New Family Of Models Research Articles

Classification of classical spin liquids: Typology and resulting landscape

Classical spin liquids (CSL) lack long-range magnetic order and are characterized by an extensive ground-state degeneracy. We propose a classification scheme of CSLs based on the structure of the flat bands of their Hamiltonians. Depending on absence or presence of the gap from the flat band, the CSL are classified as algebraic or fragile topological, respectively. Each category is further classified: the algebraic case by the nature of the emergent Gauss's law at the gap-closing point(s), and the fragile topological case by the homotopy of the eigenvector winding around the Brillouin zone. Previously identified models of CSLs fit snugly into our scheme, on a landscape where algebraic CSLs are located at transitions between fragile topological ones. It also allows us to present new families of models illustrating this landscape, which hosts both fragile topological and algebraic CSLs, as well as transitions between them. Published by the American Physical Society 2024

Discovering causal models for structural, construction and defense-related engineering phenomena

Causality, the science of cause and effect, has made it possible to create a new family of models. Such models are often referred to as causal models. Unlike those of mathematical, numerical, empirical, or machine learning (ML) nature, causal models hope to tie the cause(s) to the effect(s) pertaining to a phenomenon (i.e., data generating process) through causal principles. This paper presents one of the first works at creating causal models in the area of structural and construction engineering. To this end, this paper starts with a brief review of the principles of causality and then adopts four causal discovery algorithms, namely, PC (Peter-Clark), FCI (fast causal inference), GES (greedy equivalence search), and GRaSP (greedy relaxation of the sparsest permutation), have been used to examine four phenomena, including predicting the load-bearing capacity of axially loaded members, fire resistance of structural members, shear strength of beams, and resistance of walls against impulsive (blast) loading. Findings from this study reveal the possibility and merit of discovering complete and partial causal models. Finally, this study also proposes two simple metrics that can help assess the performance of causal discovery algorithms.

Hierarchical generalization of dual unitarity

Quantum dynamics with local interactions in lattice models display rich physics, but is notoriously hard to study. Dual-unitary circuits allow for exact answers to interesting physical questions in clean or disordered one- and higher-dimensional quantum systems. However, this family of models shows some non-universal features, like vanishing correlations inside the light-cone and instantaneous thermalization of local observables. In this work we propose a generalization of dual-unitary circuits where the exactly calculable spatial-temporal correlation functions display richer behavior, and have non-trivial thermalization of local observables. This is achieved by generalizing the single-gate condition to a hierarchy of multi-gate conditions, where the first level recovers dual-unitary models, and the second level exhibits these new interesting features. We also extend the discussion and provide exact solutions to correlators with few-site observables and discuss higher-orders, including the ones after a quantum quench. In addition, we provide exhaustive parametrizations for qubit cases, and propose a new family of models for local dimensions larger than two, which also provides a new family of dual-unitary models.

Analytical Fixed Income Pricing in Discrete-Time: A New Family of Models

Analytical Fixed Income Pricing in Discrete-Time: A New Family of Models

Revised and wider classes of isotropic space-time covariance functions

AbstractSeveral classes of space-time correlation models have been proposed by various authors in the last years. However, most of these families utilize non negative covariance functions to be adapted to different case studies: indeed, the traditional classes of covariances, such as the Whittle–Matern class and the several families constructed by applying the classical properties are not so flexible to describe covariance functions characterized by negative values. A recent analysis, regarding the difference between two isotropic covariance functions, has underlined that these new families of models are more flexible than the traditional ones because the same models are able to select covariance functions which are always positive in their domain, as well as covariance functions which could be negative in a subset of their field of definition. Moreover, within the same class of models, it is possible to select covariance models which present different behaviours in proximity of the origin. In this paper several families of isotropic space-time covariance functions, among the ones proposed in the literature, have been reviewed in order to enrich the same families including models characterized by negative values in a subset of their domain. Furthermore, the definition of separability has been revised in order to enlarge the classical definition. Apart from the theoretical importance related to the new aspects, these new classes of covariance models are characterized by an extremely simple formalism and can be easily adapted to several case studies.

