Equilibrium Response Research Articles

On the experimental identification of equilibrium relations and the separation of inelastic effects in soft biological tissues

The mechanical characterization of vascular tissues has been mainly focused on the measurement of elastic properties, while the investigation of inelastic effects has received comparatively little attention. Even the relatively simple, purely elastic description of the material behavior requires an appropriate set of experimental data that cannot be easily isolated using standard testing procedures. The presence of viscous and damage-related phenomena poses some challenges in the definition of appropriate testing protocols capable of identifying an equilibrium response, which in general does not solely represent the elastic material behavior. The primary goal of the present study is therefore to devise an experimental procedure that can distinguish and evaluate the different constitutive phenomena separately. To this end, we apply methodologies widely used in the mechanical testing of rubber-like materials and transfer them to the field of biomechanics. We performed two types of experiments in equibiaxial extension on porcine thoracic aorta: a continuous cyclic test followed by a single-step relaxation test and a cyclic multi-step relaxation test, each at varying stretch rates. We demonstrate that the approximation of quasi-stationarity through continuous testing at slow rates is inadequate for the identification of an equilibrium relation. Alternatively, a step-wise protocol allows for the separation of equilibrium and viscous effects. This motivates a thermodynamic discussion of the experimental results in terms of energy dissipation and a closer look at the interplay of inelastic phenomena.

FLARE: field line analysis and reconstruction for 3D boundary plasma modeling

Abstract The FLARE code is a magnetic mesh generator that is integrated within a suite of tools for the analysis of the magnetic geometry in toroidal fusion devices. A magnetic mesh is constructed from field line segments and permits fast reconstruction of field lines in 3D boundary plasma codes such as EMC3-EIRENE. Both intrinsically non-axisymmetric configurations (stellarators) and those with symmetry breaking perturbations of an axisymmetric equilibrium (tokamaks) are supported. The code itself is written in Modern Fortran with MPI support for parallel computing, and it incorporates object-oriented programming for the definition of the magnetic field and the material surface geometry. Extended derived types for a number of different magnetohydrodynamic equilibrium and plasma response models are implemented. The core element of FLARE is a field line tracer with adaptive step-size control, and this is integrated into tools for the construction of Poincaré maps and invariant manifolds of X-points. A collection of high-level procedures that generate output files for visualization is build on top of that. The analysis modules are build with Python frontends that facilitate customization of tasks and/or scripting of parameter scans.

High recovery speed optical humidity sensing enabled with GQD for non-contact finger distance detection

Finger distance perception plays a crucial role in enabling humanoid intelligent robotic systems to achieve smooth interaction with humans. Here, a rapidly response optical humidity sensor enabled with graphene quantum dots (GQD) for non-contact finger distance detection was proposed. The GQD was prepared through the functionalization of graphene oxide (GO) with hydrophilic groups. This modification enhances the responsiveness of GO to atmospheric humidity and promotes the deposition of conformal films of functional materials on the surfaces of optical fiber. Utilizing a light-driven coating method, the GQD was deposited onto a tilted fiber Bragg grating (TFBG) to fabricate humidity sensor. When water molecules were absorbed by GQD, the dielectric constant of GQD film was changed, causing an alteration in the intensities of the TFBG’s cladding modes. The proposed sensor shows a sensitivity of 0.032 dB/%RH with the equilibrium response and recovery time of 3.66 s and 0.92 s, respectively. The equilibrium recovery time is the fastest as far as we know. Furthermore, the sensor is capable of precisely identifying the action of a finger, such as approaching, remaining, and departing with a detection range of 0–10 mm.

