Large Values Of Parameter Research Articles

Modeling the Effect of Fear in a Prey–Predator System with Prey Refuge and Gestation Delay

Recently, some field experiments and studies show that predators affect prey not only by direct killing, they induce fear in prey which reduces the reproduction rate of prey species. Considering this fact, we propose a mathematical model to study the fear effect and prey refuge in prey–predator system with gestation time delay. It is assumed that prey population grows logistically in the absence of predators and the interaction between prey and predator is followed by Crowley–Martin type functional response. We obtained the equilibrium points and studied the local and global asymptotic behaviors of nondelayed system around them. It is observed from our analysis that the fear effect in the prey induces Hopf-bifurcation in the system. It is concluded that the refuge of prey population under a threshold level is lucrative for both the species. Further, we incorporate gestation delay of the predator population in the model. Local and global asymptotic stabilities for delayed model are carried out. The existence of stable limit cycle via Hopf-bifurcation with respect to delay parameter is established. Chaotic oscillations are also observed and confirmed by drawing the bifurcation diagram and evaluating maximum Lyapunov exponent for large values of delay parameter.

Peristaltic Flow of Non-Newtonian Fluid with Slip Effects: Analytic and Numerical Solutions

This study describes two-dimensional peristaltic flow of non-Newtonian fluid through a porous asymmetric channel under the influence of the magnetic field. The slip effect is included in the model. The flow is investigated in a wave frame of reference moving with a velocity of the wave. The momentum equations are linearized using long wavelength and low Reynolds number approximation. The transformed equations have been solved numerically. Analytic solutions for stream function, velocity and pressure gradient are also obtained. The effects of various physical parameters of interest have been explained graphically. It is found that the size of the trapped bolus reduces for large value of the velocity slip parameter.

Non-similar solution of Casson nanofluid with variable viscosity and variable thermal conductivity

PurposeThe purpose of this study is to provide a numerical investigation of Casson nanofluid along a vertical nonlinear stretching sheet with variable thermal conductivity and viscosity.Design/methodology/approachThe boundary-layer equations are presented in the dimensionless form using proper non-similar transformations. The subsequent non-dimensional nonlinear partial differential equations are solved using the implicit finite difference technique. To linearize the nonlinear terms present in these equations, the quasilinearization technique is used.FindingsThe investigation showed graphically the temperature, velocity and nanoparticle volume fraction for particular included physical parameters. It is observed that the velocity profile decreases with an increase in the values of Casson fluid parameter while increases with an increase in the viscosity variation parameter. The temperature profile enhances for large values of velocity variation parameter and thermal conductivity parameter while it reduces for large values of thermal buoyancy parameter. Further, the Nusselt number and skin-friction coefficient are introduced which are helpful in determining the physical aspects of Casson nanofluid flow.Practical implicationsThe immediate control of heat transfer in the industrial system is crucial because of increasing energy prices. Recently, nanotechnology is proposed to control the heat transfer phenomenon. Ongoing research in complex nanofluid has been fruitful in various applications such as solar thermal collectors, nuclear reactors, electronic equipment and diesel–electric conductor. A reasonable amount of nanoparticle when added to the base fluid in solar thermal collectors serves to deeper absorption of incident radiation, and hence it upgrades the efficiency of the solar thermal collectors.Originality/valueThe non-similar solution of Casson nanofluid due to a vertical nonlinear stretching sheet with variable viscosity and thermal conductivity is discussed in this work.

Thermodynamics of static solutions in ( n+1 )-dimensional quintic quasitopological gravity

Based on the fact that some important theories like string and M-theories predict spacetime with higher dimensions, so, in this paper, we aim to construct a theory of quintic quasitopological gravity in higher dimensions ($n\geq5$). This $(n+1)$-dimensional quintic quasitopological gravity can also lead to the most second-order linearized field equations in the spherically symmetric spacetimes. These equations can not be solved exactly and so, we obtain a new class of $(n+1)$-dimensional static solutions with numeric methods. For large values of mass parameter $m$, these solutions yield to black holes with two horizons in AdS and flat spacetimes. For dS solutions, there are two values, $m_{\rm ext}$ and $m_{\rm cri}$, which yield to a black hole with three horizons for $m_{\rm ext}<m<m_{\rm cri}$. We also calculate thermodynamic quantities for this black hole such as entropy and temperature and check the first law of thermodynamics. Finally, we analyze thermal stability of the $(n+1)$-dimensional static black hole at the horizon $r_{+}$. Unlike dS solutions, AdS ones have thermal stability for each values of $k$, but flat solutions are stable with just $k=1$.

