Crossover Behavior Research Articles

Universal Non-Extensive Statistical Physics Temporal Pattern of Major Subduction Zone Aftershock Sequences.

Large subduction-zone earthquakes generate long-lasting and wide-spread aftershock sequences. The physical and statistical patterns of these aftershock sequences are of considerable importance for better understanding earthquake dynamics and for seismic hazard assessments and earthquake risk mitigation. In this work, we analyzed the statistical properties of 42 aftershock sequences in terms of their temporal evolution. These aftershock sequences followed recent large subduction-zone earthquakes of M ≥ 7.0 with focal depths less than 70 km that have occurred worldwide since 1976. Their temporal properties were analyzed by investigating the probability distribution of the interevent times between successive aftershocks in terms of non-extensive statistical physics (NESP). We demonstrate the presence of a crossover behavior from power-law (q ≠ 1) to exponential (q = 1) scaling for greater interevent times. The estimated entropic q-values characterizing the observed distributions range from 1.67 to 1.83. The q-exponential behavior, along with the crossover behavior observed for greater interevent times, are further discussed in terms of superstatistics and in view of a stochastic mechanism with memory effects, which could generate the observed scaling patterns of the interevent time evolution in earthquake aftershock sequences.

Spin Crossover Coordination Polymers with Pyridine-Like Modification through Selective Guest Molecules

A porous 3D FeII coordination polymer made of 4,4′-bipyridine ligands (bipy) and [N(CN)2]− (dca) organic bridges, [Fe(bipy)2dca]ClO4·CHCl3·CH3OH (1·CHCl3·CH3OH), has been synthesized as single crystals, by a slow diffusion technique at room temperature. Single-crystal X-ray diffraction analysis has shown that the structure of 1·CHCl3·CH3OH presents large volume values of porosity (1790 Å3 per iron atom). It crystallizes in the orthorhombic Cmc21 space group but undergoes a phase transition to Cmca at 298 K, presumably due to solvent release. According to magnetic data, this material displays a gradual spin crossover behavior, along with a thermal hysteresis loop of 15 K around 190 K. However, when lattice solvent molecules are removed, the magnetic behavior changes drastically resulting in more gradual spin conversion or even silencing the spin crossover behavior of the as-synthesized complex (1·CHCl3·CH3OH), evidencing the influence of guest molecules on the magnetic properties by host–guest interactions. This property was confirmed by spatiotemporal optical microscopy studies, performed on several single crystals. The generation of a host lattice that interacts with exchangeable guest species in a switchable fashion has implications for the generation of previously undeveloped advanced materials with applications in areas such as molecular sensing.

Rational Design of Iron Spin-Crossover Complexes Using Heteroscorpionate Chelates.

The optical, structural, and magnetic properties of iron(II,III) sandwich complexes, Fe(Tp')2n+ (Tp' = bis(3,5-dimethylpyrazolyl)benzotriazolylborate), are described. The intensely colored FeII(Tp')2 (orange) and FeIII(Tp')2+ (purple) show strong MLCT bands. Geometric isomerism for M(Tp')2 is established crystallographically in the racemate of chiral cis-Fe(Tp')2. For the first time, paramagnetic 11B NMR describes solution-phase low-spin (LS, S = 0) to high-spin (HS, S = 2) crossover behavior in Fe(Tp')2. Thermochemical parameters for solution-phase SCO of Fe(Tp')2 demonstrate the endothermic LS to HS conversion and entropic preference of the HS state. Entropy changes for both Fe(Tp')2 isomers are significantly larger than for the majority of iron scorpionate SCO systems. Solid-state magnetic and thermochemical measurements show cis-Fe(Tp')2 to be thermally stable up to 520 K, allowing experimental investigation of a solid-state SCO magnetic hysteresis of over 45 K. A large solution vs solid-state SCO difference was observed: cis-Fe(Tp')2 shows Tc ≈ 270 K (solution) and Tc ≈ 385 K (solid), with the remarkably wide ΔTc ≈ 115 K; trans-Fe(Tp')2 shows Tc ≈ 278 K (solution) and Tc ≈ 372 K (solid). Solid-state Tc values are among the highest seen for iron(II) molecular systems. The large solution/solid ΔTc difference is explained by "anchoring" intermolecular interactions in the solid state that prevent thermal expansion of the LS iron(II) coordination sphere in its transition to the HS state. DFT calculations, validated against LS cis-Fe(Tp')2 crystallography and LS to HS SCO thermochemical parameters, demonstrate the role the benzotriazole rings play in its structural and optical properties. The Lewis basicity of M(Tp')2 is shown with the structural characterization of the air-stable tin(II) adduct [cis-Fe(Tp')2-SnCl2]; tin(II) coordination does not alter the iron(II) spin state. The Tp' chelate adds functionality (asymmetry, chirality, chemical reactivity) to the array of iron SCO materials for potential incorporation into nanoscale magnetic switches and spintronic devices.