Optimizing multi-energy systems with enhanced robust planning for cost-effective and reliable operation

This paper introduces a comprehensive and resilient multi-energy system (MES) designed for independent planning and real-time implementation. A robust daily coordinated planning model is proposed, incorporating adjustable optimization with fundamental operational and uncertainty constraints. The model integrates various energy sources and systems, including photovoltaics, wind turbines, combined heat and power (CHP) units, energy storage system (ESS), electric vehicle (EV), electric boilers, and power-to-gas (P2G) facilities, to manage electricity, natural gas, and heat demands. The objective is to minimize MES operational costs while meeting electricity and heat requirements, considering renewable energy uncertainties. It includes the development of a two-stage flexible robust optimization model that accounts for energy equilibrium, capacity constraints, and demand response mechanisms. The model incorporates price-based demand response with both switchable and interruptible loads, enhancing system controllability and flexibility. Additionally, a scenario generation and reduction technique based on the Kantorovich distance is employed to effectively manage forecast errors and uncertainties. A novel modified Slime Mold Algorithm (SMA) is utilized to solve the optimization problem, demonstrating superior convergence and computational efficiency compared to traditional meta-heuristics. The slime mold algorithm is further enhanced with chaos theory, using a sine map to introduce dynamic exploration capabilities. The findings indicate that the proposed multi-energy system model effectively balances electricity, natural gas, and heat loads while accommodating renewable energy fluctuations. The enhanced slime mold algorithm provides optimal solutions swiftly, ensuring reliable and cost-effective multi-energy system operation.

Hybrid platforms with free entry: demand-enhancing activities

AbstractWe study the decision of a platform as to the quantity and quality of the products to sell directly on its own marketplace, where also third-party sellers decide how much to invest in the quality of their products. Using a representative agent framework that is based on a quasi-linear quality-augmented indirect utility function, we show that, under free entry, the quality investments of sellers do not change with platform entry, while the number of joining sellers does. Moreover, contrarily to what is found in the received literature, the platform may go hybrid even in the case it does not enjoy a competitive advantage vis-á-vis third-party sellers. We then study the welfare implications of a platform’s entry decision and show that promoting sellers’ investments and/or contrasting platform entry may lead to a larger as well as a lower consumer welfare. This depends on the platform’s response in equilibrium, both in terms of changes of its quality-enhancing investments and the fee charged on the revenues of third-party sellers.

Role of cytokines in immunomodulation during malaria clearance.

Malaria remains a significant global health challenge, demanding a deeper understanding of host immune responses for effective clearance of the parasitic infection. Cytokines, as crucial mediators of the immune system, orchestrate a complex interplay during the various stages of malaria infection. Throughout the course of the disease, an intricate balance of pro-inflammatory and anti-inflammatory cytokines dictate the immune response's outcome, influencing parasitic clearance and disease severity. During the initial stages, interleukins such as interleukin-12 (IL-12), interferon-gamma (IFN-γ), and tumour necrosis factor-alpha (TNF-α) play pivotal roles in activating innate immune cells, initiating the anti-parasitic response. Simultaneously, regulatory cytokines like interleukin-10 (IL-10) and transforming growth factor-beta (TGF-β) modulate this immune activation, preventing excessive inflammation and tissue damage. As the infection progresses, a delicate shift occurs, characterized by a transition to adaptive immunity, guided by cytokines like interleukin-4 (IL-4), interleukin-5 (IL-5), and interleukin-13 (IL-13), promoting antibody production and T-cell responses. Notably, the resolution of malaria infection crucially relies on a fine-tuned balance of cytokine networks. Dysregulation or imbalances in these mediators often result in immune hyperactivation, contributing to severe manifestations and prolonged infection. Understanding the multi-faceted roles of cytokines in malaria clearance offers promising avenues for therapeutic interventions. Targeting cytokine pathways to restore immune equilibrium or bolster protective responses could potentially enhance treatment strategies and vaccine development. In conclusion, the pivotal role of cytokines in immunomodulation during malaria clearance underscores their significance as potential targets for therapeutic interventions, offering promising prospects in the global fight against this infectious disease.

