Steady Perturbation Research Articles

Periodic dynamics in viscous fingering

The displacement of a viscous liquid by air inside a Hele-Shaw channel is an archetype for nonlinear pattern-forming systems. Typically, bubbles or fingers of air propagate steadily at low values of the capillary number Ca = μ U * / σ , where μ is the viscosity of the liquid, U * is the speed of the bubble or finger and σ is the surface tension at the air–liquid interface. However, as the capillary number increases, the advancing interface can exhibit disordered pattern-forming dynamics. We demonstrate experimentally that a sustained, remote perturbation of the bubble tip can drive time-periodic dynamics. We exploit the propensity of a group of bubbles to propagate in steady spatial arrangements inside a Hele-Shaw channel with a centralized depth-reduction to apply a sustained pressure perturbation ahead of the bubble as it propagates. The oscillation cycle is initiated by the splitting of the bubble tip, via the Saffman–Taylor instability, which is promoted by the local flow-field conditions. The restoral of the bubble tip follows naturally because the system is driven by a fixed flow rate and the perturbed bubble is attracted to the weakly unstable, steadily propagating state that is set by the ratio of imposed viscous and capillary forces. The splitting and restoral mechanisms do not rely on the specific perturbation used in this study, suggesting a generic mechanism for periodic dynamics of propagating curved fronts subject to steady flow-field perturbations.

Nonmodal stability analysis of Poiseuille flow through a porous medium

We unravel the nonmodal stability of a three-dimensional nonstratified Poiseuille flow in a saturated hyperporous medium constrained by impermeable rigid parallel plates. The primary objective is to broaden the scope of previous studies that conducted modal stability analysis for two-dimensional disturbances. Here, we explore both temporal and spatial transient disturbance energy growths for three-dimensional disturbances when the Reynolds number and porosity of the material are high, based on evolution equations with respect to time and space, respectively. Modal stability analysis reveals that the critical Reynolds number for the onset of shear mode instability increases as porosity increases. Moreover, the Darcy viscous drag term stabilizes shear mode instability, resulting in a delay in the transition from laminar flow to turbulence. In addition, it demonstrates the suppression of three-dimensional shear mode instability as the spanwise wavenumber increases, thereby confirming the statement of Squire’s theorem. By contrast, nonmodal stability analysis discloses that both temporal and spatial transient disturbance energy growths curtail as the effect of the Darcy viscous drag force intensifies. But their maximum values behave like O(Re2) for a fixed porous material, where Re is the Reynolds number. However, for different porous materials, the scalings for both temporal and spatial transient disturbance energy growths are different. Furthermore, increasing porosity also suppresses both temporal and spatial disturbance energy growths. Finally, we observe that temporal transient disturbance energy growth becomes larger for a spanwise perturbation, while spatial transient disturbance energy growth becomes larger for a steady perturbation when angular frequency vanishes. The initial disturbance that excites the largest temporal energy amplification generates two sets of alternating high-speed and low-speed elongated streaks in the streamwise direction.

Response of sound propagation characteristics to Luzon cold eddy coupled with tide in the Northern South China Sea

The northern part of the South China Sea is a complex ocean environment with a large range of tidal waves and the stable Luzon cold eddy, which significantly influence the sound propagation characteristics through their impact on sound speed. This study uses a 3D ocean-acoustic framework consisting of MITgcm and BELLHOP ray model to investigate the coupled effects of the Luzon cold eddy and tidal waves. Firstly, the model incorporates tidal assimilation to reconstruct the hydrographic field and compute the sound speed field. Subsequently, the sound propagation in a representative region in the northern South China Sea is simulated to compare the response of sound propagation characteristics to the Luzon cold eddy only, tide only, and the coupled effect of both. The results demonstrate that the cold eddy shifts the location of the convergence zone forward by over 5 km at most. Further, it also makes the acoustic energy focus on the first few arrivals and delays the arrival time of rays by about 0.1 s. The tidal waves intensify these effects, resulting in a further increase of the forward distance of the convergence zone by 2-5 km and a delay in arrival time by 0.02 s. Sound propagation in the coupled influence of these two dynamic processes is exposed to steady perturbations from the cold eddy and spatial-temporal perturbations from tidal waves. The model in this study provides valuable insight for underwater detection and positioning in the realistic ocean environment.

