Parameter Space Research Articles

QPOs from charged particles around magnetized black holes in braneworlds

Quasiperiodic oscillations (QPOs) are a powerful tool for testing gravity theories, probing gravitational and electromagnetic field properties, and obtaining constraints on the black hole and field parameters. This work considers charged particle dynamics near uniformly magnetized black holes in braneworlds. First, we obtain the solution of the Maxwell equation for magnetic fields and calculate the radial and angular magnetic field components. We derive and analyze the effective potential of charged particles for circular orbits and investigate the energy and angular momentum for the circular orbits. We also analyze the combined effects of magnetic interaction and braneworlds on the charged particles’ innermost stable circular orbits (ISCOs). We calculate the angular momentum of charged particles in Keplerian orbits in the presence of an external magnetic field and braneworlds. Also, we investigate frequencies of the particle oscillations along vertical and angular directions. We applied our studies on particle oscillations to the QPO studies in the relativistic precession model. Finally, we obtain constraints on magnetic interaction and braneworld parameters together with the black hole mass and QPO orbits using Monte Carlo Markov Chain (MCMC) simulation in the four-dimensional parameter space for the QPOs observed in the microquasars XTE J1550-564, GRO J1655-40 & GRS 1915-105, and at the center of galaxies M82 and Milky Way.

Na-Promoted Bimetallic Hydroxide Nanoparticles for Aerobic C-H Activation: Catalyst Design Principles and Insights into Reaction Mechanism.

A precious metal-free bimetallic FexMn1-x(OH)y hydroxide catalyst was developed that is capable of catalyzing aerobic C-H oxidation reactions at low temperatures, without the need for an initiator, relying sustainably on molecular oxygen. Through a systematic synthetic effort, we scanned a wide nanoparticle synthesis parameter space to lay out a detailed set of catalyst design principles unraveling how the Fe/Mn cation ratio, NaOH(aq) concentration used in the synthesis, catalyst washing procedures, extent of residual Na+ promoters on the catalyst surface, reaction temperature, and catalyst loading influence catalytic C-H activation performance as a function of the electronic, surface chemical, and crystal structure of FexMn1-x(OH)y bimetallic hydroxide nanostructures. Our comprehensive XRD, XPS, BET, ICP-MS, 1H NMR, and XANES structural/product characterization results as well as mechanistic kinetic isotope effect (KIE) studies provided the following valuable insights into the molecular level origins of the catalytic performance of the bimetallic FexMn1-x(OH)y hydroxide nanostructures: (i) catalytic reactivity is due to the coexistence and synergistic operation of Fe3+ and Mn3+ cationic sites (with minor contributions from Fe2+ and Mn2+ sites) on the catalyst surface, where in the absence of one of these synergistic sites (i.e., in the presence of monometallic hydroxides), catalytic activity almost entirely vanishes, (ii) residual Na+ species on the catalyst surface act as efficient electronic promoters by increasing the electron density on the Fe3+ and Mn3+ cationic sites, which in turn, presumably enhance the electrophilic adsorption of organic reactants and strengthen the interaction between molecular oxygen and the catalyst surface, (iii) in the fluorene oxidation reaction the step dictating the reaction rate likely involved the breaking of a C-H bond (kH/kD = 2.4), (iv) reactivity patterns of a variety of alkylarene substrates indicate that the C-H bond cleavage follows a stepwise PT-ET (proton transfer-electron transfer) pathway.

Influence of new states in searches for negative gauge-Higgs couplings

In this work, we explore how constraints based on interference effects for the negative gauge-Higgs coupling scenario are affected by new physics. Models that achieve this wrong-sign gauge-Higgs coupling inevitably have new charged Higgs states. These states affect the interpretation of interference effects. We recast the ATLAS analysis for VBF Wh, showing that the previously excluded negative gauge-Higgs coupling scenario is still experimentally viable for charged Higgs masses below 370 GeV. We show that it is possible to weaken this bound further with mild tuning in the parameter space. We discuss how to further constrain the wrong-sign gauge-Higgs coupling hypothesis and point out the potential of VBF Zh to exclude this scenario in a model-independent way.

