Commensurate Ones Research Articles

Robust global synchronization of delayed incommensurate fractional-order gene regulatory networks

This paper investigates the issue of robust synchronization for delayed incommensurate fractional-order gene regularity networks (IFOGRNs). The common stability analyzing methods for commensurate fractional-order models cannot be used for incommensurate cases. Therefore, the synchronization of the GRNs with incommensurate order models is more challenging than the commensurate ones. This paper employs a novel fractional Lyapunov-based scheme that can be used for incommensurate cases without conversion to a commensurate model. Moreover, this method can analyze the IFOGRNs without linearization, which guarantees global stability. Firstly, some sufficient conditions are proposed for robust controller design when the parameter uncertainties are similar between two such IFOGRNs. It is shown that asymptotic stability is not guaranteed when the parameter uncertainties are not the same. In this paper, a novel adaptive based controller is introduced, which leads to asymptotic stability even for dissimilar parameter uncertainties. Finally, to evaluate the efficiency of the proposed method, some numerical examples are investigated.

Corona-19 Pandemic and Altering Dynamics of Human Resource Management: A Multifarious Approach

This study is an attempt to bring forth some of the human resource predicaments which will be ushered by the ubiquitous venom of the Corona Virus. Regardless of the deliberation operating at the back of Corona and the availability of the requisite vaccine, the executives need to adapt themselves with the new paradigm and contemplate on the enactment of novel and apposite ways of managing human capital. The global economy is feared to sink such that the world might be coerced to relive the 1930’s global recession; thus each economy is entwined in the cruel jaws of havoc. The study presents various dimensions of the pandemic and after analytic discussion, puts forth some important suggestions for the reader that he resort lies in self-reliance, caution and adaptability. Since the business activity is by and large a function of superior human capital, the HRM interventions need to be the most commensurate ones.

Emergent Geometric Frustration and Flat Band in Moiré Bilayer Graphene.

So far the physics of moiré graphene bilayers at large, incommensurate rotation angles has been considered uninteresting. It has been held that the interlayer coupling in such structures is weak and the system can be thought of as a pair of decoupled single graphene sheets to a good approximation. Here, we demonstrate that for large rotation angles near commensurate ones, the interlayer coupling, far from being weak, is able to completely localize electrons to within a large scale, geometrically frustrated network of topologically protected modes. The emergent geometric frustration of the system gives rise to completely flat bands, with strong correlation physics as a result. All of this arises although in the lattice structure no large scale pattern appears to the unguided eye. Sufficiently close to commensuration the low-energy physics of this remarkable system has an exact solution.

Direct observation of incommensurate charge-density wave in overdoped manganites

The origin of the charge and orbital ordering is still the subject of debate. In manganites, charge ordering (CO) has been traditionally identified as an ordered arrangement of Mn3+ and Mn4+ ions. Here, by high-resolution transmission electron microscopy (HRTEM) in combination with image deconvolution technique and the high-dimensional space description, the nature of CO related to the structural modulation is revealed as an incommensurate charge-density wave (CDW) in real-space for overdoped manganites La0.8Ca2.2Mn2O7. This result resolves the current controversy and confirms the incommensurate CO is not simply a mixture of commensurate ones with different periodicities. In this sense, we provide the first HRTEM imaging evidence for a CDW picture.

Sufficient stability conditions of fractional systems with perturbed differentiation orders

In this paper sufficient stability conditions are established for fractional systems with perturbed differentiation orders. It is an extension of the recently published paper Rapaic and Malti [2016] which allows henceforth increasing the highest differentiation order. The maximum allowable variation on all differentiation orders is computed so that the stability (respectively instability) is preserved when differentiation orders are perturbed away from the commensurate ones. The maximum allowable variations are compared in both cases: when the highest order is allowed to be increased and when it is not. The established conditions allow concluding on the stability of incommensurate fractional systems on the basis of Matignon’s theorem and the additional sufficient condition.

