Parameter Λc Research Articles

Stability analysis of dual solutions for nonlinear radiative magnetohydrodynamic flow of [formula omitted] hybrid nanofluid over a nonlinearly shrinking surface

The present work explores the existence and temporal stability of dual solutions with the consequence of nonlinear thermal radiation on hybrid nanofluid flow (including Silver and Titanium dioxide nanoparticles in water) past a permeable shrinking sheet. The analysis also considers the united outcomes of suction/injection, Joule heating, viscous dissipation, and magnetohydrodynamics. Employing realistic assumptions and suitable similarity transformations, the governing nonlinear partial differential equations are formulated and altered into a nonlinear ordinary differential equations system. These equations are then solved numerically using the Lobatto IIIA technique. It is observed that dual solutions can occur within a precise range of the shrinking surface parameter. Analyzing the temporal stability of these dual solutions under small disturbances shows that the upper solution branch is stable and represents a physically realistic solution to the problem. In contrast, the lower solution branch is unstable and not physically realizable. No solution exists beyond the critical λc=−1.3915 for the shrinking parameter. The critical values of shrinking parameter λc=−1.2565,−1.3188, and −1.4161 correspond to volume fractions of hybrid nanofluid with φAg−TiO2 of 2%,4%, and 8%, respectively. No solution exists beyond this critical point. The graphical representation and quantitative explanation demonstrate how various emergent characteristics affect momentum and thermal boundary layer profiles, Nusselt number, and skin friction. The velocity and temperature profile of hybrid nanofluid can be improved by adding a small volume of nanoparticle volume fraction. Thermal boundary layer thickness is amplified by an accumulation in the shrinking parameter, power index of velocity component, thermal radiation parameter, and temperature difference ratio. Sheering stress and heat transfer coefficient improve with adding more nanoparticles in the base fluid for the first solution braches, but opposite effects are found in the second solutions. The contributions of this research are significant both theoretically, in terms of advancing the mathematical modeling of hybrid nanofluid flow with heat transfer in engineering systems, and practically, in terms of applications to engineering cooling systems.

Nonlinear hardening/softening dynamic analysis and its application to cables: A geometrical framework

Competing mechanisms like quadratic/cubic nonlinearities associated with continuous structures lead to complicated dynamics, and it is meaningful to identify the dominant mechanism in a specific parameter domain. However, when the same parameter arises simultaneously in different competing mechanisms, either hardening (H) or softening (S), it implies that a certain constraint between various parameters and thus leads to difficulties for identifying its dominant dynamics with reference to physics parameters. For example, in a nonlinear cable model, its stiffness α, initial sag f, and Irvine parameter λc are all closely related to H/S behaviors, but they are not independent. A novel nonlinear hardening/softening dynamic analysis procedure is asymptotically developed by geometrically interpreting the underlying constraint between parameters as a curved surface located in an auxiliary parameter space. For cables, it consists of stiffness α, initial sag f, and Irvine parameter λc. Further, iso-λc curves on this curved constraint surface is properly defined, which represents a family of cable models with the same Irvine parameter and turn out to be useful for the proposed hardening/softening analysis. Though currently developed for a cable model, the framework can be meaningfully extended to other nonlinear structures with an initial curvature like shallow arches, buckled beams, or imperfect beams, etc.

Theoretical Analysis of the Effects of Exothermic Catalytic Chemical Reaction on Transient Mixed Convection Flow along a Curved Shaped Surface.

The present problem addressed the transient behavior of convective heat and mass transfer characteristics across a curved surface under the influence of exothermic catalytic chemical reactions. The governing non-linear mathematical model wastransformed into a convenient form with the help of a primitive variable formulation. The final primitive formed model wassolved numerically by applying the finite difference method. The analysis of the above said computed numerical data in terms of oscillatory heat transfer, skin friction, and oscillatory mass transfer for various emerging parameters, such as the mixed convection parameter λT, modified mixed convection parameter λc, index parameter n, activation energy parameter E, exothermicparameter β, temperature relative parameter γ, chemical reaction parameter λ, and Schmidt number Sc is plotted in graphical form. An excellent agreement is depicted for oscillatory heat transfer behavior at the large value of activation energy E. The amplitude of heat transfer and prominent fluctuating response in mass transfer with a certain height is found at each value of the index parameter n with a good alteration. An increase in the activation energy led to an increase in the surface temperature, which yielded more transient heat transfer in the above-said mechanism. The main novelty of the current study is that first, we ensured the numerical results for the steady state heat and fluid flow and then these obtained results wereused in the unsteady part to obtain numerical results for the transient behavior of the heat and mass transfer mechanism.