Role of ionospheric Pedersen conductance and its gradient in field-aligned currents

Field-aligned current (FAC) is one of the most important aspects in the coupling of magnetosphere and the ionosphere. This paper presents a systematic numerical study of the magnetospheric and ionospheric influences on the evolution and modification of FACs, with focus on the role of ionospheric Pedersen conductance and its gradient. FACs are typically generated in the magnetosphere and are carried into the ionosphere by Alfvén waves. During their reflection from the ionosphere, these FACs are modified. The nature of modifications depends on the magnitude and distribution of ionospheric Pedersen conductance. A uniform ionosphere, having a high Pedersen conductance, enhances such a magnetospheric FAC strongly. For conductance-gradients perpendicular to the wave-polarization, FACs are generated after the reflection of simple Alfvénic perturbations, which are not carrying any FACs. A suitable arrangement of ionospheric Pedersen conductance can create a pair of antiparallel FACs, with consequent generation of a strong Pedersen current at the ionospheric boundary. For conductance-gradients along the polarization of the wave, the steady state velocity perturbation assumes an average value of the imposed Pedersen conductance over the entire region after reflection from the ionosphere. This configuration is comparable to the situation where the Cowling conductance operates.

Role of Ionospheric Pedersen Conductance and its Gradient in Field-Aligned Currents

Field-aligned current (FAC) is one of the most important aspects in the coupling of magnetosphere and the ionosphere. This paper presents a systematic numerical study of the magnetospheric and ionospheric influences on the evolution and modification of FACs, with focus on the role of ionospheric Pedersen conductance and its gradient. FACs are typically generated in the magnetosphere and are carried into the ionosphere by Alfven waves. During their reflection from the ionosphere, these FACs are modified. The nature of modifications depends on the magnitude and distribution of ionospheric Pedersen conductance. A uniform ionosphere, having a high Pedersen conductance, enhances such a magnetospheric FAC strongly. For conductance-gradients perpendicular to the wave-polarization, FACs are generated after the reflection of simple Alfvenic perturbations, which are not carrying any FACs. A suitable arrangement of ionospheric Pedersen conductance can create a pair of antiparallel FACs, with consequent generation of a strong Pedersen current at the ionospheric boundary. For conductance-gradients along the polarization of the wave, the steady state velocity perturbation assumes an average value of the imposed Pedersen conductance over the entire region after reflection from the ionosphere. This configuration is comparable to the situation where the Cowling conductance operates.

Repeated exposure to tripping like perturbations elicits more precise control and lower toe clearance of the swinging foot during steady walking.

Controlling minimum toe clearance (MTC) is considered an important factor in preventing tripping. In the current study, we investigated modifications of neuro-muscular control underlying toe clearance during steady locomotion induced by repeated exposure to tripping-like perturbations of the right swing foot. Fourteen healthy young adults (mean age 26.4±3.1years) participated in the study. The experimental protocol consisted of three identical trials, each involving three phases: steady walking (baseline), perturbation, and steady walking (post-perturbation). During the perturbation, participants experienced 30 tripping-like perturbations at unexpected timing delivered by a custom-made mechatronic perturbation device. The temporal parameters (cadence and stance phase%), mean, and standard deviation of MTC were computed across approximately 90 strides collected during both baseline and post-perturbation phases, for all trials. The effects of trial (three levels), phase (two levels: baseline and post-perturbation) and foot (two levels: right and left) on the outcome variables were analyzed using a three-way repeated measures analysis of variance. The results revealed that exposure to repeated trip-like perturbations modified MTC toward more precise control and lower toe clearance of the swinging foot, which appeared to reflect both the expectation of potential forthcoming perturbations and a quicker compensatory response in cases of a lack of balance. Moreover, locomotion control enabled subjects to maintain symmetric rhythmic features during post-perturbation steady walking. Finally, the effects of exposure to perturbation quickly disappeared among consecutive trials.

