Island Of Stability Research Articles

Four-wave interactions: islands of stability surrounded by instability

Four-wave interactions: islands of stability surrounded by instability

Chaos over order: mapping 3D rotation of triaxial asteroids and minor planets

ABSTRACT Celestial bodies approximated with rigid triaxial ellipsoids in a two-body system can rotate chaotically due to the time-varying gravitational torque from the central mass. At small orbital eccentricity values, rotation is short-term orderly and predictable within the commensurate spin–orbit resonances, while at eccentricity approaching unity, chaos completely takes over. Here, we present the full three-dimensional rotational equations of motion around all three principal axes for triaxial minor planets and two independent methods of numerical solution based on Euler rotations and quaternion algebra. The domains of chaotic rotation are numerically investigated over the entire range of eccentricity with a combination of trial integrations of Euler’s equations of motion and the GALI(k) (Generalized Alignment Index) method. We quantify the dependence of the order–chaos boundaries on shape by changing a prolateness parameter, and find that the main 1:1 spin–orbit resonance disappears for specific moderately prolate shapes already at eccentricities as low as 0.3. The island of short-term stability around the main 1:1 resonance shrinks with increasing eccentricity at a fixed low degree of prolateness and completely vanishes at approximately 0.8. This island is also encroached by chaos on longer time-scales, indicating longer Lyapunov exponents. Trajectories in the close vicinity of the 3:2 spin–orbit resonance become chaotic at smaller eccentricities, but separated enclaves of orderly rotation emerge at eccentricities as high as 0.8. Initial perturbations of rotational velocity in latitude away from the exact equilibrium result in a spectrum of free libration, nutation, and polar wander, which is not well matched by the linearized analysis omitting the inertial terms.

How to approach the island of stability: Reactions using multinucleon transfer or radioactive neutron-rich beams?

The multinucleon transfer (MNT) process and radioactive beam induced fusion-evaporation (FE) reactions are the considered routines to explore the island of stability. We make the first direct comparison of the two approaches for producing neutron-rich superheavy nuclei, especially the predicted double magic isotope 298Fl. The radioactive beams 49−59Ca induced hot FE reactions with actinide targets and the MNT reaction 238U + 252Cf are investigated within the framework of the dinuclear system model. Based on the beam intensities proposed by Argonne Tandem Linac Accelerator System, we find that the MNT and FE processes are comparable for producing 298Fl. The influence of the shell structures uncertainties on the production cross section of 298Fl is evaluated. It is found that the shell structures weakly influence the production cross sections of 298Fl around the optimal incident energy, although, the double shell closures could strongly enhance the stability of 298Fl. We also quantitatively estimated the relative proportion of shell effects on cross sections in the transfer stage of the MNT reaction 238U + 252Cf. It is demonstrated that the shell effects on production cross section of 298Fl are mainly from de-excitation process. The general conclusion of this work is that the radioactive beam induced FE reactions show advantages for the excursion toward N=184 from current status.

Unpredictability in Hamiltonian systems with a hierarchical phase space

One of the main consequences of the complex hierarchical structure of chaotic regions and stability islands in the phase space of a typical nonlinear Hamiltonian system is the phenomenon of stickiness. The chaotic orbits that approach an island are trapped in its neighborhood for arbitrarily long times, in which the orbits behave similarly as quasiperiodic orbits. In this paper, we characterize the boundary between chaos and regular motion in the phase space of the standard map for distinct parameter values. The orbits are distinguished between regular and chaotic employing a recently proposed method of weighted Birkhoff averages. We quantify the dimension of the boundaries of the islands using the uncertainty exponent. In our simulations, we show that the dimension of the island's boundary depends on the scale of the initial condition uncertainty and the level of the hierarchical structure. We also show that the trapping in the vicinity of the islands causes an obstruction in the predictability of the final state of an orbit. We present how this loss of predictability results in larger dimensions at the inner levels of the islands.

Massless preheating and electroweak vacuum metastability

Current measurements of Standard Model parameters suggest that the electroweak vacuum is metastable. This metastability has important cosmological implications, because large fluctuations in the Higgs field could trigger vacuum decay in the early universe. For the false vacuum to survive, interactions which stabilize the Higgs during inflation -- e.g., inflaton-Higgs interactions or non-minimal couplings to gravity -- are typically necessary. However, the post-inflationary preheating dynamics of these same interactions could also trigger vacuum decay, thereby recreating the problem we sought to avoid. This dynamics is often assumed catastrophic for models exhibiting scale invariance since these generically allow for unimpeded growth of fluctuations. In this paper, we examine the dynamics of such "massless preheating" scenarios and show that the competing threats to metastability can nonetheless be balanced to ensure viability. We find that fully accounting for both the backreaction from particle production and the effects of perturbative decays reveals a large number of disjoint "islands of (meta)stability" over the parameter space of couplings. Ultimately, the interplay among Higgs-stabilizing interactions plays a significant role, leading to a sequence of dynamical phases that effectively extend the metastable regions to large Higgs-curvature couplings.

