Critical Number Research Articles

Pulsating traveling fronts of a discrete periodic system with a quiescent stage

In this paper, we study the pulsating traveling fronts for a spatially discrete periodic reaction–diffusion system with a quiescent stage. It is known that there exists a critical number [Formula: see text] (called minimal wave speed) such that a pulsating traveling front exists if and only if its speed is above [Formula: see text]. In this paper, we derive a uniqueness theorem for supercritical pulsating traveling fronts. Further, we show that all supercritical pulsating traveling fronts are exponentially stable.

Thermo-magnetic convection and convective magneto-gravitational parametric resonance in a horizontal ferrofluid layer under time quasi-periodic vibrations: A balance harmonic analysis

Convective instability in a horizontal ferromagnetic liquid layer with rigid boundaries is investigated in the presence of both an uniform magnetic field and a vertical quasi-periodic forcing having two incommensurate frequencies ω1 and ω2. A linearized convective instability analysis predicting the onset of convection is performed and by means of a Galerkin projection truncated to the first order, the linear dynamic of the system is reduced to a damped quasi-periodic Mathieu oscillator. Using a balance harmonic analysis, it turns out that at sufficiently low vibration frequencies, we recover the critical instability parameters related to the unmodulated case where the convection is mainly due to the magnetic mechanism. This feature means that the buoyancy mechanism does not contribute into the convective cells formation and consequently heating from below or from above does not alter the onset of convection. However, at sufficiently high vibration frequencies, both the magnetic and buoyancy mechanisms are operative and here we are dealing with a magneto-gravitational parametric resonance convection. The transition between these convective modes is occurred via bicritical states giving rise to cusp points in the magnetic Rayleigh number besides discontinuities in its corresponding critical wave number. In addition, it is shown that a proper tuning of the irrational frequency ratio ω=ω2/ω1 provides a control of the convection onset as well as the nature of its mechanism. Moreover, special attention is devoted to highlight the effect of the Prandtl number on the dynamic of the system at different values of the frequency ratio ω.

Dissipation induced instability in porous medium using Brinkman model: Thermal non-equilibrium effect

The convective instability that arises in a porous layer solely because of dissipative energy in the medium is studied. The thermal non-equilibrium model is considered for energy equation. The boundary at top is kept at constant temperature, and an adiabatic lower boundary is considered. The momentum equation is written according to the Brinkman model. A basic flow in the horizontal plane is considered, and the basic velocity and temperature profile have been derived. A comparison between the basic temperature profiles for solid and fluid of the porous medium is presented for Darcy and Brinkman models. Infinitesimal disturbance is introduced to the basic flow. A linear stability analysis has been carried out to study the stability of the basic flow. The parameters influencing the stability of the system are critical Rayleigh number (RaC), Gebhart number (Ge), ξ associated with the Darcy number (Da), and interphase heat transfer coefficient (H). The values of the critical Rayleigh number and wavenumber are compared by varying other variables. The flow is more stable when the Brinkman medium is considered. With the increase in interphase heat transfer coefficient, the critical Rayleigh number increases in both Darcy and Brinkman media. The longitudinal rolls appear as the most unstable rolls for all cases. The variation of convective rolls with respect to ξ and heat transfer coefficient is presented.

Plateau-Rayleigh instability of a soft layer coated on a rigid cylinder.

We study the Plateau-Rayleigh instability of a soft viscoelastic solid layer coated on a rigid cylinder i.e., a soft fibre with a rigid core. The onset of instability is examined using a linear stability analysis. We find that increasing the rigid cylinder radius or the stiffness of the layer reduces the growth rate of the fastest growing mode. For each rigid cylinder radius, a critical elastocapillary number is found below which all wavelengths of disturbances are stable. The critical value for a soft fibre with a thick rigid cylindrical core can be several orders of magnitudes larger than that for a totally soft fibre (no rigid core). This highlights the strong stabilizing effect of the rigid core on the system. Increasing the relaxation timescale of the viscoelastic material also slows down the growth of disturbances, but has no effect on the critical elastocapillary number. Interestingly, the wavelength of the fastest growing mode is independent of the rigid cylinder radius for the purely elastic case.

