Areas Of Parameter Space Research Articles

The QCD axion sum rule

We demonstrate that the true QCD axion that solves the strong CP problem can be found in all generality outside the customary standard QCD band, with QCD being the sole source of Peccei-Quinn breaking. The essential reason is that the basis of axion-gluon interactions does not need to coincide with the mass basis. Specifically, we consider the case in which the QCD axion field is not the only singlet scalar in Nature but it mixes with other singlet scalars (besides the η′). We determine the exact mathematical condition for an arbitrary N-scalar potential to be Peccei-Quinn invariant. Such potentials provide extra sources of mass for the customary axion without enlarging the Standard Model gauge symmetry. The contribution to the axion mass stemming from the QCD topological susceptibility is shown to be shared then among the N axion eigenstates through a precise sum rule. Their location can only be displaced to the right of the standard QCD band. We demonstrate that the axion closest to this band can be displaced from it by a factor of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{N} $$\\end{document} at most, and this corresponds to the case in which all axion signals are maximally deviated. Conversely, if one axion is found on the standard QCD band, the other eigenstates will be out of experimental reach. Our results imply that any ALP experiment which finds a signal to the right of the standard QCD axion band can be solving the strong CP problem within QCD, with the associated N − 1 excitations to be found in an area of parameter space that we determine. We illustrate the results and phenomenology in some particular cases.

A simple three-dimensional quadratic flow with an attracting torus

Attracting torus is a rare phenomenon in the dynamics of low-dimensional autonomous systems. Adding an anti-damping term to the well-known Nosé-Hoover oscillator, this paper introduces a new system exhibiting attracting torus in a wide range of parameter values. This system has a variety of dynamical solutions like limit cycles, strange attractors, attracting tori, invariant tori, and chaotic sea. It is also demonstrated that the system is multistable in some regions of parameter space wherein different types of attractors coexist. However, the attracting torus is the leading bounded solution in a considerable area of parameter space. Moreover, the coexistence of four limit cycles is found in the time-reversed system. The study of the system's basin of attraction shows that the system owns a solid basin of attraction with rounded boundaries for the attracting torus, which is an exciting property.

A novel interpretable machine learning algorithm to identify optimal parameter space for cancer growth.

Recent years have seen an increase in the application of machine learning to the analysis of physical and biological systems, including cancer progression. A fundamental downside to these tools is that their complexity and nonlinearity makes it almost impossible to establish a deterministic, a priori relationship between their input and output, and thus their predictions are not wholly accountable. We begin with a series of proofs establishing that this holds even for the simplest possible model of a neural network; the effects of specific loss functions are explored more fully in Appendices. We return to first principles and consider how to construct a physics-inspired model of tumor growth without resorting to stochastic gradient descent or artificial nonlinearities. We derive an algorithm which explores the space of possible parameters in a model of tumor growth and identifies candidate equations much faster than a simulated annealing approach. We test this algorithm on synthetic tumor-growth trajectories and show that it can efficiently and reliably narrow down the area of parameter space where the correct values are located. This approach has the potential to greatly improve the speed and reliability with which patient-specific models of cancer growth can be identified in a clinical setting.

Chaos in the border-collision normal form: A computer-assisted proof using induced maps and invariant expanding cones

In some maps the existence of an attractor with a positive Lyapunov exponent can be proved by constructing a trapping region in phase space and an invariant expanding cone in tangent space. If this approach fails it may be possible to adapt the strategy by considering an induced map (a first return map for a well-chosen subset of phase space). In this paper we show that such a construction can be applied to the two-dimensional border-collision normal form (a continuous piecewise-linear map) if a certain set of conditions are satisfied and develop an algorithm for checking these conditions. The algorithm requires relatively few computations, so it is a more efficient method than, for example, estimating the Lyapunov exponent from a single orbit in terms of speed, numerical accuracy, and rigor. The algorithm is used to prove the existence of an attractor with a positive Lyapunov exponent numerically in an area of parameter space where the map has strong rotational characteristics and the consideration of an induced map is critical for the proof of robust chaos.

Cramér-Rao bound-informed training of neural networks for quantitative MRI.

