma cyclodextrin (γCD) and 1,1'-diethyl,2,2'-dicarbocyanine (DDI) demonstrates extension of the known 1:2 host:guest complex to form a previously unreported 2:2 complex near the γCD solubility limit. Though DDI is predominantly hosted as a non-fluorescent H-aggregate, both complexes exist in respective equilibria with two secondary complexes hosting unaggregated DDI as 1:1 and 2:1 complexes. The 2:1 complex exhibits significant fluorescence emission, with a quantum yield six times that of DDI in organic solvents, but ten times lower than that of an analogous indodicarbocyanine. Fragment Molecular Orbital calculations suggest that the 2:1 complex has the tail-to-tail conformation, and that solvent access to the dye strongly favors photoisomerization. In the host-guest complex, γCD limits solvent access to the dye and hinders rotation of the quinolyl terminal groups, but nevertheless pairwise rotation of methine carbons within the γCD cavity likely remains as a significant nonradiative relaxation pathway for the excited state.
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Affiliation(s)
- Olivia M Bernstein
- Department of Chemistry, Physics, and Engineering, Biola University, 13800 Biola Avenue, La Mirada, CA 90639, USA
| | - Tiffany E McGee
- Department of Chemistry, Physics, and Engineering, Biola University, 13800 Biola Avenue, La Mirada, CA 90639, USA
| | - Lisa E Silzel
- Department of Chemistry, Physics, and Engineering, Biola University, 13800 Biola Avenue, La Mirada, CA 90639, USA
| | - John W Silzel
- Department of Chemistry, Physics, and Engineering, Biola University, 13800 Biola Avenue, La Mirada, CA 90639, USA.
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de Billy M. Crossing of acoustic envelope solitary waves in homogeneous elastic rods: Experiments. Ultrasonics 2016; 72:42-46. [PMID: 27476118 DOI: 10.1016/j.ultras.2016.07.009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2016] [Revised: 07/16/2016] [Accepted: 07/18/2016] [Indexed: 06/06/2023]
Abstract
In this letter we focused on the problem in which two shear envelope solitary waves traveling in 1-D homogeneous system (elastic PMMA rod of constant cross-section) and incoming in opposite directions, meet one another and head-on collide. The properties of incident acoustic waves after collision are investigated. Two cases are experimentally examined: incoming waves with close amplitudes and quite large difference in magnitude. No phase shift and no variation of polarization are experimentally detected after the collision.
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Affiliation(s)
- M de Billy
- Sorbonne Universités, UPMC Univ. Paris 06, CNRS, UMR 7190, Institut Jean Le Rond d'Alembert - Site de St Cyr, 2 place de la Gare de Ceinture, 78210 St Cyr l'Ecole, France.
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Abstract
We present here biophysical models to gain deeper insights into how an acoustic stimulus might influence or modulate neuronal activity. There is clear evidence that neural activity is not only associated with electrical and chemical changes but that an electro-mechanical coupling is also involved. Currently, there is no theory that unifies the electrical, chemical, and mechanical aspects of neuronal activity. Here, we discuss biophysical models and hypotheses that can explain some of the mechanical aspects associated with neuronal activity: the soliton model, the neuronal intramembrane cavitation excitation model, and the flexoelectricity hypothesis. We analyze these models and discuss their implications on stimulation and modulation of neuronal activity by ultrasound.
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Affiliation(s)
- Elisabetta Sassaroli
- Department of Radiology, Brigham and Women’s Hospital, Focused Ultrasound Lab, 221 Longwood Ave., Boston, MA 02115 USA
| | - Natalia Vykhodtseva
- Department of Radiology, Brigham and Women’s Hospital, Focused Ultrasound Lab, 221 Longwood Ave., Boston, MA 02115 USA
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Shikhovtseva ES, Nazarov VN. Non-linear longitudinal compression effect on dynamics of the transcription bubble in DNA. Biophys Chem 2016; 214-215:47-53. [PMID: 27232455 DOI: 10.1016/j.bpc.2016.05.005] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2016] [Revised: 05/11/2016] [Accepted: 05/14/2016] [Indexed: 01/28/2023]
Abstract
The dependence of the dynamics of transcription bubble on the parameters of non-linear longitudinal compression is presented on the base of simple model of soliton-like conformational switchings in two-component bistable polymer molecules with energetically non-equivalent stable states. It has been shown that under certain conditions the longitudinal compression may be a trap for a conformational switching.
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Affiliation(s)
- E S Shikhovtseva
- Institute of Molecule and Crystal Physics Ufa Research Centre of Russian Academy of Sciences, Prospekt Oktyabrya 151, Ufa 450075, Russia.
| | - V N Nazarov
- Institute of Molecule and Crystal Physics Ufa Research Centre of Russian Academy of Sciences, Prospekt Oktyabrya 151, Ufa 450075, Russia.
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Akbar MA, Hj Mohd Ali N. Solitary wave solutions of the fourth order Boussinesq equation through the exp(-Ф(η))-expansion method. Springerplus 2014; 3:344. [PMID: 25105084 PMCID: PMC4124106 DOI: 10.1186/2193-1801-3-344] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/03/2014] [Accepted: 06/10/2014] [Indexed: 11/25/2022]
Abstract
Abstract The exp(–Ф(η))-expansion method is an ascending method for obtaining exact and solitary wave solutions for nonlinear evolution equations. In this article, we implement the exp(–Ф(η))-expansion method to build solitary wave solutions to the fourth order Boussinesq equation. The procedure is simple, direct and useful with the help of computer algebra. By using this method, we obtain solitary wave solutions in terms of the hyperbolic functions, the trigonometric functions and elementary functions. The results show that the exp(–Ф(η))-expansion method is straightforward and effective mathematical tool for the treatment of nonlinear evolution equations in mathematical physics and engineering. Mathematics subject classifications 35C07; 35C08; 35P99
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Affiliation(s)
- M Ali Akbar
- Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh
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Abstract
Two models for energy and charge transport and storage in biomolecules are considered. A model based on the discrete nonlinear Schrödinger equation with long-range dispersive interactions (LRI's) between base pairs of DNA is offered for the description of nonlinear dynamics of the DNA molecule. We show that LRI's are responsible for the existence of an interval of bistability where two stable stationary states, a narrow, pinned state and a broad, mobile state, coexist at each value of the total energy. The possibility of controlled switching between pinned and mobile states is demonstrated. The mechanism could be important for controlling energy storage and transport in DNA molecules. Another model is offered for the description of nonlinear excitations in proteins and other anharmonic biomolecules. We show that in the highly anharmonic systems a bound state of Davydov and Boussinesq solitons can exist.
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Affiliation(s)
- S F Mingaleev
- Bogolyubov Institute for Theoretical Physics, 14-b Metrologichna Str., 252143 Kiev, Ukraine
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