Power-law Growth Research Articles

Cumulative geometric frustration and superextensive energy scaling in a nonlinear classical XY -spin model

Geometric frustration results from a discrepancy between the locally favored arrangement of the constituents of a system and the geometry of the embedding space. Geometric frustration can be either noncumulative, which implies an extensive energy growth, or cumulative, which implies superextensive energy scaling and highly cooperative ground-state configurations which may depend on the dimensions of the system. Cumulative geometric frustration was identified in a variety of continuous systems including liquid crystals, filament bundles, and molecular crystals. However, a spin-lattice model which clearly demonstrates cumulative geometric frustration was lacking. In this paper we describe a nonlinear variation of the XY-spin model on a triangular lattice that displays cumulative geometric frustration. The model is studied numerically and analyzed in three distinct parameter regimes, which are associated with different energy minimizing configurations. We show that, despite the difference in the ground-state structure in the different regimes, in all cases the superextensive power-law growth of the frustration energy for small domains grows with the same universal exponent that is predicted from the structure of the underlying compatibility condition.

Growth kinetics and power laws indicate distinct mechanisms of cell-cell interactions in the aggregation process

Cellular aggregation is a complex process orchestrated by various kinds of interactions depending on the environment. Different interactions give rise to different pathways of cellular rearrangement and the development of specialized tissues. To distinguish the underlying mechanisms, in this theoretical work, we investigate the spontaneous emergence of tissue patterns from an ensemble of single cells on a substrate following three leading pathways of cell-cell interactions, namely, direct cell adhesion contacts, matrix-mediated mechanical interaction, and chemical signaling. Our analysis shows that the growth kinetics of the aggregation process are distinctly different for each pathway and bear the signature of the specific cell-cell interactions. Interestingly, we find that the average domain size and the mass of the clusters exhibit a power law growth in time under certain interaction mechanisms hitherto unexplored. Further, as observed in experiments, the cluster size distribution can be characterized by stretched exponential functions showing distinct cellular organization processes.

Water Availability Controls the Biomass Increment of Melia dubia in South India

Farmland tree cultivation is considered an important option for enhancing wood production. In South India, the native leaf-deciduous tree species Melia dubia is popular for short-rotation plantations. Across a rainfall gradient from 420 to 2170 mm year–1, we studied 186 farmland woodlots between one and nine years in age. The objectives were to identify the main factors controlling aboveground biomass (AGB) and growth rates. A power-law growth model predicts an average stand-level AGB of 93.8 Mg ha–1 for nine-year-old woodlots. The resulting average annual AGB increment over the length of the rotation cycle is 10.4 Mg ha–1 year–1, which falls within the range reported for other tropical tree plantations. When expressing the parameters of the growth model as functions of management, climate and soil variables, it explains 65% of the variance in AGB. The results indicate that water availability is the main driver of the growth of M. dubia. Compared to the effects of water availability, the effects of soil nutrients are 26% to 60% smaller. We conclude that because of its high biomass accumulation rates in farm forestry, M. dubia is a promising candidate for short-rotation plantations in South India and beyond.

Controlled Release Study on Bifidocin A from a Polyvinyl Alcohol/Chitosan Blend Particle-Based Biodegradable and Active Packaging Coupled with Mechanistic Assessment and Experimental Modeling.

On the basis of PVA-CS, which is incorporated with Bifidocin A, anti-microbial biodegradable films were prepared, characterized by their abilities to control the Bifidocin A's total release rate into foods as needed for packaging of active foods. This study aimed to explore the anti-microbial effects and release kinetics of active substances in polyvinyl alcoholchitosan (PVA-CS) particle composite films added with Bifidocin A. Pseudomonas fluorescens was used as indicator bacteria to evaluate the anti-microbial activity of the films. Fick's law, power law and negative exponential growth model were applied to further study the release kinetics of Bifidocin A. The results revealed that the composite films of PVA and CS had better mechanical properties and anti-microbial activity when the content of Bifidocin A was 50% with 1:1 PVA/CS, but it impairs the structure of the film, which can be resolved by including a suitable amount of grycerol. The anti-microbial was released faster at higher temperature and concentration of Bifidocin A, and the diffusion coeffcients increased significantlywith the increase of temperature and concentration. According to the thermodynamic parameters, the release of Bifidocin A was endothermic and spontaneous. High correlation factors (R² > 0.99) were acquired by fitting the release data of the Bifidocin A with the negative exponential growth model. The potential of Bifidocin A to deliver from the films into the food analog appropriately at low temperatures favored the obtained active films to be applied on food packaging, especially suitable for refrigerated foods.