Bypass transition in flow over a vibrating flat plate

Abstract

Practical approach of linear hydro-elasticity effect on vessel with forward speed in the frequency domain

In this study, a practical approach to incorporate forward speed and hydro-elasticity effect in the frequency domain is developed. By utilizing the discrete-module-beam (DMB) method, flexible structures are partitioned into multiple rigid bodies that are connected by beam elements. The forward speed effect is taken into consideration in the multi-body hydrodynamics through the slender body and low uniform flow speed approximation, which is called the uniform flow approximation (due to no steady perturbation coupling term considered). By implementing the uniform flow approximation into the multi-body hydrodynamics formulation and then coupling it with the DMB method, any multi-rigid-body radiation–diffraction simulation tools can be extended to solve the linear hydro-elasticity problem with forward speed effect. The present numerical results compare well with published experimental and computational results, including a more direct but much more time-consuming FEM–BEM coupling method. By using the developed computer program, the increase of elastic response and change in dynamic bending moment are assessed for various wave lengths and forward speeds in the case of Wigley hull. The occurrence of hydro-elastic resonance at the first bending mode at certain forward speed is illustrated for a typical operational sea state. The forward speed also changes the wet mode shape, dynamic elastic response, and dynamic bending moment and its distribution along the ship. Encounter frequency, convective term in the pressure formulation and the m-terms contribute to their changes. The effect of local structural damage on the modal characteristics and the resulting hydro-elasticity is also investigated It needs to be noted that due to several approximations (e.g., uniform flow and free-surface approximations), care should be exercised when applying the proposed method.

Frequency-Resolved X-Ray Absorption Spectroscopy: A Synchrotron-Based Technique for Extracting Kinetic and Transport Parameters