THE INFLUENCE OF THE MARANGONI EFFECT ON THE ONSET OF GRAVITACTIC BIOCONVECTION

Self-movement of such microorganisms as Tetrahymena against gravity leads to the accumulation of cells at the free surface and, as a consequence, to an unstable density distribution. The study considers the onset of gravitactic bioconvection in a horizontal layer of a nonisothermal liquid with a free nondeformable boundary, taking into account the dependence of surface tension on the concentration of microorganisms. The dependence of the critical concentration Rayleigh number characterizing the onset of instability on the Marangoni number is analytically obtained in the long-wave approximation. It is shown that the long-wave concentration Rayleigh number does not depend on the thermal Rayleigh number, as well as on the Schmidt and Lewis numbers. The parameter ranges (the Marangoni and thermal Rayleigh numbers) in which the long-wave instability exists are found. Critical wave numbers and critical concentration Rayleigh numbers are determined from the numerical solution of the linear stability problem.

Effect of Archimedes number on the dynamics of free-falling perforated disks

The dynamics of perforated disks falling freely in a large expanse of viscous fluid at rest is investigated numerically. This complex fluid–structure interaction is solved via large eddy simulation. This numerical algorithm is verified and validated with available experimental results. The influence of Archimedes number expressing the ratio between the gravity-buoyancy and viscosity effects is discussed thoroughly, including kinematics and dynamics. Two critical Archimedes numbers are identified, Arcr1≈450 and Arcr2≈950, respectively. At these two critical Archimedes numbers, both kinematic and dynamic variables change trends. In this paper, we focus on the statistics of free-falling perforated disks. With the Archimedes number Ar increasing, the average angle of attack ⟨AoA⟩ and descent velocity ⟨Uz⟩ decrease gradually, and they arrive at a fixed value finally (here, ⟨·⟩ represents a time-average result); On the contrary, the other kinetic variables change violently when Ar is around 900, for example, terminal velocity ⟨Ut⟩. Additionally, phase differences of kinematic and dynamic variables are analyzed. A constant phase difference between the nutation angle θ and normal force FN is identified, about 66°, which is independent of Ar. Vortex structures are visualized using Q-criterion, and triangular vortex is omnipresent around holes. During the descent, a helical vortex always attaches to the perforated disk outer edge. With Ar increasing, complex vortex interaction appears, for example, merging and stretching. Some unusual behaviors in the numerical results are analyzed from the perspective of wake dynamics.

Подкритическая конвекция в коллоидах и жидких бинарных смесях с положительной термодиффузией

The paper analyzes convection of molecular binary mixtures and colloids with positive thermal diffusion that occurs in the case of heating from below and below the equilibrium stability threshold for a homogeneous liquid. The convection is pulsed in nature and is realized in the form of periodic bursts. Positive thermal diffusion displaces the heavy component into the upper cold layers of the liquid. There, the heavy component accumulates in the boundary layer, forming a growing unstable density stratification. When the inhomogeneity exceeds the critical value for a given geometry, a convective surge occurs, and the heavy component moves down to a stable position. The study has found the critical thickness of the boundary layer, the critical concentration difference at the boundaries of the cavity, and the time at which instability occurs. Based on the analysis of the problem of the concentration profile dynamics under the influence of gravitational sedimentation and thermal diffusion, experimental facts are explained – periodic convective bursts of the binary mixture in channels and in the Hele-Shaw cell below the critical Rayleigh number. The described mechanism probably explains the convection observed by other experimenters in a horizontal flat layer of magnetic fluids below the critical Rayleigh number at Ra < 1708.