A new logistic growth model applied to COVID-19 fatality data

Background:Recent work showed that the temporal growth of the novel coronavirus disease (COVID-19) follows a sub-exponential power-law scaling whenever effective control interventions are in place. Taking this into consideration, we present a new phenomenological logistic model that is well-suited for such power-law epidemic growth. Methods:We empirically develop the logistic growth model using simple scaling arguments, known boundary conditions and a comparison with available data from four countries, Belgium, China, Denmark and Germany, where (arguably) effective containment measures were put in place during the first wave of the pandemic. A non-linear least-squares minimization algorithm is used to map the parameter space and make optimal predictions. Results:Unlike other logistic growth models, our presented model is shown to consistently make accurate predictions of peak heights, peak locations and cumulative saturation values for incomplete epidemic growth curves. We further show that the power-law growth model also works reasonably well when containment and lock down strategies are not as stringent as they were during the first wave of infections in 2020. On the basis of this agreement, the model was used to forecast COVID-19 fatalities for the third wave in South Africa, which was in progress during the time of this work. Conclusion:We anticipate that our presented model will be useful for a similar forecasting of COVID-19 induced infections/deaths in other regions as well as other cases of infectious disease outbreaks, particularly when power-law scaling is observed.

Antigen receptor therapy in bone metastasis via optimal control for different human life stages

In this work we propose a bone metastasis model using power law growth functions in order to describe the biochemical interactions between bone cells and cancer cells. Experimental studies indicate that bone remodeling cycles are different for human life stages: childhood, young adulthood, and adulthood. In order to include such differences in our study, we estimate the model parameter values for each human life stage via bifurcation analysis. Results reveal an intrinsic relationship between the active period of remodeling cycles and the proliferation of cancer cells. Subsequently, using optimal control theory we analyze a possible antigen receptor therapy as a new treatment for bone metastasis. Theoretical results such as existence of optimal solutions are proved. Numerical simulations for late stages of bone metastasis are presented and a discussion of our results is carried out.

Stability of expanding accretion shocks for an arbitrary equation of state

We present a theoretical stability analysis for an expanding accretion shock that does not involve a rarefaction wave behind it. The dispersion equation that determines the eigenvalues of the problem and the explicit formulae for the corresponding eigenfunction profiles are presented for an arbitrary equation of state and finite-strength shocks. For spherically and cylindrically expanding steady shock waves, we demonstrate the possibility of instability in a literal sense, a power-law growth of shock-front perturbations with time, in the range of$h_c< h<1+2 {\mathcal {M}}_2$, where$h$is the D'yakov-Kontorovich parameter,$h_c$is its critical value corresponding to the onset of the instability and${\mathcal {M}}_2$is the downstream Mach number. Shock divergence is a stabilizing factor and, therefore, instability is found for high angular mode numbers. As the parameter$h$increases from$h_c$to$1+2 {\mathcal {M}}_2$, the instability power index grows from zero to infinity. This result contrasts with the classic theory applicable to planar isolated shocks, which predicts spontaneous acoustic emission associated with constant-amplitude oscillations of the perturbed shock in the range$h_c< h<1+2 {\mathcal {M}}_2$. Examples are given for three different equations of state: ideal gas, van der Waals gas and three-terms constitutive equation for simple metals.

Subdiffusive dynamics and critical quantum correlations in a disorder-free localized Kitaev honeycomb model out of equilibrium

Disorder-free localization has recently emerged as a mechanism for ergodicity breaking in homogeneous lattice gauge theories. In this work we show that this mechanism can lead to unconventional states of quantum matter as the absence of thermalization lifts constraints imposed by equilibrium statistical physics. We study a Kitaev honeycomb model in a skew magnetic field subject to a quantum quench from a fully polarized initial product state and observe nonergodic dynamics as a consequence of disorder-free localization. We find that the system exhibits a subballistic power-law entanglement growth and quantum correlation spreading, which is otherwise typically associated with thermalizing systems. In the asymptotic steady state the Kitaev model develops volume-law entanglement and power-law decaying dimer quantum correlations even at a finite energy density. Our work sheds light onto the potential for disorder-free localized lattice gauge theories to realize quantum states in two dimensions with properties beyond what is possible in an equilibrium context.

Nontrivial maturation metastate-average state in a one-dimensional long-range Ising spin glass: Above and below the upper critical range.

