Dominant Balance Research Articles

The evolution of a front in turbulent thermal wind balance. Part 1. Theory

Here, we examine the influence of small-scale turbulence on the evolution of fronts in the ocean and atmosphere. Specifically, we consider the evolution of an initially balanced density front subject to an imposed viscosity and diffusivity as a simple analogue for small-scale turbulence. At late times, the dominant balance is found to be the quasisteady turbulent thermal wind balance with time evolution due to an advection–diffusion balance in the buoyancy equation. We use the leading-order balance to determine analytical similarity solutions for the spreading of a front and find that the spreading rate is maximum for an intermediate value of the Ekman number, with the spreading resulting from shear dispersion associated with the cross-front flow and vertical diffusion of density. In response to shear dispersion, the front evolves towards a density profile that is nearly linear in the cross-front coordinate. At the edges of the frontal zone, the density field develops large curvature, and these regions are associated with narrow bands of intense vertical velocity.

Study of finite-time singularities of loop quantum cosmology interacting multifluids

In this work we study the occurrence of finite-time cosmological singularities in a cosmological system comprising from three fluids. Particularly, the system contains two dark fluids, namely that of dark energy and dark matter, which are interacting, and of a non-interacting baryonic fluid. For the study we adopt the phase space approach by constructing the cosmological dynamical system in such a way so that it rendered to be an autonomous polynomial dynamical system, and in order to achieve this, we appropriately choose the variables of the dynamical system. By employing a rigid mathematical framework, that of dominant balances analysis, we demonstrate that there exist non-singular solutions of the dynamical system, which correspond to a general set of initial conditions, which proves that no Big Rip or Type III finite-time singularities occur in this LQC multifluid dynamical system. Thus the new feature of this work is that we are able to do this using an analytic technique instead of adopting a numerical approach. In addition, we perform a fixed point analysis of the cosmological dynamical system, and we examine the behavior of the total effective equation of state parameter, at the fixed points, as a function of the free parameters of the system. Finally, we investigate the phenomenological implications of the dark energy equation of state which we assumed that it governs the dark energy fluid.

Axial flow in a two-dimensional microchannel induced by a travelling temperature wave imposed at the bottom wall

Fluid flow in microchannels has wide industrial and scientific applications. Hence, it is important to explore different driving mechanisms. In this paper, we study the net transport or fluid pumping in a two-dimensional channel induced by a travelling temperature wave applied at the bottom wall. The Navier–Stokes equations with the Boussinesq approximation and the convection–diffusion heat equation are made dimensionless by the height of the channel and a velocity scale obtained by a dominant balance between buoyancy and viscous resistance in the momentum equation. The system of equations is transformed to an axial coordinate that moves with the travelling temperature wave, and we seek steady solutions in this moving frame. Four dimensionless numbers emerge from the governing equations and boundary conditions: the Reynolds number $Re$, a Reynolds number $Rc$ based on the wave speed, the Prandtl number $Pr$ and the dimensionless wavenumber $K$. The system of equations is solved by a finite-volume method and by a perturbation method in the limit $Re\rightarrow 0$. Surprisingly, the leading and first-order perturbation solutions agree well with the computed axial flow for $Re\leqslant 10^{3}$. Thus, the analytic perturbation solutions are used to study systematically the effects of $Re$, $Rc$, $Pr$ and $K$ on the dimensionless induced axial flow $Q$. We find that $Q$ varies linearly with $Re$, and $Q/Re$ versus any of the three remaining dimensionless groups always exhibits a maximum. The global maximum of $Q/Re$ in the parameter space is subsequently determined for the first time. This induced axial flow is driven solely by the Reynolds stress.

Transient gas flow in elastic microchannels

We study pressure-driven propagation of gas into a two-dimensional microchannel bounded by linearly elastic substrates. Relevant fields of application include lab-on-a-chip devices, soft robotics and respiratory flows. Applying the lubrication approximation, the flow field is governed by the interaction between elasticity and viscosity, as well as weak rarefaction and low-Mach-number compressibility effects, characteristic of gaseous microflows. A governing equation describing the evolution of channel height is derived for the problem. Several physical limits allow simplification of the governing equation and solution by self-similarity. These limits, representing different physical regimes and their corresponding time scales, include compressibility–elasticity–viscosity, compressibility–viscosity and elasticity–viscosity dominant balances. Transition of the flow field between these regimes and corresponding exact solutions is illustrated for the case of an impulsive mass insertion in which the order of magnitude of the deflection evolves in time. For an initial channel thickness which is similar to the elastic deformation generated by the background pressure, a symmetry between compressibility and elasticity allows us to obtain a self-similar solution which includes weak rarefaction effects. The presented results are validated by numerical solutions of the evolution equation.