Non-linear matter power spectrum modeling in interacting dark energy cosmologies

AbstractUnderstanding the behavior of the matter power spectrum on non-linear scales beyond the $$\Lambda $$ Λ CDM model is crucial for accurately predicting the large-scale structure (LSS) of the Universe in non-standard cosmologies. In this work, we present an analysis of the non-linear matter power spectrum within the framework of interacting dark energy-dark matter cosmologies (IDE). We employ N-body simulations and theoretical models to investigate the impact of IDE on these non-linear scales. Beginning with N-body simulations characterized by a fixed parameter space delineated by prior observational research, we adeptly fit the simulated spectra with a simple parametric function, achieving accuracy within 5%. Subsequently, we refine a modified halo model tailored to the IDE cosmology, exhibiting exceptional precision in fitting the simulations down to scales of approximately 1 h/Mpc. To assess the model’s robustness, we conduct a forecast analysis for the Euclid survey, employing our refined model. We find that the coupling parameter $$\xi $$ ξ will be constrained to $$\sigma (\xi ) = 0.0110$$ σ ( ξ ) = 0.0110 . This marks a significant improvement by an order of magnitude compared to any other current observational tests documented in the literature. These primary findings pave the way for a novel preliminary approach, enabling the utilization of IDE models for observational constraints concerning LSS data on non-linear scales.

Inertial effects on free surface pumping with an undulating surface

Free surface flows driven by boundary undulations are observed in many biological phenomena, including the feeding and locomotion of water snails. To simulate the feeding strategy of apple snails, we develop a centimetric robotic undulator that drives a thin viscous film of liquid with the wave speed $V_w$ . Our experimental results demonstrate that the behaviour of the net fluid flux $Q$ strongly depends on the Reynolds number $Re$ . Specifically, in the limit of vanishing $Re$ , we observe that $Q$ varies non-monotonically with $V_w$ , which has been successfully rationalised by Pandey et al. (Nat. Commun., vol. 14, no. 1, 2023, p. 7735) with the lubrication model. By contrast, in the regime of finite inertia ( ${Re} \sim O(1)$ ), the fluid flux continues to increase with $V_w$ and completely deviates from the prediction of lubrication theory. To explain the inertia-enhanced pumping rate, we build a thin-film, two-dimensional model via the asymptotic expansion in which we linearise the effects of inertia. Our model results match the experimental data with no fitting parameters and also show the connection to the corresponding free surface shapes $h_2$ . Going beyond the experimental data, we derive analytical expressions of $Q$ and $h_2$ , which allow us to decouple the effects of inertia, gravity, viscosity and surface tension on free surface pumping over a wide range of parameter space.

Theoretical constraints on models with vectorlike fermions

We provide a set of theoretical constraints on models in which the Standard Model field content is extended by vectorlike fermions and in some cases also by a real scalar singlet. Our approach is based on the study of electroweak vacuum stability, perturbativity of model couplings, and gauge couplings unification with the use of renormalization group equations. We show that careful analysis of these issues leads to strong constraints on the parameter space of the considered models. This, in turn, has important implications for phenomenology, as we show using examples of the double Higgs boson production, electroweak precision observables, and the electroweak phase transition. Published by the American Physical Society 2024

Tackling the multitude of uncertainties in energy systems analysis by model coupling and high-performance computing

This paper identifies and addresses three key challenges in energy systems analysis—varying assumptions, computational limitations, and coverage of a few indicators only. First, results depend strongly on assumptions, i.e., varying input data. Hence, comparisons and robust results are hard to achieve. To address this, we use a broad range of possible inputs through an extensive literature review by scenario experts. Second, we overcome computational limitations using high-performance computing (HPC) and an automated workflow. Third, by coupling models and developing 13 indicators to evaluate the overall quality of energy systems in Germany for 2030, we include many aspects of security of supply, market impact, life cycle analysis and cost optimization. A cluster analysis of scenarios by indicators reveals three recognizable clusters, separating systems with a high share of renewables clearly from more conventional sets. Additionally, scenarios can be identified which perform very positive for many of the 13 indicators. We conclude that an automated, coupled workflow on supercomputers based on a broad parameter space is able to produce robust results for many important aspects of future energy systems. Since all models and software components are released as open-source, all components of a multi-perspective model-chain are now available to the energy system modeling community.