«Дорогой Михаил Михайлович! Я назначен редактором Вашей книги...»: из истории издания «Проблем поэтики Достоевского»

The background and publication history of Problems of Dostoevsky’s Poetics is an important part of the scholarly biography and reception of Mikhail Bakhtin’s personality and ideas. The second edition of this work, which appeared in 1963, marked a new milestone in the development of Russian literary studies, combining the best traditions of the literary scholarship of the pre-revolutionary period and the first post-revolutionary decade and the new trends of the post-Stalin era humanities. Refuting the myth that the 1929 book on Dostoevsky had been forgotten, the authors emphasize that by the mid-1950s and early 1960s it was well remembered by a large number of Soviet literary critics. Anatoly Lunacharsky’s review in the anthology F.M. Dostoevsky in Russian Criticism (1956) only strengthened the authority and relevance of Bakhtin’s old monograph, which was borne out by the extensive polemic with this work, in particular in Viktor Shklovsky’s book Pro et Contra (1957) and in the collection F.M. Dostoevsky’s Oeuvre (1959), whose authors strongly objected to Bakhtin’s polyphonic novel theory. The article pays special attention to the activities of Sergey Bocharov as the editor of the book, revealing his contribution to the work on the manuscript. The article introduces a number of previously unknown archival documents, including fragments of correspondence between Bocharov and Bakhtin in 1962-1963. It also contains the memoirs of Bocharov and Vadim Kozhinov, studies by Nikolay Pankov, etc. The letters of Bakhtin and Bocharov represent a kind of a dialogue between the author and the editor, in which the proposed changes were discussed. Bocharov’s editorial “intervention” was quite limited and as tactful as possible. None of the principles of the 1929 book was corrected. All of Bakhtin’s additions, including the new fourth chapter, were approved. The alterations affected the philosophical terminology of the book (it became simpler and clearer to the modern reader), individual quotations from Dostoyevsky were expanded, and the structure of paragraphs was partially changed. On this basis, it is concluded that Bocharov’s efforts to revise the manuscript were in fact more significant than what he claimed to have done in his lifetime, and the words of gratitude expressed by Bakhtin to his editor in his letters receive further validation. The authors declare no conflicts of interests.

A MAXIMUM ENTROPY PRINCIPLE MODEL FOR THE INITIALIZATION OF EULERIAN–LAGRANGIAN SPRAY SIMULATIONS

NOx emission regulations have become more and more restrictive for internal combustion engine-powered vehicles, especially for road transport applications. To minimize emissions and comply with regulations, selective catalytic reduction (SCR) systems are the most efficient deNOx technology thanks to the injection of a urea-water solution (UWS). State-of-the-art computational fluid dynamics (CFD) techniques employ Eulerian-Lagrangian frameworks to deal with the two phases of such problems. Still, the associated low velocities of UWS applications make it difficult to use standard breakup models (Kelvin-Helmholtz, Rayleigh-Taylor, Taylor analogy breakup) to generate initial drop size distributions. Hence, these specific studies end up needing experimentally characterized drop size distributions to initialize the CFD simulations or using expensive Eulerian-Eulerian simulations to obtain the outcomes of the primary breakup of the liquid jet. The maximum entropy principle (MEP) allows generating a droplet size-velocity probability distribution function (PDF) from initial injection conditions and injector characteristics while satisfying conservation equations. The most probable PDF curve is determined by the distribution that maximizes the entropy of the problem. A critical Weber number has been proposed to select which droplets will break up subsequently after the initial droplet break up. The model has been validated against experimental results obtained by high-resolution laser backlight imaging. Comparable results have been found and realistic tendencies were achieved, decreasing the expected droplet size with increasing injection pressures. The proposed model could help with introducing alternative breakup models for low-velocity applications without the need for prior droplet size knowledge.

Thermosolutal convection in a Brinkman–Darcy–Kelvin–Voigt fluid with a bidisperse porous medium

A model for thermosolutal convection of a category of viscoelastic fluids in a bidisperse porous medium is comprehensively investigated. The Brinkman model is employed in macropores, whereas the Darcy model is utilized in micropores. In the momentum equations, the densities are considered a linear function of temperature and concentration. The concentration of solutes at equilibrium is assumed to be a linear function of temperature. There are two situations considered, where we have study systems that are heated below and salted above and heated and salted below. The fluids are of the Kelvin–Voigt type. The critical Rayleigh numbers for linear instability and nonlinear stability are computed.