Phase transitions and the quantum effect in A2BX4-type ferroelectric crystals

ABSTRACTPhase diagrams for modulated phases are constructed based on a competing interactive ISING model. Commensurate phases with the wave number q = 0, 1/6, 1/3 and 1/2 are stable at zero temperature, if the model Hamiltonian is treated classically. On the other hand, the regions of incommensurate wave number as well as high-order commensurate ones extend down to 0 K, if the quantum statistical mechanics is employed. Based on the calculated phase diagram, phase transitions of K2SeO4, Rb2MoO4, Rb2SeO4, and Cs2WO4 are discussed.

Bounds of imaginary spectra of LTI systems in the domain of two of the multiple time delays

The stability of linear time invariant (LTI) systems with independent multiple time delays and the cluster treatment of characteristic roots (CTCR) paradigm are investigated from a new perspective. It is known that for such systems, all the imaginary characteristic roots can be detected completely on a small set of hypersurfaces in the domain of the delays (Sipahi and Olgac, 2006a). They are called kernel hypersurfaces (KH). The complete description of KH is the only prerequisite for the CTCR stability assessment procedure. As the number of delays increases, however, their evaluation becomes infeasible. Instead, we present a procedure to extract the 2-D cross-sections of these hypersurfaces in the domain of any two of the delays by fixing the remaining delays. In the 2-delay domain of interest, the exact upper and lower bounds of the imaginary spectra are determined. For this, a combination of half-angle tangent representation of the characteristic equation and the Dixon resultant theory is used as the main contributions of this paper. The complete KH are obtained by sweeping the root crossing frequency in this interval. Using this knowledge CTCR creates the cross-section of the stability map in the domain of the two arbitrarily selected delays. We demonstrate the effectiveness of this methodology over an example case study with three independent delays and two commensurate ones.

Probe-type of superconductivity by impurity in materials with short coherence length: the s-wave and η-wave phases study

The effects of a single non-magnetic impurity on superconducting states in the Penson–Kolb–Hubbard model have been analyzed. The investigations have been performed within the Hartree–Fock mean field approximation in two steps: (i) the homogeneous system is analysed using the Bogoliubov transformation, whereas (ii) the inhomogeneous system is investigated by self-consistent Bogoliubov-de Gennes equations (with the exact diagonalization and the kernel polynomial method). We analysed both signs of the pair hopping, which correspond to s-wave and η-wave superconductivity. Our results show that an enhancement of the local superconducting gap at the impurity-site occurs for both cases. We obtained that Cooper pairs are scattered (at the impurity site) into the states which are from the neighborhoods of the states, which are commensurate ones with the crystal lattice. Additionally, in the η-phase there are peaks in the local-energy gap (in momentum space), which are connected with long-range oscillations in the spatial distribution of the energy gap, superconducting order parameter (SOP), as well as effective pairing potential. Our results can be contrasted with the experiment and predicts how to experimentally differentiate these two different symmetries of SOP by the scanning tunneling microscopy technique.

(In)commensurability, scaling, and multiplicity of friction in nanocrystals and application to gold nanocrystals on graphite

The scaling of friction with the contact size $A$ and (in)commensurabilty of nanoscopic and mesoscopic crystals on a regular substrate are investigated analytically for triangular nanocrystals on hexagonal substrates. The crystals are assumed to be stiff, but not completely rigid. Commensurate and incommensurate configurations are identified systematically. It is shown that three distinct friction branches coexist, an incommensurate one that does not scale with the contact size ($A^0$) and two commensurate ones which scale differently (with $A^{1/2}$ and $A$) and are associated with various combinations of commensurate and incommensurate lattice parameters and orientations. This coexistence is a direct consequence of the two-dimensional nature of the contact layer, and such multiplicity exists in all geometries consisting of regular lattices. To demonstrate this, the procedure is repeated for rectangular geometry. The scaling of irregularly shaped crystals is also considered, and again three branches are found ($A^{1/4}, A^{3/4}, A$). Based on the scaling properties, a quantity is defined which can be used to classify commensurability in infinite as well as finite contacts. Finally, the consequences for friction experiments on gold nanocrystals on graphite are discussed.