Understanding the low-temperature pure state structure of spin glasses remains an open problem in the field of statistical mechanics of disordered systems. Here we study Monte Carlo dynamics, performing simulations of the growth of correlations following a quench from infinite temperature to a temperature well below the spin-glass transition temperature T_{c} for a one-dimensional Ising spin-glass model with diluted long-range interactions. In this model, the probability P_{ij} that an edge {i,j} has nonvanishing interaction falls as a power law with chord distance, P_{ij}∝1/R_{ij}^{2σ}, and we study a range of values of σ with 1/2<σ<1. We consider a correlation function C_{4}(r,t). A dynamic correlation length that shows power-law growth with time ξ(t)∝t^{1/z} can be identified in the data and, for large time t,C_{4}(r,t) decays as a power law r^{-α_{d}} with distance r when r≪ξ(t). The calculation can be interpreted in terms of the maturation metastate averaged Gibbs state, or MMAS, and the decay exponent α_{d} differentiates between a trivial MMAS (α_{d}=0), as expected in the droplet picture of spin glasses, and a nontrivial MMAS (α_{d}≠0), as in the replica-symmetry-breaking (RSB) or chaotic pairs pictures. We find nonzero α_{d} even in the regime σ>2/3 which corresponds to short-range systems below six dimensions. For σ<2/3, the decay exponent α_{d} follows the RSB prediction for the decay exponent α_{s}=3-4σ of the static metastate, consistent with a conjectured statics-dynamics relation, while it approaches α_{d}=1-σ in the regime 2/3<σ<1; however, it deviates from both lines in the vicinity of σ=2/3.

A Refutation of Finite-State Language Models through Zipf's Law for Factual Knowledge.

We present a hypothetical argument against finite-state processes in statistical language modeling that is based on semantics rather than syntax. In this theoretical model, we suppose that the semantic properties of texts in a natural language could be approximately captured by a recently introduced concept of a perigraphic process. Perigraphic processes are a class of stochastic processes that satisfy a Zipf-law accumulation of a subset of factual knowledge, which is time-independent, compressed, and effectively inferrable from the process. We show that the classes of finite-state processes and of perigraphic processes are disjoint, and we present a new simple example of perigraphic processes over a finite alphabet called Oracle processes. The disjointness result makes use of the Hilberg condition, i.e., the almost sure power-law growth of algorithmic mutual information. Using a strongly consistent estimator of the number of hidden states, we show that finite-state processes do not satisfy the Hilberg condition whereas Oracle processes satisfy the Hilberg condition via the data-processing inequality. We discuss the relevance of these mathematical results for theoretical and computational linguistics.

Power-Law Growth of the Oxide in the Self-Limiting Oxidation of Si Nanowires

Thermal oxidation of Si nanowires (SiNWs) is studied by two steps. First, it is studied by numerically integrating a reaction–diffusion equation in which the effects of stress in the oxide layer ar...

A unified description of mechanical and actuation fatigue crack growth in shape memory alloys

The damage tolerance approaches to fatigue rely on fracture mechanics concepts to explicitly account for the fatigue crack growth process. These approaches typically adopt the Paris equation, which relates the crack growth per cycle to the range of variation of the stress intensity factor, ΔK, during cyclic loading by means of experimentally calibrated parameters. Conditions on the validity of a single parameter description of the near crack tip stress and strain fields restrict the applicability of ΔK to fatigue crack growth resistance in Shape Memory Alloys (SMAs) under general thermomechanical loading paths. These conditions are substantially relaxed for the cyclic ΔJ–integral approach, which can achieve similitude over a wider range of loading conditions and geometric configurations. Thus, ΔJ qualifies as a potential unified descriptor of thermomechanical fatigue crack growth resistance in SMAs, an assertion, which is tested in this work for data from both purely mechanical and actuation fatigue crack growth experiments of a high temperature SMA, Ni50.3Ti29.7Hf20. In the latter, compact tension specimens are subjected to thermal cycling under constant load between an upper and a lower cycle temperature that allows for the stable phase to alternate in each cycle. It is shown here that a Paris-type power-law crack growth expression based on the ΔJ-integral can fit fatigue crack growth rate data from both types of experiments with a single set of parameters. This new analysis method for both actuation and mechanical fatigue crack growth rates provides a unified description for fatigue crack growth in SMAs and can allow estimating actuation fatigue crack growth rates, laborious and challenging to measure, from easier to detect mechanical fatigue crack growth rates.

