A Hausdorff fractal Nizhnik-Novikov-Veselov model arising in the incompressible fluid

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yasir Khan
Keyword(s):  
Incompressible Fluid ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Fractal Model ◽  
Scale Transformation ◽  
Physical Parameters ◽  
Content Type ◽  
Soliton Theory ◽  
Solitary Solutions ◽  
And Mathematics

Purpose Nizhnik–Novikov–Veselov system (NNVS) is a well-known isotropic extension of the Lax (1 + 1) dimensional Korteweg-deVries equation that is also used as a paradigm for an incompressible fluid. The purpose of this paper is to present a fractal model of the NNVS based on the Hausdorff fractal derivative fundamental concept. Design/methodology/approach A two-scale transformation is used to convert the proposed fractal model into regular NNVS. The variational strategy of well-known Chinese scientist Prof. Ji Huan He is used to generate bright and exponential soliton solutions for the proposed fractal system. Findings The NNV fractal model and its variational principle are introduced in this paper. Solitons are created with a variety of restriction interactions that must all be applied equally. Finally, the three-dimensional diagrams are displayed using an appropriate range of physical parameters. The results of the solitary solutions demonstrated that the suggested method is very accurate and effective. The proposed methodology is extremely useful and nearly preferable for use in such problems. Practical implications The research study of the soliton theory has already played a pioneering role in modern nonlinear science. It is widely used in many natural sciences, including communication, biology, chemistry and mathematics, as well as almost all branches of physics, including nonlinear optics, plasma physics, fluid dynamics, condensed matter physics and field theory, among others. As a result, while constructing possible soliton solutions to a nonlinear NNV model arising from the field of an incompressible fluid is a popular topic, solving nonlinear fluid mechanics problems is significantly more difficult than solving linear ones. Originality/value To the best of the authors’ knowledge, for the first time in the literature, this study presents Prof. Ji Huan He's variational algorithm for finding and studying solitary solutions of the fractal NNV model. The reported solutions are novel and present a valuable addition to the literature in soliton theory.

A variational approach for novel solitary solutions of FitzHugh–Nagumo equation arising in the nonlinear reaction–diffusion equation

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yasir Khan
Keyword(s):  
Differential Equation ◽  
Variational Approach ◽  
Reaction Diffusion ◽  
Nonlinear Ordinary Differential Equation ◽  
Fractal Model ◽  
Reaction Diffusion Equation ◽  
Content Type ◽  
Nonlinear Reaction Diffusion Equation ◽  
Solitary Solutions ◽  
Nagumo Equation

Purpose In the nonlinear model of reaction–diffusion, the Fitzhugh–Nagumo equation plays a very significant role. This paper aims to generate innovative solitary solutions of the Fitzhugh–Nagumo equation through the use of variational formulation. Design/methodology/approach The partial differential equation of Fitzhugh–Nagumo is modified by the appropriate wave transforms into a dimensionless nonlinear ordinary differential equation, which is solved by a semi-inverse variational method. Findings This paper uses a variational approach to the Fitzhugh–Nagumo equation developing new solitary solutions. The condition for the continuation of new solitary solutions has been met. In addition, this paper sets out the Fitzhugh–Nagumo equation fractal model and its variational principle. The findings of the solitary solutions have shown that the suggested method is very reliable and efficient. The suggested algorithm is very effective and is almost ideal for use in such problems. Originality/value The Fitzhugh–Nagumo equation is an important nonlinear equation for reaction–diffusion and is typically used for modeling nerve impulses transmission. The Fitzhugh–Nagumo equation is reduced to the real Newell–Whitehead equation if β = −1. This study provides researchers with an extremely useful source of information in this area.

