Space Of Free Parameters Research Articles

A modern reappraisal of the U-Zr phase diagram

By integrating published experimental data on the uranium-zirconium (U-Zr) system into a machine learning framework, insight into the two differing views on the thermochemical equilibrium, particularly on the U-rich portion of the phase diagram (PD) was developed, ultimately resulting in a new U-Zr PD. Phase diagram sensitivity to model parameters, tolerances, physical preconceptions and experimental biases, are considered to establish the validity of the generated PDs. A systematic assessment of the most reliable and most recent thermochemical data was made, and the traditional modeling bias to search the space of free energy parameters was removed by using recently developed machine learning strategies. The readily validated methodology enables a thermodynamically consistent search of free energy parameters by leveraging modern experimental work from an array of sources including phase transformations, phase transition temperatures, and enthalpy changes between 723-1173 K (450-900°C). These changes include the truncation of β-U stability at 6 at.% Zr, prominent isotherms at 884 K (611°C) and 961 K (688°C), and δ-U-Zr phase boundaries ranging from 66.5 to 80.2 at.% Zr at 823 K (550°C). The newly proposed PD captures fundamental constants measured experimentally and improves the agreement with phase transformation studies such as neutron diffraction with in situ heating. As such, it is proposed that the new U-Zr PD developed in this work be used to resolve the historically opposing views.

Biophysical Analysis of a Minimalistic Kidney Model Expressing SGLT1 Reveals Crosstalk between Luminal and Lateral Membranes and a Plausible Mechanism of Isosmotic Transport.

We extended our model of the S1 tubular segment to address the mechanisms by which SGLT1 interacts with lateral Na/K pumps and tight junctional complexes to generate isosmotic fluid reabsorption via tubular segment S3. The strategy applied allowed for simulation of laboratory experiments. Reproducing known experimental results constrained the range of acceptable model outputs and contributed to minimizing the free parameter space. (1) In experimental conditions, published Na and K concentrations of proximal kidney cells were found to deviate substantially from their normal physiological levels. Analysis of the mechanisms involved suggested insufficient oxygen supply as the cause and, indirectly, that a main function of the Na/H exchanger (NHE3) is to extrude protons stemming from mitochondrial energy metabolism. (2) The water path from the lumen to the peritubular space passed through aquaporins on the cell membrane and claudin-2 at paracellular tight junctions, with an additional contribution to water transport by the coupling of 1 glucose:2 Na:400 H2O in SGLT1. (3) A Na-uptake component passed through paracellular junctions via solvent drag in Na- and water-permeable claudin-2, thus bypassing the Na/K pump, in agreement with the findings of early studies. (4) Electrical crosstalk between apical rheogenic SGLT1 and lateral rheogenic Na/K pumps resulted in tight coupling of luminal glucose uptake and transepithelial water flow. (5) Isosmotic transport was achieved by Na-mediated ion recirculation at the peritubular membrane.

A mathematical representation of an automated system designed to monitor critical infrastructure objects using seismic and acoustic signals

The article considers the mathematical model of the automated system of seismoacoustic monitoring of critical infrastructure objects. In the monitoring approach, the object is identified with a point in the multidimensional space of free model parameters. Thus, the forecast about the state of the object is a forecast of a significant shift in the position of the parameter vector in the parameters space. When choosing a mathematical model, it is necessary to select a space of informative parameters to reduce the probability of errors of two types. First of all, it is necessary to build a mathematical model of the dynamics of the OKI, which reflects the most significant moments of the monitoring process, including both the process itself and the disturbances accompanying this process and the noise background superimposed on the process of the dynamics of the state of the OKI. A priori knowledge of the interference of an arbitrary process will significantly weaken its influence on obtaining estimates of the parameters of the process, which is perceived as a useful signal. This attenuation is achieved by optimizing processing procedures that take into account the a priori statistics of the random interference process. A new mathematical model in the form of a superposition of Berlasi pulses in the seismoacoustic frequency range and constructive algorithms for its implementation are proposed. The mathematical properties of the model were studied. Thus, the state of OKI is reflected in the vector of free parameters of the above model. To evaluate the informative parameters of the proposed model of the automated seismo-acoustic monitoring system, the work solves the problem of nonlinear regression, considering them as the point of the criterion optimum in the n-dimensional space. In the situation that has developed in our country, related to the conduct of military operations on its territory and missile attacks, the creation of automated seismo-acoustic monitoring systems of critical infrastructure objects is a necessary task.