Off-diagonal long-range order in arrays of dipolar droplets

We report quantum Monte Carlo results of harmonically confined quantum Bose dipoles within a range of interactions covering the evolution from a gas phase to the formation of an array of droplets. Scaling the experimental setup to a computationally accessible domain we characterize that evolution in qualitative agreement with experiments. Our microscopic approach generates ground-state results free from approximations, albeit with some controlled statistical noise. The simultaneous estimation of the static structure factor and the one-body density matrix allows for a better knowledge of the quantum coherence between droplets. Our results show a narrow window of interaction strengths where diagonal and off-diagonal long-range order can coexist. This domain, which is the key signal of a supersolid state, is reduced with respect to the one predicted by the extended Gross–Pitaevskii equation. Differences are probably due to an increase of attraction in our model, observed previously in the calculation of critical atom numbers for single dipolar drops.

ON THERMAL CONVECTION IN ROTATING CASSON NANOFLUID PERMEATED WITH SUSPENDED PARTICLES IN A DARCY-BRINKMAN POROUS MEDIUM

The present paper investigates the effect of suspended particles on thermal convection in rotating Casson nanofluids saturating a Darcy-Brinkman porous medium which has various applications in different sectors, including those that process food, paint, water generators, electricity generators, hydrology, and geophysics, heavily rely on rotation in thermal convection. With the aid of the Galerkin 1st approximation technique, the numerical examination is carried out. The Darcy-Brinkman porous media and particles suspension are taken into consideration throughout the conduct of this study. The non-Newtonian Casson nanofluid, Darcy-Brinkman porous medium, particle suspension and rotation parameter, and their impact on thermal convection have been analyzed and presented graphically for free-free, rigid-rigid, and rigid-free boundaries. It is found that for all boundary conditions the Casson nanofluid and suspended particle parameters have destabilizing impact on the stationary convection, whereas the parameter which occurred due to presence of rotation, i.e., Taylor number and Brinkman porous medium parameters, both delayed the stationary convection. In addition, we have discovered that for realistic rigid-rigid boundary condition, the system is determined to be more stable than for the other two boundary conditions. Also, on the basis of several approximations on the Taylor number and other parameters, the critical wave number and value for stationary convection are determined.

Exact ideal magnetohydrodynamic Riemann solutions considering the strength of intermediate shocks

Exact magnetohydrodynamic (MHD) Riemann solutions are the basis of constructing numerical schemes and benchmarks for verifying the schemes. However, non-strict hyperbolicity and nonconvexity of MHD equations contribute to the appearance of intermediate shocks, causing low efficiency of existing exact solvers and high dependence on iterative initials. Utilizing the magnetic critical Mach number proposed in this paper, all possible intermediate shocks are analyzed, parameterized, and categorized. Moreover, the possible wave structures on one side of contact discontinuity are revealed to have 25 cases, and initial conditions are classified into three categories according to the coplanar properties. Based on our findings, a new exact MHD Riemann solver is built. The robustness has been significantly improved after avoiding considerable judgments and the dependence on iterative initials. The analysis of the exact MHD Riemann solution is carried out by the characteristic properties of MHD shocks in the parameterization, and it is found that a solution space exists with the highest dimension of two dimensions under the given initial condition. It is proposed to adopt the intensities of 2 → 3 intermediate shocks as the free parameters of solution space, which can completely express the degree of solution space freedom. Finally, two examples that possess the solution space are used as verifications. The physical properties of MHD equations show that the dominant factor for the solution space is the unique characteristic property of 2 → 3 intermediate shock: the existence of an additional free parameter with tangential symmetry simultaneously.