The intrinsic rarity of equilibrium response in stratigraphic processes

Conventional sequence stratigraphy is based, explicitly or implicitly, on the hypothesis that steady external forcing results in a steady stratigraphic configuration (equilibrium response), so that an unsteady stratigraphic configuration is usually believed to result from unsteady external forcing. Recent advances in autostratigraphy, on the other hand, have led to a significantly different notion that steady external forcing generally results in an unsteady stratigraphic configuration (non-equilibrium response). To advance this debate, it is necessary to clarify what exactly is meant by a steady stratigraphic configuration. Here, we propose a quantitative criterion for defining the latter concept in terms of the straightness of the shoreline trajectory, and specifically a straight shoreline trajectory or the shoreline being held still as a sign to express steady stratigraphic configurations. In such a definition, a steady stratigraphic configuration means that the ratio of the rate of aggradation and the rate of progradation is constant, or one of these two rates is zero. Based on this criterion, a total of 7 types of steady stratigraphic configurations can be clarified, most of which require unsteady external forcing and are thus realized by non-equilibrium response, although special cases exist. The reason that non-equilibrium responses dominate the stacking of strata is that it is common for a growing basin-margin depositional system to change its surface area. The size-changing system will easily change the stacking pattern (unsteady stratigraphic configuration) if the external forcing is steady, or, if the steady stratigraphic configuration is maintained, the rate of external forcing must change in a particular pattern (unsteady external forcing). Equilibrium responses can occur, but in very special cases. Conventional sequence stratigraphy should take into account the importance of non-equilibrium response.

Local employment multiplier: Evidence from relocation of public-sector entities in South Korea

We exploit a series of public-sector entity relocations in South Korea as an exogenous source of variation in public sector employment to estimate the local employment multiplier. We find that the introduction of one public sector employment position increases private sector employment by one unit, primarily driven by the service sector. Consistent with existing literature, we document that the effect of public employment on private employment is highly localized. In addition to changes in private employment, we also discover that the relocations led to a positive net influx of residents into the treated neighborhoods; this effect is also localized. Lastly, by estimating the local employment multiplier for each relocation site, we document the heterogeneity of the local employment multiplier and provide suggestive evidence that this heterogeneity is shaped by the local economic environment’s capacity to accommodate additional general equilibrium responses.

Diagnosing the Quasi-Equilibrium Response of ENSO Variability under a Range of CO2 Levels

Abstract Several recent studies have highlighted differences in simulated properties of El Niño–Southern Oscillation (ENSO) under transient and equilibrium responses to increasing CO2. However, the reasons behind these disparate responses and the extent to which they are robust to different scales of CO2 forcing remain unclear. In this study, we adopt a climate system model with reduced SST bias in the eastern tropical Pacific and incrementally apply abrupt increases in CO2, analyzing outputs after each simulation reaches quasi-equilibrium with the imposed forcing. The results suggest that ENSO activity under quasi-equilibrium first increases and then decreases with increasing CO2, peaking in simulations with CO2 concentrations similar to the present day. Bjerknes–Jin stability analysis indicates that changes in the ENSO growth rate result primarily from changes in the thermocline feedback and thermodynamic damping terms. While thermodynamic damping increases monotonically with increasing CO2, the positive thermocline feedback varies within the range of internal variability up to twice the preindustrial value of CO2 and then weakens sharply with further increases. The mechanisms behind these changes include weaker mean ocean upwelling and weaker dynamical coupling between the atmosphere and subsurface ocean associated with substantial near-surface freshening at higher levels of CO2. These changes steepen the thermodynamic barrier to mixing between the surface and subsurface, weakening the east–west temperature gradient in the mean state and suppressing variability in the cold tongue. Analysis of similar model simulations from the Coupled Model Intercomparison Project (CMIP6) archive indicates that changes in the Bjerknes–Jin stability index are robust but do not establish a consensus as to the mechanisms behind them. Significance Statement This study investigates how El Niño–Southern Oscillation changes with increasing CO2 forcing by using a global model with improved tropical Pacific climate. The simulations roughly correspond to scenarios in which emissions are reduced to maintain CO2 concentrations at near-constant values over a long period, with levels ranging from about 2/3 to more than 5 times the present-day concentration. Analysis of these simulations suggests that ENSO activity is strongest when CO2 concentrations are similar to the present-day and becomes substantially weaker when CO2 is more than double its present-day value. Reduced ENSO activity with further increases in CO2 is caused by weaker interactions between the atmosphere and the subsurface ocean. Both the amplitude of warm (El Niño) events and the occurrence frequency of warm and cold (La Niña) events decrease as ENSO events become first more difficult to grow and then more difficult to trigger with increasing CO2.

