Two-dimensional Parameter Space Research Articles

Novel dynamical Scenario of the two-stage Colpitts oscillator

Abstract The paper performs a systematic investigation on the complexities in a two-stage Colpitts oscillator. An abundance of novel dynamical behaviors in the two-stage Colpitts oscillator are investigated by plotting stability diagrams, i.e., Lyapunov stability phase diagram and isospike diagrams, in two-dimensional parameter space. It not only covers some conventional structures, such as periodicity hubs and spirals, but also plenty of novel organizations, such as “eye of chaos”, split shrimp-shaped period island, periodic islands with fancy geometric distributions, and zig-zag networks. Beyond these, it also exhibits a new distribution regularity of spikes. It first finds the coexistence of these structures in a two-stage Colpitts oscillator, indicating that there are a number of elusive and undetected dynamical behaviors in the two-stage Colpitts oscillator. It will be beneficial to the profound understanding for the dynamical information of the two-stage Colpitts oscillator in the field of electronics.

A Holling Type II Discrete Switching Host-Parasitoid System with a Nonlinear Threshold Policy for Integrated Pest Management

A nonlinear discrete switching host-parasitoid model with Holling type II functional response function, in which the switch is guided by an economic threshold (ET), is proposed. Thus, if the weighted density of two generations of the host population increases and exceeds the ET, then integrated pest management (IPM) measures are enacted, i.e., biological and chemical measures are implemented together, assuming that the chemical immediately precedes the biological inputs to avoid pesticide-induced deaths of the natural enemies. First, the existence and local stability of the equilibria of two subsystems were studied, and the existence and coexistence of several types of equilibria of a nonlinear switching system were analysed. Next, the nonlinear switching system was investigated by numerical simulation, showing that the system exhibits quite complex dynamic behaviour. A two-dimensional bifurcation diagram revealed the existence and coexistence regions of different types of equilibria including regular and virtual equilibria. Moreover, period-adding bifurcations in two-dimensional parameter spaces were found. One-dimensional bifurcation diagrams revealed that the system has periodic, quasiperiodic, and chaotic solutions, Neimark–Sacker bifurcation, multiple coexisting attractors, period-doubling bifurcations, period-halving bifurcations, and so on. Finally, the initial densities of hosts and parasitoids associated with host outbreaks and their biological implications are discussed.

Fear the Shadows of the Giants: On Secular Perturbations in Circumstellar Habitable Zones of Double Stars

Abstract After the detection of extrasolar planets in binary- and multiple-star systems, questions arose about their dynamics and habitability. In this study we investigate a five-dimensional parameter space for wide binary stars with a massive planet beyond the habitable zone (HZ). Our aim is to reveal those orbital and physical parameter combinations that expose bodies in the primary star’s HZ to secular perturbations. Building on an established semianalytical model, we combine two separate analytical models into a new one to treat the restricted four-body problem. We apply this new Combined Analytical Model (CAM) to different synthetic systems and systematically map the occurrence of secular resonances (SRs). These maps are then visualized as two-dimensional sections of the parameter space. The CAM model has a median error below 3% relative to numerical reference simulations. We also derive a simplified CAM that performs well for hierarchical systems with moderate to large separations between the bodies. Our results show that SRs appear in the HZ even for large secondary-star distances (up to >1000 au) if either (i) the planet’s distance is larger than Jupiter’s or (ii) its mass is about Saturn’s or lower. Changes in the secondary star’s eccentricity by stellar flybys or galactic tides can push a formerly dynamically quiet HZ to a high-eccentricity state. Based on these results, we provide the easy-to-use online tool “SHaDoS” that evaluates the CAM for a given user input and traces the locations of SRs in the HZ in two-dimensional parameter space plots.

Analysis of liquids, gases, and supercritical fluids by a two-dimensional replica-exchange Monte Carlo method in temperature and chemical potential space.

We investigate the liquid, gas, and supercritical fluid phases of a Lennard-Jones 12-6 potential system by a two-dimensional replica-exchange method in which not only temperature but also chemical potential is exchanged. The method is referred to as the grand canonical replica-exchange method (GCREM). While one-dimensional replica exchange, which exchanges only temperature, cannot cross first-order phase transition points, GCREM can avoid this problem by making a detour in the two-dimensional parameter space. From only one simulation run, we can obtain probability distributions in the grand canonical ensemble for wide temperature and chemical potential values using the multiple-histogram reweighting techniques. We define a phase diagram near the critical point using thermodynamic quantities. Moreover, we discuss structures in each defined phase and at phase transition points.

