Steady-state Dynamics Research Articles

Spontaneous symmetry breaking in generative diffusion models*

Abstract Generative diffusion models have recently emerged as a leading approach for generating high-dimensional data. In this paper, we show that the dynamics of these models exhibit a spontaneous symmetry breaking phenomenon that divides the generative dynamics into two distinct phases: (1) a linear steady-state dynamics around a central fixed-point and, (2) an attractor dynamics directed towards the data manifold. These two ‘phases’ are separated by the change in stability of the central fixed-point, with the resulting window of instability being responsible for the diversity of the generated samples. Using both theoretical and empirical evidence, we show that an accurate simulation of the early dynamics does not significantly contribute to the final generation, since early fluctuations are reverted to the central fixed point. To leverage this insight, we propose a Gaussian late initialization scheme, which significantly improves model performance, achieving up to 3× Fréchet inception distance improvements on fast samplers, while also increasing sample diversity (e.g. racial composition of generated CelebA images). Our work offers a new way to understand the generative dynamics of diffusion models that has the potential to bring about higher performance and less biased fast-samplers.

The Impact of Flow-Thermal Characteristics in Ship-Board Solid Oxide Fuel Cells

Hydrogen is increasingly recognized as a clean and reliable energy vector for decarbonization in the future. In the marine sector, marine solid oxide fuel cells (SOFCs) that employ hydrogen as an energy source have already been developed. In this study, a multi-channel plate-anode-loaded SOFC was taken as the research object. A three-dimensional steady-state computational fluid dynamics (CFD) model for anode-supported SOFC was established, which is based on the mass conservation, energy conservation, momentum conservation, electrochemical reactions, and charge transport equations, including detailed geometric shapes, model boundary condition settings, and the numerical methods employed. The polarization curves calculated from the numerical simulation were compared with experimental results from the literature to verify the model’s accuracy. The curved model was applied by enlarging the flow channels or adding blocks. Numerical calculations were employed to obtain the current density, temperature distribution, and component concentration distribution under the operating conditions of the SOFC. Subsequently, the distribution patterns of various physical parameters during the SOFC operation were analyzed. Compared to the classical model, the temperature of the curved model was reduced by 1.3%, and the velocities of the cathode and anode were increased by 4.9% and 5.0%, respectively, with a 2.42% enhancement in performance. The findings of this study provide robust support for research into and the application of marine SOFCs, and offer they insights into how we may achieving “dual carbon” goals.

Frequency domain solution method for electromagnetic influence analysis on torsional vibrations

In electric motor-driven machines, mechanical torsional dynamics are nonlinearly coupled with the electrical system through the electromagnetic torque and the counter-electromotive force. In this paper, an approach based on small-signal linearization is proposed for modeling the steady-state torsional dynamics of the coupled system. Using the linearized model, resonance interference diagrams, torsional response, and stability can be evaluated rapidly across numerous operating points, while accurately accounting for the electromagnetic effects. The model is validated with conventional time-stepping simulations of two induction machines. An example analysis of a 3 MW motor-driven compressor train displays the modification of torsional properties due to the electromagnetic coupling effect and explains the mechanism of torsional destabilization. Finally, previously published measurements of a 37 kW motor test bench are considered to validate the instability of the elastic torsional mode predicted by the model.

Modeling the Effects of Increased Hurricane Frequency on the Tropical Forest Carbon Cycle