Circuits of space and time quantum channels

Exact solutions in interacting many-body systems are scarce but extremely valuable since they provide insights into the dynamics. Dual-unitary models are examples in one spatial dimension where this is possible. These brick-wall quantum circuits consist of local gates, which remain unitary not only in time, but also when interpreted as evolutions along the spatial directions. However, this setting of unitary dynamics does not directly apply to real-world systems due to their imperfect isolation, and it is thus imperative to consider the impact of noise to dual-unitary dynamics and its exact solvability. In this work we generalise the ideas of dual-unitarity to obtain exact solutions in noisy quantum circuits, where each unitary gate is substituted by a local quantum channel. Exact solutions are obtained by demanding that the noisy gates yield a valid quantum channel not only in time, but also when interpreted as evolutions along one or both of the spatial directions and possibly backwards in time. This gives rise to new families of models that satisfy different combinations of unitality constraints along the space and time directions. We provide exact solutions for the spatio-temporal correlation functions, spatial correlations after a quantum quench, and the structure of steady states for these families of models. We show that noise unbiased around the dual-unitary family leads to exactly solvable models, even if dual-unitarity is strongly violated. We prove that any channel unital in both space and time directions can be written as an affine combination of a particular class of dual-unitary gates. Finally, we extend the definition of solvable initial states to matrix-product density operators. We completely classify them when their tensor admits a local purification.

Special classes of isotropic covariance functions

In the literature classical properties concerning the class of covariance functions are well illustrated. A recent analysis has provided the conditions under which the difference between two covariance functions is still a covariance function. In this paper the properties of these new classes of models have been explored; in particular, the present analysis has been given for isotropic covariance functions, because of their importance in many applied areas; moreover, isotropic covariance functions can be considered the starting point to construct anisotropic models. It has been pointed out that these new families of models are more flexible than the traditional ones because the same models, according to the values of their parameters, are able to select covariance functions which are always positive in their domain, as well as covariance functions which could be negative in a subset of their field of definition. Moreover, within the same class of models, it is possible to select covariance models which present a parabolic behaviour near the origin from covariance models which present a linear behaviour in proximity of the origin. Apart from the theoretical importance related to the new aspects presented throughout the paper, it is relevant to underline the practical aspects, since these new classes of isotropic covariance models are characterized by an extremely simple formalism and can be easily adapted to several case studies, hence they result very useful for many practitioners.

The effect of screening on the health burden of chlamydia: An evaluation of compartmental models based on person-days of infection.

Sexually transmitted diseases (STDs) are detrimental to the health and economic well-being of society. Consequently, predicting outbreaks and identifying effective disease interventions through epidemiological tools, such as compartmental models, is of the utmost importance. Unfortunately, the ordinary differential equation compartmental models attributed to the work of Kermack and McKendrick require a duration of infection that follows the exponential or Erlang distribution, despite the biological invalidity of such assumptions. As these assumptions negatively impact the quality of predictions, alternative approaches are required that capture how the variability in the duration of infection affects the trajectory of disease and the evaluation of disease interventions. So, we apply a new family of ordinary differential equation compartmental models based on the quantity person-days of infection to predict the trajectory of disease. Importantly, this new family of models features non-exponential and non-Erlang duration of infection distributions without requiring more complex integral and integrodifferential equation compartmental model formulations. As proof of concept, we calibrate our model to recent trends of chlamydia incidence in the U.S. and utilize a novel duration of infection distribution that features periodic hazard rates. We then evaluate how increasing STD screening rates alter predictions of incidence and disability adjusted life-years over a five-year horizon. Our findings illustrate that our family of compartmental models provides a better fit to chlamydia incidence trends than traditional compartmental models, based on Akaike information criterion. They also show new asymptomatic and symptomatic infections of chlamydia peak over drastically different time frames and that increasing the annual STD screening rates from 35% to 40%-70% would annually avert 6.1-40.3 incidence while saving 1.68-11.14 disability adjusted life-years per 1000 people. This suggests increasing the STD screening rate in the U.S. would greatly aid in ongoing public health efforts to curtail the rising trends in preventable STDs.