Vulnerable window of yield strength for swelling-driven fracture of phase-transforming battery materials

Despite numerous experimental and theoretical investigations of the mechanical behavior of high-capacity Si and Ge Li-ion battery anodes, our basic understanding of swelling-driven fracture in these materials remains limited. Existing theoretical studies have provided insights into elasto-plastic deformations caused by large volume change phase transformations, but have not modeled fracture explicitly beyond Griffith’s criterion. Here, we use a multi-physics phase-field approach to model self-consistently anisotropic phase transformation, elasto-plastic deformation, and crack initiation and propagation during lithiation of Si nanopillars. Our computational results reveal that fracture occurs within a “vulnerable window” inside the two-dimensional parameter space of yield strength and fracture energy and highlight the importance of taking into account the surface localization of plastic deformation to accurately predict the magnitude of tensile stresses at the onset of fracture. They further demonstrate how the increased robustness of hollow nanopillars can be understood as a direct effect of anode geometry on the size of this vulnerable window. Those insights provide an improved theoretical basis for designing next-generation mechanically stable phase-transforming battery materials undergoing large volume changes.

Effects of atom numbers on the miscibility-immiscibility transition of a binary Bose-Einstein condensate

The effects of atom numbers on the miscibility-immiscibility transition of a harmonically trapped population imbalanced binary Bose-Einstein condensate are investigated. In two-dimensional parameter space expanded by the strength of interspecies interaction and the ratio of atom numbers between two components, we have mapped out the ground-state phase diagrams for the ideal model without intraspecies interactions, and for the $^{23}\mathrm{Na}\text{\ensuremath{-}}^{23}\mathrm{Na}$ mixture and the $^{87}\mathrm{Rb}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ mixture with experimentally accessible intraspecies scattering lengths, respectively. It is found that all the phase diagrams include the miscible, symmetric immiscible, and asymmetric immiscible phases, and there exists a tricritical point where those three different phases merge. Furthermore, the phase boundaries among those three phases show a strong dependence on the atom numbers of two components. These results can be observed in current experiments.

Double Hopf Bifurcation in Microbubble Oscillators with Delay Coupling

Using center manifold reduction methodswe investigate the double Hopf bifurcation in the dynamics of microbubble with delay couplingwith main attention focused on nonresonant double Hopf bifurcation. We obtain the normal form of the system in the vicinity of the double Hopf point and classify the bifurcations in a two-dimensional parameter space near the critical point. Some numerical simulations support the applicability of the theoretical results. In particularwe give the explanation for some physical phenomena of the system using the obtained mathematical results.

Nonconductive Noncharging Composites: Tunable and Stretchable Materials for Adaptive Prevention of Charging by Contact Electrification.

Static charge generated by contact electrification can cause a wide range of undesirable consequences in our lives and in industry (e.g., adhesion of particles on surfaces, damage to electronics, and explosions). It has, however, been challenging to develop methods to prevent charging due to the vast types of materials that charge easily by contact electrification and the frequent changes in process and environmental conditions. The most common method is to use conductive materials for dissipating charge away; however, it is ineffective for many circumstances. Here, we propose a general and effective materials framework that involves a two-level consideration for preparing noncharging materials: (1) the variation of the proportion of a two-material composite and (2) the extent of stretching the composite material. This materials strategy is achieved by infusing particles within a stretchable bulk material. Importantly, the preparation of the noncharging surface for (1) is based on a novel fundamental mechanism that involves combining an appropriate amount of a material (e.g., the particles) that tends to charge positively with another material (e.g., the bulk material) that tends to charge negatively. This mechanism does not rely on conductivity; both the contacting materials naturally prevent the generation of static charge even when only nonconductive materials are involved. When the composite material is stretchable, the change in proportion of the surface coverage of the particles allows the charging response to be changed. Therefore, the variation in composition and stretching provide a wide two-dimensional parameter space for achieving noncharging response for the vast range of contacting materials that are used in industry and our lives. In addition, stretchability allows the composite material to flexibly adapt to changes in process and environmental conditions. This stretchable composite material was also demonstrated to be capable of preventing the adhesion of particles and separating particles of different materials.