Effect of A-site Gd3+ substitution on structural, optical and electrical properties of La2−xGdxCrMnO6 double perovskites

Nanocrystalline new double perovskites La2-xGdxCrMnO6 (x = 0.5, 1.0, 1.5 and 2.0) have been prepared by employing auto-combustion sol-gel method. Herein, we investigate the influence of Gd3+ on structural, optical and transport properties of La2CrMnO6. The Rietveld refinement reveals that the said materials crystallize in orthorhombic structure with Pbnm space group symmetry. The vibrational phonon modes have been examined using the infrared reflectance technique and were fitted using the Lorentz oscillator model. The spectra contain various IR active phonon modes. The position and width of these modes were determined and correlated with ionic substitution at the A-site. The optical conductivity shows the semiconducting nature of the series. The Raman spectra with active modes were also studied in connection with substitution. The optical bandgap varies from (1.62–1.67 eV) which has been estimated from diffuse reflectance spectra and found to increase with substitution whereas the Urbach energy decreases with increasing Gd3+ content. A significant change has been observed in resistive response and the resistivity vary from to The crossover behaviour at ∼ from variable range hopping to small polaron hopping has been observed.

Model of conversion of flow from confined to unconfined with the generalized Mittag-Leffler process

We considered in the paper a mathematical model used to replicate the conversion from confined to unconfined flow due to groundwater abstraction. We argued that the existing model, while very useful, however, does not capture the effect of the aquitard with fractures, as in such media there is a crossover behavior from stretched exponential to power law. We modified the model by replacing the exponential decay component with the generalized Mittag-Leffler function, which yields a model with nonlocal properties. To solve the system, we consider two different approaches, the first consists of discretizing the model directly using the forward Euler method, and the second consists of converting the model to an integral equation and deriving the solution by employing a polynomial interpolation approach. We presented using the Von Neumann stability approach for the confined part and both yield stability unconditionally. Some numerical simulations are performed.

Push and Pull Effect of Methoxy and Nitro Groups Modifies the Spin-State Switching Temperature in Fe(III) Complexes.

We have explored the impact of electron-donating (methoxy) and electron-withdrawing (nitro) substituents on SalEen ligand based spin crossover (SCO) behavior of Fe(III) complexes. Thus, 3-X-substituted SalEen ligands were employed to prepare [Fe(3-X-SalEen)2]·NCSe, where X = OMe (1), H (2), and NO2 (3) (3-X-SalEen is the condensation product of 3-substituted salicylaldehyde and N-ethylethylenediamine). The characteristic spin transition temperature (T 1/2) is shown to shift to a lower temperature when an electron-donating substituent (OMe) is used and to a higher temperature when an electron-withdrawing substituent (NO2) is used. We used experimental and theoretical methods to determine the reasons for this behavior. The solid-state magnetic data revealed the transition temperatures for complexes 1, 2, and 3 to be 219, 251, and 366 K, respectively. The solution-state magnetic data also support this trend in T 1/2 values. UV-vis spectra analysis indicates that there is greater delocalization in the π-manifold of the ligand when the nitro group is the substituent. Theoretical studies through density functional theory methods suggest the methoxy substituent decreases the energy gap between the t2g and eg orbitals (explaining the lower T 1/2 value), while the nitro substituent increases the energy gap between the t2g and eg orbitals and thus increases the T 1/2 value.