Local limit theorem for a Markov additive process on with a null recurrent internal Markov chain

AbstractIn the classical framework, a random walk on a group is a Markov chain with independent and identically distributed increments. In some sense, random walks are time and space homogeneous. This paper is devoted to a class of inhomogeneous random walks on $\mathbb{Z}^d$ termed ‘Markov additive processes’ (also known as Markov random walks, random walks with internal degrees of freedom, or semi-Markov processes). In this model, the increments of the walk are still independent but their distributions are dictated by a Markov chain, termed the internal Markov chain. While this model is largely studied in the literature, most of the results involve internal Markov chains whose operator is quasi-compact. This paper extends two results for more general internal operators: a local limit theorem and a sufficient criterion for their transience. These results are thereafter applied to a new family of models of drifted random walks on the lattice $\mathbb{Z}^d$ .

A comparison of turbine mass flow models based on pragmatic identification data sets for turbogenerator model development

The use of turbogenerators as a means of waste heat recovery has gained interest from industry and academia in recent years. Accurate mass flow models of turbogenerators are required for assessing their impact on overall engine performance during design–development. This paper presents the results of an experimental model identification program for a commercially available turbogenerator. The experimental data was categorised into training and validation data sets. Training data sets were selected using a simulation based method to bound data within a region representative of turbocharger turbine operation. A comprehensive review of promulgated models is presented, and the replication and extrapolation performance with respect to the experimental data sets is assessed. A new family of models is proposed which is applicable to a large class of radial flow turbines. Application of a systematic model selection process based on Akaike Information Criteria yields models from this family with improved performance. Furthermore, the robustness of the proposed family of models is assessed using published experimental data sets from a range of turbine designs, demonstrating the versatility of the proposed model family and model selection techniques.

Spins, percolation and height functions

To highlight certain similarities in graphical representations of several well known two-dimensional models of statistical mechanics, we introduce and study a new family of models which specializes to these cases after a proper tuning of the parameters. To be precise, our model consists of two independent standard Potts models, with possibly different numbers of spins and different coupling constants (the four parameters of the model), defined jointly on a graph embedded in a surface and its dual graph, and conditioned on the event that the primal and dual interfaces between spins of different value do not intersect. We also introduce naturally coupled height function and bond percolation models, and we discuss fundamental properties of the resulting joint coupling. As special cases we recover the standard Potts and random cluster model, the six-vertex model and loop O(n) model, the random current, double random current and XOR-Ising model.

Seeking SUSY fixed points in the 4 \u2212 \u03f5 expansion

We use the 4 − ϵ expansion to search for fixed points corresponding to 2 + 1 dimensional mathcal{N} =1 Wess-Zumino models of NΦ scalar superfields interacting through a cubic superpotential. In the NΦ = 3 case we classify all SUSY fixed points that are perturbatively unitary. In the NΦ = 4 and NΦ = 5 cases, we focus on fixed points where the scalar superfields form a single irreducible representation of the symmetry group (irreducible fixed points). For NΦ = 4 we show that the S5 invariant super Potts model is the only irreducible fixed point where the four scalar superfields are fully interacting. For NΦ = 5, we go through all Lie subgroups of O(5) and use the GAP system for computational discrete algebra to study finite subgroups of O(5) up to order 800. This analysis gives us three fully interacting irreducible fixed points. Of particular interest is a subgroup of O(5) that exhibits O(3)/Z2 symmetry. It turns out this fixed point can be generalized to a new family of models, with NΦ = frac{mathrm{N}left(mathrm{N}-1right)}{2} − 1 and O(N)/Z2 symmetry, that exists for arbitrary integer N≥3.