AbstractModels project that climate change is increasing the frequency of severe storm events such as hurricanes. Hurricanes are an important driver of ecosystem structure and function in tropical coastal and island regions and thus impact tropical forest carbon (C) cycling. We used the DayCent model to explore the effects of increased hurricane frequency on humid tropical forest C stocks and fluxes at decadal and centennial timescales. The model was parameterized with empirical data from the Luquillo Experimental Forest (LEF), Puerto Rico. The DayCent model replicated the well-documented cyclical pattern of forest biomass fluctuations in hurricane-impacted forests such as the LEF. At the historical hurricane frequency (60 years), the dynamic steady state mean forest biomass was 80.9 ± 0.8 Mg C/ha during the 500-year study period. Increasing hurricane frequency to 30 and 10 years did not significantly affect net primary productivity but resulted in a significant decrease in mean forest biomass to 61.1 ± 0.6 and 33.2 ± 0.2 Mg C/ha, respectively (p < 0.001). Hurricane events at all intervals had a positive effect on soil C stocks, although the magnitude and rate of change of soil C varied with hurricane frequency. However, the gain in soil C stocks was insufficient to offset the larger losses from aboveground biomass C over the time period. Heterotrophic respiration increased with hurricane frequency by 1.6 to 4.8%. Overall, we found that an increasing frequency of tropical hurricanes led to a decrease in net ecosystem production by − 0.2 ± 0.08 Mg C/ha/y to − 0.4 ± 0.04 Mg C/ha/y for 30–10-year hurricane intervals, respectively, significantly increasing the C source strength of this forest. These results demonstrate how changes in hurricane frequency can have major implications for the tropical forest C cycle and limit the potential for this ecosystem to serve as a net C sink.

Analyzing steady-state equilibria and bifurcations in a time-delayed SIR epidemic model featuring Crowley-Martin incidence and Holling type II treatment rates

This article presents a time-delayed SIR epidemiological model that has been quantitatively examined. The model incorporates a logistic growth function for the susceptible population, a Crowley-Martin type incidence, and Holling type II treatment rates. We investigated two separate time delays. The first delay refers to the rate at which new infections occur, allowing us to evaluate the impact of the latent period. The second delay relates to the rate of treatment for those who have contracted the infection, which allows us to examine the consequences of postponed access to therapy. The investigation of the steady-state behavior of the model emphasizes two equilibria, namely, the infection-free equilibrium and the endemic equilibrium. The determination of critical values involves the use of the fundamental reproduction number, denoted R0, which serves as a predictive measure to determine the potential elimination of a disease within a specific population. Using the fundamental reproduction number, it can be shown that infection-free equilibrium exhibits local asymptotic stability when the value of R0 is less than 1. In contrast, when R0 exceeds 1, the infection-free equilibrium becomes unstable in the context of the time-delayed system. Furthermore, an analysis of the steady-state dynamics of the endemic equilibrium indicates the appearance of oscillations and periodic solutions with the Hopf bifurcation for all feasible combinations of two-time delays as the bifurcated parameter. In sensitivity analysis, a sensitivity index is utilized to evaluate the relative modification in the fundamental reproduction number caused by each parameter. In summary, numerical simulations are employed to offer empirical evidence for the theoretical findings.

Modeling nitrogen behavior in Tigris River using system dynamics approach

Nitrogen behavior across multimedia environment like Tigris River is complex process resulting in a number of interactions of the biogeochemical processes. A solid understanding of the interacted processes is critical to evaluate river system performance. Inorganic nitrogen including ammonium ion (NH4+), free ammonia (NH3), total ammoniacal nitrogen (NHx), nitrite (NO2−), nitrate (NO3−), total oxidized nitrogen (NOx), and total inorganic nitrogen (TIN) in Tigris River were examined from April 2018 to March 2020. A simple system model was implemented to simulate and to help interpret the trend of inorganic N forms based on datasets collected from the river system. It is indicated that the obtained results revealed that the dynamic model was able to represent and predict NHx and NOx behavior in Tigris River. Root mean squared errors between actual and predicted concentrations for NHx and NOx were 0.053 and 0.312 g m−3, respectively. Modeling analysis confirmed the steady-state dynamics of NHx and NOx over the course of the study. Average concentration for NHx was 0.37 ± 0.05 g m−3, while mean value of NOx levels was 2.18 ± 0.33 g m−3 in the Tigris river water. The results from this study also supported by the changes of the water budget, chemical oxygen demand, pH, dissolved oxygen, electrical conductivity, and water temperature in the river system. The results suggest that the microbial mechanisms are the principal N transformation processes in the river system. Findings presented in this research could help to improve conceptual understanding of N behavior in Tigris River, and therefore could assist decision makers to select best management practices and to develop mitigation strategies to sustain water quality in Tigris River.