A new similarity solution with stability analysis for the three-dimensional boundary layer of hybrid nanofluids

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Najiyah Safwa Khashi'ie ◽  
Norihan M. Arifin ◽  
Ioan Pop ◽  
Roslinda Nazar ◽  
Ezad Hafidz Hafidzuddin
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Differential Equations ◽  
Similarity Transformation ◽  
Three Dimensional ◽  
Physical Parameters ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Boundary Layer Equations ◽  
Dimensional Boundary

Purpose The purpose of this study is to implement a new class of similarity transformation in analyzing the three-dimensional boundary layer flow of hybrid nanofluid. The Cu-Al2O3/water hybrid nanofluid is formulated using the single-phase nanofluid model with modified thermophysical properties. Design/methodology/approach The governing partial differential equations are reduced to the ordinary (similarity) differential equations using the proposed similarity transformation. The resulting equations are programmed in Matlab software through the bvp4c solver to obtain their solutions. The features of the reduced skin frictions and the velocity profiles for different values of the physical parameters are analyzed and discussed. Findings The non-uniqueness of the solutions is observed for certain physical parameters. The dual solutions are perceived for both permeable and impermeable cases and being the main agenda of the work. The execution of stability analysis proves that the first solution is undoubtedly stable than the second solution. An increase in the mass transpiration parameter leads to the uniqueness of the solution. Oppositely, as the injection parameter increase, the two solutions remain. However, no separation point is detected in this problem within the considered parameter values. The present results are decisive to the pair of alumina and copper only. Originality/value The present findings are original and can benefit other researchers particularly in the field of fluid dynamics. This study can provide a different insight of the transformation that is applicable to reduce the complexity of the boundary layer equations.

Numerical modeling of hybrid laser welding taking into account phase change of material

2017 ◽  
Vol 36 (2) ◽  
pp. 417-426 ◽  
Author(s):  
Ivo Doležel ◽  
Václav Kotlan ◽  
Roman Hamar ◽  
David Pánek
Keyword(s):  
Laser Beam ◽  
Laser Welding ◽  
Phase Change ◽  
3D Model ◽  
Three Dimensional ◽  
Physical Parameters ◽  
Saturation Curve ◽  
Plasma Cloud ◽  
Content Type ◽  
Liquid Phases

Purpose This paper aims to present a three-dimensional (3D) model of hybrid laser welding of a steel plate. Before welding, the plate is pre- and/or post-heated by induction to avoid mechanical stresses in material due to high gradients of temperature. Welding itself is realized by laser beam without welding rod. The model takes into account existence of both solid and liquid phases in the weld. Design/methodology/approach Presented is the complete mathematical model of the above heat treatment process, taking into account all relevant nonlinearities (saturation curve of the processed steel material and temperature dependences of its physical parameters). Its numerical solution is realized by the finite element method. Some important results are compared with experimental data. Findings In comparison with the former model developed by the authors that did not take into account the phase change, the results are more realistic and exhibit a better accordance with measurements. On the other hand, they strongly depend on sufficiently accurate knowledge of material parameters in both solid and liquid levels (that represent the input data). Research limitations/implications The quality of calculated results strongly depends on the material properties and their temperature dependencies. In case of alloys (whose chemical composition may vary in some range), such data are often unavailable and must be estimated on the basis of experiments. Another quantity that has to be calibrated is the time dependence of power delivered by the laser beam, which is due to the production of a plasma cloud above the exposed spot. Practical implications The presented model and methodology of its solution may represent a basis for design of the complete technology of laser welding with induction pre-heating and/or post-heating. Originality/value Fully 3D model of hybrid laser welding (supplemented with pre- and/or post-heating by magnetic induction) taking into account both solid and liquid phases of welded metal and influence of the plasma cloud is presented.

Three-dimensional flow of Eyring Powell nanofluid over an exponentially stretching sheet

2015 ◽  
Vol 25 (3) ◽  
pp. 593-616 ◽  
Author(s):  
Tasawar Hayat ◽  
Bilal Ashraf ◽  
Sabir Ali Shehzad ◽  
Elbaz Abouelmagd
Keyword(s):  
Differential Equations ◽  
Stretching Sheet ◽  
Three Dimensional ◽  
Physical Parameters ◽  
Stretching Surface ◽  
Three Dimensional Flow ◽  
Content Type ◽  
Exponentially Stretching Surface ◽  
Exponentially Stretching ◽  
Made In

Purpose – The purpose of this paper is to analyze the Eyring Powell fluid over an exponentially stretching surface. Heat and mass transfer effects are taken into account with nanoparticles. Design/methodology/approach – Appropriate transformations are employed to reduce the boundary layer partial differential equations into ordinary differential equations. Series solutions of the problem are obtained and impacts of physical parameters on the velocities, temperature and concentration profiles are discussed. Findings – Numerical values of local Nusselt and Sherwood numbers for all the involved physical parameters are computed and analyzed. A comparative study between the present and previous results is made in a limiting sense. Local Nusselt number −′(0) increases by increasing ε, Pr, λ and N while it decreases for δ, N_{t{, N_{b} and Sc. Originality/value – This analysis has not been discussed in the literature yet.