Dynamics and stability results for novel coronavirus (2019-nCov) model via Caputo-Fabrizio fractional derivative

Recently, many mathematical models have been studied to better understand the coronavirus infection. Most of these models are based on classical integer-order derivatives which cannot capture the fading memory and crossover behavior found in many biological phenomena. Therefore, the aim of this paper is to establish the existence and uniqueness of solutions to novel coronavirus (COVID-19) model including Caputo-Fabrizio (CF)-fractional derivative. We derive existence and uniqueness results with the help of properties of CF-fractional calculus, fixed-point theorem and iterative method. Finally, the model is proved to have a disease-free and an endemic equilibrium point.

Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer

We construct the exact solution for a family of one-half spin chains explicitly. The spin chains Hamiltonian corresponds to an isotropic Heisenberg Hamiltonian, with staggered exchange couplings (ECs) that take only two different values. We work out the exact solutions in the one-excitation subspace. Regarding the problem of quantum state transfer, we use the solution and some theorems concerning the approximation of irrational numbers, to show the appearance of conclusive pretty good transmission for chains with particular lengths. We present numerical evidence that pretty good transmission is achieved by chains whose length is not a power of two. The set of spin chains that shows pretty good transmission is a subset of the family with an exact solution. Using perturbation theory, we thoroughly analyze the case when one of the EC strengths is orders of magnitude larger than the other. This strong coupling limit (SCL) allows us to study, in a simple way, the appearance of pretty good transmission. The use of analytical closed expressions for the eigenvalues, eigenvectors, and transmission probabilities allows us to obtain the precise asymptotic behavior of the time where the pretty good transmission is observed. Moreover, we show that this time scales as a power law whose exponent is an increasing function of the chain length. We also discuss the crossover behavior obtained for the pretty good transmission time between the regimes of SCL and the one observed when the ECs are of the same order of magnitude.

Oscillatory, crossover behavior and chaos analysis of HIV-1 infection model using piece-wise Atangana–Baleanu fractional operator: Real data approach

There are many fatal diseases which are caused by virus. Different types of viruses cause different infections. One of them is HIV-1 infection which caused by retrovirus. HIV-1 infection is a hazardous disease that can lead to cancer, AIDS, and other serious illnesses. Several mathematical models have been proposed in the field and examined using various methods. In this manuscript, the newly suggested piece-wise (PW) Atangana–Baleanu (AB) fractional operator is used to examine HIV-1 infection. Some theorems related to the existence of the solution to the examined model are proved through fixed point results. The Ulam–Hyers (UH) stability and its different forms are presented for the proposed PW HIV-1 infection model. The considered model’s numerical results are attained via the Newton interpolation method. The results are graphically illustrated via MATLAB software to show the behavior of the considered model. Oscillatory and complex dynamics are obtained for some fractional orders and show the crossover behavior of the proposed model. The model’s simulation of infected class is fitted with the real data taken for six different countries. It proves the validity and accuracy of the suggested approach.