Whence and wherefore IgE?

Despite the near ubiquitous presence of Ig-based antibodies in vertebrates, IgE is unique to mammals. How and why it emerged remains mysterious. IgE expression is greatly constrained compared to other IgH isotypes. While other IgH isotypes are relatively abundant, soluble IgE has a truncated half-life, and IgE plasma cells are mostly short-lived. Despite its rarity, IgE is consequential and can trigger life-threatening anaphylaxis. IgE production reflects a dynamic steady state with IgG memory B cells feeding short-lived IgE production. Emerging evidence suggests that IgE may also potentially be produced in longer-lived plasma cells as well, perhaps as an aberrancy stemming from its evolutionary roots from an antibody isotype that likely functioned more like IgG. As a late derivative of an ancient systemic antibody system, the benefits of IgE in mammals likely stems from the antibody system's adaptive recognition and response capability. However, the tendency for massive, systemic, and long-lived production, common to IgH isotypes like IgG, were likely not a good fit for IgE. The evolutionary derivation of IgE from an antibody system that for millions of years was good at antigen de-sensitization to now functioning as a highly specialized antigen-sensitization function required heavy restrictions on antibody production-insufficiency of which may contribute to allergic disease.

Measuring the Equilibrium Spreading Pressure-A Tale of Three Amphiphiles.

A surfactant's equilibrium spreading pressure (ESP) is the maximum decrease in surface tension achievable at equilibrium below the Krafft point. Difficulties in measuring the ESP have been noted previously but no well-established experimental protocols to overcome them exist. We present a case study of three solid amphiphiles with different propensities to spread on the air-water interface. Starting with the partially water soluble n-dodecanol (C12H25OH), which spreads instantaneously. The strong Marangoni flows associated with the spreading result in the dislocating of the Wilhelmy plate or crystals attaching to it. A temporary mechanical barrier in front of the spreading crystals mitigates the flows disturbing the plate. Presaturating the subphase with the amphiphile prevents the establishment of dynamic steady states, reduces the standard error by a factor of three and causes faster equilibration. The perfluoroalkylated analog of dodecanol (11:1 fluorotelomer alcohol, C11F23CH2OH) is slow spreading. With surfactant crystals on the interface, the surface pressure reaches a pre-equilibrium plateau within an hour, followed by equilibration on day-long timescales. We show that it is better to estimate the ESP by averaging the values of multiple pre-equilibrium plateaus rather than waiting for equilibrium to be established. Finally, the nonspreading amphiphile DPPC exhibits a large barrier for the mass transfer from the DPPC crystal to the aqueous surface. This was overcome by introducing a volatile, water-immiscible solvent deposited on the surface next to the crystals to facilitate the spreading process and leave behind a monolayer.

An introduction to phase ordering in scalar active matter

AbstractThese notes provide an introduction to phase ordering in dry, scalar active matter. We first briefly review Model A and Model B, the long-standing continuum descriptions of ordering in systems with a non-conserved and conserved scalar order parameter. We then contrast different ways in which the field theories can be extended so that the phase ordering persists, but in systems that are active and do not reach thermodynamic equilibrium. The active models allow a wide range of dynamical steady states not seen in their passive counterparts. These include microphase separation, active foams and travelling density bands.

Rigid flocks, undulatory gaits, and chiral foldamers in a chemically active polymer

Active matter systems—such as a collection of active colloidal particles—operate far from equilibrium with complex inter-particle interactions that govern their collective dynamics. Predicting the collective dynamics of such systems may aid the design of self-shaping structures comprised of active colloidal units with a prescribed dynamical function. Here, using simulations and theory, we study the collective dynamics of a chain consisting of active Brownian particles with internal interactions via trail-mediated chemicals, connected by harmonic springs in two dimensions to obtain design principles for active colloidal molecules. We show that two-dimensional confinement and chemo-repulsive interactions between the freely-jointed particles lead to an emergent rigidity of the chain in the steady-state dynamics. In the chemo-attractive regime, the chain collapses into crystals that abruptly halt their motion. Further, in a chain consisting of a binary mixture of monomers, we show that non-reciprocal chemical affinities between distinct species give rise to novel phenomena, such as chiral molecules with tunable dynamics, sustained undulatory gaits and reversal of the direction of motion. Our results suggest a novel interpretation of the role of trail-mediated interactions, in addition to providing active self-assembly principles arising due to non-reciprocal interactions.