Stereotactic radiosurgery versus stereotactic radiotherapy for patients with vestibular schwannoma: a Leksell Gamma Knife Society 2000 debate

2000 ◽  
Vol 93 (supplement_3) ◽  
pp. 90-92 ◽  
Author(s):  
Mark E. Linskey
Keyword(s):  
Gamma Knife ◽  
Stereotactic Radiotherapy ◽  
Three Dimensional ◽  
Late Recurrence ◽  
Vestibular Schwannomas ◽  
Tumor Control ◽  
Complication Rates ◽  
Content Type ◽  
Single Fraction ◽  
Fine Print

✓ By definition, the term “radiosurgery” refers to the delivery of a therapeutic radiation dose in a single fraction, not simply the use of stereotaxy. Multiple-fraction delivery is better termed “stereotactic radiotherapy.” There are compelling radiobiological principles supporting the biological superiority of single-fraction radiation for achieving an optimal therapeutic response for the slowly proliferating, late-responding, tissue of a schwannoma. It is axiomatic that complication avoidance requires precise three-dimensional conformality between treatment and tumor volumes. This degree of conformality can only be achieved through complex multiisocenter planning. Alternative radiosurgery devices are generally limited to delivering one to four isocenters in a single treatment session. Although they can reproduce dose plans similar in conformality to early gamma knife dose plans by using a similar number of isocenters, they cannot reproduce the conformality of modern gamma knife plans based on magnetic resonance image—targeted localization and five to 30 isocenters. A disturbing trend is developing in which institutions without nongamma knife radiosurgery (GKS) centers are championing and/or shifting to hypofractionated stereotactic radiotherapy for vestibular schwannomas. This trend appears to be driven by a desire to reduce complication rates to compete with modern GKS results by using complex multiisocenter planning. Aggressive advertising and marketing from some of these centers even paradoxically suggests biological superiority of hypofractionation approaches over single-dose radiosurgery for vestibular schwannomas. At the same time these centers continue to use the term radiosurgery to describe their hypofractionated radiotherapy approach in an apparent effort to benefit from a GKS “halo effect.” It must be reemphasized that as neurosurgeons our primary duty is to achieve permanent tumor control for our patients and not to eliminate complications at the expense of potential late recurrence. The answer to minimizing complications while maintaining maximum tumor control is improved conformality of radiosurgery dose planning and not resorting to homeopathic radiosurgery doses or hypofractionation radiotherapy schemes.

The dialectics of authoring expansive learning: tracing the long tail of a Change Laboratory

2016 ◽  
Vol 28 (4) ◽  
pp. 245-262 ◽  
Author(s):  
Annalisa Sannino ◽  
Yrjö Engeström ◽  
Johanna Lahikainen
Keyword(s):  
Large Scale ◽  
Scale Transformation ◽  
Dialectical Tensions ◽  
Content Type ◽  
Organization Model ◽  
Expansive Learning ◽  
Conceptual Argument ◽  
University Library ◽  
Dialectical Process ◽  
Cultural Historical Activity