MEDEA: A New Model for Emulating Radio Antenna Beam Patterns for 21 cm Cosmology and Antenna Design Studies

In 21 cm experimental cosmology, accurate characterization of a radio telescope’s antenna beam response is essential to measure the 21 cm signal. Computational electromagnetic (CEM) simulations estimate the antenna beam pattern and frequency response by subjecting the EM model to different dependencies, or beam hyperparameters, such as soil dielectric constant or orientation with the environment. However, it is computationally expensive to search all possible parameter spaces to optimize the antenna design or accurately represent the beam to the level required for use as a systematic model in 21 cm cosmology. We therefore present the Model for Emulating Directivities and Electric fields of Antennas (MEDEA), an emulator that rapidly and accurately generates far-field radiation patterns over a large hyperparameter space. MEDEA takes a subset of beams simulated by CEM software, spatially decomposes them into coefficients on a complete, linear basis, and then interpolates them to form new beams at arbitrary hyperparameters. We test MEDEA on an analytical dipole and two numerical beams motivated by upcoming lunar lander missions, and then employ MEDEA as a model to fit mock radio spectrometer data to extract covariances on the input beam hyperparameters. We find that the interpolated beams have rms relative errors of at most 10−2 using 20 input beams or less, and that fits to mock data are able to recover the input beam hyperparameters when the model and mock are derived from the same set of beams. When a systematic bias is introduced into the mock data, extracted beam hyperparameters exhibit bias, as expected. We propose several extensions to MEDEA to potentially account for such bias.

Theoretical framework for the response of barotropic shelf current to along-shelf bathymetric perturbations

Abstract The mechanism underlying the response of barotropic shelf current to along-shelf bathymetric perturbations is rationalized by a one-dimensional vorticity equation. Fourier analysis of the equation in the wavenumber domain suggests that bathymetric features with relatively short length scales in the alongshore direction drive steady cross-shelf velocity undulations when the shelf circulation is against the direction of Kelvin wave propagation (upwelling regime). In contrast, much weaker and non-oscillatory cross-shelf velocity is expected when the shelf circulation is in alignment with propagating Kelvin waves (downwelling regime). The velocity undulations in the upwelling regime result from a positive feedback mechanism associated with potential vorticity (PV) advection; however, the presence of bottom friction restricts such undulations within a few wavelengths. The characteristic wavelength of undulations is determined by when the normalized drag coefficient , where u is the along-shelf mean flow speed, Hs is shelf depth, αs is the bottom slope, f is the Coriolis parameter, and r is the linear drag coefficient. Using this formula, a scale of the cross-shelf displacement distance Yt is proposed, aligning with one-layer barotropic simulations over a large parameter space. The study provides a framework for investigating barotropic cross-shelf exchange caused by shelf circulation over irregular bottom bathymetries.

Bayesian inference: more than Bayes’s theorem

Bayesian inference gets its name from Bayes’s theorem, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference uses all of probability theory, not just Bayes’s theorem. Many hypotheses of scientific interest are composite hypotheses, with the strength of evidence for the hypothesis dependent on knowledge about auxiliary factors, such as the values of nuisance parameters (e.g., uncertain background rates or calibration factors). Many important capabilities of Bayesian methods arise from use of the law of total probability, which instructs analysts to compute probabilities for composite hypotheses by marginalization over auxiliary factors. This tutorial targets relative newcomers to Bayesian inference, aiming to complement tutorials that focus on Bayes’s theorem and how priors modulate likelihoods. The emphasis here is on marginalization over parameter spaces—both how it is the foundation for important capabilities, and how it may motivate caution when parameter spaces are large. Topics covered include the difference between likelihood and probability, understanding the impact of priors beyond merely shifting the maximum likelihood estimate, and the role of marginalization in accounting for uncertainty in nuisance parameters, systematic error, and model misspecification.