A simple model for arbitrary pollution effects on rotating free-surface flows

In an experimental context, the contamination of an air–liquid interface by ambient pollutants can strongly affect the dynamics and the stability of a given flow. In some configurations, the interfacial flow can even be blocked by surface tension effects. A cylindrical free-surface flow driven by a slow rotating disc is considered here as a generic example of such effects and is investigated both experimentally and numerically. We suggest here a simple numerical model, without any superficial transport of the pollutants, adaptable into any code for single-phase flows. For the stationary axisymmetric base flow, the radial velocity at the interface is set to zero whereas the usual stress-free boundary conditions are retained for the perturbations. The model does not feature any free parameter. For a geometrical aspect ratio of 1/4, known to display ambiguous behaviour regarding stability thresholds, the modal selection as well as a nonlinear stability island found in the experiments are well reproduced by the model, both qualitatively and quantitatively. The robustness of the model has also been validated by replacing the radial velocity profile by a more accurate experimental fit, with very little influence on the stability results.

Nonmonotonic Photostability of BA2MAn-1PbnI3n+1 Homologous Layered Perovskites.

Layered lead halide perovskites (2D LHPs) are attracting considerable attention as a promising material for a new generation of solar cell devices. LHPs have been presented as a more stable alternative to the more widespread 3D bulk perovskite materials; however, a critical analysis of their photostability is still lacking. In this work, we perform a comparative study between BA2MAn-1PbnI3n+1 (BA─butylammonium and MA─methylammonium) 2D LHPs with different dimensionalities (n = 1-3) and MAPbI3 3D perovskites. We compare different stability testing protocols including photometrical determination of iodine-containing products in nonpolar solvents, X-ray diffraction, and photoluminescence (PL) spectroscopy. The resulting trends of the photostability in an inert atmosphere based on PL spectroscopy measurements demonstrate a nonmonotonic dependence of the degradation rate on the perovskite layer thickness n with a "stability island" at n ≥ 3, which is caused by a combination of antibate factors of electronic structures and chemical compositions in the family of 2D perovskites. We also identify a critical oxygen concentration in the surrounding environment that affects the mechanism and strongly enhances the rate of layered perovskite photodegradation.

Landscape of the island of stability with self-consistent mean-field potentials

Incorporating effective nucleon mass from the noncovariant energy-density functional, the Schr\"odinger-equivalent central and spin-orbit mean-field potentials are determined and used in the microscopic-macroscopic method to calculate the ground-state shell corrections in superheavy nuclei with the charge numbers $Z=112--126$. The island of stability of superheavy nuclei is found to be rather flat and looks like one of coral reef origin due to the interplay between the proton shells at $Z=114$ and 120, and neutron shells at $N=174$ and 184, respectively. The shape coexistence in superheavy nuclei depends on spin-orbit potentials and can affect the spectrum of $\ensuremath{\alpha}$ decay. The one-quasiparticle spectra, isomeric states, and possible $\ensuremath{\alpha}$-decay energies are predicted in the nuclei of $\ensuremath{\alpha}$-decay chains of $^{295}119$ and $^{295--297,299}120$.

Fusion cross section of the superheavy Z=120 nuclei within the relativistic mean-field formalism