Periodic, permanent, and extinct solutions to population models

The existence of a critical parameter λc>0 is proven for some population models, that splits the set of parameters into two parts where the existence, resp. nonexistence, of a positive periodic solution is guaranteed. Moreover, it is shown that in a quite wide class of population models, all the positive solutions are permanent, resp. extinct ones, provided there exists, resp. does not exist, a positive periodic solution. The results are based on a theoretical research dealing with a boundary value problem for functional differential equation with a real parameteru′(t)=ℓ(u)(t)+λF(u)(t)for a.e. t∈[a,b],h(u)=0, where ℓ and F:C([a,b];R)→L([a,b];R) are, respectively, linear and nonlinear operators, h:C([a,b];R)→R is a linear functional, and λ∈R is a real parameter. The results are illustrated by numerical simulations.

A mass correction method for the aerosol particle mass analyzer to measure the particle mass of sub-50 nm nanoparticles

The particle mass measurement instrument of the aerosol particle mass analyzer (APM) tends to underestimate the particle mass of sub-50 nm nanoparticles, limiting the APM mass measurement to larger particles. In the present work, a mass correction method was developed based on a calibration reference to correct the APM mass underestimation according to a measured mass-based dimensionless parameter λc,PmAPM. The correction was tested using laboratory generated silver nanoparticles and ambient nanoparticles. It was found that the measured effective density variations of silver nanoparticles due to different extent of APM mass underestimation at different operating conditions were reduced by the correction method with a significant improvement of R-squared from 0.40 to 0.87. In addition, about 20% increase in the effective density from 0.91 to 1.09 g/cm3 was observed for 30 nm ambient wet nanoparticles using the correction method. The difference between the raw and corrected effective densities is due to the mass underestimation by the APM itself, which should be corrected in the data analysis program of the APM.Copyright © 2019 American Association for Aerosol Research

CCA2 secure public‐key encryption scheme tolerating continual leakage attacks

AbstractFor a public‐key encryption scheme to be applied in practical applications, it should withstand various leakage attacks (e.g., side‐channel attacks and cold‐boot attacks). To this end, we present a way of construct the more practical CCA2 secure public‐key encryption scheme tolerating leakage attacks, and the scheme's security is based on the hardness of classical decisional Diffie–Hellman assumption and the target collision resistant of one‐way hash function. Additionally, our proposal enjoys better performance, for example, all of elements of ciphertext will be random from the adversary's view, and any probabilistic polynomial‐time adversary cannot obtain leakage on the secret key from the ciphertext, and so on. In the bounded‐leakage setting, for any leakage parameter λ⩽logq − ω(logk)(q is the prime order of the underlying group, and k denotes the security parameter.), our proposal is secure against leakage‐resilient chosen‐ciphertext attacks, where λ is independent of the plaintext space, and has the constant size. However, in the real world, an adversary can continuously learn information on the secret key through a variety of leakage attacks and can trivially break the security of public‐key encryption scheme under the continual leakage attacks. Thus, we will improve our method to resist the continual leakage attacks. Similarly, for any round leakage parameter λC⩽logq − ω(logk), we can prove the security of the improvement scheme based on the hardness of decisional Diffie–Hellman assuming and the target collision resistant of one‐way hash function. With this important performance, our proposal may have some significant value in the practical applications, such as our proposal can provide the leakage‐resilient security for outsourcing data in the cloud computing environment. Copyright © 2016 John Wiley & Sons, Ltd.

Decay property of stopped Markovian bulk-arriving queues with c-servers

ABSTRACTThis article concentrates on investigating decay properties of Markovian bulk-arriving queues with c-servers which stop immediately after hitting the state zero. The exact value of the decay parameter λC for the case B′c(1) > 0 is first given. Then, by using the generating functions of the corresponding q-matrix, a test function Fλ(s) is constructed. The exact value of the decay parameter λC for the case B′c(1) ⩽ 0 is then obtained according to the sign of .