Buckling of an Elastic Plate/Layer Along a Rigid Base With Adhesion

Abstract An infinitely long elastic plate/layer is under uniaxial compression with its long dimension held by adhesion to a flat rigid base without friction. A prescribed length of the plate/layer is free of adhesion. This configuration is similar to a pre-stressed elastic film for which buckling of an unbonded section is a necessary, but not sufficient, condition for delamination. For that configuration, buckling occurs at the Euler buckling load of a fixed–fixed plate. Although the present study does not include friction or tangential interface stresses, the onset of buckling should be similar for these two cases. For the case of an elastic plate, a cohesive zone is used and it is found that the fixed–fixed buckling load is not attained except for extremely large values of a cohesive zone parameter. For realistic values, the buckling load is about half of that value. For the situation of an elastic layer with adhesion (without a cohesive zone), the buckling load approaches the fixed–fixed value only for very large values of the ratio of the unbonded length to the thickness.

Effect of heat and mass transfer on the peristaltic flow of a Jeffrey nanofluid in a tapered flexible channel in the presence of aligned magnetic field

In this paper, we have studied the influence of wall properties and aligned magnetic field on the peristaltic transport and heat and mass transfer of a Jeffrey/Newtonian nanofluid in a tapered channel. The analytical solutions are obtained for the stream function, the temperature and the concentration. Further, we obtained the Nusselt and Sherwood numbers at the wall. The effects of all important parameters on the physical quantities of the flow for both Jeffrey and Newtonian fluids are investigated through graphs and deliberated in detail. The velocity and temperatures are high for Newtonian fluid than Jeffrey fluid and the opposite situation is observed for concentration field. The large values of the magnetic parameter suppress the velocity and temperature fields but the reverse situation is seen in the case of concentration field. Also observed that the inclination angle of magnetic field and wall parameters have shown a significant effect on this investigation.

Impact of photon addition and subtraction on nonclassical and phase properties of a displaced Fock state

Various nonclassical and quantum phase properties of photon added then subtracted displaced Fock state have been examined systematically and rigorously. Higher-order moments of the relevant bosonic operators are computed to test the nonclassicality of the state of interest, which reduces to various quantum states (having applications in quantum optics, metrology and information processing) in different limits ranging from the coherent (classical) state to the Fock (most nonclassical) states. The nonclassical features are discussed using Klyshko’s, Vogel’s, and Agarwal–Tara’s criteria as well as the criteria of lower- and higher-order antibunching, sub-Poissonian photon statistics and squeezing. In addition, phase distribution function and quantum phase fluctuation have been studied. These properties are examined for various combinations of number of photon addition and/or subtraction and Fock parameter. The examination has revealed that photon addition generally improves nonclassicality, and this advantage enhances for the large (small) values of displacement parameter using photon subtraction (Fock parameter). The higher-order sub-Poissonian photon statistics is only observed for the odd orders. In general, higher-order nonclassicality criteria are found to detect nonclassicality even in the cases when corresponding lower-order criteria failed to do so. Photon subtraction is observed to induce squeezing, but only large number of photon addition can be used to probe squeezing for large values of displacement parameter. Further, photon subtraction is found to alter the phase properties more than photon addition, while Fock parameter has an opposite effect of the photon addition/subtraction. Finally, nonclassicality and non-Gaussianity is also established using Q function.

Correlations in area preserving maps: A Shannon entropy approach

In the present work we extend and generalize the formulation of the Shannon entropy as a measure of correlations in the phase space variables of any dynamical system. By means of theoretical arguments we show that the Shannon entropy is a quite sensitive approach to detect correlations in the state variables. The formulation given herein includes the analysis of the evolution of a single variable of the system, for instance a given phase; the phase space variables of a 2-dimensional model or the action space of a 4-dimensional map or a 3dof Hamiltonian. We show that the Shannon entropy provides a direct measure of the volume of the phase space occupied by a given trajectory as well as a direct measure of the correlations among the successive values of the phase space variables in any dynamical system, in particular when the motion is highly chaotic. We use the standard map model at large values of the perturbation parameter to confront all the analytical estimates with the numerical simulations. The numerical–experimental results show the efficiency of the entropy in revealing the fine structure of the phase space, in particular the existence of small stability domains (islands around periodic solutions) that affect the diffusion.