Probing energy transfer in luminescent CaMoO4:Tb3+ by steady state and decay dynamics

Polyvinylpyrrolidone functionalized CaMoO4:Tb3+ were synthesized hydrothermally. The formation of tetragonal phase CaMoO4:Tb3+ and morphology of nanoparticles are thoroughly studied with XRD, TEM and FT-IR spectroscopy. Nanophosphors show green emission of Tb3+ at 544 nm when excited at 290 nm due to MoO42− absorption. The energy transfer from the host MoO42− to the activator Tb3+ is occurred mainly through dipole-dipole interactions. The decay lifetime of MoO42− emission decreases from ∼13 to 1 μs with the increase in Tb3+ concentration indicating occurrence of energy transfer. This is further corroborated with the calculation of radiative and non-radiative decay rates. The quantum yield and CIE color chromaticity are also studied.

Collisionless Magnetorotational Turbulence in Pair Plasmas: Steady-State Dynamics, Particle Acceleration, and Radiative Cooling.

We present 3D fully kinetic shearing-box simulations of pair-plasma magnetorotational turbulence with unprecedented macro-to-microscopic scale separation. While retrieving the expected fluid behavior of the plasma at large scales, we observe a steepening of turbulent spectra at kinetic scales and substantial angular-momentum transport linked with kinetic processes. For the first time, we provide a definitive demonstration of nonthermal particle acceleration in kinetic magnetorotational turbulence agnostically of shearing-box initial conditions by means of a novel strategy exploiting synchrotron cooling.

Dynamic swarms regulate the morphology and distribution of soft membrane domains.

We study the dynamic structure of lipid domain inclusions embedded within a phase-separated reconstituted lipid bilayer in contact with a swarming flow of gliding filamentous actin. Passive circular domains transition into highly deformed morphologies that continuously elongate, rotate, and pinch off into smaller fragments, leading to a dynamic steady state with ≈23× speedup in the relaxation of the intermediate scattering function compared with passive membrane domains driven by purely thermal forces. To corroborate experimental results, we develop a phase-field model of the lipid domains with two-way coupling to the Toner-Tu equations. We report phase domains that become entrained in the chaotic eddy patterns, with oscillating waves of domains that correlate with the dominant wavelengths of the Toner-Tu flow fields.

Inferring potential landscapes: A Schrödinger bridge approach to maximum caliber

Schrödinger bridges have emerged as an enabling framework for unveiling the stochastic dynamics of systems based on marginal observations at different points in time. The terminology “bridge” refers to a probability law that suitably interpolates such marginals. The theory plays a pivotal role in a variety of contemporary developments in machine learning, stochastic control, thermodynamics, and biology, to name a few, impacting disciplines such as single-cell genomics, meteorology, and robotics. In this work, we extend Schrödinger's paradigm of bridges to account for integral constraints along paths, in a way akin to maximum caliber—a maximum entropy principle applied in a dynamic context. The maximum caliber principle has proven useful to infer the dynamics of complex systems, e.g., model gene circuits and protein folding. We unify these two problems via a maximum likelihood formulation to reconcile stochastic dynamics with ensemble-path data. A variety of data types can be encompassed, ranging from distribution moments to average currents along paths. The framework enables inference of time-varying potential landscapes that drive the process. The resulting forces can be interpreted as the optimal control that drives the system in a way that abides by specified integral constraints. This, in turn, relates to a similarly constrained optimal mass transport problem in the zero-noise limit. Analogous results are presented in a discrete-time, discrete-space setting and specialized to steady-state dynamics. We finish by illustrating the practical applicability of the framework through paradigmatic examples, such as that of bit erasure or protein folding. In doing so, we highlight the strengths of the proposed framework, namely, the generality of the theory, its elegant analytical structure, the ease of computation, and the ability to interpret results in terms of system dynamics. This is in contrast to maximum caliber problems where the focus is typically on updating a probability law on paths. Published by the American Physical Society 2024