To improve the performance of neural networks for parameter estimation in quantitative MRI, in particular when the noise propagation varies throughout the space of biophysical parameters. A theoretically well-founded loss function is proposed that normalizes the squared error of each estimate with respective Cramér-Rao bound (CRB)-a theoretical lower bound for the variance of an unbiased estimator. This avoids a dominance of hard-to-estimate parameters and areas in parameter space, which are often of little interest. The normalization with corresponding CRB balances the large errors of fundamentally more noisy estimates and the small errors of fundamentally less noisy estimates, allowing the network to better learn to estimate the latter. Further, proposed loss function provides an absolute evaluation metric for performance: A network has an average loss of 1 if it is a maximally efficient unbiased estimator, which can be considered the ideal performance. The performance gain with proposed loss function is demonstrated at the example of an eight-parameter magnetization transfer model that is fitted to phantom and in vivo data. Networks trained with proposed loss function perform close to optimal, that is, their loss converges to approximately 1, and their performance is superior to networks trained with the standard mean-squared error (MSE). The proposed loss function reduces the bias of the estimates compared to the MSE loss, and improves the match of the noise variance to the CRB. This performance gain translates to in vivo maps that align better with the literature. Normalizing the squared error with the CRB during the training of neural networks improves their performance in estimating biophysical parameters.

Control of firing mode in nonlinear neuron circuit driven by photocurrent

Firing patterns discern the electrical activities in biological neurons when intracellular and extracellular ions are pumped into cells and exchanged there. Artificial neural circuits can be tamed to reproduce similar firing modes from biological neurons by applying appropriate physical stimuli. Photocurrent generated in the phototube can be used as a signal source, which can stimulate the neural circuits, while the involvement of which branch circuit will be much different because the channel current can control the dynamics of functional neuron to a different degree. In this paper, based on a nonlinear (FitzHugh-Nagumo, FHN) neural circuit composed of one capacitor, induction coil, nonlinear resistor, two ideal resistors and one periodical stimulus, the phototube is incorporated into different branch circuits for changing the channel current and the biophysical role of photocurrent is investigated. The dynamical equations of three types of system are unified, though they fall in different areas in parameter space. The membrane potential can be directly changed and firing modes are switched when photocurrent is activated to change the channel current by connecting the phototube to the capacitor. The induced current across the induction coil is regulated to balance the external stimulus when the phototube is connected to the induction coil in series. The two types of photosensitive neuron models constructed in this paper are compared with the photocurrent driven inductive branch showing that the photocurrent driven capacitive branch can very effectively regulate the membrane potential and greatly improve the photosensitive sensitivity.

Magnetic and charge susceptibilities in the half-filled triangular lattice Hubbard model

We study magnetic and charge susceptibilities in the half-filled two-dimensional triangular Hubbard model within the dual fermion approximation in the metallic, Mott insulating, and crossover regions of parameter space. In the \textcolor{black}{insulating state}, we find strong spin fluctuations at the K point at low energy corresponding to the \textcolor{black}{120$^{\circ}$} antiferromagnetic order. These spin fluctuations persist into the metallic phase and move to higher energy. We also present data for simulated neutron spectroscopy and \textcolor{black}{spin-lattice} relaxation times, and perform direct comparisons to inelastic neutron spectroscopy experiments on the triangular material Ba$_8$CoNb$_6$O$_{24}$ and to the relaxation times on $\kappa$-(ET)$_2$Cu$_2$(CN)$_3$. Finally, we present charge susceptibilities in different areas of parameter space, which should correspond to momentum-resolved electron-loss spectroscopy measurements on triangular compounds.