SpheCow: Flexible dynamical models for galaxies and dark matter haloes

Simple but flexible dynamical models are useful for many purposes, including serving as the starting point for more complex models or numerical simulations of galaxies, clusters, or dark matter haloes. We present SpheCow, a new light-weight and flexible code that allows one to easily explore the structure and dynamics of any spherical model. Assuming an isotropic or Osipkov-Merritt anisotropic orbital structure, the code can automatically calculate the dynamical properties of any model with either an analytical density profile or an analytical surface density profile as starting point. We have extensively validated SpheCow using a combination of comparisons to analytical and high-precision numerical calculations, as well as the calculation of inverse formulae. SpheCow contains readily usable implementations for many standard models, including the Plummer, Hernquist, NFW, Einasto, Sérsic, and Nuker models. The code is publicly available as a set of C++ routines and as a Python module, and it is designed to be easily extendable, in the sense that new models can be added in a straightforward way. We demonstrate this by adding two new families of models in which either the density slope or the surface density slope is described by an algebraic sigmoid function. We advocate the use of the SpheCow code to investigate the full dynamical structure for models for which the distribution function cannot be expressed analytically and to explore a much wider range of models than is possible using analytical models alone.

Generalized extended Weibull power series family of distributions

In this study, we introduce a new family of models for lifetime data called generalized extended Weibull power series family of distributions by compounding generalized extended Weibull distributions and power series distributions. The compounding procedure follows the same setup carried out by Adamidis (1998). The proposed family contains all types of combinations between truncated discrete with generalized and non-generalized Weibull distributions. Some existing power series and subclasses of mixed lifetime distributions become special cases of the proposed family, such as the compound class of extended Weibull power series distributions proposed by Silva et al. (2013) and the generalized exponential power series distributions introduced by Mahmoudi and Jafari (2012). Some mathematical properties of the new class are studied, including the cumulative distribution function, density function, survival function, and hazard rate function. The method of maximum likelihood is used for obtaining a general setup for estimating the parameters of any distribution in this class. An expectation-maximization algorithm is introduced for estimating maximum likelihood estimates. Special subclasses and applications for some models in a real dataset are introduced to demonstrate the flexibility and the benefit of this new family.

A Comparison of Turbine Mass Flow Models Based on Pragmatic Identification Data Sets for Turbogenerator Model Development

The use of turbogenerators as a means of waste heat recovery has gained interest from industry and academia in recent years. Accurate mass flow models of turbogenerators are required for assessing their impact on overall engine performance during design–development. This paper presents the results of an experimental model identification program for a commercially available turbogenerator. The experimental data was categorised into training and validation data sets. Training data sets were selected using a simulation based method to bound data within a region representative of turbocharger turbine operation. A comprehensive review of promulgated models is presented, and the replication and extrapolation performance with respect to the experimental data sets is assessed. A new family of models is proposed which is applicable to a large class of radial flow turbines. Application of a systematic model selection process based on Akaike Information Criteria yields models from this family with improved performance. Furthermore, the robustness of the proposed family of models is assessed using published experimental data sets from a range of turbine designs, demonstrating the versatility of the proposed model family and model selection techniques.

A methodology for adding thixotropy to Oldroyd-8 family of viscoelastic models for characterization of human blood

Recent work modeling the rheological behavior of human blood indicates that blood has all the hallmark features of a complex material, including shear-thinning, viscoelastic behavior, a yield stress, and thixotropy. After decades of modeling only the steady state blood data, steady state models, such as the Casson, Carreau–Yasuda, and Herschel–Bulkley models, have been developed. The advancement and evolution of blood modeling to transient flow conditions now has renewed interest. Using recently collected human blood rheological data from a strain-controlled rheometer, we show and compare a new modeling effort using the Oldroyd-8 viscoelastic framework as a foundation. This foundation is enhanced with the application of a recent thixotropic framework recently published to model elastic and viscoelastic contributions from the microstructure to three Oldroyd-8 families of models: the corotational Jeffreys model, the convected Maxwell model, and the Oldroyd 4-constant model. The elastic and viscoelastic stress contributions from the microstructure are then linearly superimposed with the viscoelastic backbone solution for stress given by the Oldroyd-8 family of models. Demonstrated here is a parametric analysis, model comparison, and a comparison of the new approaches made using the ability to predict large amplitude oscillatory shear and uni-directional large amplitude oscillatory shear flow. The new family of models can solve components of the full stress tensor, making them ideal for use with a future conformation tensor to evolve, model, and better understand the effects of the microstructure of human blood. In addition, there is now a methodology to model the normal forces of blood.