Slave spins away from half filling: Cluster mean-field theory of the Hubbard and extended Hubbard models

A slave-spin representation of fermion operators has recently been proposed for the half-filled single and multiband Hubbard model. We show that with the addition of a gauge variable, the formalism can be extended to finite doping. We solve the resulting spin problem using the cluster mean-field approximation. This approximation takes short-range correlations into account by exact diagonalization on the cluster, whereas long-range correlations beyond the size of clusters are treated at the mean-field level. In the limit where the cluster has only one site and the interaction strength $U$ is infinite, this approach reduces to the Gutzwiller approximation. There are some qualitative differences when the size of the cluster is finite. We first compute the critical $U$ for the Mott transition as a function of a frustrating nearest-neighbor interaction on lattices relevant for various correlated systems, namely, the cobaltates, the layered organic superconductors and the high-temperature superconductors. For the triangular lattice, we also study the extended Hubbard model with nearest-neighbor repulsion. In addition to a uniform metallic state, we find a $\sqrt{(3)}\ifmmode\times\else\texttimes\fi{}\sqrt{(3)}$ charge density wave in a broad doping regime, including commensurate ones. We find that in the large $U$ limit, intersite Coulomb repulsion $V$ strongly suppresses the single-particle weight of the metallic state.

Phenomenological theory of spin excitations in La- and Y-based cuprates

Motivated by recent inelastic neutron scattering experiments on La-based cuprates and based on the fermiology theories, we study the spin susceptibility for La-based (e.g., ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$) and Y-based (e.g., $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{y}$) cuprates, respectively. The spin excitation in $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{y}$ is dominated by a sharp resonance peak at the frequency $40\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ in the superconducting state. Below and above the resonance frequency, the incommensurate (IC) peaks develop and the intensity of the peaks decreases dramatically. In the normal state, the resonant excitation does not occur and the IC peaks are merged into commensurate ones. The spin excitation of ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$ is significantly different from that of Y-based ones, namely, the resonance peak does not exist due to the decreasing of the superconducting gap and the presence of the possible spin-stripe order. The spectra are only enhanced at the expected resonance frequency (about $18\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$) while they are still incommensurate. On the other hand, another frequency scale is also revealed, namely, the spectra are commensurate and show local maximum at the frequency of $55\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. We elaborate all the results based on the Fermi surface topology and the $d$-wave superconductivity and suggest that the spin-stripe order is also important in determining the spin excitation of La-based cuprates. A coherent picture for the spin excitations is presented for Y-based and La-based cuprates.

Magnetic structures of RAuGe (R = Pr, Nd, Tb, Ho, Er) compounds

RAuGe compounds crystallize in hexagonal LiGeGa-type structure at room temperature. Magnetic susceptibility measurements reveal that the investigated compounds order antiferromagnetically at low temperatures except PrAuGe which is a paramagnet down to 4.2 K. In case of other compounds, neutron diffraction data showed variety of magnetic structures from commensurate ones (propagation vector k=[ 1 2 , 0, 0] ) to incommensurate ones (propagation vector k=[k x,0,0] , where 0.3< k x <0.5) – see main text for details.

Effect of Hydrostatic Pressure on the Low-Temperature Phase Transitions in Rb2ZnBr4

The effect of hydrostatic pressure on the low-temperature structural phase transitions in Rb 2 ZnBr 4 has been investigated by the use of neutron scattering technique. The phase III-to-IV transition temperature, T 3 =112 K at atmospheric pressure, increased by applying pressure with a rate of 7 K/kbar. The phase IV-to-V transition temperature, T 4 =76 K at atmospheric pressure, decreased by applying pressure with a rate of -45 K/kbar. At high pressure, two high-order pseudo-commensurate phases characterized by wave vectors q z ≃ \(\frac{3}{11}\) and \(\frac{4}{15}\) were observed in addition to the already known commensurate ones of \(q_z=\frac{2}{7}\) and \(\frac{1}{4}\). The space group of the commensurate phase of \(q_z=\frac{1}{4}\) under high pressure was suggested to be P 2 1 / c 11 from the extinction rule.