Revisiting [formula omitted] cosmologies

We review the status of f(R,T) cosmological models, where T is the trace of the energy momentum tensor Tμν. We start focusing on the modified Friedmann equations for the minimally coupled gravitational Lagrangian of the type f(R,T)=R+αeβT+γnTn. We show that in such a minimally coupled case there exists a useful constraining relation between the effective fractionary total matter density with an arbitrary equation of state parameter and the modified gravity parameters. With this association the modified gravity sector can be independently constrained using estimations of the gas mass fraction in galaxy clusters. Using cosmological background cosmic chronometers data and demanding the universe is old enough to accommodate the existence of Galactic globular clusters with ages of at least ∼14 Gyrs we find a narrow range of the modified gravity free parameter space in which this class of theories remains viable for the late time cosmological evolution. This preferred parameter space region accommodates the ΛCDM limit of f(R,T) models. We also work out the non-minimally coupled case in the metric-affine formalism and find that there are no viable cosmologies in the latter situation. However, when analyzing the cosmological dynamics including a radiation component, we find that this energy density interacts with the matter field and it does not scale according to the typical behavior. We conclude stating that f(R,T) gravity is not able to provide a full cosmological scenario and should be ruled out as a modified gravity alternative to the dark energy phenomena.

Sign-changeable interacting ghost dark energy model versus the cosmic age

In this paper, we discuss cosmic age problem in the case of ghost dark energy (GDE) model. To this end, we use two observational data sets to constrain the free parameter space of the models. Next, we try to set new limits on the mentioned free parameter space using the age of the universe. In this work, both of these tasks are done for the GDE model in the presence of the sign-changeable interaction terms. To this end, three classes of interaction terms are considered that provide a sign-changeability possibility. For one of these cases, the age problem passes completely and there is no new bound of free parameters. For two others the age test sets some constrains on the models. In addition to cosmic age problem, we investigate some other properties of these three models including ability to cross the phantom line, accelerating phase of cosmic expansion and the stability against cosmic perturbations.

Determinant quantum Monte Carlo for the half-filled Hubbard model with nonlocal density-density interactions

We design a novel formalism of determinant quantum Monte Carlo method for the half-filled Hubbard model with on-site Hubbard interaction $U$ and nearest neighbor density-density interaction $V$ on the square lattice. The formalism is free of sign problem for $|U|\ge 4|V|$, and is achieved by introducing discrete auxiliary fields on the nearest-neighbor bonds alone. Based on this formalism, we study the ground state phase diagram of the model systematically using the projector algorithm. Within the sign-problem free parameter space $|U|\ge 4|V|$, we obtain antiferromagnetism for $U\ge 4|V|>0$, charge density wave for $U0$, s-wave superconductivity for $U<0$ and small negative $V$, and phase separation for $U<0$ and a larger negative $V$. We also obtain the single particle gap and spin excitation spectra, and by comparison to mean field results, as well as available literatures, we discuss the possible phase boundary beyond the sign-problem free region. The unbiased numerically exact results can be taken as benchmarks in future studies. Finally, we discuss possible extension for longer-range interactions in the model.

Multi-equation bifurcation analysis of a free radical polymerization in a CSTR

The materials and composites prepared via a synthesis route of free radical homopolymerization are known in industrial practice. The dimensionless steady state equations of this reaction in a reactor were presented and parameter regions were explored to study occurrence of steady state patterns. These diagrams are useful in determining an operating point in free parameter space. The operating points can be further useful in design of the chemical reactor. A system of nonlinear steady state equations can encounter singularities. Our objective is to compute various branching points using a new and novel method presented by Karimi and Inamdar (2002) that gives rise to bifurcation patterns and construct the steady state diagrams.

Is policy causing chaos in the United Kingdom?

We study the stability properties and conditions for the onset of Shilnikov chaos in the UK New Keynesian macroeconomy, as well as the shifts in equilibrium dynamics under various policy regimes. Shilnikov chaos emerges for a restricted part of the free parameter space in the baseline rational expectations UK model with no regime switching. Chaos did not occur, when the UK's central bank showed a weak response to inflation in the high-inflation regime, while it appears easily in the low-inflation regime associated with the central bank's use of aggressive monetary policy in recent years. As a policy alternative for restoring uniqueness, the local analysis proposes tightening the monetary policy rule via the Taylor coefficient along with passive fiscal policy. But we find that doing so could hasten the emergence of Shilnikov's chaotic dynamics. The magnitude of the Taylor coefficient thus becomes central in attaining the desired long run steady-state.