Islandness within climate change narratives of small island developing states (SIDS)

Small island developing states (SIDS) are portrayed as icons of climate change impacts, with assumed islandness characteristics being used to emphasise vulnerability. Meanwhile, island resilience expressed as the stability of island “paradises” is said to be undermined by climate change. Two dominant counternarratives have been emerging. Physical science demonstrates the limited empirical evidence at the moment for SIDS being destroyed due to climate change. Notwithstanding that such empirical evidence could appear in the future, social science counternarratives are challenging notions of SIDS’ peoples inevitably fleeing their homes as climate refugees. Instead, SIDS’ peoples have strong abilities and desires to make their own mobility decisions, whether due to climate change or other impetuses. Consequently, islandness within SIDS’ climate change narratives is not necessarily problematic, but instead can help islanders address climate change and wider challenges. The counternarratives, even if not entirely contradicting the dominant narratives, provide needed nuances, balance, and contextualisation to provide a full picture of SIDS, islandness, and climate change.

KAJIAN TENTANG METODE PERSAMAAN RICCATI PROYEKTIF

Abstract. In this paper, we discuss the derivation and application of a projective Riccatiequation method in solving nonlinear partial dierential equations. We also study themathematical aspects of the method and its limitations in some particular cases.Kata Kunci: Nonlinear partial dierential equations, projective Riccati equation method,dominant balance principle

Static response of coated microbubbles compressed between rigid plates: Simulations and asymptotic analysis including elastic and adhesive forces

The static response of coated microbubbles is investigated with a novel approach employed for modeling contact between a microbubble and the cantilever of an atomic force microscope. Elastic tensions and moments are described via appropriate constitutive laws. The encapsulated gas is assumed to undergo isothermal variations. Due to the hydrophilic nature of the cantilever, an ultrathin aqueous film is formed, which transfers the force onto the shell. An interaction potential describes the local pressure applied on the shell. The problem is solved in axisymmetric form with the finite element method. The response is governed by the dimensionless bending, k^b=kb/χR02, pressure, P^A=PAR0/χ, and interaction potential, W^=w0/χ. Hard polymeric shells have negligible resistance to gas compression, while for the softer lipid shells gas compressibility is comparable with shell elasticity. As the external force increases, numerical simulations reveal that the force versus deformation (f vs d) curve of polymeric shells exhibits a transition from the linear O(d) (Reissner) regime, marked by flattened shapes around the contact region, to a non-linear O(d1/2) (Pogorelov) regime dominated by shapes exhibiting crater formation due to buckling. When lipid shells are tested, buckling is bypassed as the external force increases and flattened shapes prevail in an initially linear f vs d curve. Transition to a curved upwards regime is observed as the force increases, where gas compression and area dilatation form the dominant balance providing a nonlinear regime with an O(d3) dependence. Asymptotic analysis recovers the above patterns and facilitates estimation of the shell mechanical properties.