Markov equilibrium of social security: An analytic solution under CRRA utility and the future of social security

The politico-economic sustainability of pay-as-you-go social security has been studied with the help of two-period overlapping generation models under Markovian equilibrium concepts. The literature has mostly used logarithmic utility for tractability, whereas versions under the more general isoelastic CRRA utility have only been analyzed computationally. This paper demonstrates that a prototypical social security model under CRRA utility has a closed-form solution; it revisits previously obtained computational conclusions and presents new findings and extensions. Quantitatively, the model can explain the observed path of payroll tax rates in the USA and predicts increased tax rates as the equilibrium response to lower future population growth rates. The model predicts a gradual increase in tax rates, from the current 12.4% to about 15% or so in 2060, and then staying at that level. Benefits are expected to decrease slowly, by about 2% (or less) per decade, starting in 2030.

Networks, Barriers, and Trade

We study a flexible class of trade models with international production networks and arbitrary wedge‐like distortions like markups, tariffs, or nominal rigidities. We characterize the general equilibrium response of variables to shocks in terms of microeconomic statistics. Our results are useful for decomposing the sources of real GDP and welfare growth, and for computing counterfactuals. Using the same set of microeconomic sufficient statistics, we also characterize societal losses from increases in tariffs and iceberg trade costs and dissect the qualitative and quantitative importance of accounting for disaggregated details. Our results, which can be used to compute approximate and exact counterfactuals, provide an analytical toolbox for studying large‐scale trade models and help to bridge the gap between computation and theory.

Equilibrium Responses to Price Controls: A Supply-Chain Approach

Equilibrium Responses to Price Controls: A Supply-Chain Approach

Use of DNA forceps to measure receptor-ligand dissociation equilibrium constants in a single-molecule competition assay.

The ability of biophysicists to decipher the behavior of individual biomolecules has steadily improved over the past thirty years. However, it still remains unclear how an ensemble of data acquired at the single-molecule level compares with the data acquired on an ensemble of the same molecules. We here propose an assay to tackle this question in the context of dissociation equilibrium constant measurements. A sensor is built by engrafting a receptor and a ligand onto a flexible dsDNA scaffold and mounting this assembly on magnetic tweezers. This way, looking at the position of the magnetic bead enables one to determine in real-time if the two molecular partners are associated or not. Next, to quantify the affinity of the scrutinized single-receptor for a given competitor, various amounts of the latter molecule are introduced in solution and the equilibrium response of the sensor is monitored throughout the titration protocol. Proofs of concept are established for the binding of three rapamycin analogs to the FKBP12 cis-trans prolyl isomerase. For each of these drugs the mean affinity constant obtained on a ten of individual receptors agrees with the one previously determined in a bulk assay. Furthermore, experimental contingencies are sufficient to explain the dispersion observed over the single-molecule values.

Impact of Transport Mechanism on Binding Kinematics and Sensitivity of FET Biosensors

In this work, the impact of bioanalyte concentration and the dominant transport mechanism of biomolecules on the binding kinematics of the target biomolecules at the sensing surface have been investigated in detail. A comprehensive analysis of the fundamental parameters such as equilibrium response time and equilibrium density of the binding molecules at the sensing surface considering different concentrations of the analytes and their transport mechanisms has been performed. The impact of these realistic artifacts on the current sensitivity of emerging junctionless field effect transistors (JLFETs) and tunnel field effect transistors (TFETs)-based ion-sensitive field effect transistor (ISFET) has been investigated. Moreover, depending on the bioanalyte concentration, design guidelines for the dimensions of the sensing surface have been provided for a minimum limit of detection (LOD). The impact of charge screening and nonspecific binding on current sensitivity has also been discussed in depth. We believe that the guidelines presented in this work will enable the community to conceptualize, understand, and design novel label-free biosensors more rationally considering the practical scenario.

A Novel Fiber-Reinforced Poroviscoelastic Bovine Intervertebral Disc Finite Element Model For Organ Culture Experiment Simulations.