Impact of deforestation on the hydrogen, oxygen and iron isotope compositions of Amazonian streams

We examined the consequences of deforestation and pasture establishment on H, O and Fe isotope cycling in the hydrosphere, with focus on small watersheds from the central and eastern part of Brazilian Amazonia. The δ18O- δD relationships in stream water samples show that the evaporation effect is greater in pasture than in forest, thereby highlighting the impact of deforestation on atmospheric water circulation and rainfall.A clear effect of deforestation was also found on the dissolved load of these streams. Water temperature, pH, conductivity, major cations and dissolved carbon organic content are lower in forest streams compared to those from deforested areas. Dissolved (i.e., filtrate <0.45 μm) iron concentrations are typically higher in these tropical forest streams. They also show δ57Fe signatures commonly higher than that of the continental crust (i.e., > 0.1‰). In these black waters enriched in organic matter, the heavier iron isotope composition in the forested areas is related to the oxidized Fe strongly bound to colloidal organic matter. On the other hand, dissolved iron from streams draining older deforested areas shows isotopic compositions usually lighter than the continental crust (δ57Fe < 0.1‰). The negative δ57Fe signatures of these areas are likely caused by deforestation involving erosion and rejuvenation of soils in valleys, which leads to the occurrence of a partial iron reduction in the soils. These modifications increased the proportion of isotopically light, dissolved and more reduced Fe in the streams.Those effects are less obvious on more recent pastures since they display more chemical and isotopic scatter along the sampling months. In a stream flowing through an area undergoing slash and burned deforestation within the year, dissolved iron concentrations and isotopic compositions are much more scattered, with δ57Fe values varying by >10 ‰ as a result of fire or heavy rain events. This likely depicts the disruption of the iron cycling in the water-soil-plant system with strong changes in the soil mineralogy, organic matter characteristics and biomass activity resulting from the forest fire. Our results suggest that more than a decade is needed to reach a new dynamic steady state of the Fe biogeochemical cycle in pastures.Hence, the contrasted Fe isotopic compositions between the streams draining pristine tropical forests and those from deforested areas indicate that, like H and O isotopes, Fe isotopes are a sensitive indicator of the transformations affecting the biogeochemical cycling of tropical environment in response to deforestation. However, in contrast to hydrogen and oxygen isotopes that reveal the exchanges between surface waters and atmosphere, iron isotopes rather highlight the physical-chemical reactions occurring between surface waters and the soils, but with the biomass mediation for all three isotopic tracers.

Symmetry and stability of orientationally ordered collective motions of self-propelled, semiflexible filaments

Ordered, collective motions commonly arise spontaneously in systems of many interacting, active units, ranging from cellular tissues and bacterial colonies to self-propelled colloids and animal flocks. Active phases are especially rich when the active units are sufficiently anisotropic to produce liquid crystalline order and thus active nematic phenomena, with important biophysical examples provided by cytoskeletal filaments including microtubules and actin. Gliding assay experiments have provided a test bed to study the collective motions of these cytoskeletal filaments and unlocked diverse collective active phases, including states with long-range orientational order. However, it is not well understood how such long-range order emerges from the interplay of passive and active aligning mechanisms. We use Brownian dynamics simulations to study the collective motions of semiflexible filaments that self-propel in quasi-two-dimensions, in order to gain insights into the aligning mechanisms at work in these gliding assay systems. We find that, without aligning torques in the microscopic model, long-range orientational order can only be achieved when the filaments are able to overlap. The symmetry (nematic or polar) of the long-range order that first emerges is shown to depend on the energy cost of filament overlap and on filament flexibility. However, our model also predicts that a long-range-ordered active nematic state is merely transient, whereas long-range polar order is the only active dynamical steady state in systems with finite filament rigidity. Published by the American Physical Society 2024