East Asia VLBI Network observations of the TeV Gamma-Ray Burst 190114C

Observations of gamma-ray bursts (GRBs) at Very High Energy (VHE) offer a unique opportunity to investigate particle acceleration processes, magnetic fields and radiation fields in these events. Very Long Baseline Interferometry (VLBI) observations have been proven to be a powerful tool providing unique information on the source size of the GRBs at mas scales, as well as their accurate positions and possible expansion speeds. This paper reports on the follow-up observations of GRB 190114C, the first ever GRB detected with high significance at TeV photon energies by the MAGIC telescope, conducted with the East Asia VLBI Network (EAVN) at 22 GHz on three epochs, corresponding to 6, 15 and 32 days after the burst. The derived maps do not show any significant source above 5 sigma. The inferred upper limits on the GRB 190114C flux density at 22 GHz are used here to constrain the allowable two-dimensional parameter space for the afterglow emission. We find that our limits are consistent with most afterglow parameter combinations proposed so far in the literature. This is the first effort for the EAVN to search and monitor a radio transient in the Target of Opportunity mode. In addition to the useful constraints on GRB 190114C radio emission, experience gained from these observations is very helpful for future routine operation of EAVN transient program.

Confined-walking mode for an elliptical polarized undulator and its application.

Elliptical polarized undulators (EPUs) are broadly used in the soft X-ray energy range. They have the advantage of providing photons with both varied energy and polarization through adjustments to the value of the gap and/or shift magnet arrays in an undulator. Yet these adjustments may create a disturbance on the stability of the electron beam in a storage ring. To correct such a disturbance, it is necessary to establish a feed-forward table of key nodes in the gap-shift-defined two-dimensional parameter space. Such a table can only be scanned during machine-study time. For a free-walking mode, whereby an undulator is allowed to manoeuvre in the whole gap-shift space, all the key nodes need to be scanned at the expense of a large amount of machine-study time. This will greatly delay the employment of a full-polarization capable undulator (especially circularly polarized). By analyzing data-collecting patterns of user experiments, this paper defines a reduced set of key nodes in gap-shift parameter space, with the number of key nodes to be scanned for feed-forwarding scaled down to one-third of the original; and introduces a new walking mode for EPUs: confined-walking mode, whereby the undulator is manoeuvred only within the reduced set of key nodes. Such a mode is firstly realized on the EPUs at the DREAMLINE beamline at Shanghai Synchrotron Radiation Facility (SSRF). Under confined-walking mode, the undulator movements are stable and there is no obvious disturbance to the electron beam with the feed-forward system in operation. Successful experiments have been carried out using the circularly polarized light obtained via the new walking mode. This mode is expected to be applied to future EPUs at SSRF with the increasing requirements for various polarization modes.

Reduced-Dimension DOA and Polarization Parameters Joint Estimation Method for Electromagnetic Vector Sensor Array

MUSIC algorithm is a very typical algorithm in the joint estimation of DOA and polarization parameters. But the two spectral peak searches of two-dimensional parameter space in the algorithm cause a damaging effect on calculation, which limits the application of the algorithm in practice. Therefore, this paper proposes a joint estimation algorithm of dimensionality reduction DOA and polarization parameters based on successive MUSIC in the case of uniform linear array arrangement of the electromagnetic vector sensor. The proposed algorithm improves the classical MUSIC algorithm from two two-dimensional parameter searches to four one-dimensional parameter searches in the joint estimation of DOA and polarization parameters, which greatly reduces the computational complexity of the algorithm and can lead to the automatic matching of DOA and polarization parameters. Simulation results show that the computational complexity of the proposed algorithm is reduced by 104 orders of magnitude compared to the classical MUSIC algorithm. And the performance of the polarization parameter estimation of this algorithm is about 72%∼85% higher than that of the ESPRIT algorithm. Therefore, the algorithm is more applicable.