Stability of natural convection in a vertical dielectric couple stress fluid layer in the presence of a horizontal AC electric field

The combined effect of couple stresses and a uniform horizontal AC electric field on the stability of buoyancy-driven parallel shear flow of a vertical dielectric fluid between vertical surfaces maintained at constant but different temperatures is investigated. Applying linear stability theory, stability equations are derived and solved numerically using the Galerkin method with wave speed as the eigenvalue. The critical Grashof number Gc, the critical wave number ac and the critical wave speed cc are computed for wide ranges of couple stress parameter Λc, AC electric Rayleigh number Rea and the Prandtl number Pr. Based on these parameters, the stability characteristics of the system are discussed in detail. The value of Prandtl number at which the transition from stationary to travelling-wave mode takes place is found to be independent of AC electric Rayleigh number even in the presence of couple stresses but increases significantly with increasing Λc. Moreover, the effect of increasing Rea is to instill instability, while the couple stress parameter shows destabilizing effect in the stationary mode but it exhibits a dual behavior if the instability is via travelling-wave mode. The streamlines and isotherms presented demonstrate the development of complex dynamics at the critical state.

Uniqueness and Decay Properties of Markov Branching Processes with Disasters

In this paper we discuss the decay properties of Markov branching processes with disasters, including the decay parameter, invariant measures, and quasistationary distributions. After showing that the corresponding q-matrix Q is always regular and, thus, that the Feller minimal Q-process is honest, we obtain the exact value of the decay parameter λC. We show that the decay parameter can be easily expressed explicitly. We further show that the Markov branching process with disaster is always λC-positive. The invariant vectors, the invariant measures, and the quasidistributions are given explicitly.

Uniqueness and Decay Properties of Markov Branching Processes with Disasters

In this paper we discuss the decay properties of Markov branching processes with disasters, including the decay parameter, invariant measures, and quasistationary distributions. After showing that the corresponding q-matrix Q is always regular and, thus, that the Feller minimal Q-process is honest, we obtain the exact value of the decay parameter λ C . We show that the decay parameter can be easily expressed explicitly. We further show that the Markov branching process with disaster is always λ C -positive. The invariant vectors, the invariant measures, and the quasidistributions are given explicitly.

Stability of natural convection in a vertical couple stress fluid layer

The stability of buoyancy-driven parallel shear flow of a couple stress fluid confined between vertical plates is investigated by performing a classical linear stability analysis. The plates are maintained at constant but different temperatures. A modified Orr–Sommerfeld equation is derived and solved numerically using the Galerkin method with wave speed as the eigenvalue. The critical Grashof number Gc, critical wave number ac and critical wave speed cc are computed for wide ranges of couple stress parameter Λc and the Prandtl number Pr. Based on these parameters, the stability characteristics of the system are discussed in detail. The value of Prandtl number, at which the transition from stationary to travelling-wave mode takes place, increases with increasing Λc. The couple stress parameter shows destabilising effect on the convective flow against stationary mode, while it exhibits a dual behaviour if the instability is via travelling-wave mode. The streamlines and isotherms presented demonstrate the development of complex dynamics at the critical state.

Vibration and Acoustic Emission Measurements Evaluating the Separation of the Balls and Raceways With Lubricating Film in a Linear Bearing Under Grease Lubrication

This paper deals with vibration and acoustic emission (AE) measurements evaluating the separation of the balls and raceways with lubricating film in a linear-guideway–type recirculating ball bearing (linear bearing) under grease lubrication. In the experiments, three types of commercial grease, AS2, LG2, and PS2, were used. The vibratory acceleration, AE, temperature, and electric conductivity (contact voltage) in the test bearing were measured, while a carriage of the test bearing was driven at a certain linear velocity. Experimental results showed that the measured vibratory acceleration, AE, and contact voltage of the test bearing were affected by the linear velocity and the base oil viscosity of the grease. Next, the rail side film parameter ΛR and the carriage side film parameter ΛC were examined for the test bearing in operation, and it was shown that the ΛR value was lower than the ΛC value. In addition, a condition for the separation of all the balls and raceways with lubricating film was presented. Finally, it was shown that the measured root-mean-square (RMS) values of vibratory acceleration or AE can be used for evaluating the separation of all the balls and raceways with lubricating film in the test bearing.

Decay property of stopped Markovian bulk-arriving queues

We consider decay properties including the decay parameter, invariant measures, invariant vectors, and quasistationary distributions of a Markovian bulk-arriving queue that stops immediately after hitting the zero state. Investigating such behavior is crucial in realizing the busy period and some other related properties of Markovian bulk-arriving queues. The exact value of the decay parameter λC is obtained and expressed explicitly. The invariant measures, invariant vectors, and quasistationary distributions are then presented. We show that there exists a family of invariant measures indexed by λ ∈ [0, λC]. We then show that, under some conditions, there exists a family of quasistationary distributions, also indexed by λ ∈ [0, λC]. The generating functions of these invariant measures and quasistationary distributions are presented. We further show that a stopped Markovian bulk-arriving queue is always λC-transient and some deep properties are revealed. The clear geometric interpretation of the decay parameter is explained. A few examples are then provided to illustrate the results obtained in this paper.