High precision accelerator for our hybrid model of the redshift space power spectrum

Abstract Upcoming Large Scale Structure surveys aim to achieve an unprecedented level of precision in measuring galaxy clustering. However, accurately modelling these statistics may require theoretical templates that go beyond two-loop order perturbation theory, especially for achieving precision at smaller scales. In our previous work, we introduced a hybrid model for the redshift space power spectrum of galaxies. This model combines two-loop order templates with N-body simulations to capture the influence of scale-independent parameters on the galaxy power spectrum. However, the impact of scale-dependent parameters was addressed by precomputing a set of input statistics derived from computationally expensive N-body simulations. As a result, exploring the scale-dependent parameter space was not feasible in this approach. To address this challenge, we present an accelerated methodology that utilizes Gaussian processes, a machine learning technique, to emulate these input statistics. Our emulators exhibit remarkable accuracy, achieving reliable results with just 13 N-body simulations for training. Our emulators can reproduce the set of statistics we are interested in with less than 0.1% error in the parameter space within 5σ of the Planck ΛCDM predictions, specifically for scales around k > 0.1 h Mpc−1. Following the training of our emulators, we can predict all inputs for our hybrid model in approximately 0.2 seconds at a specified redshift. Given that performing 13 N-body simulations is a manageable task, our present methodology enables us to construct efficient and highly accurate models of the galaxy power spectra within a manageable time frame.

Noise aware parameter estimation in bioprocesses: Using neural network surrogate models with nonuniform data sampling

AbstractThis article demonstrates a parameter estimation technique for bioprocesses that utilizes measurement noise in experimental data to determine credible intervals on parameter estimates, with this information of potential use in prediction, robust control, and optimization. To determine these estimates, the work implements Bayesian inference using nested sampling, presenting an approach to develop neural network‐ (NN) based surrogate models. To address challenges associated with nonuniform sampling of experimental measurements, an NN structure is proposed. The resultant surrogate model is utilized within a Nested Sampling Algorithm that samples possible parameter values from the parameter space and uses the NN to calculate model output for use in the likelihood function based on the joint probability distribution of the noise of output variables. This method is illustrated against simulated data, then with experimental data from a Sartorius fed‐batch bioprocess. Results demonstrate the feasibility of the proposed technique to enable rapid parameter estimation for bioprocesses.

POD and mesh-adaptivity based reduce order model: Application to solve PDEs and inviscid flows

Time efficiency is a critical concern in Computational Fluid Dynamics (CFD) simulations of industrial applications. Despite the extensive research to improve the underlying numerical schemes to reduce the processing time, many CFD applications still need to improve on this issue. Reduced-Order Models (ROM) appeared as a promising alternative for significantly enhancing cost-effectiveness. The dimension of the initial problem is reduced significantly while keeping an acceptable level of accuracy. Proper Orthogonal Decomposition (POD), a data analysis technique, is widely used to construct a ROM to solve Euler and Navier-Stokes equations in CFD. Many aspects, however, need to be improved. In this paper, first, a general upper-bound error formula is derived, and second, a mesh-adaptivity based algorithm for snapshot locations in parameter space is provided (a sensitive step for POD-based ROM) in the context of Partial Differential Equations (PDE). The method’s efficiency is demonstrated through numerical tests by comparison to exact solutions and numerical results of a finite volume scheme on inviscid flow over a NACA0012.