Quantum-critical phase from frustrated magnetism in a strongly correlated metal

Strange-metal phenomena often develop at the border of antiferromagnetic order in strongly correlated metals. It has been well established that they can originate from the fluctuations anchored by the point of continuous quantum phase transition out of the antiferromagnetic order, i.e., a quantum critical point. What has been unclear is how these phenomena can be associated with a potential new phase of matter at zero temperature. Here we show that magnetic frustration of the 4f-local moments in the distorted Kagome intermetallic compound CePdAl gives rise to such a paramagnetic quantum-critical phase. Moreover, we demonstrate that this phase turns into a Fermi liquid through a Mott-like crossover; in a two-dimensional parameter space of pressure and magnetic field, this crossover is linked to a line of zero-temperature 4f-electron localization-delocalization phase transitions at low and moderate pressures. Our discovery motivates a new design principle for strongly correlated metallic states with unconventional excitations that may underlie the development of such effects as high temperature superconductivity.

Simulations and experimental results of cloud thermodynamic phase classification with three SWIR spectral bands

Knowing the thermodynamic phase of a cloud–whether it is composed of spherical water droplets or polyhedral ice crystals–is critical in remote sensing applications and in climate studies. Liquid water and ice have different absorptive properties in certain spectral bands that can be exploited to identify the phase of clouds using ground-based, passive remote sensing. Our simulations found that ground-based radiance measurements at three spectral channels (1.55, 1.64, and 1.70 μm) provide improved discrimination when analyzed in three spectral dimensions as opposed to previous approaches based in two-dimensional parameter space. Our simulations show that these bands provide good discrimination between liquid-water and ice clouds when the optical depth is large. We also show measurements from a ground-based spectrometer confirming the cloud-phase sensing ability of these three channels, with validation provided by a dual-polarization lidar system.

Period doubling bifurcation analysis and isolated sub-harmonic resonances in an oscillator with asymmetric clearances

In this paper, a frequency-domain characterization of the period doubling bifurcation is proposed. This allows an efficient detection and localization of such points along frequency response curves computed through continuation and the harmonic balance method. A simple strategy for branch switching to sub-harmonic regimes is presented as well. Furthermore, these bifurcations are tracked in a two-dimensional parameter space, and extremum points with respect to the tracking parameter are characterized and linked to sub-harmonic isola formation. As a test case for these methods, a forced Duffing oscillator with asymmetric clearances is studied numerically. The results, which include the prediction of period doubling cascades and sub-harmonic isolas, are then compared to experimental results, yielding an excellent agreement.

Computation of Cusp Bifurcation Point in a Two-Prey One Predator Model using Lagrange Multiplier Method

In this paper we introduce a new method for computing cusp bifurcation point in a system of two prey one predator dynamical system. The method consists of rewriting the system of equations for the equilibria in a constrained optimization problem at where the classical Lagrange Multiplier Method can be applied to derive the fold bifurcation point. By having one extra parameter as free parameter we construct two fold curves which intersect each other nontransversally in a cusp bifurcation point. This result is verified by looking at three section in two-dimensional parameter space by taking one of the parameter constant and study the stability of the equilibria.

Influence of Hopf Bifurcation Dynamics on Conduction Failure of Action Potentials Along Nerve C-Fiber

Contrary to faithful conduction of every action potential or spike along the axon, some spikes induced by the external stimulation with a high frequency at one end of the unmyelinated nerve fiber (C-fiber) disappear during the conduction process to the other end, which leads to conduction failure. Many physiological functions such as information coding or pathological pain are involved. In the present paper, the dynamic mechanism of the conduction failure is well interpreted by two characteristics of the focus near Hopf bifurcation of the Hodgkin–Huxley (HH) model. One is that the current threshold to evoke a spike from the after-potential corresponding to the focus exhibits damping oscillations, and the other is that the damping oscillations exhibit an internal period. A chain network model composed of HH neurons and stimulated by the external periodic stimulation is used to stimulate C-fiber. In the two-dimensional parameter space of the stimulation period and coupling strength, the conduction failure appears for the coupling strength lower than that of the faithful conduction, which is due to some maximal values of the coupling current for low coupling strength not being strong enough to evoke spikes, and the coupling strength threshold between the faithful conduction and conduction failure exhibiting damping oscillations with respect to the stimulation period, due to the damping oscillations of the current threshold. The damping oscillations of the coupling strength exhibit close correlations to those of the current threshold. The coupling strength for the conduction failure exhibits maximal values as the stimulation period is approximated to 1-, 2-, 3- or 4-times of the internal period and the maximal values decrease with increasing stimulation period. In addition, the correspondence between the simulation results and the previous experimental observations is discussed. The results present deep insights into the dynamics of the conduction failure with Hopf bifurcation and are helpful to investigate the influence of other modulation factors on the conduction failure.