MHD Casson Nanofluid Past a Stretching Sheet with the Effects of Viscous Dissipation, Chemical Reaction and Heat Source/Sink

The effects of viscous dissipation, chemical reaction and activation energy on the two-dimensional hydromagnetic convective heat and mass transfer flow of a Casson nanofluid fluid over a stretching sheet with thermal radiation, have been discussed in detail. The formulated highly nonlinear equations for the above-mentioned flow are converted into first-order ordinary differential equations (ODEs). The shooting method along with Adams-Bash forth Moulton method is used to solve the BVP by using the Fortran language program. The numerical results are computed by choosing different values of the involved physical parameters and compared with earlier published results and excellent validation of the present numerical results has been achieved for local Nusselt number and local Sherwood number. The graphical numerical results of different physical quantities of interest are presented to analyze their dynamics under the varying physical quantities. From the results, it has been remarked that the heat transfer rate escalates for the large values of radiation parameter, viscous dissipation for the Casson nanofluid.

Physical and thermodynamic properties of quartic quasitopological black holes and rotating black branes with a nonlinear source

In this paper, we find the solutions of quartic quasitopological black holes and branes coupled to logarithmic and exponential forms of nonlinear electrodynamics. These solutions have an essential singularity at $r=0$. Depending on the value of charge parameter $q$, we have an extreme black hole/brane, a black hole/brane with two horizons or a naked singularity. For small values of parameter $q$, the solutions lead to a black hole/brane with two horizons. The values of the horizons are independent of the values of quasitopological parameters and depend only on the values of $q$, dimensions $n$, nonlinear parameter $\beta$ and mass parameter. Also, the solutions are not thermally stable for dS and flat spacetimes. However, AdS solutions are stable for $r_{+}>{r_{+}}_{\rm{ext}}$ which the temperature is zero for $r_{+}={r_{+}}_{\rm{ext}}$. The value of ${r_{+}}_{\rm{ext}}$ also depends on the values of parameters $q$, $\beta$, $n$ and $m$. As the value of ${r_{+}}_{\rm{ext}}$ decreases, the region of stability becomes larger. We also use HPEM metric to probe GTD formalism for our solutions. This metric is successful to predict the divergences of the scalar curvature exactly at the phase transition points. For large values of parameter $\Xi$, the black hole/brane has a transition to a stable state and stays stable.

Cyclic (Aryl)(Amido)Carbenes: NHCs with Triplet‐like Reactivity

AbstractThe synthesis and study of a library of cyclic (aryl)(amido)carbenes (CArAmCs), which represent a class of electrophilic NHCs that feature low calculated singlet‐triplet gaps (ΔEST=19.9 kcal mol−1; B3LYP/def2‐TZVP) and exhibit reactivity profiles expected from triplet carbenes, are described. The electrophilic properties of the CArAmCs were quantified by analyzing their respective selenium adducts, which exhibited the largest downfield 77Se NMR chemical shifts (up to 1645 ppm) measured for any NHC derivative known to date, as well as their Ir carbonyl complexes, from which large Tolman electronic parameter (TEP) values (up to 2064 cm−1) were ascertained. The CArAmCs were found to engage in reactions that are typically observed with triplet carbenes, including C−H insertions, [2+1] cycloadditions with alkenes as well as alkynes, and spontaneous oxidation upon exposure to oxygen.

Cyclic (Aryl)(Amido)Carbenes: NHCs with Triplet-like Reactivity.

The synthesis and study of a library of cyclic (aryl)(amido)carbenes (CArAmCs), which represent a class of electrophilic NHCs that feature low calculated singlet-triplet gaps (ΔEST =19.9 kcal mol-1 ; B3LYP/def2-TZVP) and exhibit reactivity profiles expected from triplet carbenes, are described. The electrophilic properties of the CArAmCs were quantified by analyzing their respective selenium adducts, which exhibited the largest downfield 77 Se NMR chemical shifts (up to 1645 ppm) measured for any NHC derivative known to date, as well as their Ir carbonyl complexes, from which large Tolman electronic parameter (TEP) values (up to 2064 cm-1 ) were ascertained. The CArAmCs were found to engage in reactions that are typically observed with triplet carbenes, including C-H insertions, [2+1] cycloadditions with alkenes as well as alkynes, and spontaneous oxidation upon exposure to oxygen.

The Effect of Beta on the Downstream Development of Unstable, Chaotic Baroclinic Waves

AbstractThe weakly unstable, two-layer model of baroclinic instability is studied in a configuration in which the flow is perturbed at the inflow section of a channel by a slow and periodic perturbation. In a parameter regime where the governing equation would be the Lorenz equations for chaos if the development occurs only in time, the solution behavior becomes considerably more complex as a function of time and downstream coordinate. In the absence of the beta effect it has earlier been shown that the chaotic behavior along characteristics renders the solution nearly discontinuous in the slow downstream coordinate of the asymptotic model. The additional presence of the beta effect, although expunging the chaos for large enough values of the beta parameter, also provides an additional mechanism for abrupt spatial change.