Hydraulic behavior of fault zones in pump tests of geothermal wells: a parametric analysis using numerical simulations for the Upper Jurassic aquifer of the North Alpine Foreland Basin

Fault zones in the Upper Jurassic aquifer of the North Alpine Foreland Basin are generally regions with possibly increased hydraulic properties. They are consequently often part of the geothermal exploration concepts in this area and a primary target for the drilling operation. Data from this aquifer, gathered in pump tests, however, show that only four out of 41 successful wells exhibit hydraulic proof for the presence of such a fault zone in terms of a bi-/linear flow regime. Besides technical effects, also the contrast in hydraulic properties itself, between fault zone and surrounding host rock, can prevent the detection of a fault zone in pump test data. This means a certain threshold has to be surpassed until its effects become clearly visible. A simplified realistic numerical model was constructed and calibrated with pressure data from an exploration site in the south of Munich. This model was then used to observe the presence of linear and bilinear flows in dependence on the Malm aquifers parameter space. Sampling the possible hydraulic property combinations with the help of an HPC (high-performance computing) cluster and automating the detection of the corresponding main flow type allowed to quantify the areas in parameter space where the fault zone-related flow regimes of interest are present. Through the investigation of more than 30,000 combinations between fault zone permeability, matrix permeability, fault zone storage, matrix storage and fault zone thickness, it was found that, in the parameter space of the Malm aquifer, a bilinear flow can be observed for the first time only if the matrix permeability is lower than 2.0 × 10−13 m2, and a linear flow for matrix permeability values below 6.0 × 10−14 m2. Additionally, it was shown that fault zones, which have better hydraulic properties than the surrounding matrix, can indeed be hidden in pumping tests due to the parameter setting.

The chaotic dynamics and multistability of two coupled Fitzhugh–Nagumo model neurons

In this short article, we present a detailed analysis of the dynamics of a system of two coupled Fitzhugh–Nagumo neuron equations with tonic descending command signals, suitable for modelling circuits underlying the generation of motor behaviours. We conduct a search of possible attractors and calculate dynamical quantities, such as the largest Lyapunov exponents (LLEs), at a fine resolution over the areas of parameter space where complex and chaotic dynamics are most likely, to build a more detailed picture of the dynamical regimes of the system, focusing on the most complex solutions. By building a precise LLE map, we identify a narrow region of parameter space of particular interest, rich with chaotic and multistable dynamics, and show that it is on the border of criticality. This allows us to draw conclusions about possible neural mechanisms underlying the generation of chaotic dynamics. We illustrate the detailed ecology of multiple attractors in the system by listing, characterising and grouping all the stable attractors in the parameter range of interest. This allows us to pinpoint the regions with complex multistability. The greater understanding thus provided is intended to help future studies on the roles of chaotic dynamics in biological motor control, and their application in robotics, particularly by giving a deeper insight into how input signals and control parameters shape the system’s dynamics which can be exploited in chaos-driven adaptation.

Exploring axionlike particles beyond the canonical setup

Axionlike particles (ALPs) are interesting dark matter candidates from both the theoretical and the experimental perspective. Usually they are motivated as pseudo-Nambu-Goldstone bosons. In this case one of their most important features is that their coupling to other particles is suppressed by a large scale, the vacuum expectation value of the field breaking the symmetry that gives rise to them. This naturally endows them with very weak interactions but also restricts the maximal field value and therefore the regions where sufficient dark matter is produced. In this paper we investigate deviations from this simplest setup, where the potential and interactions are as expected for a pseudo-Nambu-Goldstone boson, but the kinetic term has singularities. This leads to a significantly increased area in parameter space where such particles can be dark matter and can be probed by current and near future experiments. We discuss cosmological limits and in the course of this give a simple derivation of a formula for isocurvature fluctuations in models with general anharmonic potentials. As an application of this formula we give an update of the isocurvature constraints for QCD axion dark matter models, using the most recent results for the QCD topological susceptibility and the newest Planck data.

Remerging Feigenbaum trees, and multiple coexisting bifurcations in a novel hybrid diode-based hyperjerk circuit with offset boosting

This paper proposes a novel chaotic hyperjerk circuit obtained from the autonomous 4-D hyperjerk circuit (Leutcho et al. in Chaos Solitons Fractals 107:67–87, 2018) via substituting the nonlinear component (pair of anti-parallel diodes) with a first order hybrid diode circuit. The nonlinear component (i.e. hybrid diode) is characterized by a frequency dependent nonlinear I–V characteristic which is responsible for complex behaviours of the whole circuit. The essential dynamic properties of the model are investigated by exploiting numerical tools of nonlinear theory such as bifurcation diagrams, graphs of Lyapunov exponents, as well as phase portraits. Some interesting features are found including period-doubling bifurcation, coexisting bifurcations, symmetry recovering crises, antimonotonicity, and offset-boosting. One of the most interesting features of the new hyperjerk circuit is the presence of various areas of parameter space in which the hyperjerk system exhibits the attractive and intricate property of coexisting bifurcation and several coexisting attractors (e.g. coexistence of two, three, four, five, six, or seven disconnected periodic and chaotic attractors) for the same parameter’ set. Laboratory experimental results show a very good agreement with the theoretical analysis.