Worldwide energy infrastructures are shifting to renewable, but intermittent sources, requiring new solutions for energy storage and conversion. Solid oxide fuel cells are attractive for their high energetic efficiencies, but poor performance in oxygen electrodes contributes to high material costs preventing their widespread adoption. Improving the performance of these technologies is often hindered by inadequate knowledge of localized kinetic and transport behavior. Spatial averaging across the electrode structure makes these properties inaccessible to typical bulk electrochemical characterization techniques like DC polarization and AC impedance spectroscopy. Conversely, chemically sensitive operando and in situ techniques spatially resolve local behavior but struggle to separate physics by timescale. We aim to bridge this gap by extending on previous work using synchrotron-based operando micro X-ray absorption spectroscopy (µ-XAS)1–3 with steady periodic voltage perturbations to isolate and spatiotemporally resolve physics.We introduce this technique – called frequency-resolved X-ray absorption spectroscopy (fr-XAS)– by showing one-dimensional oxygen vacancy distribution images in a patterned thin film La0.6Sr0.4CoO3-δ electrode. Oxygen vacancies in the electrode are compensated by Co oxidation state, resulting in Co K-edge absorption shifts. At a fixed incident X-ray energy, the edge shifts appear as vertical changes, providing a direct measure of electrode oxidation state in the irradiated volume. Scanning the X-ray beam across the electrode and measuring the absorption shift at each point over time (with Fourier analysis to accurately distinguish shifts caused by the voltage perturbation from noise in the signal) allows us to construct the oxygen vacancy distribution images. The oxygen chemical potential is equilibrated at the electrode/electrolyte interface controlled by the voltage with gradients extending away from the interface determined by surface exchange and ionic transport processes. Changing the perturbation frequency separates observed physics by timescale and allows for directly extracting kinetic and transport parameters.Initial results show good quantitative agreement with a one-dimensional Gerischer model, and extracted vacancy diffusion coefficients and surface exchange rates are within a factor of 10 from literature values on porous electrodes.4,5 Impedance results from the same sample are obfuscated by extraneous processes past the point of reasonable interpretation, thereby highlighting the power of fr-XAS to extract meaningful parameters despite extraneous factors. These promising results demonstrate proof-of-concept for fr-XAS and provide motivation for the community to adapt this framework for other material systems relevant to energy storage and conversion technologies.(1) Fujimaki, Y.; Watanabe, H.; Terada, Y.; Nakamura, T.; Yashiro, K.; Hashimoto, S.; Kawada, T.; Amezawa, K. Direct Evaluation of Oxygen Chemical Potential Distribution in an SOFC Cathode by In Situ X-Ray Absorption Spectroscopy. ECS Trans. 2013, 57 (1), 1925–1932. https://doi.org/10.1149/05701.1925ecst.(2) Amezawa, K.; Fujimaki, Y.; Nakamura, T.; Bagarinao, K. D.-; Yamaji, K.; Nitta, K.; Terada, Y.; Iguchi, F.; Yashiro, K.; Yugami, H.; Kawada, T. (Invited) Determination of Effective Reaction Area in a Mixed-Conducting SOFC Cathode. ECS Trans. 2015, 66 (2), 129–135. https://doi.org/10.1149/06602.0129ecst.(3) Amezawa, K.; Fujimaki, Y.; Mizuno, K.; Kimura, Y.; Nakamura, T.; Nitta, K.; Terada, Y.; Iguchi, F.; Yugami, H.; Yashiro, K.; Kawada, T. (Invited) Triple Phase Boundary Reaction in a Mixed-Conducting SOFC Cathode. ECS Trans. 2017, 77 (10), 41–47. https://doi.org/10.1149/07710.0041ecst.(4) Lu, Y.; Kreller, C.; Adler, S. B. Measurement and Modeling of the Impedance Characteristics of Porous La1 − x Sr x CoO3 − δ Electrodes. J. Electrochem. Soc. 2009, 156 (4), B513–B525. https://doi.org/10.1149/1.3079337.(5) Søgaard, M.; Hendriksen, P. V.; Mogensen, M.; Poulsen, F. W.; Skou, E. Oxygen Nonstoichiometry and Transport Properties of Strontium Substituted Lanthanum Cobaltite. Solid State Ionics 2006, 177 (37), 3285–3296. https://doi.org/10.1016/j.ssi.2006.09.005.

Peristaltic thrusting of a thermal-viscosity nanofluid through a resilient vertical pipe

Abstract In the article, the effects of the thermal viscosity and magnetohydrodynamic on the peristalsis of nanofluid are analyzed. The dominant neutralization is deduced through long wavelength approximation. The analytical solution of velocity and temperature is extracted by using steady perturbation. The pressure gradient and friction forces are obtained. Numerical results are calculated and contrasted with the debated theoretical results. These results are calculated for various values of Hartmann number, variable viscosity parameter and amplitude ratio. It is observed that the pressure gradient is reduced with an increase in the thermal viscosity parameter and that the Hartmann number enhances the pressure difference.

Robustness of a biomolecular oscillator to pulse perturbations.

Biomolecular oscillators can function robustly in the presence of environmental perturbations, which can either be static or dynamic. While the effect of different circuit parameters and mechanisms on the robustness to steady perturbations has been investigated, the scenario for dynamic perturbations is relatively unclear. To address this, the authors use a benchmark three protein oscillator design – the repressilator – and investigate its robustness to pulse perturbations, computationally as well as use analytical tools of Floquet theory. They found that the metric provided by direct computations of the time it takes for the oscillator to settle after pulse perturbation is applied, correlates well with the metric provided by Floquet theory. They investigated the parametric dependence of the Floquet metric, finding that the parameters that increase the effective delay enhance robustness to pulse perturbation. They found that the structural changes such as increasing the number of proteins in a ring oscillator as well as adding positive feedback, both of which increase effective delay, facilitates such robustness. These results highlight such design principles, especially the role of delay, for designing an oscillator that is robust to pulse perturbation.