Correlations and degeneracies among the NSI parameters with tunable beams at DUNE

The Deep Underground Neutrino Experiment (DUNE) is a leading experiment in neutrino physics which is presently under construction. DUNE aims to measure the yet unknown parameters in the three flavour oscillation scenario which includes discovery of leptonic CP violation, determination of the mass hierarchy and determination of the octant of $\theta_{23}$. Additionally, the ancillary goals of DUNE include probing the sub-dominant effects induced by new physics. A widely studied new physics scenario is that of nonstandard neutrino interactions (NSI) in propagation which impacts the oscillations of neutrinos. We consider some of the essential NSI parameters impacting the oscillation signals at DUNE and explore the space of NSI parameters as well as study their correlations among themselves and with the yet unknown CP violating phase, $\delta$ appearing in the standard paradigm. The experiment utilizes a wide band beam and provides us with a unique opportunity to utilize different beam tunes at DUNE. We demonstrate that combining information from different beam tunes (low energy, LE and medium energy, ME) available at DUNE impacts the ability to probe some of these parameters and leads to altering the allowed regions in two-dimensional space of parameters considered.

Spica and the annual cycle of PKS B1322–110 scintillations

PKS B1322-110 is a radio quasar that is located only 8.5' in angular separation from the bright B star Spica. It exhibits intra-day variability in its flux density at GHz frequencies attributed to scintillations from plasma inhomogeneities. We have tracked the rate of scintillation of this source for over a year with the Australia Telescope Compact Array, recording a strong annual cycle that includes a near-standstill in August and another in December. The cycle is consistent with scattering by highly anisotropic plasma microstructure, and we fit our data to that model in order to determine the kinematic parameters of the plasma. Because of the low ecliptic latitude of PKS B1322-110, the orientation of the plasma microstructure is poorly constrained. Nonetheless at each possible orientation our data single out a narrow range of the corresponding velocity component, leading to a one-dimensional constraint in a two-dimensional parameter space. The constrained region is consistent with a published model in which the scattering material is associated with Spica and consists of filaments that are radially oriented around the star. This result has a 1% probability of arising by chance.

Minimal spin-one isotriplet dark matter

In this work we present a simple extension of the Standard Model that contains, as the only new physics component, a massive spin-one matter field in the adjoint representation of $SU(2)_{L}$. In order to be consistent with perturbative unitarity, the vector field must be odd under a $Z_{2}$ symmetry. Radiative corrections make the neutral component of the triplet ($V^{0}$) slightly lighter than the charged ones. We show that $V^{0}$ can be the dark matter particle while satisfying all current bounds if it has a mass between $2.8$ and $3.8$ TeV. We present the current limit on the model parameter space from highly complementary experimental constraints including dark matter relic density measurement, dark matter direct and indirect detection searches, LHC data on Higgs couplings to photons and LHC data on disappearing track searches. We show that the two-dimensional parameter space can be substantially covered by disappearing track searches at a future 100 TeV hadron collider, which will probe DM mass upto about 1.2 TeV.

Optimization of a 3-D isothermal plug-flow model of a monolith reactor featuring first order reactions

In this work, monolith reactor optimization is carried out. A 3-D monolith reactor model is first developed for a plug flow, isothermal, reactor featuring first order irreversible volumetric and surface reactions, then solved analytically using a series-based solution method, and finally optimized by establishing a number of mathematical model properties, and carrying out a broad search of the resulting reduced two-dimensional design parameter space. It is shown that maximum conversion is attained at a fluid velocity upper bound determined by the channel’s width, height, and capital cost to compression cost ratio. For reactors featuring only a surface reaction, maximum conversion is also attained at the maximum allowable channel width, and the minimum allowable channel hydraulic diameter. The optimum reactor residence time is inversely proportional (proportional) to the channel’s optimum hydraulic diameter (the reactor’s capital cost to production ratio).