Nonequilibrium dynamic phases and plastic flow of driven vortex lattices in superconductors with periodic arrays of pinning sites

We present results from an extensive series of simulations and analytical work on driven vortex lattices interacting with periodic arrays of pinning sites. An extremely rich variety of dynamical plastic flow phases, very distinct from those observed in random arrays, are found as a function of an applied driving force. Signatures of the transitions between these different dynamical phases appear as very pronounced jumps and dips in striking voltage-current $V(I)$ curves that exhibit hysteresis, reentrant behavior, and negative differential conductivity. By monitoring the moving vortex lattice, we show that these features coincide with pronounced changes in the microscopic structure and transport behavior of the driven lattice. For the case when the number of vortices is greater than the number of pinning sites, the plastic flow regimes include a one-dimensional (1D) interstitial flow of vortices between the rows of pinned vortices, a disordered flow regime where 2D pin-to-pin and winding interstitial motion of vortices occurs, and a 1D incommensurate flow regime where vortex motion is confined along the pinning rows. In the last case, flux-line channels with an incommensurate number of vortices contain mobile flux discommensurations or ``flux solitons,'' and commensurate channels remain pinned. At high driving forces, the 1D incommensurate paths of moving vortices persist with the entire vortex lattice flowing. In this regime, the incommensurate channels move at a higher velocity than the commensurate ones, causing incommensurate and commensurate rows of moving vortices to slide past one another. Thus there is no recrystallization at large driving forces. Moreover, these phases cannot be described by elastic theories. Different system parameters produce other phases, including an ordered channel flow regime, where a small number of vortices are pinned and the rest of the lattice flows through the interstitial regions, and a vacancy flow regime, which occurs when the number of vortices is less than the number of pinning sites. We also find a striking reentrant disordered-motion regime in which the vortex lattice undergoes a series of order-disorder transitions that display unusual hysteresis properties. By varying a wide range of values for the microscopic pinning parameters, including pinning strength, radius, density, and the degree of ordering, as well as varying the commensurability of the vortex lattice with its pinning substrate, we obtain a series of interesting dynamic phase diagrams that outline the onset of the different dynamical phases. We show that many of these phases and the phase boundaries can be well understood in terms of analytical arguments.

Evidence of High Critical Temperature Charge Density Wave Transitions in the (PO2)4(WO3)2m Family of Low Dimensional Conductors for m ${\bf\geq}$ 8

The monophosphate tungsten bronzes with pentagonal tunnels (MPTBp) of general formula (PO 2 ) 4 (WO 3 ) 2m form a family of layered conductors where the average number of conduction electrons per tungsten atom 2/m can be changed while keeping the same structural array. Previous investigation of the low m = 4, 6 and 7 members of this family have shown that this series is subject to several successive incommensurate charge density wave (CDW) long range orders below room temperature (RT). Here we present an X-ray scattering study of the m = 8, 9, 10, 11, 12, 13 and 14 members of this family. A very rich and diverse structural phase diagram is observed. The m = 8 member shows only short range order below RT at two different incommensurate wave vectors while commensurate and/or incommensurate long range order is observed above RT for m ≥ 9. Incommensurate modulations are observed for the m = 11 and 13 members and commensurate ones for the other members. In most of the 7 ≥ m ≥ 13 members the observation of several harmonics suggests that the CDW modulation is non-sinusoidal, which could be the fingerprint of electron localization phenomena due either to strong electron-phonon or electron-electron interactions. These CDW instabilities have been tentatively attributed to chains a and a ± b of WO 6 octahedra into which the ReO3 type layers of (PO 2 ) 4 (WO 3 ) 2m can be decomposed. In addition, the observation for m ≥ 9 of a commensurate (1/2,0,0) or (1/2, 0, 1/2) modulation or (1/2, 0, l) diffuse scattering suggests the occurrence of an incipient WO 3 type antiferroelectric instability which interacts with the CDW for m ≤ 13. We further discuss the division between high m value and low m value members in relation to the z dependence of the physical properties of some M x WO 3 tungsten bronzes families and finally propose a dielectric to magnetic duality between CDW tungsten oxides and superconducting copper oxides.