Symplectic Computations of Fast Ion Trajectory and Radial Diffusion Coefficient in MHD Perturbed Tokamak

The magneto-hydrodynamics (MHD) modes existing in conducting plasmas can greatly affect charged particle’s dynamics. Low frequency MHD perturbations, called the neo-classical tearing (NTM) modes, give rise to magnetic islands which can deteriorate fast ion confinement, especially in tokamak plasmas. Here, a Hamiltonian guiding-center code, based on symplectic algorithm which allows efficient computations of energetic ion trajectories and transport coefficients, has been applied to magnetically perturbed tokamak plasmas. The effects of NTM perturbations on the energetic ion trajectories and diffusion coefficient have been presented. It is demonstrated that the inclusion of such steady state magnetic perturbations in the guiding center drift orbit computations escalates the loss of energetic ions via radial diffusion. Moreover, the broader NTMs lead to a significant enhancement of the radial diffusion coefficient.

Optimal suppression of a separation bubble in a laminar boundary layer

By means of nonlinear optimization, we seek the velocity disturbances at a given upstream position that suppress a laminar separation bubble as effectively as possible. Both steady and unsteady disturbances are examined and compared. For steady disturbances, an informed guess based on linear analysis of transient perturbation growth leads to significant delay of separation and serves as a starting point for the nonlinear optimization algorithm. It is found that the linear analysis largely captures the suppression of the separation bubble attained by the nonlinear optimal perturbations. The mechanism of separation delay is the generation of a mean flow distortion by nonlinear interactions during the perturbation growth. The mean flow distortion enhances the momentum close to the wall, counteracting the deceleration of the flow in that region. An examination of the effect of the disturbance spanwise wavenumber reveals that perturbations maximizing the mean flow distortion also approximately maximize the peak wall pressure, which is beneficial for lowering form drag. The optimal spanwise wavenumber leading to maximal peak wall pressure is significantly larger than the one maximizing the shift in separation onset. For unsteady disturbances, the mechanism of separation delay relies on enhancing wall-normal momentum transfer by triggering instabilities of the separated shear layer. It is found that Tollmien–Schlichting waves obtained from linear stability theory provide accurate estimates of the nonlinearly optimal disturbances. Comparison of optimal steady and unsteady perturbations reveals that the latter are able to obtain a higher time-averaged peak wall pressure.

Effect of flame interaction on swirl-stabilized mesoscale burner array performance

Individual flames in a swirl-stabilized mesoscale burner array can interact with neighboring flames for optimum burner array operation, particularly at lean equivalence ratios. Understanding these interactions are therefore critical for optimizing the mesoscale burner array. This study probes the effect of burner performance and stability based on experimental data of two burner array configurations (dense and sparse) under steady and acoustic perturbation conditions. First, the dense lean blow off equivalence ratios and flame temperatures were examined. The dense burner array lean blow off limits were 8.8 % lower than the sparse burner array. Maximum flame temperature of the dense burner array was 56.4 K higher compared to its sparse counterpart at the equivalence ratio of 0.65. Second, various flame structures from both mesoscale burner arrays were visualized using OH planar laser induced fluorescence imaging. Results showed that flame structures from the dense mesoscale burner array produced a wider range of stable power outputs. Lastly, proper orthogonal decomposition, phase-averaging, and Rayleigh index-based stability analyses were performed using 10 kHz OH* chemiluminescence imaging. Results showed that the dense mesoscale burner array exhibited better thermal-acoustic damping with smaller heat release fluctuations under acoustic perturbation range from 80 to 270 Hz compared to the sparse mesoscale burner array.