Diagnosis and Prediction of IIGPS’ Countries Bubble Crashes during BREXIT

We herein employ an alternative approach to model the financial bubbles prior to crashes and fit a log-periodic power law (LPPL) to IIGPS countries (Italy, Ireland, Greece, Portugal, and Spain) during Brexit. These countries represent the five financially troubled economies of the Eurozone that have suffered the most during the Brexit referendum. It was found that all 77 crashes across the five IIGPS nations from 19 January 2015 until 17 February 2020 strictly followed a log-periodic power law or other LPPL signature. They all had a speculative bubble phase (following the power law growth) that was then followed by a sudden crash immediately after reaching a critical point. Furthermore, their pattern coefficients were similar as well. This study would surely assist policymakers around the Eurozone to predict future crashes with the help of these parameters.

A random walk Monte Carlo simulation study of COVID-19-like infection spread

Recent analysis of early COVID-19 data from China showed that the number of confirmed cases followed a subexponential power-law increase, with a growth exponent of around 2.2 (Maier and Brockmann, 2020). The power-law behavior was attributed to a combination of effective containment and mitigation measures employed as well as behavioral changes by the population. In this work, we report a random walk Monte Carlo simulation study of proximity-based infection spread. Control interventions such as lockdown measures and mobility restrictions are incorporated in the simulations through a single parameter, the size of each step in the random walk process. The step size l is taken to be a multiple of 〈r〉, which is the average separation between individuals. Three temporal growth regimes (quadratic, intermediate power-law and exponential) are shown to emerge naturally from our simulations. For l=〈r〉, we get intermediate power-law growth exponents that are in general agreement with available data from China. On the other hand, we obtain a quadratic growth for smaller step sizes l≲〈r〉∕2, while for large l the growth is found to be exponential. We further performed a comparative case study of early fatality data (under varying levels of lockdown conditions) from three other countries, India, Brazil and South Africa. We show that reasonable agreement with these data can be obtained by incorporating small-world-like connections in our simulations.

Evaporation Kinetics of Sessile Water Droplets on a Smooth Stainless Steel Surface at Elevated Temperatures and Pressures.

The evaporation of water droplets on a solid surface at elevated temperatures under a pressurized condition has not yet been well understood, although this phenomenon is of both theoretical and practical significance. In this work, water droplet evaporation on smooth stainless steel surfaces in nitrogen gas atmosphere at elevated pressures and temperatures (up to 2 MPa and 202.4 °C, respectively) was investigated experimentally. It was observed that the increase in pressure diminishes the proportion of the constant contact radius stage over the entire evaporation time, whereas an opposite trend was found when raising the temperature, due to the change in the surface pinning ability with pressure (and temperature). The results also suggested that the evaporation mode transition is mainly affected by temperature rather than pressure. In addition, the evaporation rate was calculated under various degrees of subcooling, revealing that the evaporation rate increases almost linearly with pressure when keeping the degree of subcooling constant. However, when fixing the test temperature, a nonlinear decrease of the evaporation rate with pressure was observed. A power law growth of the evaporation rate with temperature was also found at a constant pressure. Last, it was uncovered by a theoretical analysis that the saturated vapor concentration is the dominant factor dictating the evaporation rate.

Reynolds number dependence of Lyapunov exponents of turbulence and fluid particles.

The Navier-Stokes equations generate an infinite set of generalized Lyapunov exponents defined by different ways of measuring the distance between exponentially diverging perturbed and unperturbed solutions. This set is demonstrated to be similar, yet different, from the generalized Lyapunov exponent that provides moments of distance between two fluid particles below the Kolmogorov scale. We derive rigorous upper bounds on dimensionless Lyapunov exponent of the fluid particles that demonstrate the exponent's decay with Reynolds number Re in accord with previous studies. In contrast, terms of cumulant series for exponents of the moments have power-law growth with Re. We demonstrate as an application that the growth of small fluctuations of magnetic field in ideal conducting turbulence is hyperintermittent, being exponential in both time and Reynolds number. We resolve the existing contradiction between the theory, that predicts slow decrease of dimensionless Lyapunov exponent of turbulence with Re, and observations exhibiting quite fast growth. We demonstrate that it is highly plausible that a pointwise limit for the growth of small perturbations of the Navier-Stokes equations exists.

From diffusion in compartmentalized media to non-Gaussian random walks

In this work we establish a link between two different phenomena that were studied in a large and growing number of biological, composite and soft media: the diffusion in compartmentalized environment and the non-Gaussian diffusion that exhibits linear or power-law growth of the mean square displacement joined by the exponential shape of the positional probability density. We explore a microscopic model that gives rise to transient confinement, similar to the one observed for hop-diffusion on top of a cellular membrane. The compartmentalization of the media is achieved by introducing randomly placed, identical barriers. Using this model of a heterogeneous medium we derive a general class of random walks with simple jump rules that are dictated by the geometry of the compartments. Exponential decay of positional probability density is observed and we also quantify the significant decrease of the long time diffusion constant. Our results suggest that the observed exponential decay is a general feature of the transient regime in compartmentalized media.