Intervertebral disc (IVD) degeneration and methods for repair and regeneration have commonly been studied in organ cultures with animal IVDs under compressive loading. With the recent establishment of novel multiaxial organ culture systems, accurate predictions of the global and local mechanical response of the IVD are needed for control system development and to aid in experiment planning. This study aimed to establish a finite element model of bovine IVD capable of predicting IVD behavior at physiological and detrimental load levels. A finite element model was created based on the dimensions and shape of a typical bovine IVD used in organ culture. The nucleus pulposus (NP) was modelled as a neo-Hookean poroelastic material and the annulus fibrosus (AF) as a fiber-reinforced poroviscoelastic material. The AF consisted of 10 lamella layers and the material properties were distributed in radial direction. The model outcome was compared to a bovine IVD in a compressive stress-relaxation experiment. A parametric study was conducted to investigate the effect of different material parameters on the overall IVD response. The model was able to capture the equilibrium response, and the relaxation response at physiological and higher strain levels. Permeability and elastic stiffness of the AF fiber network affected the overall response most prominently. The established model can be used to evaluate the response of the bovine IVD at strain levels typical for organ culture experiments, to define relevant boundaries for such studies and to aid in the development and use of new multiaxial organ culture systems.

Demand, growth, and deleveraging

We present empirical evidence that weak household demand contributed to a reduction in firm entry in the Great Recession. Motivated by this evidence, we study the general equilibrium response of aggregate economic growth to a severe deleveraging event. To do so, we combine a standard incomplete markets model with a class of endogenous growth models. A large reduction in credit access causes the zero lower bound to bind, inducing a drop in demand via employment rationing. Decreased demand in turn lowers the return to entrepreneurship and innovation, endogenously lowering productivity. We find that a persistent recession induced by deleveraging can significantly influence growth in productivity. Our main result is a powerful feedback effect: households increase savings in response to future slow growth, exacerbate the fall in demand, and further slow the recovery.

The impact of a uniform ocean warming on the West African monsoon

Projections of West African Monsoon (WAM) precipitation are uncertain. To address this, an improved understanding of the mechanisms driving WAM precipitation change is needed to shed light on inter-model differences and aid model development. The full forcing of increased CO2 can be decomposed into different components such as the impact of ocean warming, or the direct radiative effect of increased CO2. This paper investigates such a decomposition, analysing the effect of a uniform 4K ocean warming whilst keeping atmospheric CO2 concentrations constant. The analysis highlights several mechanisms acting to decrease WAM precipitation over a range of timescales, from days after the abrupt ocean warming, to the long-term equilibrium response. The initial decrease in WAM precipitation is caused by warming and enhanced convection over the ocean, stabilising the atmosphere inland and disrupting the monsoon inflow at low levels. Later in the response (after about 5 days), the WAM precipitation is reduced through a strengthening of the shallow circulation over West Africa, associated with changes in the large-scale temperature gradients and a local warming of the atmosphere related to a soil moisture feedback mechanism over the Sahel. Finally, from around 20 days after the SST increase, the WAM precipitation is also reduced through changes in specific humidity gradients that lead to increased potency of dry air advection into the monsoon rainband. The analysis concludes by demonstrating that the processes affecting precipitation in the early stages of the response are also relevant to the long-term equilibrium response.

Inherited anthropogenic disturbance and decadal sediment dynamics in a mountain fluvial system: The case of the Marecchia River canyon, Northern Apennines

