Moment Stability Research Articles

Electronic structure and magnetic properties of dilute U impurities in metals

The electronic structure and magnetic moment of dilute U impurity in metallic hosts have been calculated from first principles. The calculations have been performed within local density approximation of the density functional theory using Augmented plane wave+local orbital (APW+lo) technique, taking account of spin–orbit coupling and Coulomb correlation through LDA+U approach. We present here our results for the local density of states, magnetic moment and hyperfine field calculated for an isolated U impurity embedded in hosts with sp-, d- and f-type conduction electrons. The results of our systematic study provide a comprehensive insight on the pressure dependence of 5f local magnetism in metallic systems. The unpolarized local density of states (LDOS), analyzed within the frame work of Stoner model suggest the occurrence of local moment for U in sp-elements, noble metals and f-block hosts like La, Ce, Lu and Th. In contrast, U is predicted to be nonmagnetic in most transition metal hosts except in Sc, Ti, Y, Zr, and Hf consistent with the results obtained from spin polarized calculation. The spin and orbital magnetic moments of U computed within the frame of LDA+U formalism show a scaling behavior with lattice compression. We have also computed the spin and orbital hyperfine fields and a detail analysis has been carried out. The host dependent trends for the magnetic moment, hyperfine field and 5f occupation reflect pressure induced change of electronic structure with U valency changing from 3+ to 4+ under lattice compression. In addition, we have made a detailed analysis of the impurity induced host spin polarization suggesting qualitatively different roles of f-band electrons on moment stability. The results presented in this work would be helpful towards understanding magnetism and spin fluctuation in U based alloys.

Inverse energy cascade in developed turbulence at the breaking of the symmetry of helical modes

The interactions breaking the symmetry of the positive and negative components of the total helicity have been considered with quasinormal approximations and the cascade model of helical turbulence. In the ideal case of the absence of one of them, the equations have two sign-definite integrals of motion; as a result, an inverse energy cascade occurs, as for two-dimensional turbulence. Owing to the instability of the second moments, whose mechanism was proposed in A. Belian, O. Chkhetiani, E. Golbraikh, and S. Moiseev, Physica A 258, 55 (1998), the generation of large-scale modes has been considered within the Fourier equations of hydrodynamics under the assumption of a quasinormal velocity field. The presence of background turbulence with large-scale helical perturbations and small-scale sources of the energy and helicity is a determining circumstance in this mechanism. The possibility of the inverse cascade in the case of incomplete degeneracy of one of the helicity components has been studied in the numerical experiments with the cascade model. It has been shown that the existence of the inverse (toward large scales) energy flux from small-scale perturbations requires a certain external-action-generated level of helical noise in large modes, which depends on the degree of “mixing” of different-sign helical components of the velocity field.

Nilsson-SU3 self-consistency in heavy N=Z nuclei

It is argued that there exist natural shell model spaces optimally adapted to the operation of two variants of Elliott' SU3 symmetry that provide accurate predictions of quadrupole moments of deformed states. A selfconsistent Nilsson-like calculation describes the competition between the realistic quadrupole force and the central field, indicating a {\em remarkable stability of the quadruplole moments}---which remain close to their quasi and pseudo SU3 values---as the single particle splittings increase. A detailed study of the $N=Z$ even nuclei from $^{56}$Ni to $^{96}$Cd reveals that the region of prolate deformation is bounded by a pair of transitional nuclei $^{72}$Kr and $^{84}$Mo in which prolate ground state bands are predicted to dominate, though coexisting with oblate ones,

Stabilization of weak ferromagnetism by strong magnetic response to epitaxial strain in multiferroic BiFeO3.