Effect of scattered/diffuse flux on the phototactic bioconvection in the absence of collimated flux

The main objective of this paper is to investigate the impact of diffuse/scattered flux in the absence of collimated flux on the stability of an isotropic scattering algal suspension. The linear stability analysis predicts an unstable mode of disturbance shifts from a non-oscillatory (an overstable) to an overstable (a non-oscillatory) state at the variation of diffuse flux for fixed parameters at the bioconvective instability. However, overstable solutions are observed only at the higher cell swimming speed and a higher extinction coefficient. The critical Rayleigh number increases as the magnitude of diffuse flux intensifies. This indicates that a suspension illuminated by higher levels of diffuse flux is more stable. Furthermore, the lower (higher) swimming speed enhances (diminishes) the suspension's stability, especially in low (high) light conditions. Also, the horizontal component of swimming orientation becomes more influential with a higher level of diffuse flux, particularly at smaller pattern wavelengths, resulting in behavior akin to gyrotaxis in certain instances.

Floquet-based analysis on three-dimensional non-axisymmetric instabilities in oscillatory-driven Taylor–Couette flows and their low-frequency asymptotic behavior using Wentzel–Kramers–Brillouin method

This paper revisits the linear stability analysis of oscillatory-driven flows between two oscillating cylinders against non-axisymmetric disturbances. This study is motivated by the lack of a sufficiently reliable theoretical analysis giving insight into the experimentally observed spiral-like non-axisymmetric patterns when the cylinders are counter-oscillating. A new generalized time-dependent algebraic eigenvalue problem is constructed from the linearized set of the three-dimensional Navier–Stokes equations around the purely azimuthal basic state. Numerical evaluation of the critical eigenvalues combining both Floquet theory and spectral method reveals the existence of frequency ranges where this basic state becomes unstable against three-dimensional non-axisymmetric disturbances before it does so for two-dimensional axisymmetric ones. Indeed, as the oscillation frequency of the cylinders increases, the azimuthal wave number of the critical eigensolution is found to change from 0 to 2 to 1 and then back to 0. The primary bifurcation exchange between two instability modes with different azimuthal wave numbers occurs via different types of codimension-2 bifurcation points giving rise to discontinuities in the critical axial wave number where reversing and non-reversing non-axisymmetric Taylor vortex flows are identified. In addition, by extending our numerical calculations to the co-oscillating case, we show that the axisymmetric disturbances are the most unstable confirming thus existing experimental findings. Furthermore, a Wentzel–Kramers–Brillouin (WKB) analysis is performed to shed light on the asymptotic behavior of these time-dependent flows in the low-frequency limit when the cylinders are slowly oscillating.

Распространение магнитогидродинамических волн и гравитационная неустойчивость в астрофизической анизотропной и теплопроводной плазме

The hydrodynamic instability of a magnetised, self-gravitating rotating anisotropic plasma is analysed in the collisionless approximation and taking into account the heat flux vector on the basis of the modified Chew-Goldberger-Low equations. The dispersion relation is derived and simplified cases of propagation of small-amplitude perturbation waves are discussed, with modified analytical criteria for hydrodynamic instability obtained. In accordance with the general dispersion relation, three cases when the propagation of the perturbation wave passes across, along, and obliquely to the magnetic field vector are specifically considered. It is shown that anisotropic pressure and heat flux not only modify the classical Jeans instability criterion but also induce new unstable regions. It is found that the presence of uniform plasma rotation reduces the critical wave number and has a stabilising effect on the gravitational instability criterion for transverse propagation of the perturbation wave and has no effect in the case of its longitudinal propagation. The inclusion of thermal flows leads to the appearance of two additional wave modes. The results obtained are important for the construction of evolutionary magnetohydrodynamic models of collisionless astrophysical plasma.