Streamwise-travelling viscous waves in channel flows

The unsteady viscous flow induced by streamwise-travelling waves of spanwise wall velocity in an incompressible laminar channel flow is investigated. Wall waves belonging to this category have found important practical applications, such as microfluidic flow manipulation via electro-osmosis and surface acoustic forcing and reduction of wall friction in turbulent wall-bounded flows. An analytical solution composed of the classical streamwise Poiseuille flow and a spanwise velocity profile described by the parabolic cylinder function is found. The solution depends on the bulk Reynolds number R, the scaled streamwise wavelength lambda , and the scaled wave phase speed U. Numerical solutions are discussed for various combinations of these parameters. The flow is studied by the boundary-layer theory, thereby revealing the dominant physical balances and quantifying the thickness of the near-wall spanwise flow. The Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) theory is also employed to obtain an analytical solution, which is valid across the whole channel. For positive wave speeds which are smaller than or equal to the maximum streamwise velocity, a turning-point behaviour emerges through the WKBJ analysis. Between the wall and the turning point, the wall-normal viscous effects are balanced solely by the convection driven by the wall forcing, while between the turning point and the centreline, the Poiseuille convection balances the wall-normal diffusion. At the turning point, the Poiseuille convection and the convection from the wall forcing cancel each other out, which leads to a constant viscous stress and to the break down of the WKBJ solution. This flow regime is analysed through a WKBJ composite expansion and the Langer method. The Langer solution is simpler and more accurate than the WKBJ composite solution, while the latter quantifies the thickness of the turning-point region. We also discuss how these waves can be generated via surface acoustic forcing and electro-osmosis and propose their use as microfluidic flow mixing devices. For the electro-osmosis case, the Helmholtz–Smoluchowski velocity at the edge of the Debye–Hückel layer, which drives the bulk electrically neutral flow, is obtained by matched asymptotic expansion.

Asymptotic Analysis of a Silicon Furnace Model

Silicon is produced from quartz rock in electrode-heated furnaces by using carbon as a reduction agent. We perform an asymptotic analysis of a heat and mass transfer model of an experimental pilot furnace in order to determine the dominant chemical and thermal behavior of the system. First, by prescribing a steady-state temperature profile in the furnace we explore the leading order reactions in different spatial regions, as well as early time behavior. We are able to obtain asymptotic solutions which compare well with numerical simulations. Utilizing the dominant balances found when the temperature is prescribed, we next reduce the full model to two coupled partial differential equations for the time-variable temperature profile within the furnace and the concentration of solid quartz. These equations account for diffusion, an endothermic reaction, and the external heating input to the system. A moving boundary is found and the behavior on either side of this boundary explored in the asymptotic limit of small diffusion. We note how the simplifications derived may be useful for future models and industrial furnace operation and comment on insights from the model about furnace crust formation.

Power Politics Behind the Transforming Geopolitics in East Asia

Current geopolitical dynamics in East Asia is generated by the US rebalancing and China’s counterbalancing. The US rebalancing has so far ended in an encircling of China, whereas China counteracts to extend into the seas and the lands as typified by the Belt and Road Initiative and assertive activities in the South China Sea. China under Xi Jinping’s leadership has set up a new guideline of ‘great power foreign policy’ (大国外交) to realize Xi Jinping’s ambitious vision of ‘China dream’. As delivered in the ‘New Model of Great Power Relations’, China under Xi Jinping’s leadership seeks clearly for ‘regional dominance’, while for ‘global balance’ with the USA. With rebalancing, however, the USA seeks to restore power balance in East Asia by adding up to military and economic resources already deployed there. By doing so, the USA aims to achieve its strategic goal of ‘regional balance’, while maintaining ‘global dominance’. These two distinct strategic goals, regional dominance and global balance for China and regional balance and global dominance for the USA, interact to result in currently transforming geopolitics in East Asia.

Behavior of a vacuum and naked singularity under a smooth gauge function in Lyra geometry

Lyra geometry is a conformal geometry that originated from Weyl geometry. In this article, we derive the exterior field equation under a spherically symmetric gauge function x0(r) and metric in Lyra geometry. When we impose a specific form of the gauge function x0(r), the radial differential equation of the metric component g00 will possess an irregular singular point (ISP) at r = 0. Moreover, we can apply the method of dominant balance to get the asymptotic behavior of the new space–time solution. The significance of this work is that we can use a series of smooth gauge functions x0(r) to modulate the degree of divergence of the singularity at r = 0, which will become a naked singularity under certain conditions. Furthermore, we investigate the physical meaning of this novel behavior of space–time in Lyra geometry and find out that no spaceship with finite integrated acceleration can arrive at this singularity at r = 0. The physical meaning of the gauge function and integrability is also discussed.

A Pilot RCT Investigating the Effects of Targeted Compression on Athletes With Pelvic/Groin Pain.