Background: Isotopes of $Z=107\text{--}118$ have been synthesized using cold fusion at GSI, Darmstadt, and hot fusion reactions at JINR, Dubna. Recently theoretical models have predicted $Z=120$ with $N=184$ as an island of stability in the superheavy valley. Hence it is crucial and exciting to predict theoretically the possible combination of projectiles and targets for the synthesis of $Z=120$, which can be informative for upcoming experiments.Purpose: Present theoretical investigations aim to explore the fusion characteristics of various isotopes of $Z=120$ within the relativistic mean-field formalism. We predict the most suitable projectile-target combination for the synthesis of element $Z=120$. The increase in fusion cross section of nuclei in the superheavy island directly signals the nuclear shell effects. Besides these, the analysis will be crucial and relevant for future experiments to synthesize superheavy nuclei.Methods: The microscopic nucleon-nucleon R3Y interaction and the density distributions for targets and projectiles are calculated using a relativistic mean-field formalism with the ${\mathrm{NL3}}^{*}$ parameter set. These densities and R3Y nucleon-nucleon (NN) interaction are then used to calculate the nuclear interaction potential using the double folding approach. Seventeen different projectile-target combinations that allow a high $N$/$Z$ ratio are considered in the present analysis to calculate the capture and/or fusion cross sections of various isotopes of $Z=120$ within the $\ensuremath{\ell}$-summed Wong formula.Results: The nuclear density distributions for the interacting projectile and target nuclei are obtained from relativistic mean-field Lagrangian for the ${\mathrm{NL3}}^{*}$ parameter set. The nucleus-nucleus interaction potential is estimated for seventeen possible projectile-target combinations using the mean-field density and the R3Y NN potential via a double folding approach. The fusion barriers are obtained by adding the Coulomb potential to the nucleus-nucleus interaction potential. Finally, the fusion and/or capture cross section is calculated for all the systems within the $\ensuremath{\ell}$-summed Wong formula. Further, the equivalent surface diffusion parameter is estimated to correlate the surface properties of interacting nuclei with the fusion cross section.Conclusions: The four Ti-based reactions with the heaviest available target $^{\mathrm{x}}\mathrm{Cf}$, namely, $^{46}\mathrm{Ti}+^{248}\mathrm{Cf}$, $^{46}\mathrm{Ti}+^{249}\mathrm{Cf}$, $^{50}\mathrm{Ti}+^{249}\mathrm{Cf}$, and $^{50}\mathrm{Ti}+^{252}\mathrm{Cf}$, and also $^{54}\mathrm{Cr}+^{250}\mathrm{Cm}$ are found to have the most suitable target-projectile combinations for the synthesis of various isotopes $Z=120$. We also notice that $^{48}\mathrm{Ca}$ beams merely provide the required number of protons to synthesize the element with $Z=120$. We established a correlation among the surface properties of interacting nuclei with the fusion characteristics in terms of the equivalent surface diffusion parameter.

Structural and decay properties of nuclei appearing in the α-decay chains of 296,298,300,302,304120 within the relativistic mean field formalism

An extensive study of [Formula: see text]-decay half-lives for various decay chains of isotopes of [Formula: see text] is performed within the axially deformed relativistic mean-field (RMF) formalism by employing the NL3, NL3[Formula: see text], and DD-ME2 parameter set. The structural properties of the nuclei appearing in the decay chains are explored. The binding energy, quadrupole deformation parameter, root-mean-square charge radius, and pairing energy are calculated for the even–even isotopes of [Formula: see text], which are produced in five different [Formula: see text]-decay chains, namely, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]. A superdeformed prolate ground state is observed for the heavier nuclei, and gradually the deformation decreases towards the lighter nuclei in the considered decay chains. The RMF results are compared with various theoretical predictions and experimental data. The [Formula: see text]-decay energies are calculated for each decay chain. To determine the relative numerical dependency of the half-life for a specific [Formula: see text]-decay energy, the decay half-lives are calculated using four different formulas, namely, Viola–Seaborg, Alex–Brown, Parkhomenko–Sobiczewski and Royer for the above said five [Formula: see text]-decay chain. We notice a firm dependency of the half-life on the [Formula: see text]-decay formula in terms of [Formula: see text]-values for all decay chains. Further, this study also strengthens the prediction for the island of stability in terms of magic number at the superheavy valley in the laboratories.

Function Composition from Sine Function and Skew Tent Map and Its Application to Pseudorandom Number Generators

In cryptography, the pseudorandom number sequences must have random appearance to be used in secure information systems. The skew tent map (STM) is an attractive map to produce pseudorandom sequences due to its easy implementation and the absence of stability islands when it is in chaotic behavior. Using the STM and sine function, we propose and analyze a function composition to propose a pseudorandom number generator (PRNG). In the analysis of the function composition, we use the bifurcation diagram and the Lyapunov exponent to perform a behavioral comparison against the STM. We show that the proposed function composition is more sensitive to initial conditions than the STM, and then it is a better option than the STM for cryptography applications. For the proposed function we determine and avoid the chaos annulling traps. The proposed PRNG can be configured to generate pseudorandom numbers of 8, 16 or 32 bits and it can be implemented on microcontrollers with different architectures. We evaluate the pseudorandomness of the proposed PRNG using the NIST SP 800-22 and TestU01 suites. Additionally, to evaluate its quality, we apply tests such as correlation coefficient, key sensitivity, statistical and entropy analysis, key space, linear complexity, and speed. Finally, we performed a comparison with similar PRNGs that produce pseudorandom sequences considering numbers of 8 and 32 bits. The results show that the proposed PRNG maintains its security regardless of the selected configuration. The proposed PRNG has five important features: easy implementation, configurable to produce number with 8, 16 or 32 bits, high processing speed, high linear complexity, and wide key space. These features are necessary for cryptographic systems.