Multiferroic BiFeO3 exhibits excellent magnetoelectric coupling critical for magnetic information processing with minimal power consumption. However, the degenerate nature of the easy spin axis in the (111) plane presents roadblocks for real world applications. Here, we explore the stabilization and switchability of the weak ferromagnetic moments under applied epitaxial strain using a combination of first-principles calculations and group-theoretic analyses. We demonstrate that the antiferromagnetic moment vector can be stabilized along unique crystallographic directions ([110] and [–110]) under compressive and tensile strains. A direct coupling between the anisotropic antiferrodistortive rotations and the Dzyaloshinskii-Moria interactions drives the stabilization of the weak ferromagnetism. Furthermore, energetically competing C- and G-type magnetic orderings are observed at high compressive strains, suggesting that it may be possible to switch the weak ferromagnetism “on” and “off” under the application of strain. These findings emphasize the importance of strain and antiferrodistortive rotations as routes to enhancing induced weak ferromagnetism in multiferroic oxides.

Delay-independent stability of moments of a linear oscillator with delayed state feedback and parametric white noise

The stability of a linear oscillator with delayed state feedback driven by parametric Gaussian white noise is studied in this paper. The first and second order moment equations of the system response are derived by using moment method and Itô differential rule. Based on the moment equations, the delay-independent stable conditions of both moments are proposed: For the first order moment, the sufficient and necessary condition that guarantee delay-independent stability is identified to that of the deterministic system; for the second order moment, the sufficient condition that ensure delay-independent stability depends on noise intensity. The theoretical results are also illustrated with numerical simulations.

Admission Control for Multidimensional Workload input with Heavy Tails and Fractional Ornstein-Uhlenbeck Process

The infinite source Poisson arrival model with heavy-tailed workload distributions has attracted much attention, especially in the modeling of data packet traffic in communication networks. In particular, it is well known that under suitable assumptions on the source arrival rate, the centered and scaled cumulative workload input process for the underlying processing system can be approximated by fractional Brownian motion. In many applications one is interested in the stabilization of the work inflow to the system by modifying the net input rate, using an appropriate admission control policy. In this paper we study a natural family of admission control policies which keep the associated scaled cumulative workload input asymptotically close to a prespecified linear trajectory, uniformly over time. Under such admission control policies and with natural assumptions on arrival distributions, suitably scaled and centered cumulative workload input processes are shown to converge weakly in the path space to the solution of a d-dimensional stochastic differential equation driven by a Gaussian process. It is shown that the admission control policy achieves moment stabilization in that the second moment of the solution to the stochastic differential equation (averaged over the d-stations) is bounded uniformly for all times. In one special case of control policies, as time approaches ∞, we obtain a fractional version of a stationary Ornstein-Uhlenbeck process that is driven by fractional Brownian motion with Hurst parameter H > ½.

Admission Control for Multidimensional Workload input with Heavy Tails and Fractional Ornstein-Uhlenbeck Process

The infinite source Poisson arrival model with heavy-tailed workload distributions has attracted much attention, especially in the modeling of data packet traffic in communication networks. In particular, it is well known that under suitable assumptions on the source arrival rate, the centered and scaled cumulative workload input process for the underlying processing system can be approximated by fractional Brownian motion. In many applications one is interested in the stabilization of the work inflow to the system by modifying the net input rate, using an appropriate admission control policy. In this paper we study a natural family of admission control policies which keep the associated scaled cumulative workload input asymptotically close to a prespecified linear trajectory, uniformly over time. Under such admission control policies and with natural assumptions on arrival distributions, suitably scaled and centered cumulative workload input processes are shown to converge weakly in the path space to the solution of a d-dimensional stochastic differential equation driven by a Gaussian process. It is shown that the admission control policy achieves moment stabilization in that the second moment of the solution to the stochastic differential equation (averaged over the d-stations) is bounded uniformly for all times. In one special case of control policies, as time approaches ∞, we obtain a fractional version of a stationary Ornstein-Uhlenbeck process that is driven by fractional Brownian motion with Hurst parameter H > ½.

EFFECT OF RESISTANCE TRAINING OF THE WRIST JOINT MUSCLES ON MULTI-DIGIT COORDINATION.