Thermal Radiation Effects on Heat and Mass Transfer of Magnetohydrodynamics Dusty Jeffrey Fluid past an Exponentially Stretching Sheet

The heat and mass transfer of steady magnetohydrodynamics of dusty Jeffrey fluid past an exponentially stretching sheet in the presence of thermal radiation have been investigated. The main purpose of this study is to conduct a detailed analysis of flow behaviour of suspended dust particles in non-Newtonian fluid. The governing equations hav been converted into dimensionless form, and then solved numerically via the Keller-box method. The expression of Sherwood number, Nusselt number and skin friction have been evaluated, and then displayed in tabular forms. Velocity, temperature and concentration profiles are presented graphically. It is observed that large value of dust particles mass concentration parameter has reduced the flow velocity significantly. Increase in radiation parameter enhances the temperature, whereas the increment in Schmidt number parameter reduces the concentration.

Ground State Phases of Distorted S = 1 Diamond Chains

The ground states of distorted $S=1$ diamond chains are investigated for two types of distortion called type A and B [J. Phys. Soc. Jpn. 79 (2010) 114703]. For the type A distortion, Haldane phases with and without spontaneous translational symmetry breakdown are present for large values of parameter $\lambda$ that parametrize the strength of frustration. For small $\lambda$, the Haldane phase and two quantized ferrimagnetic phases in the undistorted chain remain stable even for strong distortion. In contrast, for the type B distortion, the quantized ferrimagnetic phases with and without spontaneous translational symmetry breakdown are present for large $\lambda$. The partial ferrimagnetic phases emerge between them. For small $\lambda$, two quantized ferrimagnetic phases remain and the partial ferrimagnetic phases also emerge between them. The Haldane phase between the two kinds of ferrimagnetic phases turns into a topologically trivial double Haldane phase for strong distortion.

Emission of electromagnetic waves from walls of esophagus under domination of wall slip effect

Abstract On explanation of biomedical applications and its complexity, the contraction and relaxation of Eyring-Powell fluid in esophagus has turned out to be notable amongst the challenging research fields of fluid mechanics. Therefore, the main idea of this paper is to classify the simultaneous significances of compliant walls and emission of electromagnetic waves from walls of electrically conducting Eyring-Powell fluid. Conductivity of the fluid is increased by adding the Brownian motion and thermophoresis effects. Moreover, the velocity of the channel and the fluid particles near the surfaces are assumed to be different. Due to vertical contraction and relaxation, the body forces are taken in the form of mixed convection. The dimensionless variables are utilized to convert the required partial differential equations including mass, momentum and energy into dimensionless form. The solutions of the reduced partial differential equations subject to the given boundary conditions are calculated by using Mathematica. Moreover, the various solutions for dimensionless fluid concentration, velocity, and temperature distributions are captured for different values of embedded parameters. The different dimensionless parameters governing the flow, heat and mass transfer characteristics are the Schmidt number, radiation parameter, Hartmann number, local temperature Grashof number, slip parameters, local nanoparticles Grashof number, thermophoresis parameter, Brownian motion parameter, fluid parameters and Prandtl number. Maximum velocity is noted an increasing function of velocity slip parameter. Further maximum temperature enhances by increasing Brownian motion and thermophoresis parameters. More specifically the effects of slip parameters, Brownian motion and thermophoresis parameters on the flow stream have been examined. The velocity profile shows enhance behavior for large values of velocity parameter and mixed convection, whereas, reverse impact is noticed for magnetic field. Increasing concentration slip parameter causes reduction in nanoparticle volume fraction, while temperature of the fluid rises by increasing thermal slip parameter.