EFFECTS OF ROTATIONAL MODULATION ON CONVECTION IN ETHYLENE GLYCOL-BASED HYBRID NANOFLUIDS WITH INTERNAL HEATING

The rotational modulation effects on Rayleigh-Bénard convection in ethylene glycol-based hybrid nanofluids with internal heating are investigated. Due to their improved thermophysical properties as compared to base fluid, nanofluids are frequently used in numerous heat transfer applications. Hybrid nanofluids with suitable nanoparticle combinations can have better thermophysical characteristics than mono nanofluids. As a result, this study investigates the impact of hybridizing the base fluid on system stability and heat transfer. A single-phase model is employed to perform a linear and weakly nonlinear stability analysis of the nanofluid. The nonautonomous Ginzburg-Landau equation is derived and solved, and the solution is used to obtain the Nusselt number expression. Based on the linear analysis, the critical Rayleigh number attained in the case of hybrid nanofluids is less than the value found in the case of mono nanofluids. Therefore, the convection onset is faster in a hybrid nanofluid than in a mono nanofluid. The study further shows that hybrid nanofluid ethylene glycol-alumina-copper increases the heat transportation rate as compared to the mono nanofluid ethylene glycol-alumina, presenting evidence that hybrid nanofluid facilitates heat transfer better than the mono nanofluid. Increasing the volume of hybrid nanoparticles qualitatively improved heat transfer by up to 5.96%. Further, the effects of important fluid parameters on heat transfer are presented. Among other results, we found that increasing the modulation's amplitude improves heat transmission in the hybrid nanofluid.

The effect of the formal organizer strategy on the achievement and visual thinking skills of first-year intermediate female students in social studies subject

Due to Large number of criticisms directed at educational institutions such as being negligent in developing students’ ideas and teaching them how to develop these ideas, this paper came to fill in the gap by tackling the strategy of formal organizer and to show how effective this strategy was on the achievement and visual thinking skills among first-year intermediate female students in social studies subject. The current research was applied to sample of intermediate schools for girls in Iraq composed of (282) female students chosen randomly from number of intermediate schools for girls in the city of Diwaniyah for (2023-24) to identify the range of this strategy effectiveness in teaching the subject of social studies. The result indicated that there was a statistically significant difference between the average grades of the female students of the experimental group who studied social studies according to the formal organizer strategy, and the average grades of the female students of the control group who studied the same subject in the usual way in the achievement variable in favor of the female students of the experimental group. In light of the results, the researcher concluded teaching social studies based on the strategy of formal organizer raised the level of achievement, worked to give students a positive role in the learning process and raised visual thinking skills.

Examining the role of the diaspora in addressing the interconnections between human health and environmental change: The case of northern Senegalese communities

Diaspora communities are a growing source of external assistance and resources to meet unmet needs and to strengthen existing health systems in their home countries. Although a growing number of articles have been published in this realm, very few have looked at diaspora communities’ role and the place translocal communities give to health (care) in the various remittance dynamics, whilst including power relationships and environmental change. This article examines the motivations and practices through which Senegalese diasporas engage with the health system in their origin country and what barriers they face in their interventions. The results of the migration-environment-health nexus are critically discussed with a political ecology approach. We found that households and villages with a critical number of members abroad, and with strong political and/or international networks, are better off and less exposed to health risks in the face of adverse extreme climate impacts.

The Problem with Longtermism

Moral circle expansion has been occurring faster than ever before in the last forty years, with moral agency fully extended to all humans regardless of their ethnicity, and regardless of their geographical location, as well as to animals, plants, ecosystems and even artificial intelligence. This process has made even more headway in recent years with the establishment of moral obligations towards future generations. Responsible for this development is the moral theory – and its associated movement – of longtermism, the bible of which is What We Owe the Future (London: Oneworld, 2022) by William MacAskill, whose book Doing Good Better (London: Guardian Faber, 2015) set the cornerstone of the effective altruist movement of which longtermism forms a part. With its novelty comes great excitement, but longtermism and the arguments on its behalf are not yet well thought out, suffering from various problems and entailing various uncomfortable positions on population axiology and the philosophy of history. This essay advances a number of novel criticisms of longtermism; its aim is to identify further avenues for research required by longtermists, and to establish a standard for the future development of the movement if it is to ever be widely considered as sound. Some of the issues raised here are about the arguments for the moral value of the future; the quantification of that value with the longtermist ethical calculus – or the conjunction of expected value theory with the ‘significance, persistence, contingency’ (SPC) framework; the moral value of making happy people; and our ability to affect the future and the fragility of history. Perhaps the most significant finding of this study is that longtermism currently constitutes a shorterm view on the longterm future, and that a properly longterm view reduces to absurdity.