Direct observation of coexisting Kondo hybridization and antiferromagnetic state in UAs2

In $f$-electron heavy fermion systems, a wide variety of fascinating magnetic and electronic properties arise, and they are often thought to be related to a crossover behavior between localized and itinerant regimes for $f$ electrons. Uranium-based compounds with partially occupied $5f$ orbitals provide an ideal platform to elucidate the outstanding issue of the competition between magnetic order and Kondo entanglement. Using angle-resolved photoemission spectroscopy, complemented by density functional theory simulations, we probe the temperature-dependent evolution of the low-energy electronic structure of ${\mathrm{UAs}}_{2}$ and observe two nearly flat bands of different origin in the antiferromagnetic (AFM) state. A nearly flat band which behaves with quasi-two-dimensional character has been observed and contributed to the heavy spectral weight at the \cyrchar\CYRG{} point around ${E}_{\mathrm{F}}$. This flat band reveals typical Kondo hybridization. Another flat band around the $M$ point is closely related to paramagnetic (PM)-AFM phase transition, which opens an energy gap below the transition temperature \ensuremath{\sim}273 K. Our results provide direct spectral demonstration of the electronic structure evolution across the $f\text{\ensuremath{-}}c$ hybridization and PM-AFM transition in ${\mathrm{UAs}}_{2}$.

Modern and generalized analysis of exogenous growth models

The work presents a critical analysis of the model that could replicate the dynamic of long-run economic growth by regarding the capital accumulation, the labor or the population growth and increases in productivity that depends on technological progress. In this case, we calculated the equilibrium point and gave the model’s existence and uniqueness conditions. We introduced an analysis of the Lyapunov function for the first and second derivatives. Infections point analysis was presented in detail, and a numerical scheme based on the Lagrange polynomial interpolation was used to derive the numerical solution of the classical model. To introduce into mathematical formulation nonlocal behaviors, four cases were considered, including the effect of the power-law, the impact of fading memory, the development of crossover from stretched exponential to power-law and crossover behaviors from power law to stochastic. For each case, Linear growth and Lipschitz conditions were used to establish the uniqueness of the exact solution. Further, different numerical techniques were used to prove convergence of the used numerical scheme. Finally, numerical simulations were performed for other cases.

Effect of pressure on electrical and optical properties of metal doped TiO2

A comparative study of electrical and optical properties of powder and its corresponding pellets has been done on 3d-doped TiO2. Ti1-xMxO2 (M = Sc, V, Cr, Mn, Fe, Co, Ni, Cu, Zn) powder and its corresponding pellet with doping concentration x = 0.05 has been prepared using solid state route. Optical and electrical measurements have been performed for all prepared samples and interestingly, it is observed that due to having external pressure (i.e. strain) both the properties change significantly. A rigorous theoretical calculation has been carried out to verify the experimental band gap obtained from optical absorption spectroscopy. In case of pellet sample band gap decreases as compared to the powder sample due to variation of pressure inside the structures. Role of doping has also been investigated both in pellet and powder forms and found that the band gap decreases as the atomic number of dopants increases. A cross-over behavior seen in pellet sample on doping with Ni, Cu and Zn (i.e. band gap increases with increase in atomic number of dopant). Electrical resistivity measurements have been carried out for both pellet and powder samples and it is found that in case of strain free samples the value of resistivity is smaller while in case of strained sample it is quite large. We believe that the present study suggests a novel approach for tuning the electrical and optical properties of semiconducting oxides either from doping or from applied pressure (or strain).

Off-critical wetting layer divergence at the liquid/vapor interface of binary liquid mixtures.

Surface wetting phenomena impact chemistry, physics, biology, and engineering. The wetting behaviors of partially miscible binary liquid systems are especially complex. Here, we report evidence of universal behavior in the divergence of wetting layer growth at liquid-vapor interfaces of the cyclohexane + aniline, hexane + o-toluidine, and methanol + carbon disulfide systems. Layer growth on the micron scale was followed using visible light scattering from stirred samples. The layer thicknesses were found to diverge with decreasing temperature when coexistence was approached from the one-phase region, but only for solutions richer in the higher density/higher surface tension component. The onset of divergence was <1K above the bulk coexistence temperature; nearer the critical composition, the onset temperature was the critical temperature itself. All three systems showed identical divergent wetting properties after variable normalization. In contrast, no divergent wetting layer formation was seen in the benzene + 1,2-propanediol or water + phenol systems. The mathematical signof the Hamaker constant correlates with the contrasting behaviors. Collectively, these results have implications for theoretical descriptions of adsorption layer growth and crossover behavior, for measurements of complete wetting temperatures, and for practical applications.