Non-similar solutions of the boundary layers equations with favorable and adverse pressure gradients, isothermal wall and slip boundary conditions: Application to Falkner–Skan gaseous flow

Abstract This article presents the non-similar solutions of the steady incompressible two-dimensional boundary layers equations of momentum and energy for Falkner–Skan gaseous flow with favorable and adverse pressure gradient under slip boundary conditions at a relatively low Mach number. By considering the slip boundary conditions at the fluid–wallinterface for the velocity and temperature, the non-dimensional boundary layer equations are solved numerically by using the centered implicit finite difference Keller Box methods. The results of the effects of different dimensionless parameters involved in the problem, namely the modified boundary layer Knudsen number, i.e., the slip parameter K and the shape parameter β on the local hydrodynamic and heat transfer characteristics of the flow are investigated and discussed. The results of these characteristics obtained from non-similar solutions are compared to those obtained from local similarity approach often used by several authors in the last decades. We show that for small shape parameter β and moderate or large values of the slip parameter, the self-similarity of the Falkner–Skan flows is generally lost because of slip boundary conditions. Therefore, the use of the local similarity approach may produce substantial errors for hydrodynamic and thermal characteristics of the flow as compared to non-similar solution. But in contrast, when β becomes larger than 2/3 up to 1, the flow regains its self-similarity character, in this case, the local similarity approach remains valid and may be used. While for β > 1 up to 2, the solutions of the boundary layer equations again become non-similar. Furthermore, a special attention was made to evaluate the separation point under rarefaction, the results show that the effect of slip parameter leads to decrease the separation point β s and it is concluded that separation of the boundary layer should be delayed in the slip flow regime.

Change in viscosity of Maxwell fluid flow due to thermal and solutal stratifications

The objective of this article is to explore the computational aspects of temperature dependent dynamic viscosity of Maxwell nanofluid flow over a variable thicked surface. The dynamic viscosity of the fluid is assumed to depend on temperature and due to thermal and solutal stratifications, viscosity of the liquid also depends on thermal and concentration diffusions. Temperature dependent dynamic viscosity model causes change in thermal and solutal stratifications. The basic mathematical model (system of PDEs) is reduced into nonlinear ODEs by applying similarity variables. Computational solutions of the differential system are obtained by efficient numerical approach (fifth order Rung-Kutta Fehlberg method) along the Cash and Karp. The consequential solutions are sketched for different values of physical constraints. Parameters like the temperature dependent viscosity, the fluid relaxation parameter, the wall thickness parameter and the Hartmann number are found to control the flow field. In addition, the Prandtl number, the Brownian motion parameter, the activation energy parameter, the chemical reaction rate parameter, the thermophoresis parameter, the thermal stratification parameter, the Lewis number, and the solutal stratification parameter are found to control the concentration and temperature distributions inside the stretching surface. It can be seen that for large values of the fluid relaxation parameter, the temperature dependent viscosity and the wall thickness parameter the velocity profile declines whereas reverse behavior is noticed for Hartmann number. Moreover, for large values the Lewis number, solutal stratification parameter and activation energy parameter the concentration profile shows decrease behavior.

On Herman's positive entropy conjecture

We show that any area-preserving Cr-diffeomorphism of a two-dimensional surface displaying an elliptic fixed point can be Cr-perturbed to one exhibiting a chaotic island whose metric entropy is positive, for every 1≤r≤∞. This proves a conjecture of Herman stating that the identity map of the disk can be C∞-perturbed to a conservative diffeomorphism with positive metric entropy. This implies also that the Chirikov standard map for large and small parameter values can be C∞-approximated by a conservative diffeomorphisms displaying a positive metric entropy (a weak version of Sinai's positive metric entropy conjecture). Finally, this sheds light onto a Herman's question on the density of Cr-conservative diffeomorphisms displaying a positive metric entropy: we show the existence of a dense set formed by conservative diffeomorphisms which either are weakly stable (so, conjecturally, uniformly hyperbolic) or display a chaotic island of positive metric entropy.

Numerical treatment for fluidic system of activation energy with non-linear mixed convective and radiative flow of magneto nanomaterials with Navier’s velocity slip

A novel application of Lobatto IIIA computing solver is presented for the solution of nanofluidic Buongiorno model in the porous space. Incompressible electrically conducting fluid mixed with nanomaterial is considered. Flow expression is modelled via nonlinear mixed convection and Navier’s slip condition. Activation energy, Joule heating and non-liner thermal radiation characterise the heat/mass transport. The governing PDEs of the considered problem are transformed into an equivalent system of ODEs using similarity variables. The resulting system is solved numerically by exploiting the strength of Lobatto IIIA computing solver. Numerical and graphical illustrations are utilized to interpret the behaviour of sundry physical parameters on velocity, concentration and temperature profiles. Skin friction, temperature and concentration gradients for different scenarios of embedding variables are tabulated and analysed. Furthermore, numerical data for mesh points, error analysis, ODEs and boundary conditions evaluation are also displayed. Our computed analysis indicates that velocity of nanofluid increases for large value of slip parameter while it decreases with the increase of porosity parameter. In addition, concentration distribution is decaying and increasing functions of chemical reaction and activation energy parameters respectively.