Purpose The paper aims to examine organizational authoring understood as a longitudinal, material and dialectical process of transformation efforts. The following questions are asked: To which extent can a Change Laboratory intervention help practitioners author their own learning? Are the authored outcomes of a Change Laboratory intervention futile if a workplace subsequently undergoes large-scale organizational transformations? Does the expansive learning authored in a Change Laboratory intervention survive large-scale organizational transformations, and if so, why does it survive and how? Design/methodology/approach The paper develops a conceptual argument based on cultural–historical activity theory. The conceptual argument is grounded in the examination of a case of eight years of change efforts in a university library, including a Change Laboratory (CL) intervention. Follow-up interview data are used to discuss and illuminate our argument in relation to the three research questions. Findings The idea of knotworking constructed in the CL process became a “germ cell” that generates novel solutions in the library activity. A large-scale transformation from the local organization model developed in the CL process to the organization model of the entire university library was not experienced as a loss. The dialectical tension between the local and global models became a source of movement driven by the emerging expansive object. Practitioners are modeling their own collective future competences, expanding them both in socio-spatial scope and interactive depth. Originality/value The article offers an expanded view of authorship, calling attention to material changes and practical change actions. The dialectical tensions identified serve as heuristic guidelines for future studies and interventions.

scholarly journals Agent-Based Modeling Demonstrates How Local Chemotactic Behavior Can Shape Biofilm Architecture

mSphere ◽  
2019 ◽  
Vol 4 (3) ◽  
Author(s):  
Emily G. Sweeney ◽  
Andrew Nishida ◽  
Alexandra Weston ◽  
Maria S. Bañuelos ◽  
Kristin Potter ◽  
...  
Keyword(s):  
Helicobacter Pylori ◽  
Three Dimensional ◽  
Structural Features ◽  
Agent Based Modeling ◽  
Emergent Properties ◽  
Cellular Interactions ◽  
Biofilm Growth ◽  
Content Type ◽  
Agent Based ◽  
H Pylori

ABSTRACTBacteria are often found living in aggregated multicellular communities known as biofilms. Biofilms are three-dimensional structures that confer distinct physical and biological properties to the collective of cells living within them. We used agent-based modeling to explore whether local cellular interactions were sufficient to give rise to global structural features of biofilms. Specifically, we asked whether chemorepulsion from a self-produced quorum-sensing molecule, autoinducer-2 (AI-2), was sufficient to recapitulate biofilm growth and cellular organization observed for biofilms ofHelicobacter pylori, a common bacterial resident of human stomachs. To carry out this modeling, we modified an existing platform, Individual-based Dynamics of Microbial Communities Simulator (iDynoMiCS), to incorporate three-dimensional chemotaxis, planktonic cells that could join or leave the biofilm structure, and cellular production of AI-2. We simulated biofilm growth of previously characterizedH. pyloristrains with various AI-2 production and sensing capacities. Using biologically plausible parameters, we were able to recapitulate both the variation in biofilm mass and cellular distributions observed with these strains. Specifically, the strains that were competent to chemotax away from AI-2 produced smaller and more heterogeneously spaced biofilms, whereas the AI-2 chemotaxis-defective strains produced larger and more homogeneously spaced biofilms. The model also provided new insights into the cellular demographics contributing to the biofilm patterning of each strain. Our analysis supports the idea that cellular interactions at small spatial and temporal scales are sufficient to give rise to larger-scale emergent properties of biofilms.IMPORTANCEMost bacteria exist in aggregated, three-dimensional structures called biofilms. Although biofilms play important ecological roles in natural and engineered settings, they can also pose societal problems, for example, when they grow in plumbing systems or on medical implants. Understanding the processes that promote the growth and disassembly of biofilms could lead to better strategies to manage these structures. We had previously shown thatHelicobacter pyloribacteria are repulsed by high concentrations of a self-produced molecule, AI-2, and thatH. pylorimutants deficient in AI-2 sensing form larger and more homogeneously spaced biofilms. Here, we used computer simulations of biofilm formation to show that localH. pyloribehavior of repulsion from high AI-2 could explain the overall architecture ofH. pyloribiofilms. Our findings demonstrate that it is possible to change global biofilm organization by manipulating local cell behaviors, which suggests that simple strategies targeting cells at local scales could be useful for controlling biofilms in industrial and medical settings.

scholarly journals Modelling of Applied Magnetic Field and Thermal Radiations Due to the Stretching of Cylinder

Processes ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 1077
Author(s):  
Muhammad Tamoor ◽  
Muhammad Kamran ◽  
Sadique Rehman ◽  
Aamir Farooq ◽  
Rewayat Khan ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Boundary Layer Equations ◽  
Convective Parameter ◽  
Momentum And Heat Transfer ◽  
Dimensional Boundary