New results on nuclear magicity and possible extension of the nuclear landscape

In nuclear theory, there is always a quest for possible extensions of the nuclear landscape and extending our knowledge to the limits of nuclear existence. In this study, we examine the stability and structural properties of a wide range of nuclei in super- and ultra-heavy region in a phenomenological semi-microscopic approach. we calculated the shell correlation energy, residual pairing correction energy, two-nucleon separation energy and two-nucleon energy gap for 3670 even–even nuclei along [Formula: see text]-stability line and two-neutron driplines in the ranges [Formula: see text] with [Formula: see text] and [Formula: see text] with [Formula: see text], respectively. To assure reliability and confidence of the new results in the ultra-heavy region, we extended the search space to include heavy and super-heavy nuclei. We report 83 double magic nuclei and address the predominance of proton and neutron magic numbers. Our calculations reproduced known results on nuclear magicity and present strong evidences on islands of stability and magic numbers in super- and ultra-heavy regions. We also address shifts in nuclear magicity along the nuclear landscape close to the [Formula: see text]-stability line and close to the neutron rich regions.

Modified empirical formulas and machine learning for α-decay systematics

Latest experimental and evaluated α-decay half-lives between 82 ⩽ Z ⩽ 118 have been used to modify two empirical formulas: (i) Horoi scaling law (2004 J. Phys. G: Nucl. Part. Phys. 30 945), and Sobiczewski formula (2005 Acta Phys. Pol. B 36 3095) by adding asymmetry dependent terms (I and I 2) and refitting of the coefficients. The results of these modified formulas are found with significant improvement while compared with other 21 formulas, and, therefore, are used to predict α-decay half-lives with more precision in the unknown superheavy region. The formula of spontaneous fission (SF) half-life proposed by Bao et al (2015 J. Phys. G: Nucl. Part. Phys. 42 085101) is further modified by using ground-state shell-plus-pairing correction taken from FRDM-2012 and using the latest experimental and evaluated SF half-lives between 82 ⩽ Z ⩽ 118. Using these modified formulas, contest between α-decay and SF is probed for the nuclei within the range 112 ⩽ Z ⩽ 118 and consequently probable half-lives and decay modes are estimated. Potential decay chains of 286−302Og and 287−303119 (168 ⩽ N ⩽ 184: island of stability) are analyzed which are found to be in excellent agreement with available experimental data. In addition, four different machine learning models: XGBoost, random forest, decision trees, and multilayer perceptron (MLP) neural network are used to train a predictor for α-decay and SF half-lives prediction. The prediction of decay modes using XGBoost and MLP are found to be in excellent agreement with available experimental decay modes along with our predictions obtained by the above-mentioned modified formulas.

Hyperheavy spherical and toroidal nuclei: The role of shell structure

The properties of toroidal hyperheavy even-even nuclei and the role of toroidal shell structure are extensively studied within covariant density functional theory. The general trends in the evolution of toroidal shapes in the $Z\approx 130-180$ region of nuclear chart are established for the first time. These nuclei are stable with respect of breathing deformations. The most compact fat toroidal nuclei are located in the $Z\approx 136, N\approx 206$ region of nuclear chart, but thin toroidal nuclei become dominant with increasing proton number and on moving towards proton and neutron drip lines. The role of toroidal shell structure, its regularity, supershell structure, shell gaps as well as the role of different groups of the pairs of the orbitals in its formation are investigated in detail. The lowest in energy solutions at axial symmetry are characterized either by large shell gaps or low density of the single-particle states in the vicinity of the Fermi level in at least one of the subsystems (proton or neutron). Related quantum shell effects are expected to act against the instabilities in breathing and sausage deformations for these subsystems. The investigation with large set of covariant energy density functionals reveals that substantial proton $Z=154$ and 186 and neutron $N=228$, 308 and 406 spherical shell gaps exist in all functionals. The nuclei in the vicinity of the combination of these particle numbers form the islands of stability of spherical hyperheavy nuclei. The study suggests that the $N=210$ toroidal shell gap plays a substantial role in the stabilization of fat toroidal nuclei.

Internal chaotic sea structure and chaos-chaos intermittency in Hamiltonian systems.