Origin of the Acoustic Bandgaps in Hypersonic Colloidal Phononics: The Role of the Elastic Impedance.

How phonons propagate in nanostructures determines the flow of elastic and thermal energy in dielectric materials. However, a reliable theoretical prediction of the phonon dispersion relation requires experimental verification both near to and far from the Brillouin zone of the nanostructure. We report on the experimental hypersonic phonon dispersion of hard (SiO2) and soft (polymer) fcc colloidal crystals infiltrated in liquid polydimethylsiloxane with different elastic impedance contrast using Brillouin light spectroscopy. We discuss the distinct differences with first-principles full elastodynamic calculations involving a multiple-scattering theory. Interparticle contacts strongly impact the long-wavelength speed of sound and the nature of the particle vibration resonance-induced hybridization hypersonic bandgap. The absence of the order-induced Bragg bandgap in SiO2 and its presence in soft opals cannot be fully accounted for by the theory, limiting its predictive power. Bridging the elasticity of the two colloidal crystals with suitable SiO2 core–shell (polymer) particles reveals an unprecedented crossover behavior in the dispersion relation. In view of many conversational parameters, the control tuning of phonon propagation in soft matter-based hypersonic phononics remains challenging.

Control of quantum dynamics: non-Markovianity and speedup of a massive particle evolution due to gravity

We illustrate two linear configurations (one-side model and two-side model) for implementing a non-Markovian speedup evolution of a massive particle gravitationally coupled with a controllable environment: multiple massive particles. By controlling the environment, for instance by choosing a judicious the mass of the environmental particles or by changing the separation distance of each massive particle, two dynamical crossover behaviors from Markovian to non-Markovian and from no-speedup to speedup are achieved due to the gravitational interactions between the system particle and each environmental particle. Numerical calculation also shows that the critical mass of the environmental particles or the critical separation distance for these two dynamical crossover behaviors restrict each other directly. The larger the value of the mass of the environmental particles is, the smaller the value of the critical separation distance should be requested. In this work, the non-Markovian dynamics is the principal physical reason for the speedup evolution of a quantum system. Particularly, the non-Markovianity of the system mass particle in the two-side model has better correspondence with the quantum speed limit time than that in the one-side model.

Crossover behavior of the Zika virus infection and the delayed immune response

The control of the transmission of viruses is really challenging. Zika virus is the twentieth among the most deadly viruses in world’s history. With the advancement in research and technology several epidemiological issues are controlled, yet the vector borne diseases have remained a great challenge and the most effective approach to control its spread is to strictly adhere to the precautionary measures. Computational framework is ideal to forecast the impact of precautionary measures on the crossover behavior of the Zika virus and the delay in population growth, caused by such viruses. During this research, a delayed computational model is studied and the dynamical analysis with useful thresholds are reported. The compartmental model is comprised of the interactions of Zika virus infected cells and the short lived effector cells. Based on the fetal abnormalities, associated with the Zika virus infection, delayed pregnancy is recommended by WHO. The impact of the Zika virus to the delayed pregnancies, to avoid such fetal complications is demonstrated with the aid of dynamical analysis of interactions with delay at the inter-cellular levels. The dynamics are depicted numerically relative to key parameters and useful conclusions are drawn.