Receptivity of supersonic boundary layers over smooth and wavy surfaces to impinging slow acoustic waves

In this paper, we investigate the receptivity of a supersonic boundary layer to impinging acoustic waves. Unlike previous studies of acoustic receptivity, where the sound waves have phase speeds comparable with or larger than the free-stream velocity $U_{\infty }$, the acoustic waves here have much slower ($O(R^{-1/8}U_{\infty })$) phase velocity, and their characteristic wavelength and frequency are of $O(R^{-3/8}L)$ and $O(R^{1/4}U_{\infty }/L)$ respectively, compatible with the triple-deck structure, where $L$ is the distance to the leading edge and $R$ the Reynolds number based on $L$ and $U_{\infty }$. A significant feature of a sound wave on the triple-deck scale is that an $O(\unicode[STIX]{x1D700}_{s})$ perturbation in the free stream generates much stronger ($O(\unicode[STIX]{x1D700}_{s}R^{1/8})$) velocity fluctuations in the boundary layer. Two receptivity mechanisms are considered. The first is new, involving the interaction of two such acoustic waves and operating in a boundary layer over a smooth wall. The second involves the interaction between an acoustic wave and the steady perturbation induced by a wavy wall. The sound–sound, or sound–roughness, interactions generate a forcing in resonance with a neutral Tollmien–Schlichting (T–S) wave. The latter is thus excited near the lower branch of the neutral curve, and subsequently undergoes exponential amplification. The excitation through sound–sound interaction may offer a possible explanation for the appearance of instability modes downstream of their neutral locations as was observed in a supersonic boundary layer over a smooth wall. The triple-deck formalism is adopted to describe impingement and reflection of the acoustic waves, and ensuing receptivity, allowing the coupling coefficient to be calculated. The two receptivity processes with the acoustic waves on the triple-deck scale are much more effective compared with those involving usual sound waves, with the coupling coefficient being greater by a factor of $O(R^{1/4})$ and $O(R^{1/8})$ in the sound–sound and sound–roughness interactions, respectively. A parametric study for both the reflection and coupling coefficients is conducted for representative T–S waves, to assess the influence of the streamwise and spanwise wavenumbers, and the phase speed (or frequency) of the acoustic wave.

Active control of circular cylinder flow with windward suction and leeward blowing

This study is an experimental investigation of the effectiveness and mechanism of a concept for bluff-body control characterized by combined windward suction and leeward blowing (WSLB). Wind tunnel tests are performed at a subcritical Reynolds number (Re) of 3.33 × 104. Open-loop WSLB is used to control the flow around a cylindrical test model. Distributed suction and blowing nozzles are symmetrically arranged at the front and rear stagnation points. Steady suction and blowing are implemented simultaneously on both surfaces of the cylinder. WSLB control is characterized by the dimensionless momentum of the suction/blowing relative to the incoming airflow. Instantaneous pressure distributions on the midspan of the cylinder surface for the baseline and controlled cases are measured to quantify the modifications of WSLB control to the aerodynamic coefficients of the cylinder. In addition to surface pressure measurements, a particle image velocimetry (PIV) system is used to describe the wake flow structures of the baseline and controlled cylinders. Experimental results demonstrate that WSLB control decreases sectional drag at the midspan and reduces the fluctuating amplitudes of dynamic wind loads acting on the cylinder. The Strouhal number to characterize the vortex shedding frequencies of the controlled cylinders is also found to deviate from that of the natural cylinder. PIV measurement results show that the active blowing positioned at the leeward stagnation point forms a pair of vortices into the cylinder wake that modify the original vortex shedding process. As the blowing vortices convect into the wake, they stretch the unsteady shear flows from the upper and lower sides of the cylinder, increase the vortex-formation length and push the alternative vortex shedding further downstream. It is also shown that a steady and symmetric perturbation imposed on the periodic cylinder flow can reduce the von Karman vortices and modify the mode of wake vortex shedding significantly. With active control of windward suction and leeward blowing (WSLB), blowing positioned at the leeward stagnation point forms a pair of vortices in the cylindrical wake that modifies the typical vortex shedding process. As the blowing vortices convect downstream, they contribute to detaching the unsteady shear layers from the cylinder. It is shown that a steady and symmetric perturbation imposed on the periodic cylinder flow can lead to a symmetric mode of wake vortex shedding.