Muon g−2 and semileptonic B decays in the Bélanger-Delaunay-Westhoff model with gauge kinetic mixing

In the model proposed by B\'elanger, Delaunay and Westhoff (BDW), a new sector consisted of vectorlike fermions and two complex scalars is charged under an extra Abelian symmetry $U(1)_X$. In this paper, we generalize the BDW model by introducing the kinetic mixing between the $U(1)_X$ and the standard model $U(1)_Y$ gauge fields. The new physics contributions to the muon anomalous magnetic moment and the Wilson coefficients $C_{9,10}^{(')}$ are obtained analytically. We have explored the free parameter space of the model, taking into account various constraints on the muon $g-2$ using recent data from the E989 experiment at Fermilab, the lepton universality violation in terms of $R_K$ and $R_{K^*}$, and the branching ratios of the semileptonic decays, $B^+ \rightarrow K^+ \mu^+ \mu^-$ and $B^0 \rightarrow K^{*0} \mu^+ \mu^-$, the LEP and LHC searches for sleptons and $Z'$ boson, as well as the perturbative requirement. The viable parameter regions of the model are identified. In the presence of the gauge kinetic mixing term, those regions are enlarged and significantly deformed in comparison to the case with vanishing kinetic mixing. In the near future, the E989 experiment with the projected sensitivity will be able to test significant parts of the currently allowed parameter regions.

Two-loop radiative seesaw, muon g \u2212 2, and \u03c4-lepton-flavor violation with DM constraints

The quartic scalar coupling λ5 term, which violates the lepton-number by two units in the Ma-model, is phenomenologically small when the model is applied to the lepton-flavor violation (LFV) processes. In order to dynamically generate the λ5 parameter through quantum loop effects and retain the dark matter (DM) candidate, we extend the Ma-model by adding a Z2-odd vector-like lepton doublet and a Z2-even Majorana singlet. With the new couplings to the Higgs and gauge bosons, the observed DM relic density can be explained when the upper limits from the DM-nucleon scattering cross sections are satisfied. In addition to the neutrino data and LFV constraints, it is found that the DM relic density can significantly exclude the free parameter space. Nevertheless, the resulting muon g − 2 mediated by the inert charged-Higgs can fit the 4.2σ deviation between the experimental measurement and the SM result, and the branching ratio for τ → μγ can be as large as the current upper limit when the rare μ → (eγ, 3e) decays are suppressed. In addition, it is found that the resulting BR(τ → μρ) can reach the sensitivity of Belle II with an integrated luminosity of 50 ab−1.

Process‐Based Climate Model Development Harnessing Machine Learning: II. Model Calibration From Single Column to Global

AbstractWe demonstrate a new approach for climate model tuning in a realistic situation. Our approach, the mathematical foundations and technical details of which are given in Part I, systematically uses a single‐column configuration of a global atmospheric model on test cases for which reference large‐eddy‐simulations are available. The space of free parameters is sampled running the single‐column model from which metrics are estimated in the full parameter space using emulators. The parameter space is then reduced by retaining only the values for which the emulated metrics match large eddy simulations within a given tolerance to error. The approach is applied to the 6A version of the LMDZ model which results from a long investment in the development of physics parameterizations and by‐hand tuning. The boundary layer is revisited by increasing the vertical resolution and varying parameters that were kept fixed so far, which improves the representation of clouds at process scale. The approach allows us to automatically reach a tuning of this modified configuration as good as that of the 6A version. We show how this approach helps accelerate the introduction of new parameterizations. It allows us to maintain the physical foundations of the model and to ensure that the improvement of global metrics is obtained for a reasonable behavior at process level, reducing the risk of error compensations that may arise from over‐fitting some climate metrics. That is, we get things right for the right reasons.

Fermion-boson stars with a quartic self-interaction in the boson sector

Fermion-boson stars are solutions of the gravitationally coupled Einstein-Klein-Gordon-Hydrodynamic equations system. By means of methods developed in previous works, we perform a stability analysis of fermion-boson stars that include a quartic self-interaction in their bosonic part. Additionally, we describe the complete structure of the stability and instability regions of the space of free parameters, which we argue is qualitatively the same for any value of the quartic self-interaction. The relationship between the total mass of mixed stars and their general stability is also discussed in terms of the structure identified within the stability region.