Self-similar Solutions of Oscillatory Reconnection: Parameter Study of Magnetic Field Strength and Background Temperature

Oscillatory reconnection is a specific type of time-dependent reconnection which involves periodic changes in the magnetic topology of a null point. The mechanism has been reported for a variety of magnetic field strengths and configurations, background temperatures, and densities. All these studies report an oscillation in the current density at the null point, but also report a variety of periods, amplitudes, and overall behaviors. We conduct a parametric study for equilibrium magnetic field strength and initial background temperature, solving two-dimensional resistive magnetohydrodynamic equations around a magnetic X-point. We introduce a parameter space for the ratio of internal to magnetic energy and find self-similar solutions for simulations where this ratio is below 0.1 (which represents a magnetically dominated environment or, equivalently, a low-beta plasma). Self-similarity can be seen in oscillations in the current density at the null (including amplitude and period), ohmic heating, and the temperature generated via reconnection jets. The parameter space of energy ratios also allows us to contextualize previous studies of the oscillatory reconnection mechanism and bring those different studies together into a single unified understanding.

Reconstruction error based implicit regularization method and its engineering application to lung cancer diagnosis

The automatic diagnosis of lung cancer via artificial intelligence faces two hotspot issues: (1) insufficient data and (2) excessive redundant information, which make it difficult for convolutional neural networks (CNNs) to learn discriminative information of lung cancer. In this paper, we present the reconstruction error based implicit regularization method (REbIRM) that regularizes CNNs at the loss layer. During each training iteration, the reconstruction errors introduced by the two-stage discriminative auto-encoder are used to sharpen the generalization ability of deep CNNs by improving the decision boundary. In the application process, the trained deep CNN is used for completing computed tomography (CT) diagnostics. The main clinical benefit of our approach is that it is domain independent, requiring no specialized knowledge, and can therefore be applied to different types of datasets. To the best of our knowledge, this is the first attempt to implicitly regularize CNNs based on the reconstruction errors. Finally, experimental results on three CT image classification datasets show that REbIRM can achieve impressive results and that, in conjunction with Dropout, it obtains the state-of-the-art performance. REbIRM is also robust to the selection of hyper-parameters and only has the sublinear influence on the convergence of deep CNNs. Besides, empirical and theoretical evidence are provided to indicate that REbIRM prefers to converges in a constrained parameter space with flatter minima, which explains why it can generalize to new data. Finally, the nature of REbIRM is further explored through visualization techniques to analyze how it works in training deep CNNs.

Dissipative stabilization of maximal entanglement between nonidentical emitters via two-photon excitation

Two nonidentical quantum emitters, when placed within a cavity and coherently excited at the two-photon resonance, can reach stationary states of nearly maximal entanglement. In Vivas-Viaña, Martín-Cano, and Sánchez Muñoz [], we introduce a frequency-resolved Purcell effect stabilizing entangled W states among strongly interacting quantum emitters embedded in a cavity. Here we delve deeper into a specific configuration with a particularly rich phenomenology: two interacting quantum emitters under coherent excitation at the two-photon resonance. This scenario yields two resonant cavity frequencies where the combination of two-photon driving and Purcell-enhanced decay stabilizes the system into the subradiant and superradiant states, respectively. By considering the case of nondegenerate emitters and exploring the parameter space of the system, we show that this mechanism is merely one among a complex family of phenomena that can generate both stationary and metastable entanglement when driving the emitters at the two-photon resonance. We provide a global perspective of this landscape of mechanisms and contribute analytical characterizations and insights into these phenomena, establishing connections with previous reports in the literature and discussing how some of these effects can be optically detected. Published by the American Physical Society 2024

Equilibrium States of a Liquid Bridge between Flexible Sheets.

We study the equilibrium states of a drop between flexible sheets clamped on both ends. Revisiting first the case of parallel sheets, we find multiple equilibria, which we classify in a parameter space. In solution branching diagrams, we identify hysteresis cycles and folds indicating abrupt transitions, yet not necessarily leading to channel collapse. Between nonparallel sheets, a drop can stay in equilibrium away from the ends even when the liquid is not totally wetting, which is impossible between nonparallel rigid plates. We also show that nonparallel sheets can delay or prevent collapse in comparison to straight channels, suggesting thus a mechanism that protects slender structures inside microdevices from damage by surface tension.