In this study, a numerical approach was adopted in order to explore the analysis of magneto fluid in the presence of thermal radiation combined with mixed convective and slip conditions. Using the similarity transformation, the axisymmetric three-dimensional boundary layer equations were reduced to a self-similar form. The shooting technique, combined with the Range–Kutta–Fehlberg method, was used to solve the resulting coupled nonlinear momentum and heat transfer equations numerically. When physically interpreting the data, some important observations were made. The novelty of the present study lies in finding help to control the rate of heat transfer and fluid velocity in any industrial manufacturing processes (such as the cooling of metallic plates). The numerical results revealed that the Nusselt number decrease for larger Prandtl number, curvature, and convective parameters. At the same time, the skin friction coefficient was enhanced with an increase in both slip velocity and convective parameter. The effect of emerging physical parameters on velocity and temperature profiles for a nonlinear stretching cylinder has been thoroughly studied and analyzed using plotted graphs and tables.

A biomimetic 3D airflow sensor made of an array of two piezoelectric metal-core fibers

Sensor Review ◽  
2017 ◽  
Vol 37 (3) ◽  
pp. 312-321 ◽  
Author(s):  
Yixiang Bian ◽  
Can He ◽  
Kaixuan Sun ◽  
Longchao Dai ◽  
Hui Shen ◽  
...  
Keyword(s):  
Design Methodology ◽  
Spherical Surface ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Piezoceramic Cylinder ◽  
Metal Core ◽  
Content Type ◽  
3D Space ◽  
Highly Sensitive ◽  
Airflow Sensor

Purpose The purpose of this paper is to design and fabricate a three-dimensional (3D) bionic airflow sensing array made of two multi-electrode piezoelectric metal-core fibers (MPMFs), inspired by the structure of a cricket’s highly sensitive airflow receptor (consisting of two cerci). Design/methodology/approach A metal core was positioned at the center of an MPMF and surrounded by a hollow piezoceramic cylinder. Four thin metal films were spray-coated symmetrically on the surface of the fiber that could be used as two pairs of sensor electrodes. Findings In 3D space, four output signals of the two MPMFs arrays can form three “8”-shaped spheres. Similarly, the sensing signals for the same airflow are located on a spherical surface. Originality/value Two MPMF arrays are sufficient to detect the speed and direction of airflow in all three dimensions.

Comparison of the reluctance laminated and solid rotor synchronous machine operating at high temperatures

2019 ◽  
Vol 38 (4) ◽  
pp. 1111-1119 ◽  
Author(s):  
Marcin Lefik ◽  
Krzysztof Komeza ◽  
Ewa Napieralska-Juszczak ◽  
Daniel Roger ◽  
Piotr Andrzej Napieralski
Keyword(s):  
High Speed ◽  
Design Methodology ◽  
Three Dimensional ◽  
Synchronous Machine ◽  
Point Of View ◽  
Heat Sources ◽  
Model Calculations ◽  
Content Type ◽  
Thermal Phenomenon ◽  
Practical Implications

Purpose The purpose of this paper is to present a comparison between reluctance synchronous machine-enabling work at high internal temperature (HT° machine) with laminated and solid rotor. Design/methodology/approach To obtain heat sources for the thermal model, calculations of the electromagnetic field were made using the Opera 3D program including effect of rotation and the resulting eddy current losses. To analyse the thermal phenomenon, the 3D coupled thermal-fluid (CFD) model is used. Findings The presented results show clearly that laminated construction is much better from a point of view of efficiency and temperature. However, solid construction can be interesting for high speed machines due to their mechanical robustness. Research limitations/implications The main problem, despite the use of parallel calculations, is the long calculation time. Practical implications The obtained simulation and experimental results show the possibility of building a machine operating at a much higher ambient temperature than it was previously produced for example in the vicinity of the aircraft turbines. Originality/value The paper presents the application of fully three-dimensional coupled electromagnetic and thermal analysis of new machine constructions designed for elevated temperature.

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