Adhesion and volume constraints via nonlocal interactions determine cell organisation and migration profiles

The description of the cell spatial pattern and characteristic distances is fundamental in a wide range of physio-pathological biological phenomena, from morphogenesis to cancer growth. Discrete particle models are widely used in this field, since they are focused on the cell-level of abstraction and are able to preserve the identity of single individuals reproducing their behavior. In particular, a fundamental role in determining the usefulness and the realism of a particle mathematical approach is played by the choice of the intercellular pairwise interaction kernel and by the estimate of its parameters. The aim of the paper is to demonstrate how the concept of H-stability, deriving from statistical mechanics, can have important implications in this respect. For any given interaction kernel, it in fact allows to a priori predict the regions of the free parameter space that result in stable configurations of the system characterized by a finite and strictly positive minimal interparticle distance, which is fundamental when dealing with biological phenomena. The proposed analytical arguments are indeed able to restrict the range of possible variations of selected model coefficients, whose exact estimate however requires further investigations (e.g., fitting with empirical data), as illustrated in this paper by series of representative simulations dealing with cell colony reorganization, sorting phenomena and zebrafish embryonic development.

The reconstruction of f(ϕ)R and mimetic gravity from viable slow-roll inflation

In this work, we extend the bottom-up reconstruction framework of F(R) gravity to other modified gravities, and in particular for f(ϕ)R and mimetic F(R) gravities. We investigate which are the important conditions in order for the method to work, and we study several viable cosmological evolutions, focusing on the inflationary era. Particularly, for the f(ϕ)R theory case, we specify the functional form of the Hubble rate and of the scalar-to-tensor ratio as a function of the e-foldings number and accordingly, the rest of the physical quantities and also the slow-roll and the corresponding observational indices can be calculated. The same method is applied in the mimetic F(R) gravity case, and in both cases we thoroughly analyze the resulting free parameter space, in order to show that the viability of the models presented is guaranteed and secondly that there is a wide range of values of the free parameters for which the viability of the models occurs. In addition, the reconstruction method is also studied in the context of mimetic F(R)=R gravity. As we demonstrate, the resulting theory is viable, and also in this case, only the scalar-to-tensor ratio needs to be specified, since the rest follow from this condition. Finally, we discuss in brief how the reconstruction method could function for other modified gravities.

A discrete particle model reproducing collective dynamics of a bee swarm

In this article, we present a microscopic discrete mathematical model describing collective dynamics of a bee swarm. More specifically, each bee is set to move according to individual strategies and social interactions, the former involving the desire to reach a target destination, the latter accounting for repulsive/attractive stimuli and for alignment processes. The insects tend in fact to remain sufficiently close to the rest of the population, while avoiding collisions, and they are able to track and synchronize their movement to the flight of a given set of neighbors within their visual field. The resulting collective behavior of the bee cloud therefore emerges from non-local short/long-range interactions. Differently from similar approaches present in the literature, we here test different alignment mechanisms (i.e., based either on an Euclidean or on a topological neighborhood metric), which have an impact also on the other social components characterizing insect behavior. A series of numerical realizations then shows the phenomenology of the swarm (in terms of pattern configuration, collective productive movement, and flight synchronization) in different regions of the space of free model parameters (i.e., strength of attractive/repulsive forces, extension of the interaction regions). In this respect, constraints in the possible variations of such coefficients are here given both by reasonable empirical observations and by analytical results on some stability characteristics of the defined pairwise interaction kernels, which have to assure a realistic crystalline configuration of the swarm. An analysis of the effect of unconscious random fluctuations of bee dynamics is also provided.

Sloping Saturated–Unsaturated Flow with Outflow at Seepage Face

Analytic series solutions are constructed for the phreatic free surface problem of two-dimensional steady downslope saturated–unsaturated flow, with water exiting at a seepage face. The region in free parameter space is delineated for which the water table intersects the upper surface, and the steady state with uniform constant irrigation rate, ceases to exist. The flow solution is extended to a case of the domain being more general than a parallelogram, with the upper and lower boundaries being piecewise linear. This geometry resembles that of large-scale rainfall simulators that are designed to test slope stability of wetted soil beds.