The 2004–2005 Mt. Etna Compound Lava Flow Field: A Retrospective Analysis by Combining Remote and Field Methods

AbstractMapping lava flows frequently during effusive eruptions provides crucial parameters to better understand their dynamics, in turn improving our ability to model lava flow behavior. New photogrammetric methods have recently been developed, shifting the paradigm of photogrammetry from pure method to a multidisciplinary approach able to reduce the cost of volcanic monitoring and widen the potential spectrum of application. In this work, we demonstrate how multi‐view and single‐view photogrammetry methods can be used effectively to extract accurate quantitative information from photographs taken during routine surveys over an active lava flow. One intriguing advantage of these methods is that they can re‐use images acquired previously to extract new data from past eruptions. In particular, we reconstructed quantitatively the evolution of the lava flow field emplaced during 2004–2005 at Mt. Etna, subdivided in five eruptive phases from the earliest simple lava flows to the final compound lava field about 6 months later. Our results show that, in the first week of eruption, lava field formation was characterized by an increasing lava length that followed a power law growth and by a decreasing front velocity that followed a power law as well. Thereafter, the length increasing became almost constant until the developed lava tube system was able to drain the lava for long distances, with the area inundated by lava that grew linearly in the first 20 days. Finally, we demonstrate the crucial role that the syn‐eruptive DEMs acquisition could have to improve our understanding of the emplacement dynamics of complex lava fields.

Slow scrambling in extremal BTZ and microstate geometries

Out-of-time-order correlators (OTOCs) that capture maximally chaotic properties of a black hole are determined by scattering processes near the horizon. This prompts the question to what extent OTOCs display chaotic behaviour in horizonless microstate geometries. This question is complicated by the fact that Lyapunov growth of OTOCs requires nonzero temperature, whereas constructions of microstate geometries have been mostly restricted to extremal black holes.In this paper, we compute OTOCs for a class of extremal black holes, namely maximally rotating BTZ black holes, and show that on average they display “slow scrambling”, characterized by cubic (rather than exponential) growth. Superposed on this average power-law growth is a sawtooth pattern, whose steep parts correspond to brief periods of Lyapunov growth associated to the nonzero temperature of the right-moving degrees of freedom in a dual conformal field theory.Next we study the extent to which these OTOCs are modified in certain “superstrata”, horizonless microstate geometries corresponding to these black holes. Rather than an infinite throat ending on a horizon, these geometries have a very deep but finite throat ending in a cap. We find that the superstrata display the same slow scrambling as maximally rotating BTZ black holes, except that for large enough time intervals the growth of the OTOC is cut off by effects related to the cap region, some of which we evaluate explicitly.

Epidemiological model for the inhomogeneous spatial spreading of COVID-19 and other diseases.

We suggest a novel mathematical framework for the in-homogeneous spatial spreading of an infectious disease in human population, with particular attention to COVID-19. Common epidemiological models, e.g., the well-known susceptible-exposed-infectious-recovered (SEIR) model, implicitly assume uniform (random) encounters between the infectious and susceptible sub-populations, resulting in homogeneous spatial distributions. However, in human population, especially under different levels of mobility restrictions, this assumption is likely to fail. Splitting the geographic region under study into areal nodes, and assuming infection kinetics within nodes and between nearest-neighbor nodes, we arrive into a continuous, "reaction-diffusion", spatial model. To account for COVID-19, the model includes five different sub-populations, in which the infectious sub-population is split into pre-symptomatic and symptomatic. Our model accounts for the spreading evolution of infectious population domains from initial epicenters, leading to different regimes of sub-exponential (e.g., power-law) growth. Importantly, we also account for the variable geographic density of the population, that can strongly enhance or suppress infection spreading. For instance, we show how weakly infected regions surrounding a densely populated area can cause rapid migration of the infection towards the populated area. Predicted infection "heat-maps" show remarkable similarity to publicly available heat-maps, e.g., from South Carolina. We further demonstrate how localized lockdown/quarantine conditions can slow down the spreading of disease from epicenters. Application of our model in different countries can provide a useful predictive tool for the authorities, in particular, for planning strong lockdown measures in localized areas-such as those underway in a few countries.