Athletic pelvic/groin pain is a common yet often challenging problem to both diagnose and manage. A new tool has been developed based on the clinical effects of applied force on the pelvis. Early findings indicate that this customized compression orthosis may have a positive effect on pelvic/groin pain and performance measures. To inform the design and test the practicality of procedures for a future definitively powered randomized controlled trial and to provide an estimate of the effect size of this orthosis on selected clinical and performance measures. Pilotrandomized controlled trial with participants randomly allocated to an intervention or waiting-list control group. The training location of each athlete. 24 athletes with subacute and chronic pelvic conditions were proposed to be recruited. A customized compression orthosis, delivering targeted compression to the pelvic girdle. Measures were the active straight leg raise (ASLR) test, squeeze test, broad jump, and the multiple single-leg hop-stabilization test. A total of 16 athletes completed the study. The invention group demonstrated moderate to large estimated effect sizes on the squeeze test and active straight leg raise tests (d = 0.6-1.1) while wearing the orthosis. Small effect sizes (d = 0.2) were seen on jump distance and the dominant leg balance score. Compared with the control group, the intervention group also showed moderate to large estimated effect sizes on the active straight leg raise measures (d = 0.5-0.9) when wearing sports shorts. The protocol was feasible. Effect sizes and recruitment/attrition rates suggest that the intervention holds promise and that a future definitively powered randomized controlled trial appears feasible and is indicated.

Stresses of PTT, Giesekus, and Oldroyd-B fluids in a Newtonian velocity field near the stick-slip singularity

We characterise the stress singularity of the Oldroyd-B, Phan-Thien–Tanner (PTT), and Giesekus viscoelastic models in steady planar stick-slip flows. For both PTT and Giesekus models in the presence of a solvent viscosity, the asymptotics show that the velocity field is Newtonian dominated near to the singularity at the join of the stick and slip surfaces. Polymer stress boundary layers are present at both the stick and slip surfaces. By integrating along streamlines, we verify the polymer stress behavior of r−4/11 for PTT and r−5/16 for Giesekus, where r is the radial distance from the singularity. These asymptotic results for PTT and Giesekus do not hold in the limit of vanishing quadratic stress terms for Oldroyd-B. However, we can consider the Oldroyd-B model in the fixed kinematics of a prescribed Newtonian velocity field. In contrast to PTT and Giesekus, this is not the correct balance for the momentum equation but does allow insight into the behavior of the Oldroyd-B equations near the singularity. A three-region asymptotic structure is again apparent with now a polymer stress singularity of r−4/5. The high Weissenberg boundary layer equations are found to manifest themselves at the stick surface and are of thickness r3/2. At the slip surface, dominant balance between the upper convected stress and rate-of-strain terms gives a slip boundary layer of thickness r2. The solution of the slip boundary layer shows that the polymer stress is now singular along the slip surface. These results are supported through numerical integration along streamlines of the Oldroyd-B equations in a Newtonian velocity field. The Oldroyd-B model thus extends the point singularity at the join of the stick and slip surfaces to the whole of slip surface. As such, it does not have a physically meaningful solution in a Newtonian velocity field. We would expect a similar stress behavior for this model in the true viscoelastic velocity field.

Self-similar rupture of thin films of power-law fluids on a substrate

Thinning and rupture of a thin film of a power-law fluid on a solid substrate under the balance between destabilizing van der Waals pressure and stabilizing capillary pressure is analysed. In a power-law fluid, viscosity is not constant but is proportional to the deformation rate raised to the $n-1$ power, where $0<n\leqslant 1$ is the power-law exponent ($n=1$ for a Newtonian fluid). In the first part of the paper, use is made of the slenderness of the film and the lubrication approximation is applied to the equations of motion to derive a spatially one-dimensional nonlinear evolution equation for film thickness. The variation with time remaining until rupture of the film thickness, the lateral length scale, fluid velocity and viscosity is determined analytically and confirmed by numerical simulations for both line rupture and point rupture. The self-similarity of the numerically computed film profiles in the vicinity of the location where the film thickness is a minimum is demonstrated by rescaling of the transient profiles with the scales deduced from theory. It is then shown that, in contrast to films of Newtonian fluids undergoing rupture for which inertia is always negligible, inertia can become important during thinning of films of power-law fluids in certain situations. The critical conditions for which inertia becomes important and the lubrication approximation is no longer valid are determined analytically. In the second part of the paper, thinning and rupture of thin films of power-law fluids in situations when inertia is important are simulated by solving numerically the spatially two-dimensional, transient Cauchy momentum and continuity equations. It is shown that as such films continue to thin, a change of scaling occurs from a regime in which van der Waals, capillary and viscous forces are important to one where the dominant balance of forces is between van der Waals, capillary and inertial forces while viscous force is negligible.