Two hidden scalars around 125 GeV andh→μτ

We show that the 2.4σ signal of the leptonic flavor violating (LFV) Higgs boson decay h→μτ, as observed by the CMS Collaboration recently, can be explained by a certain class of two-Higgs doublet models that allow controllable flavor-changing neutral current with a minimal number of free parameters. We postulate that (i) the alignment limit is maintained, which means the lightest neutral scalar (h) has identical couplings to that of the Standard Model Higgs boson and (ii) the signal comes from two other neutral scalars, the CP-even H and the -odd A, almost degenerate with h at 125 GeV. We also show that (i) it is entirely possible that these scalars are hidden, apart from this LFV signal; (ii) the signal strengths of bb¯, τ+τ- and γγ around 125 GeV put severe constraints on the parameter space of such models; (iii) the constraint is further enhanced by the nonobservation of processes like μ→eγ, and we predict that the branching ratio of μ→eγ cannot be even an order below the present experimental limit, highlighting the role it plays in forcing H and A to be near-degenerate; (iv) an enhancement in the τ+τ- production cross section at around 125 GeV is expected in the gluon fusion channel, and should be observed during the next run of the LHC; (v) the branching ratio in the eτ channel is enhanced and is expected to be at least about 2%. The constrained parameter space and minimum number of free parameters, along with such strong predictions, make this model easily testable and falsifiable. (Less)

Critical configurations for a system of semidegenerate fermions

We study an isothermal system of semidegenerate self-gravitating fermions in general relativity. Such systems present mass density solutions with a central degenerate core, a plateau and a tail, this last following a power law behavior r −2. The different solutions are governed by the free parameters of the model: the degeneracy and the temperature parameters at the center and the particle mass m. We then analyze in detail the free parameter space for a fixed m in the keV region, by studying the one-parameter sequences of equilibrium configurations up to the critical point, which is represented by the maximum in a central density (ρ 0) vs. core mass (M c ) diagram. We show that for fully degenerate cores, the known expression for the critical core mass M ∝ m 3 /m 2 is obtained, while for low degenerate cores, the critical core mass increases, showing temperature effects in a nonlinear way. The main result of this work is that when applying this theory to model the distribution of dark matter in galaxies from the very center to the outer halos, we do not find any critical corehalo configuration of self-gravitating fermions that would be able to explain the super-massive dark object in their centers and the outer halo simultaneously.

Transcranial magnetic stimulation for investigating causal brain-behavioral relationships and their time course.

Transcranial magnetic stimulation (TMS) is a safe, non-invasive brain stimulation technique that uses a strong electromagnet in order to temporarily disrupt information processing in a brain region, generating a short-lived “virtual lesion.” Stimulation that interferes with task performance indicates that the affected brain region is necessary to perform the task normally. In other words, unlike neuroimaging methods such as functional magnetic resonance imaging (fMRI) that indicate correlations between brain and behavior, TMS can be used to demonstrate causal brain-behavior relations. Furthermore, by varying the duration and onset of the virtual lesion, TMS can also reveal the time course of normal processing. As a result, TMS has become an important tool in cognitive neuroscience. Advantages of the technique over lesion-deficit studies include better spatial-temporal precision of the disruption effect, the ability to use participants as their own control subjects, and the accessibility of participants. Limitations include concurrent auditory and somatosensory stimulation that may influence task performance, limited access to structures more than a few centimeters from the surface of the scalp, and the relatively large space of free parameters that need to be optimized in order for the experiment to work. Experimental designs that give careful consideration to appropriate control conditions help to address these concerns. This article illustrates these issues with TMS results that investigate the spatial and temporal contributions of the left supramarginal gyrus (SMG) to reading.

Transcranial Magnetic Stimulation for Investigating Causal Brain-behavioral Relationships and their Time Course

Transcranial magnetic stimulation (TMS) is a safe, non-invasive brain stimulation technique that uses a strong electromagnet in order to temporarily disrupt information processing in a brain region, generating a short-lived “virtual lesion.” Stimulation that interferes with task performance indicates that the affected brain region is necessary to perform the task normally. In other words, unlike neuroimaging methods such as functional magnetic resonance imaging (fMRI) that indicate correlations between brain and behavior, TMS can be used to demonstrate causal brain-behavior relations. Furthermore, by varying the duration and onset of the virtual lesion, TMS can also reveal the time course of normal processing. As a result, TMS has become an important tool in cognitive neuroscience. Advantages of the technique over lesion-deficit studies include better spatial-temporal precision of the disruption effect, the ability to use participants as their own control subjects, and the accessibility of participants. Limitations include concurrent auditory and somatosensory stimulation that may influence task performance, limited access to structures more than a few centimeters from the surface of the scalp, and the relatively large space of free parameters that need to be optimized in order for the experiment to work. Experimental designs that give careful consideration to appropriate control conditions help to address these concerns. This article illustrates these issues with TMS results that investigate the spatial and temporal contributions of the left supramarginal gyrus (SMG) to reading.