Steady-state multiscale CFD simulation of a circulating fluidized bed riser

Compared to transient simulation, steady-state simulation of circulating fluidized bed risers is more efficient, but is also harder to perform due to the complex scale-dependency of dense gas-solid flows. In this work, steady-state computational fluid dynamics (CFD) simulation of a riser is performed using the steady energy-minimization multi-scale (EMMS) drag. It is found that the steady state corresponds to an extremely large scale of length and time, thus the grid size required in steady-state simulation is larger than that in transient one. The time-averaged two-fluid model (TFM) coupled with the steady-state EMMS/1M drag model enables a good prediction of the S-shaped, axial solids distribution and the choking transition, whereas the two-phase turbulence and solids stress models are important in predicting the radially core-annular distribution of solids. So far as we know, this is the first time that one can predict the choking transition in a steady-state CFD simulation. Further improvement may need an EMMS modeling of the time-averaged solid stresses.

Numerical simulation of all-vanadium redox flow battery performance optimization based on flow channel cross-sectional shape design

This paper numerically investigates optimizing trapezoidal flow channel cross-sectional shapes to improve all‑vanadium redox flow battery performance. A 3D steady-state multiphysics model coupling fluid dynamics, mass transfer, and electrochemistry was developed in COMSOL. Eight trapezoidal and one rectangular cross-section serpentine flow fields were simulated at varied flow rates. Results showed the TCS-T06 design reduced pressure drop by 12 % and pump power by 12 % versus the RCS. The concentration distribution of VO2+ was also improved, enhancing mass transfer. At 60 mA/cm2, TCS-T06 achieved 0.9 % higher pump power-based voltage efficiency. The optimized trapezoidal cross-section was proven to minimize losses, improve electrolyte distribution, and enhance VRFB performance. This work provides guidance for optimizing trapezoidal flow channel cross-sections to improve VRFB performance via enhanced mass transfer and reduced pressure drop.

Investigating binary granular mixing in a rotating drum using ultrafast X-ray computed tomography

The transient mixing dynamics of an initially segregated binary granular system in a half-filled rotating drum are experimentally investigated. The granular system consists of spherical beads having identical size. The density ratio between the two granular phases is 2.8. With its ability to scan three-dimensional opaque systems with a high frequency, the ultrafast X-ray computed tomography is used to capture the transient and steady-state segregation dynamics in the bulk. The segregation dynamics are also compared to those at the circular end-wall caps, which have been captured with a camera. The results show an axial migration of the denser particles towards the bulk and, more importantly, second-order overshooting dynamics in the radial mixing index, which tend to increase with the Froude number. The results will find application in industrial systems, where rapid mixing occurs. We also believe the presented data can serve as validation for future three-dimensional simulations focusing on the transient formation of segregation patterns in the bulk.

Transient simulation of the electrical hysteresis in a metal/polymer/metal nanostructure.

The time-dependent quantum transportation through a metal/polymer/metal system is theoretically investigated on the basis of a Su-Schrieffer-Heeger model combined with the hierarchical equations of motion formalism. Using a non-adiabatic dynamical method, the evolution of the electron subspace and lattice atoms with time can be obtained. It is found that the calculated transient currents vary with time and reach stable values after a response time under the bias voltages. However, the stable current as the system reaches its dynamical steady state exhibits a discrepancy between two sweep directions of the bias voltage, which results in pronounced electrical hysteresis loops in the current-voltage curve. By analyzing the evolution of instantaneous energy eigenstates, the occupation number of the instantaneous eigenstates, and the lattice of the polymer, we show that the formation of excitons and the delay of their annihilation are responsible for the hysteretic current-voltage characteristics, where electron-phonon interactions play the key factor. Furthermore, the hysteresis width and amplitude can also be modulated by the strength of the electron-phonon coupling, level-width broadening function, and temperature. We hope these results about past condition-dependent switching performance at a sweep voltage can provide further insight into some of the basic issues of interest in hysteresis processes in conducting polymers.