Magnetic Properties of Extendedt-JModel. I. Static Properties

Spin fluctuations in the extended t - J model have been investigated within the slave-boson mean-field approximation based on both uniform and singlet RVB states. By choosing the transfer integrals to reproduce the Fermi surface of LSCO and YBCO, we find that incommensurate spin fluctuations can be expected for the Fermi surface of LSCO-type, whereas only commensurate ones for that of YBCO-type, in agreement with experiments. Moreover effects of singlet RVB pairing have been explored and are shown to lead to the qualitative difference of the temperature dependences of the shift of nuclear magnetic resonance in the high and low doping regions as seen experimentally.

Fermi Surface and Spin Fluctuations in Extendedt-JModel

The spin fluctuations in the extended t - J model have been investigated in the slave-boson mean-field theory by extending the early work by Suzumura et al. [J. Phys. Soc. Jpn. 57 (1988) 2768] based on both uniform and singlet RVB (Resonating Valence Bond). By choosing the transfer integrals to reproduce the Fermi surface of LSCO and YBCO, which is essentially rotated by 45°, it is found that incommensurate spin fluctuations can be expected for the Fermi surface of LSCO type, whereas only commensurate ones for that of YBCO type, in agreement with experiments. Moreover, the Knight shift is shown to decrease as the temperature is lowered in the presence of the singlet RVB, while it is essentially independent of temperature in the uniform RVB state. These two cases correspond to, in our classification, T c =60 K and T c =90 K YBCO systems, which also agrees with the qualitative difference observed experimentally.

Interplay between quadrupolar and bilinear interactions in rare earth intermetallics

A survey of the properties of 4f quadrupolar moments in rare earth intermetallic compounds is proposed. The double nature, one-ion magnetoelasticity and pair interactions, of the quadrupolar couplings as well as the different types of ferro-and antiferroquadrupolar orderings are first reviewed. The quadrupolar consequences on the magnetic properties, such as the order of the magnetic transition and the nature of the magnetic structure are then discussed. This interplay between quadrupoles and spins is illustrated by the competitions between collinear and multiaxial structures or between commensurate and modulated ones, sometimes in a same compound.

Evidence of memory effects in a commensurate ferroelectric phase.

Dielectric measurements in [N${(\mathrm{C}{\mathrm{H}}_{3})}_{4}$]$_{2}\mathrm{Co}$${\mathrm{Cl}}_{4}$ crystals are reported that show that memory effects in materials exhibiting incommensurate phases are not exclusively limited to these phases but can also appear in commensurate ones. The dielectric susceptibility of the material suffers strong anomalies in the ferroelectric commensurate phase after annealing in this phase for a few hours. The characteristics of this new effect are more complex than those previously reported within incommensurate phases.

Time Evolution of the Incommensurate Phase in K2ZnCl4 Observed by Dielectric Measurements and X-Ray Scatterings

At the incommensurate-commensurate transition in K 2 ZnCl 4 , slow time variations of the dielectric constant e and the satellite reflectins were observed. With increasing temperature, the incommensurate satellites appeared and coexisted with the commensurate ones when e began to rise up, and the commensurate ones disappeared when e became maximum. On cooling, the peak of e corresponded to the appearance of the commensurate reflections. In both incommensurate and commensurate phases, the slow relaxation of e accompanied with the change of the mean modulation period and the regularization of the modulated structure. The misfit parameter approached the steady value very slowly with a logarithmic dependence on time at later stage.