Tunable deconfined quantum criticality and interplay of different valence-bond solid phases**Project supported by the NSF under Grant No.DMR-1710170 and by a Simons Investigator Grant.

We use quantum Monte Carlo simulations to study an S = 1/2 spin model with competing multi-spin interactions. We find a quantum phase transition between a columnar valence-bond solid (cVBS) and a Néel antiferromagnet (AFM), as in the scenario of deconfined quantum-critical points, as well as a transition between the AFM and a staggered valence-bond solid (sVBS). By continuously varying a parameter, the sVBS–AFM and AFM–cVBS boundaries merge into a direct sVBS–cVBS transition. Unlike previous models with putative deconfined AFM–cVBS transitions, e.g., the standard J–Q model, in our extended J–Q model with competing cVBS and sVBS inducing terms the transition can be tuned from continuous to first-order. We find the expected emergent U(1) symmetry of the microscopically Z4 symmetric cVBS order parameter when the transition is continuous. In contrast, when the transition changes to first-order, the clock-like Z4 fluctuations are absent and there is no emergent higher symmetry. We argue that the confined spinons in the sVBS phase are fracton-like. We also present results for an SU(3) symmetric model with a similar phase diagram. The new family of models can serve as a useful tool for further investigating open questions related to deconfined quantum criticality and its associated emergent symmetries.

Approximate Deconvolution with Correction: A Member of a New Class of Models for High Reynolds Number Flows

We propose a new family of models for fluid flows at high Reynolds numbers, large eddy simulation with correction (LES-C), that combines a LES approach to turbulence modeling with a defect correcti...

Spatial behavioural responses to the spread of an infectious disease can suppress Turing and Turing–Hopf patterning of the disease

Reducing risky behaviour and/or avoiding sites where the risk of infection is perceived as higher (by social and/or spatial distancing) represent the two main forms of non-pharmaceutical behavioural responses of humans to the threats of infectious diseases. Here we investigate, within a reaction–diffusion setting, a family of new models for an endemic SIR (susceptible–infective–removed) infectious disease for which no vaccine is available and individuals’ responses to the infection threat are entirely based on changes either in their social behaviour or in their mobility behaviour, that is avoiding to visit sites with a large infection prevalence.First, we derive general conditions for the onset of Turing patterns for a general family of spatially inhomogeneous SIR models with a prevalence-dependent contact rate and constant recruitment. Then, we characterize our main family of models where the behavioural response also includes a spatial component, and show the condition bringing to the mitigation, or even the destruction, of Turing patterns. The same conditions can allow the transition from Turing–Hopf spatio-temporal patterns to pure Hopf temporal patterns. The same is also done for two SIS models. These results bring an inference of interest: the reduction of spatial clustering typically observed during the course of an epidemics might be related to a combination of agents’ spontaneous social and spatial distancing. To validate our theoretical results and further explore other spatio-temporal effects of the proposed spatial behavioural responses, numerical simulations of a specific instance of the above-mentioned family of SIR models have been performed.

Measurements and modelling of the viscosity of six synthetic crude oil mixtures

The viscosity and density are reported for six synthetic mixtures, composed of up to 13 components, designed to match a light, dead crude oil of API 32° and molar mass of approximately 184 g mol−1. The measurements were made in the liquid region at temperatures between (323 and 398) K and in the pressure range from 1 MPa to 70 MPa. The viscosity was measured with a vibrating-wire viscometer, while the density was measured by means of a vibrating U-tube densimeter. The density and viscosity data have expanded relative uncertainties of 0.12% and 1.2%, respectively with a coverage factor of 2.We have used the measured viscosity data to test the predictive power of the four viscosity models, the extended hard sphere (EHS), one-component EHS (1-cEHS), three-component EHS (3-cEHS) and Vesovic-Wakeham (VW), that have their basis in kinetic theory and the molecular description of the fluid. Two of the models (EHS and VW) require full compositional description of the mixture, while the other two belong to a new family of models which dispense with full compositional characterization, but retain molecular description. On average the EHS and VW models predict the viscosity data with lower deviations than 1-cEHS and 3-cEHS models, but all four models represent the data with uncertainty of 5–10%.