Testing in GARCH‐X models: boundary, correlations and bootstrap theory

In this article, we consider the so‐called Fixed Shrinkage (FS) bootstrap for the class of GARCH models with explanatory variables (GARCH‐X). Under the assumption of stationary covariates, the proposed FS bootstrap does not require modeling the covariates, as these are kept fixed in the bootstrap generating process. Our main focus is on testing whether one or more of the covariates can be excluded in the GARCH‐X model. As is well‐known the limiting distribution of the likelihood‐ratio (LR) statistic in this setting is non‐standard and depends in particular on whether nuisance parameters are on the boundary or in the interior of the parameter space. In particular, and as detailed here, the non‐standard limiting distribution depends on correlations, or dependence, between the explanatory variables. The FS bootstrap takes the presence of nuisance parameters into account by implementing shrinking as proposed in Cavaliere et al. (2022) for pure ARCH models. We establish asymptotic validity of the FS bootstrap for GARCH‐X models, and demonstrate by simulations that the bootstrap‐based test performs extremely well even when nuisance parameters lie on the boundary of the parameter space. The empirical illustration amplifies that the presence of nuisance parameters (especially whether or not on the boundary) are vital for interpreting the dynamics of conditional volatility in financial stock market indices.

Stochastic collapse: how gradient noise attracts SGD dynamics towards simpler subnetworks*

Abstract In this work, we reveal a strong implicit bias of stochastic gradient descent (SGD) that drives overly expressive networks to much simpler subnetworks, thereby dramatically reducing the number of independent parameters, and improving generalization. To reveal this bias, we identify invariant sets, or subsets of parameter space that remain unmodified by SGD. We focus on two classes of invariant sets that correspond to simpler (sparse or low-rank) subnetworks and commonly appear in modern architectures. Our analysis uncovers that SGD exhibits a property of stochastic attractivity towards these simpler invariant sets. We establish a sufficient condition for stochastic attractivity based on a competition between the loss landscape’s curvature around the invariant set and the noise introduced by stochastic gradients. Remarkably, we find that an increased level of noise strengthens attractivity, leading to the emergence of attractive invariant sets associated with saddle-points or local maxima of the train loss. We observe empirically the existence of attractive invariant sets in trained deep neural networks, implying that SGD dynamics often collapses to simple subnetworks with either vanishing or redundant neurons. We further demonstrate how this simplifying process of stochastic collapse benefits generalization in a linear teacher-student framework. Finally, through this analysis, we mechanistically explain why early training with large learning rates for extended periods benefits subsequent generalization.

Collective behavior of active filaments with homogeneous and heterogeneous stiffness.

The collective dynamics of active biopolymers is crucial for many processes in life, such as cellular motility, intracellular transport, and division. Recent experiments revealed fascinating self-organized patterns of diverse active filaments, while an explicit parameter control strategy remains an open problem. Moreover, theoretical studies so far mostly dealt with active chains with uniform stiffness, which are inadequate in describing the more complicated class of polymers with varying stiffness along the backbone. Here, using Langevin dynamics simulations, we investigate the collective behavior of active chains with homogeneous and heterogeneous stiffness in a comparative manner. We map a detailed non-equilibrium phase diagram in activity and stiffness parameter space. A wide range of phase states, including melt, cluster, spiral, polar, and vortex, are demonstrated. The appropriate parameter combination for large-scale polar and vortex formation is identified. In addition, we find that stiffness heterogeneity can substantially modulate the phase behaviors of the system. It has an evident destructive effect on the long-ranged polar structure but benefits the stability of the vortex pattern. Intriguingly, we unravel a novel polar-vortex transition in both homogeneous and heterogeneous systems, which is closely related to the local alignment mechanism. Overall, we achieve new insights into how the interplay among activity, stiffness, and heterogeneity affects the collective dynamics of active filament systems.