This study investigated the effects of a specific regimen of resistance training on coordinated actions of human hand digits during grasping. Participants were instructed to hold a rectangular object with all five digits and to maintain the orientation of the object against transient perturbation. Indices of co-varied actions (i.e., synergies) among multi-digit grasping and rotational actions were quantified. The index of anticipatory changes of co-varied actions among digit forces (i.e., anticipatory synergy adjustment) was also quantified, which represents the controller's ability to predict an upcoming perturbation. The synergies of both grasping force and moment stabilization increased with the training. No change in the index of anticipatory synergy adjustment with training was observed. The current results suggest that the resistance training on the wrist could be an effective way to enhance both voluntary muscle force/torque production capability and ability to stabilize task performances during multi-digit prehensile tasks.

The Response of a Rectangular Thin Plate Subjected to In-Plane Narrow Band Noise Excitation

One stochastic dynamical model of a thin rectangular plate subject to in-plate parametrical narrow band noise excitation is proposed based on elastic theory and Galerkin’s approach. At first the model is simplified applying the multiple scale method and the averaged equation in Ito form is obtained. Secondly, the stochastic moment stability of the steady state responses are analyzed by Floquet theory and the moment method. Finally, the second order moment of the system is obtained, which can be used to estimate the variance of the responses. The numerical results agree with the theatrical analysis.

Robustness of Stochastic Discrete-Time Switched Linear Systems With Application to Control With Shared Resources

Motivated by control applications relying on shared resources (such as computation time or bandwidth), we analyze the stability and robustness of discrete-time switched linear systems with stochastic commutations. We show that a wide class of shared resources control strategies can be modeled by a stochastic jump linear system involving two stochastic processes. The class of systems we study encompasses Markov chains and independent and identically distributed switching processes. For these systems, we recall existing definitions of stability and robustness, by relying on the input-to-state stability (ISS) property. We show that, for the class of systems under concern, $\delta$ -moment stability is equivalent to $\delta$ -moment ISS and that they both imply almost sure ISS. Several sufficient conditions are provided to guarantee these properties. Anytime control design for a translational oscillator/rotational actuator (TORA) system is used to illustrate all these concepts.

Moment stability for a predator–prey model with parametric dichotomous noises**Project supported by the National Natural Science Foundation of China (Grant No. 11272051).

In this paper, we investigate the solution moment stability for a Harrison-type predator–prey model with parametric dichotomous noises. Using the Shapiro–Loginov formula, the equations for the first-order and second-order moments are obtained and the corresponding stable conditions are given. It is found that the solution moment stability depends on the noise intensity and correlation time of noise. The first-order and second-order moments become unstable with the decrease of correlation time. That is, the dichotomous noise can improve the solution moment stability with respect to Gaussian white noise. Finally, some numerical results are presented to verify the theoretical analyses.

Stable local moments of vacancies, substitutional and hollow site impurities in graphene

The two-sublattice nature of graphene lattice in conjunction with three-fold rotational symmetry, allows for the p-wave hybridization of the impurity state with the Bloch states of carbon atoms. Such an opportunity is not available in normal metals where the wave function is scalar. The p-wave hybridization function appears when dealing with vacancies, substitutional adatoms and the hollow site impurities while the s-wave mixing on graphene lattice pertains only to the top site impurities. In this work, we compare the local moment formation in these two cases and find that the local moments formed by p-wave mixing compared to the s-wave one are robust against the changes in the parameters of the model. Furthermore, we investigate the stability of the local moments in the above cases. We find that the quantum fluctuations can destroy the local moments in the case of s-wave hybridization, while the local moments formed by p-wave hybridization survive the quantum fluctuations. Based on these findings, we propose vacancies, substitutional adatoms, and hollow site adatoms as possible candidates to produce stable local moments in graphene.