We evaluate decadal coarse sediment dynamics along the Marecchia River of the Northern Apennines, a fluvial system with a history of gravel mining that led to the incision of a 6-km-long canyon. To this purpose, we subdivided the river into 21 reaches, seen as sediment reservoirs, to examine (1) historical variations in active channel width (1955−2019) in conjunction with (2) change in alluvial sediment storage (2009−2019), by differencing two sequential LiDAR digital elevation models (DEMs) within the active channel footprint. Combined examination of lateral (widening or narrowing) and vertical (aggradation or degradation) channel changes allowed the identification of composite styles of reservoir adjustment, as well as the refinement of geomorphic inference solely based on changes in active channel width. In particular, we find that different styles of decadal adjustment (1) are compatible with supply- and transport-limited conditions, as constrained by degree of confinement, stream channel slope, and active channel width; and (2) indicate different stages of evolution at reservoirs located upstream and downstream of the canyon head (dynamic equilibrium vs. transient response). The persistence of this geomorphic divide is supported over historical time scales by distinctive trends in planform channel changes, suggesting that sedimentary signal propagation downstream becomes abruptly interrupted at the canyon head. Over this 10-year natural experiment, the spatial pattern of erosion along the canyon exemplifies a striking case of transient response to anthropogenic forcing, where decadal topographic change, modulated by varying styles of hillslope-channel coupling, declines nonlinearly downstream. Depth of incision along the canyon increases progressively upstream, suggesting that the canyon head has been evolving toward a more unstable configuration with no significant change in sediment supply. This tendency, which points to a possible runaway style of development as bedload wearing on weak pelitic side walls continues, may hold basic implications for our understanding of channel incision into bedrock and strath terrace formation.

The Time Scales of Climate Responses to Carbon Dioxide and Aerosols

Abstract The climate system responds to changes in the amount of atmospheric greenhouse gases or aerosols through rapid processes, triggered within hours and days, and through slower processes, where the full response may only be seen after centuries. In this paper, we aim to elucidate the mechanisms operating on time scales of hours to years to better understand the response of key climate quantities such as energy fluxes, temperature, and precipitation after a sudden increase in either carbon dioxide (CO2), black carbon (BC), or sulfate (SO4) aerosols. The results are based on idealized simulations from six global climate models. We find that the effect of changing ocean temperatures kicks in after a couple of months. Rapid precipitation reductions start occurring instantly and are established after just a few days. For BC, they constitute most of the equilibrium response. For CO2 and SO4, the magnitude of the precipitation response gradually increases as surface warming/cooling evolves, and for CO2, the sign of the response changes from negative to positive after 2 years. Rapid cloud adjustments are typically established within the first 24 h, and while the magnitude of cloud feedbacks for CO2 and SO4 increases over time, the geographical pattern of the equilibrium cloud change is present already after the first year. While there are model differences, our work underscores the overall similarity of the major time-varying processes and responses simulated by current global models and hence the robustness of key features of simulated responses to historical and future anthropogenic forcing. Significance Statement How does the climate system respond to a change in the amount of atmospheric greenhouse gases or aerosols? Some processes are rapid, responding within hours and days. Others are slow, and the full response to a forcing of the climate may only be seen after centuries. In this paper, we use six global climate models to investigate the time scales of climate responses to carbon dioxide, black carbon, and sulfate, focusing on key climate quantities, such as temperature, precipitation, and clouds. While there are ample model differences, our work underscores the overall similarity of the major time-varying processes and responses simulated by current global models and hence the robustness of key features of simulated responses to historical and future anthropogenic forcing.

Equilibrium and transient response of photo-actuated Liquid Crystal Elastomer beams

Light actuation is one of the preferred and advantageous approaches to remotely induce and control deformations in soft materials such as photoactive Liquid Crystal Elastomers (LCEs). Various experimental and numerical works have been carried out in the literature to study the actuation of photoactive LCE sheets under illumination. In this study, we have developed a reduced multi-physics model to predict the equilibrium and dynamic response of photoactive LCE beams under illumination. We test our model against an experiment in which a double-clamped thin nematic LCE beam is subjected to UV light, and the stress is generated in the beam due to induced contraction under illumination. Our numerical results demonstrate reasonable agreement with the experiment regarding stress evolution trend and saturation time. We also investigate the bending response of a photoactive LCE beam subjected to UV light. Based on our parameters, we observe that the nematic beam bends towards the light only due to the photochemical strain gradient along the thickness. Finally, to test our model in a dynamic situation, we perform the simulation for the self-oscillations of an LCE beam under illumination. We show that the alternate activation of the top and bottom surfaces of the LCE beam by uniform steady illumination can pump energy into the system, resulting in the phenomenon of self-oscillations.