Bifurcation in Cross-Equatorial Airflow: A Nonlinear Characteristic of Lagrangian Modeling

Abstract Low-level monsoonal cross-equatorial airflow is investigated using a simple Lagrangian model for the tropical atmosphere. With the use of Jacobian elliptic functions, analytical solutions for the dynamic system are obtained to an extent that enables the most interesting features of the model to be demonstrated. It is found that there exists some unpredictability with the equatorial airflow, in the sense that the trajectory of the airflow can either remain in one hemisphere or cross the equator from one hemisphere to another depending upon the value of a model parameter λc being negative or positive, even when the corresponding external forcings are of little difference. By means of qualitative analysis of the dynamic system, some more esoteric properties of the model solutions are investigated. It is found that the model exhibits a very interesting bifurcation, which explains the unpredictability. The bifurcation is a characteristic attributable to the nonlinearity of the Coriolis term in the Lag...

Dijet angular distributions from p-barp collisions at sqrt s=1.8 TeV.

We have measured dijet angular distributions at √s =1.8 TeV with the Collider Detector at Fermilab and the Tevatron p¯p Collider and find agreement with leading-order QCD. By comparing the distribution for the highest dijet invariant masses with the prediction of a model of quark compositeness, we set a lower limit on the associated scale parameter Λc at 330 GeV (95% C.L.).Received 24 March 1989DOI:https://doi.org/10.1103/PhysRevLett.62.3020©1989 American Physical Society

On the Dynamic Stability of the Spiral-Grooved Gas-Lubricated Thrust Bearing

The dynamic stability of a blocked center inward pumping spiral grooved thrust bearing is investigated. For this purpose two methods are considered comparatively, namely a standard small perturbation one, and an extension of the method used previously to determine air-hammer phenomena in externally pressurized gas bearings. The first method gives a more detailed description of situations in which the film is stable or unstable, while the second one gives a limit for the speed (or compressibility parameter Λc) up to which the bearing is unconditionally stable. The second method is simpler and of practical interest since at higher speeds the critical mass furnished by the first method is of little practical interest (being too small).

Tight bounds for the critical screening parameters of the generalized exponential cosine screened Coulomb potential

Analytic expressions have been obtained for the lower and upper bounds to the critical screening parameter λc associated with the ground state of the generalized exponential cosine screened Coulomb potential, V(r)=−e−λr cos(ελr)/r employing the methods of Hulthén and Laurikainen and of Hemmer. It is found that the predicted numerical results for the range 0≤ε≤1 for the lower bound for λc are within 0.08% of the exact results, and for the upper bound, within 0.7% of the exact results. It emerges further that the critical screening parameters for the excited s-states can be determined as well in an approximate way. For the static screened Coulomb potential, we obtain λnsc =1.283 664n−2 −0.092 793n−3, where n is the principal quantum number. The predicted λc for various quantum states (n=1 to 9) are in excellent agreement with the values obtained numerically by Rogers et al. [Phys. Rev. A 1, 1577 (1970)].

Complex vs Band Formation in Perovskite Oxides

It is argued that there is a critical cation-anion covalent mixing parameter λc such that ligand-field theory is appropriate for λ<λc, but band theory must be used for λ>λc. This provides, therefore, a criterion for distinguishing metallic vs magnetic compounds in those structures, like perovskite, where cation-cation interactions are negligible. It is also argued that λσ>λc can be anticipated where the cations are in a low-spin state. The fact that LaNiO3 contains low-spin NiIII and exhibits no Jahn-Teller distortion suggested that λσ>λc in this compound. Metallic conductivity from −200° to 300°C and Pauli paramagnetism from 4° to 300°K seem to confirm this suggestion. Where λ≈λc, there is the possibility of a phase change in which λ<λc in some directions, λ>λc in others. LaCoO3 seems to illustrate this situation. It undergoes a transition at 1210°K, the cobalt ordering into alternate (111) planes of high-spin Co3+ and planes containing low-spin CoIII. Below 400°K the latter planes contain only CoIII ions. The magnetic Co3+ ions couple antiferromagnetically via Co3+-``diamagnetic CoIIIO6 complex''-Co3+ superexchange to give TN≈90°K.