Inertia-less convectively-driven dynamo models in the limit of low Rossby number and large Prandtl number

Compositional convection is thought to be an important energy source for magnetic field generation within planetary interiors. The Prandtl number, Pr, characterizing compositional convection is significantly larger than unity, suggesting that the inertial force may not be important on the small scales of convection as long as the buoyancy force is not too strong. We develop asymptotic dynamo models for the case of small Rossby number and large Prandtl number in which inertia is absent on the convective scale. The relevant diffusivity parameter for this limit is the compositional Roberts number, q=D/η, which is the ratio of compositional and magnetic diffusivities. Dynamo models are developed for both order one q and the more geophysically relevant low q limit. For both cases the ratio of magnetic to kinetic energy densities, M, is asymptotically large and reflects the fact that Alfvén waves have been filtered from the dynamics. Along with previous investigations of asymptotic dynamo models for Pr=O(1), our results show that the ratio M is not a useful indicator of dominant force balances in the momentum equation since many different asymptotic limits of M can be obtained without changing the leading order geostrophic balance. Furthermore, the present models show that inertia is not a requirement for driving low q, large-scale dynamos.

Interleukin 10 inhibits pro-inflammatory cytokine responses and killing of Burkholderia pseudomallei

Melioidosis, caused by Burkholderia pseudomallei, is endemic in northeastern Thailand and Northern Australia. Severe septicemic melioidosis is associated with high levels of pro-inflammatory cytokines and is correlated with poor clinical outcomes. IL-10 is an immunoregulatory cytokine, which in other infections can control the expression of pro-inflammatory cytokines, but its role in melioidosis has not been addressed. Here, whole blood of healthy seropositive individuals (n = 75), living in N. E. Thailand was co-cultured with B. pseudomallei and production of IL-10 and IFN-γ detected and the cellular sources identified. CD3− CD14+ monocytes were the main source of IL-10. Neutralization of IL-10 increased IFN-γ, IL-6 and TNF-α production and improved bacteria killing. IFN-γ production and microbicidal activity were impaired in individuals with diabetes mellitus (DM). In contrast, IL-10 production was unimpaired in individuals with DM, resulting in an IL-10 dominant cytokine balance. Neutralization of IL-10 restored the IFN-γ response of individuals with DM to similar levels observed in healthy individuals and improved killing of B. pseudomallei in vitro. These results demonstrate that monocyte derived IL-10 acts to inhibit potentially protective cell mediated immune responses against B. pseudomallei, but may also moderate the pathological effects of excessive cytokine production during sepsis.

Secrecy Rates and Optimal Power Allocation for Full-Duplex Decode-and-Forward Relay Wire-Tap Channels

This paper investigates the secrecy rates and optimal power allocation schemes for a decode-and-forward wiretap relay channel where the transmission from a source to a destination is aided by a relay operating in a full-duplex (FD) mode under practical residual self-interference. By first considering static channels, we address the non-convex optimal power allocation problems between the source and relay nodes under individual and joint power constraints to establish closed-form solutions. An asymptotic analysis is then given to provide important insights on the derived power allocation solutions. Specifically, by using the method of dominant balance, it is demonstrated that full power at the relay is only optimal when the power at relay is sufficiently smaller when compared with that of the source. When the power at the relay is larger than the power at the source, the power consumed at the relay saturates to a constant for an effective control of self-interference. The analysis is also helpful to demonstrate that the secrecy capacity of the FD system is twice as much as that of the half-duplex system. The extension to fast fading channels with channel state information being available at the receivers but not the transmitters is also studied. To this end, we first establish a closed-form expression of the ergodic secrecy rate using simple exponential integrals for a given power allocation scheme. The results also show that with optimal power allocation schemes, FD can significantly improve the secrecy rate in fast fading environments.