Characterization of tetragonal phases of SrRuO3 under epitaxial strain by density functional theory

Using density functional theory calculations we study the effect of strain on the magnetic and structural properties of tetragonal SrRuO3. All four different oxygen octahedra rotation patterns that are in agreement with tetragonal symmetry are considered and compared with the bulk-like orthorhombic structure. We find that among the tetragonal structures the phase with I4 /mcm symmetry is energetically most favorable. This structure is also lower in energy than the orthorhombic phase for compressive and tensile strain larger than −2.1% and +3.8%, respectively. The stability of the magnetic moment is found to be greatly dependent on the octahedra rotation pattern. The magnetic moment of the zero or one-tilt systems is quenched under tensile strain, while ferromagnetic order is preserved in the two or three-tilt systems.

Stabilizing and increasing the magnetic moment of half-metals: The role of Li in half-HeuslerLiMnZ(Z=N,P,Si)

Li-based half-Heusler alloys have attracted much attention due to their potential applications in optoelectronics and because they carry the possibility of exhibiting large magnetic moments for spintronic applications. Due to their similarities to metastable zinc blende half-metals, the half-Heusler alloys $\beta$-LiMnZ (Z = N, P and Si) were systematically examined for their electric, magnetic and stability properties at optimized lattice constants and strained lattice constants that exhibit half-metallic properties. Other phases of the half-Heusler structure ($\alpha$ and $\gamma$) are also reported here, but they are unlikely to be grown. The magnetic moments of these stable Li-based alloys are expected to reach as high as 4 $\mu_{\mathrm{B}}$ per unit cell when Z = Si and 5 $\mu_{\mathrm{B}}$ per unit cell when Z = N and P, however the antiferromagnetic spin configuration is energetically favored when Z is a pnictogen. $\beta$-LiMnSi at a lattice constant 14\% larger than its equilibrium lattice constant is a promising half-metal for spintronic applications due to its large magnetic moment and vibrational stability. The modified Slater--Pauling rule for these alloys is determined. Finally, a plausible method for developing half-metallic Li$_x$MnZ at equilibrium, by tuning $x$, is investigated, but, unlike tetragonalization, this type of alloying introduces local structural changes that destroy the half-metallicity.

On the Stability of Dynamic Spectrum Access Networks in the Presence of Heavy Tails

The heavy-tailed nature in dynamic spectrum access networks challenges the applicability of conventional network stability criterion. To counter this problem, a new stability criterion, namely moment stability, is introduced, which requires that all secondary users (SUs) with light-tailed traffic have bounded queueing delay with finite mean and variance. This stability criterion can prevent heavy-tailed traffic, e.g., video and Internet traffic, from degrading the QoS performance of light-tailed ones, e.g., email deliveries and audio/voice traffic. The critical conditions for the existence of a scheduling policy to achieve moment stability are derived. The network stability region yielded from these conditions is shown to be directly related to the primary and secondary user activities, the number of SUs, and the total number of primary user channels available to SUs. Moreover, it is shown that the maximum-weight- $\alpha$ scheduling algorithm, which makes the scheduling decision based on the queue lengths raised to the $\alpha$ -th power, is throughput optimal with respect to moment stability. It is proven that its throughput optimality holds independent of the stochastic properties of SU traffic including its marginal distribution (i.e., heavy-tailed or light-tailed distribution) and its time correlation structure (i.e., long range or short range dependence).

On the Moment Stability of Stochastic Parametrically Forced Equations with Rank One Forcing

We derive simplified formulas for analyzing the moment stability of stochastic parametrically forced linear systems. This analysis extends the results in [T. Blass and L. A. Romero, SIAM J. Control Optim., 51 (2013), pp. 1099--1127], where, under the assumption that the stochastic excitation is small, the stability of such systems was computed using a weighted sum of the extended power spectral density over the eigenvalues of the unperturbed operator. In this paper, we show how to convert this sum to a sum over the residues of the extended power spectral density. For systems where the parametric forcing term is a rank one matrix, this approach leads to an enormous simplification. We give two examples of systems with rank one forcing, including the problem of stochastically forced Faraday waves.