Multiphase environment of compact galactic nuclei: the role of the nuclear star cluster

We study the conditions for the onset of Thermal Instability in the innermost regions of compact galactic nuclei, where the properties of the interstellar environment are governed by the interplay of quasi-spherical accretion onto a supermassive black hole (SMBH) and the heating/cooling processes of gas in a dense nuclear star cluster. Stellar winds are the source of material for radiatively inefficient (quasi-spherical, non-magnetised) inflow/outflow onto the central SMBH, where a stagnation point develops within the Bondi type accretion. We study the local thermal equilibrium to determine the parameter space which allows cold and hot phases in mutual contact to co-exist. We include the effects of mechanical heating by stellar winds and radiative cooling/heating by the ambient field of the dense star cluster. We consider two examples: the Nuclear Star Cluster (NSC) in the Milky Way central region (including the gaseous Mini-spiral of Sgr~A*), and the Ultra-Compact Dwarf galaxy M60-UCD1. We find that the two systems behave in different ways because they are placed in different areas of parameter space in the instability diagram: gas temperature vs. dynamical ionization parameter. In the case of Sgr~A*, stellar heating prevents the spontaneous formation of cold clouds. The plasma from stellar winds joins the hot X-ray emitting phase and forms an outflow. In M60-UCD1 our model predicts spontaneous formation of cold clouds in the inner part of the galaxy. These cold clouds may survive since the cooling timescale is shorter than the inflow/outflow timescale.

Role of the ‘N’ in the natural NMSSM for the LHC

In this work, we present mass limits on gluinos and stops in a natural Next-to-Minimal Supersymmetric Standard Model (NMSSM) with a singlino as the lightest supersymmetric particle. Motivated by naturalness, we consider spectra with light higgsinos, sub-TeV third generation sparticles and gluinos well below the multi-TeV regime while the electroweak gauginos, the sleptons and the first and second generation squarks are decoupled. We check that our natural supersymmetry spectra satisfy all electroweak precision observables and flavour measurements as well as theoretical constraints. By reinterpreting the results from the 8 TeV ATLAS supersymmetry searches we present the 95% CL exclusion limits on the model. The results show that the presence of a singlino LSP can lengthen decay chains and soften the final state particle energies. Whilst this does reduce the strength of the bounds in some areas of parameter space, the LHC still displays good sensitivity to the model.

Latent resonance in tidal rivers, with applications to River Elbe

We describe a systematic investigation of resonance in tidal rivers, and of river oscillations influenced by resonance. That is, we explore the grey-zone between absent and fully developed resonance. Data from this study are the results of a one-dimensional numerical channel model applied to a four-dimensional parameter space comprising geometry, i.e. length and depths of rivers, and varying dissipation and forcing. Similarity of real rivers and channels from parameter space is obtained with the help of a ‘run-time depth’. We present a model-channel, which reproduces tidal oscillations of River Elbe in Hamburg, Germany with accuracy of a few centimetres. The parameter space contains resonant regions and regions with ‘latent resonance’. The latter defines tidal oscillations that are elevated yet not in full but juvenile resonance. Dissipation reduces amplitudes of resonance while creating latent resonance. That is, energy of resonance radiates into areas in parameter space where periods of Eigen-oscillations are well separated from the period of the forcing tide. Increased forcing enhances the re-distribution of resonance in parameter space. The River Elbe is diagnosed as being in a state of anthropogenic latent resonance as a consequence of ongoing deepening by dredging. Deepening the river, in conjunction with the expected sea level rise, will inevitably cause increasing tidal ranges. As a rule of thumb, we found that 1m deepening would cause 0.5m increase in tidal range.