A full, self-consistent treatment of thermal wind balance on oblate fluid planets

The nature of the flow below the cloud level on Jupiter and Saturn is still unknown. Relating the flow on these planets to perturbations in their density field is key to the analysis of the gravity measurements expected from both the Juno (Jupiter) and Cassini (Saturn) spacecrafts during 2016–2018. Both missions will provide latitude-dependent gravity fields, which in principle could be inverted to calculate the vertical structure of the observed cloud-level zonal flow on these planets. Theories to date connecting the gravity field and the flow structure have been limited to potential theories under a barotropic assumption, or estimates based on thermal wind balance that allow baroclinic wind structures to be analysed, but have made simplifying assumptions that neglected several physical effects. These include the effects of the deviations from spherical symmetry, the centrifugal force due to density perturbations and self-gravitational effects of the density perturbations. Recent studies attempted to include some of these neglected terms, but lacked an overall approach that is able to include all effects in a self-consistent manner. The present study introduces such a self-consistent perturbation approach to the thermal wind balance that incorporates all physical effects, and applies it to several example wind structures, both barotropic and baroclinic. The contribution of each term is analysed, and the results are compared in the barotropic limit with those of potential theory. It is found that the dominant balance involves the original simplified thermal wind approach. This balance produces a good order-of-magnitude estimate of the gravitational moments, and is able, therefore, to address the order one question of how deep the flows are given measurements of gravitational moments. The additional terms are significantly smaller yet can affect the gravitational moments to some degree. However, none of these terms is dominant so any approximation attempting to improve over the simplified thermal wind approach needs to include all other terms.

The momentum constraints on the shallow meridional circulation associated with the marine ITCZ

Recent studies have shown that the shallow meridional circulation (SMC) coexists with the deep circulation in the marine ITCZ. The SMC has been assumed to be forced by strong meridional gradients of Sea Surface Temperature (SST) which affect the atmosphere under hydrostatic balance. In this paper, we present a new viewpoint that the shallow meridional circulation is a part of circulation that forms when the marine ITCZ is located away from the equator. To support this view, we have used reanalysis data over east Pacific ocean to show that the shallow meridional circulation is absent when the ITCZ is located near the equator while it is strong to the south of the ITCZ when the ITCZ is located away from the equator. To further support this view, we have conducted idealized aquaplanet experiments by shifting SST maximum polewards to simulate the observed contrast in the meridional circulation associated with near equatorial and off-equatorial ITCZ. The detailed momentum budget of the flow above the boundary layer shows that, to the south of an off-equatorial ITCZ, the dominant balance between the Coriolis force and the advection of relative vorticity by the mean flow leads to cancellation of the planetary rotational effects. As a result, the net rotational effects experienced by the diverging flow above the boundary layer are negligible and a shallow meridional flow along the pressure gradients is generated. This dominant balance does not occur in the aquaplanet GCM when the ITCZ forms near the equator.

Reducing ocean model imbalances in the equatorial region caused by data assimilation

The equatorial region is a particularly challenging area for ocean data assimilation. In this region the dominant balance near the surface is between the ocean pressure gradients and the applied wind stress. When increments are applied to an ocean model near the Equator, the pressure gradients are modified and this can cause an imbalance with the unchanged wind stress. This can lead to an initialization shock where spurious equatorial waves and vertical velocities are triggered. The equatorial waves can degrade the performance of the ocean model while the increased vertical velocities have a significant negative impact on biogeochemical models forced by these physical ocean fields. Previous studies have proposed a scheme to reduce the ocean biases associated with slowly varying errors in the applied wind stress by applying a pressure correction calculated from accumulated temperature and salinity increments. This scheme has previously been shown to reduce the mean vertical velocities and improve modelled circulation. However, when applying this scheme, we still see equatorial imbalances from data assimilation on shorter time‐scales.We consider a new method which is an extension of the pressure correction and aims to act as a balance to the equatorial increments and reduce intialization shock. We refer to this as an incremental pressure correction. We provide a description of this method and an analysis of its energetics. In initial experiments with a global ocean data assimilation system, this new method is shown to suppress the generation of equatorial waves in a single observation experiment and to significantly reduce the standard deviation of vertical velocities in a re‐analysis experiment.