In this paper, we study the inhomogeneity of chaotic sea properties far from islands in billiardlike systems and its influence on distributions of particle's return times. A visibly homogeneous chaotic sea at certain parameters has a nontrivial internal structure, in particular, being divided into two chaotic phases with different properties. These phases are not separated by any obstacles, neither in phase nor in configuration spaces, and are partially overlaying. The emergence of a chaotic sea structure may be explained by the existence of remnants of integrable behavior, like sites of regular trajectories of broken islands of stability built into the chaotic sea. In the case of such chaotic seas, we find distributions of return times with two main sites of exponential decay.

Determination of the Operational Parameters for the Manufacturing of Spherical PVP Particles via Electrospray.

This work aims at bridging experimental and numerical approaches to determine the optimal operating parameters for the fabrication of well-shaped polyvinylpyrrolidone (PVP) particles via electrohydrodynamic atomization. Particular emphasis is given to the role of the PVP solution viscosity. Solutions of PVP at various concentrations dissolved in Dimethylformamide (DMF) were prepared and analyzed. Numerical simulation using a coupled electro-CFD model was used to determine the ranges of experimental flow rate and the voltage, ensuring that well-shaped spherical particles are produced. It was deduced that the optimal combination of the parameters (flow rate, voltage, and polymer concentration) can be well approximated by a scaling law. The established relationship allowed determination of a stability island that guarantees that the given polymer solution will form spherical particles. Analyzing morphology and sizes of the particles manufactured in the optimal parameters range, we show, among others, that the size of the PVP particles can be predicted as a function of the flow rate by a power scaling relationship.

Characteristic Times for the Fermi–Ulam Model

The mean Poincaré recurrence time as well as the Lyapunov time are measured for the Fermi–Ulam model. It is confirmed that the mean recurrence time is dependent on the size of the window chosen in the phase space where particles are allowed to return. The fractal dimension of the region is determined by the slope of the recurrence time against the size of the window and two numerical values are measured: (i) [Formula: see text] confirming normal diffusion for chaotic regions far from periodic domains and (ii) [Formula: see text] leading to anomalous diffusion measured inside islands of stability and invariant curves corresponding to regular orbits, a signature of local trapping of an ensemble of particles. The Lyapunov time is the inverse of the Lyapunov exponent. Therefore, the Lyapunov time is measured over different domains in the phase space through a direct determination of the Lyapunov exponent.

An Octad for Darmstadtium and Excitement for Copernicium

The discovery that copernicium can decay into a new isotope of darmstadtium and the observation of a previously unseen excited state of copernicium provide clues to the location of the “island of stability.”

Desynchronization Transitions in Adaptive Networks.

Adaptive networks change their connectivity with time, depending on their dynamical state. While synchronization in structurally static networks has been studied extensively, this problem is much more challenging for adaptive networks. In this Letter, we develop the master stability approach for a large class of adaptive networks. This approach allows for reducing the synchronization problem for adaptive networks to a low-dimensional system, by decoupling topological and dynamical properties. We show how the interplay between adaptivity and network structure gives rise to the formation of stability islands. Moreover, we report a desynchronization transition and the emergence of complex partial synchronization patterns induced by an increasing overall coupling strength. We illustrate our findings using adaptive networks of coupled phase oscillators and FitzHugh-Nagumo neurons with synaptic plasticity.

Enhanced Fusion Mechanisms Towards Synthesizing Superheavy Elements

In nature all of the heavy elements are produced by nuclear fusion reactions, mostly in supernova explosions and neutron star collisions, so, this is to date the only known and proven mechanism to produce heavy elements in usable quantities. In this work we approach a difficult challenge, namely, the possibility of fusion of heavy elements, taking as a test case the heaviest observationally stable element - ²³⁸U, showing that it is feasible, at least in principle with the help of existing technologies. The main idea behind is to show that fusion of lighter - than z=184 - nuclei is conceptually viable examining the tunnel effect assisted by an auxiliary field that will produce a Sauter like effect, and this is the pathway to explore the synthesis of elements higher than z=118. The production of theoretical untested elements like Unoctquadium-184 or close Z species could open a new chapter in the physics of super-heavy elements, and leads to a deeper understanding of nuclear decay channels and stability conditions. Nuclear fusion of heavy elements will open the breach to produce neutron rich elements, so we may obtain a deep insight into the physics of the island of stability. This work will review basic aspects of fusion physics related to the assisted fusion mechanism. An enhanced fusion perspective is found generalizing the work of [1] to space dependent fields and the cases of ²H, ¹⁰⁶Pd and ²³⁸U are presented for several test fields. A final section reviewing laser confinement fusion actual experiments capable of achieving the required energies is also reported.