Crossover behaviors via piecewise concept: A model of tumor growth and its response to radiotherapy

This study aims to combine 3 different models, which take into account the pre-treatment, during the treatment and post-treatment processes of the tumor growth, with the piecewise derivative, and to consider these processes as a whole thanks to this new concept. This concept leads us to analyze and predict the process from the beginning to the end of the tumor, as it offers the possibility to observe many behaviors from crossover to stochastic processes. Moreover, the piecewise differential operators, which can be constructed with operators such as classical, Caputo, Caputo–Fabrizio, Atangana–Baleanu and stochastic derivative, have opened new doors to readers in different disciplines and enable them to capture different behaviors in different time intervals. Thus, researchers can achieve successful results in capturing reality by applying these operators to real-world problems.

A series of new Fe(II) coordination polymers based-on [Hg(XCN)3]− or [Hg(XCN)4]2− (X = S, Se) building blocks: Synthesis, crystal structure and magnetic property

Self-assembly of the tetrahedral metalloligand building block [(HgII(XCN)4]2-, where X ​= ​S or Se, a series of bis-monodentate pyridine-like ligands and iron(II) compounds has afforded seven new heterobimetallic HgII–FeII coordination polymers. Single crystal X-ray diffraction structural analysis revealed the infinite two-dimensional (2D) sheet with different topologies for all the complexes except 3, which belonged to inherent 3D-structure. The results of the temperature dependent magnetic susceptibility investigation over all the complexes discovered the paramagnetic behavior for the high spin iron(II) ion in all the complexes within the temperature range of 2–300K, except complex 6. The thermo- and photomagnetic property study for complex 6 showed incomplete spin crossover (SCO) behaviors with interesting thermomagnetic properties and light-induced excited spin state trapping effect (LIESST). The results show that the ligand field, configurations, rigidity, and polarity of the bridging ligands, as well as the coordination mode with the Fe(II) ion of the building units, are important for the design and synthesis of the targeted coordination polymers.

Piecewise Fractional Analysis of Omicron Type Covid-19 Infection

In this article, we investigate the new type of COVID-19 caused by the Omicron virus in the sense of piece-wise fractional derivative. The total interval is divided into two sub-intervals under fractional Caputo and Atangana Baleanu operators respectively. The whole model is divided into six compartments in which the agent of infection from Omicron is included. The proposed piecewise fractional model is tested for fixed points using the different theorems of fixed point theory. The approximate solution is carried out by the technique of the piecewise fractional Adams-Bashforth method. All the agents of the considered problem are tested for graphical representation. The first sub-interval is graphed for the Caputo derivative while the second interval dynamics are checked by Atangana Baleanu fractional operator. The numerical simulation results are established at different fractional orders along with the comparison of integer orders. This consideration will also show the cross-over behavior of the Omicron dynamics in human life and will be essential for its controlling and future prediction on various sub-intervals. The sensitivity of different parameters is also checked graphically. Keywords: Piecewise Fractional Derivative, Fractional mathematical model Omicron; Qualitative analysis; Caputo derivative; Fractional Adams-Bashforth technique.

Kondo entanglement in the quasi-two-dimensional heavy fermion compound CeSb2

In the heavy fermion system, development of the Kondo coherence usually occurs as a crossover behavior. However, accurate definition of the onset temperature for complete formation of the heavy quasiparticles is to some extent controversial. Here, the electronic structure of the quasi-two-dimensional Kondo lattice ${\mathrm{CeSb}}_{2}$ has been studied by high resolution angle-resolved photoemission spectroscopy (ARPES) and dynamical mean-field theory approach combined with density functional theory. A heavy quasiparticle band, which originates from the hybridization between $f$ electrons and conduction electrons, has been observed directly. Moreover, temperature-dependent electronic structure study reveals a transition from high-temperature local spins to low-temperature itinerant electrons in ${\mathrm{CeSb}}_{2}$ and the onset temperature of the hybridized c-f spectral weight revealed by laser-ARPES is consistent with the crossover temperature from transport and magnetic measurements. Our findings are essential for a microscopic understanding of different energy scales in the heavy fermion system and demonstrate the probability of laser-ARPES in studying the bulk 4f-electron properties of Ce-based compounds.