Single top events as a source of light charged Higgs in the fully hadronic final state at LHC

The single top production proceeds through different channels at LHC. The t-channel production which has a cross section at the level of one third of the ttbar, can be regarded as a source of light charged Higgs boson through top quark decay to charged Higgs. Due to the low jet multiplicity and characteristic kinematic features of this process, a signal selection can be designed to extract charged Higgs signal from the background processes. In this paper, taking MSSM as the theoretical framework, The light charged Higgs signal from single top events is analyzed. The charged Higgs is assumed to decay to tau nu and the hadronic decay of tau leptons is analyzed. Different charged Higgs mass hypotheses are analyzed and a scan over the parameter space (mH+,tanbeta) is performed. It is shown that this process has the potential to exclude large areas of parameter space, while with enough data, a 5 sigma discovery would also be possible. Finally 95% C.L. exclusion and 5 sigma contours are provided for different integrated luminosities of LHC.

Fitting the Higgs to natural SUSY

Abstract We present a fit to the 2012 LHC Higgs data in different supersymmetric frameworks using naturalness as a guiding principle. We consider the MSSM and its D-term and F -term extensions that can raise the tree-level Higgs mass. When adding an extra chiral superfield to the MSSM, three parameters are needed determine the tree-level couplings of the lightest Higgs. Two more parameters cover the most relevant loop corrections, that affect the hγγ and hgg vertexes. Motivated by this consideration, we present the results of a five parameters fit encompassing a vast class of complete supersymmetric theories. We find meaningful bounds on singlet mixing and on the mass of the pseudoscalar Higgs m A as a function of tan β in the MSSM. We show that in the (m A , tan β) plane, Higgs couplings measurements are probing areas of parameter space currently inaccessible to direct searches. We also consider separately the two cases in which only loop effects or only tree-level effects are sizable. In the former case we study in detail stops’ and charginos’ contributions to Higgs couplings, while in the latter we show that the data point to the decoupling limit of the Higgs sector. In a particular realization of the decoupling limit, with an approximate PQ symmetry, we obtain constraints on the heavy scalar Higgs mass in a general type-II Two Higgs Doublet Model.

Experiments on synchronization in networks of nonlinear oscillators with dynamic links

This paper presents experimental results on the characterization of dynamics and synchronization of networks of nonlinear oscillators with dynamic links. The results are obtained using a new experimental setup. Accurate evaluation of synchronization with dynamic coupling is reported, with reference to a network of Chua oscillators, each settled onto a periodic orbit. The observed synchronization levels, as function of the dynamic link parameters, give a picture of the synchronization area in parameter space which is in agreement with previous theoretical predictions.

Prediction of chaos in non-salient permanent-magnet synchronous machines

This Letter tries to find the area in parameter space of a non-salient Permanent-Magnet Synchronous Machine (PMSM) in which chaos can occur. This area is briefly named as chaotic area. The predicted chaotic area is obtained by checking some conditions which are necessary for existence of chaos in a dynamical system. In this Letter, it is assumed that this machine is in the generator mode, and its model is based on direct and quadrature axis of stator voltages and currents. The information of the predicted area is used in non-chaotic maximum power control of torque in the machine.

Patterns of Morphometric Parameters in a Large Bedform Field: Development and Application of a Tool for Automated Bedform Morphometry

Patterns of Morphometric Parameters in a Large Bedform Field: Development and Application of a Tool for Automated Bedform Morphometry

Characterization of the Chaotic Magnetic Particle Dynamics

In this paper, we study the deterministic spin dynamics of an anisotropic magnetic particle in the presence of a time-dependent magnetic field using the Landau-Lifshitz equation. In particular, we study the case when the magnetic field is homogeneous with a fixed direction perpendicular to the anisotropy direction and consists of a constant and a time-periodic part. We characterize the dynamical behavior of the system by monitoring the Lyapunov exponents and by bifurcation diagrams. We focus on the dependence of the largest Lyapunov exponent on the magnitude and frequency of the applied magnetic field as well as on the anisotropy parameter of the particle. We find rather complicated landscape of sometimes closely intermingled chaotic and nonchaotic areas in parameter space with rather fuzzy boundaries in-between. For actual experiments that means the system can exhibit multiple transitions between regular and chaotic behavior.