Effects of steady wake-jets on subcritical cylinder flow

We investigate the effects of active wake-jets (characterized by a dimensionless jet momentum coefficient Cμ) on the suppression of aerodynamic forces and the manipulation of wake flow topology behind a cylindrical model through wind tunnel tests. The active jets are positioned at the rear stagnation points of the cylindrical test model. The experimental campaign is conducted at a subcritical Reynolds number of Re=3.33×104. The surface pressure distributions around the bare and controlled cylinders are obtained by using a pressure measurement system. Apart from pressure measurements, we also obtain the streamwise and spanwise flow structures around the circular cylinder with different Cμ (including Cμ=0) by employing the particle image velocimetry (PIV) technique. Pressure measurement results demonstrate that the lift force acting on the cylindrical test model is greatly reduced and drag decreased with the implementation of active wake-jets. Besides, it is found that a higher Cμ contributes to a better control effectiveness in unsteady lift forces but not necessarily a better drag reduction. PIV measurement results indicate that the mechanism of the active jet control scheme is to impose steady and symmetric perturbations into the unsteady and asymmetric flows in the cylinder wake. Owing to the dynamic competition of the wake-jet flow and shear layer flows, the vortex shedding pattern behind the controlled cylinder is greatly modified, vortex formation length significantly elongated and the fluctuations of aerodynamic forces conceivably suppressed.

Fitting mathematical models of biochemical pathways to steady state perturbation response data without simulating perturbation experiments

Fitting Ordinary Differential Equation (ODE) models of signal transduction networks (STNs) to experimental data is a challenging problem. Computational parameter fitting algorithms simulate a model many times with different sets of parameter values until the simulated STN behaviour match closely with experimental data. This process can be slow when the model is fitted to measurements of STN responses to numerous perturbations, since this requires simulating the model as many times as the number of perturbations for each set of parameter values. Here, I propose an approach that avoids simulating perturbation experiments when fitting ODE models to steady state perturbation response (SSPR) data. Instead of fitting the model directly to SSPR data, it finds model parameters which provides a close match between the scaled Jacobian matrices (SJM) of the model, which are numerically calculated using the model’s rate equations and estimated from SSPR data using modular response analysis (MRA). The numerical estimation of SJM of an ODE model does not require simulating perturbation experiments, saving significant computation time. The effectiveness of this approach is demonstrated by fitting ODE models of the Mitogen Activated Protein Kinase (MAPK) pathway using simulated and real SSPR data.

Thermodiffusion-Stipulated Anomalous Response of a Stratified Fluid to Mechanical Forcing

Steady perturbations introduced into a temperature-stratified fluid binary mixture, such as saline water, by inhomogeneous tangent stresses on its surface have been studied in a linear approximation. It has been shown that thermodiffusion may greatly increase the depth of thermal perturbation penetration into the medium despite the stable background density stratification.

A Markovian model of evolving world input-output network

The initial theoretical connections between Leontief input-output models and Markov chains were established back in 1950s. However, considering the wide variety of mathematical properties of Markov chains, so far there has not been a full investigation of evolving world economic networks with Markov chain formalism. In this work, using the recently available world input-output database, we investigated the evolution of the world economic network from 1995 to 2011 through analysis of a time series of finite Markov chains. We assessed different aspects of this evolving system via different known properties of the Markov chains such as mixing time, Kemeny constant, steady state probabilities and perturbation analysis of the transition matrices. First, we showed how the time series of mixing times and Kemeny constants could be used as an aggregate index of globalization. Next, we focused on the steady state probabilities as a measure of structural power of the economies that are comparable to GDP shares of economies as the traditional index of economies welfare. Further, we introduced two measures of systemic risk, called systemic influence and systemic fragility, where the former is the ratio of number of influenced nodes to the total number of nodes, caused by a shock in the activity of a node, and the latter is based on the number of times a specific economic node is affected by a shock in the activity of any of the other nodes. Finally, focusing on Kemeny constant as a global indicator of monetary flow across the network, we showed that there is a paradoxical effect of a change in activity levels of economic nodes on the overall flow of the world economic network. While the economic slowdown of the majority of nodes with high structural power results to a slower average monetary flow over the network, there are some nodes, where their slowdowns improve the overall quality of the network in terms of connectivity and the average flow of the money.