Stochastic stability of SDOF linear viscoelastic system under wideband noise excitation

The stochastic moment stability and almost-sure stability of a single-degree-of-freedom (SDOF) viscoelastic system subject to parametric fluctuation is investigated by using the method of higher-order stochastic averaging. The stochastic parametric excitation is modeled as a wideband noise, which is taken as Gaussian white noise and real noise. The viscoelastic material is assumed to follow ordinary Maxwell linear constitutive relation. For small damping and weak stochastic fluctuation, analytical expressions are derived for the moment Lyapunov exponent and the Lyapunov exponent, which indicate moment stability and almost-sure stability respectively. The effects of various system and loading parameters on the stochastic stability are discussed. Both analytical and simulation results show that higher-order stochastic averaging improves the accuracy compared with the first-order stochastic averaging. However, results of the third-order averaging are almost overridden by those of second-order averaging and the third-order averaging involves far more calculation. It is advisable to consider a balance between accuracy achievement and calculation endeavor when using higher-order stochastic averaging.

Moment Lyapunov exponents of the Parametrical Hill's equation under the excitation of two correlated wideband noises

The Lyapunov exponent and moment Lyapunov exponents of Hill\' s equation with frequency and damping coefficient fluctuated by correlated wideband random processes are studied in this paper. The method of stochastic averaging, both the first-order and the second-order, is applied. The averaged Ito differential equation governing the pth norm is established and the pth moment Lyapunov exponents and Lyapunov exponent are then obtained. This method is applied to the study of the almost-sure and the moment stability of the stationary solution of the thin simply supported beam subjected to time-varying axial compressions and damping which are small intensity correlated stochastic excitations. The validity of the approximate results is checked by the numerical Monte Carlo simulation method for this stochastic system.

Control of the stability and soliton formation of dipole moments in a nonlinear plasmonic finite nanoparticle array

We perform numerical analysis of a finite nanoparticle array, in which the transversal dipolar polarizations are excited by a homogenous optical field. Considering the linearly long-range dipole–dipole interaction and the cubic dipole nonlinearity of particle, the characteristics of stability of a finite number nanoparticle array should be revised, compared with that of an infinite number nanoparticle array. A critical point in the low branch of the bistable curve is found, beyond which the low branch becomes unstable for a finite number of nanoparticles. The influence of the external field intensities and detuning frequencies on this critical point are investigated in detail. When the total number of particles approaches infinity, our results become similar to that of an infinity number particle system [32]. Notably, with appropriate external optical field, a dark dipole soliton is formed. Moreover, when the scaled detuning is set to an appropriate value, a double monopole dark soliton (DMDS) consisting of two particles is formed. The DMDS may have potential applications in the subwavelength highly precise detection because of its very small width.

Magnetic percolation and inequivalence of Fe sites in YFe x Co2−x (x = 0.03 and 1) Laves phase compounds

YCo2 compound is an exchange-enhanced Pauli paramagnet on the verge of being magnetic. Topological or chemical disorder can induce in it ferromagnetic long-range ordering. The influence of Fe substitution and quenched-in topological disorder on the magnetic properties of YFe0.03Co1.97 and YFeCo is studied. Structural and magnetic properties of these compounds are analyzed by means of X-ray diffraction, vibrating sample magnetometry, Mossbauer spectroscopy and AC magnetic susceptibility measurements. All samples crystallize in cubic MgCu2-type phase with lattice constant changing from 7.223 A for YCo2 through 7.221 A for YFe0.03Co1.97 to 7.313 A for YFeCo. Fe atoms are responsible for stabilization of magnetic moments on Co, and mictomagnetism is observed in YFe0.03Co1.97 sample. Upon further substitution, as in YFeCo, long-range ordering appears. The Mossbauer spectra permitted distinction between two magnetically inequivalent Fe sites, as reported earlier for YFe2.