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The Omori-Utsu law shows the temporal power-law-like decrease of the frequency of earthquake aftershocks and, interestingly, is found in a variety of complex systems/phenomena exhibiting catastrophes. Now, it may be interpreted as a characteristic response of such systems to large events. Here, hierarchical dynamics with the fast and slow degrees of freedom is studied on the basis of the Fokker-Planck theory for the load-state distribution to formulate the law as a relaxation process, in which diffusion coefficient in the space of the load state is treated as a fluctuating slow variable. The evolution equation reduced from the full Fokker-Planck equation and its Green's function are analyzed for the subdynamics governing the load state as the fast degree of freedom. It is shown that the subsystem has the temporal translational invariance in the logarithmic time, not in the conventional time, and consequently the aging phenomenon appears. [ABSTRACT FROM AUTHOR]

We report the synthesis and structures of two base‐free alkoxide dysprosium(III) complexes of formula [Dy(L1)2(μ‐η6:η1‐Ph)2BPh2] ⋅ CH2Cl2 (1) and [Dy(L2)2(μ‐η6:η1‐Ph)2BPh2] ⋅ 3(C7H8) (2) featuring a tetraphenylborate binding (L1=2,6‐dibenzhydryl‐4‐(tert‐butyl)phenolate, L2=tri(naphtalen‐1‐yl)methanolate). Investigations of the magnetic properties for 1 in line with theoretical calculations reveal the occurrence of a field‐induced slow relaxation of the magnetization. [ABSTRACT FROM AUTHOR]

A mononuclear Co(II) complex of a Schiff base ligand derived from 5-Bromo-vanillin and 4-aminoantipyrine, that has a compressed tetragonal bipyramidal geometry and exhibiting field-induced slow magnetic relaxation, has been synthesized and characterized by single crystal X-ray diffraction, elemental analysis and molecular spectroscopy. In the crystal packing, a hydrogen-bonded dimer structural topology has been observed with two distinct metal centers having slightly different bond parameters. The complex has been further investigated for its magnetic nature on a SQUID magnetometer. The DC magnetic data confirm that the complex behaves as a typical S = 3/2 spin system with a sizable axial zero-field splitting parameter D/hc = 38 cm−1. The AC susceptibility data reveal that the relaxation time for the single-mode relaxation process is τ = 0.16(1) ms at T = 2.0 K and BDC = 0.12 T. [ABSTRACT FROM AUTHOR]

The Omori-Utsu law shows the temporal power-law-like decrease of the frequency of earthquake aftershocks and, interestingly, is found in a variety of complex systems/phenomena exhibiting catastrophes. Now, it may be interpreted as a characteristic response of such systems to large events. Here, hierarchical dynamics with the fast and slow degrees of freedom is studied on the basis of the Fokker-Planck theory for the load-state distribution to formulate the law as a relaxation process, in which diffusion coefficient in the space of the load state is treated as a fluctuating slow variable. The evolution equation reduced from the full Fokker-Planck equation and its Green’s function are analyzed for the subdynamics governing the load state as the fast degree of freedom. It is shown that the subsystem has the temporal translational invariance in the logarithmic time, not in the conventional time, and consequently the aging phenomenon appears.

The development of methyl transverse relaxation optimized spectroscopy has greatly facilitated the study of macromolecular assemblies by solution NMR spectroscopy. However, limited sample solubility and stability has hindered application of this technique to ongoing studies of complexes formed on membranes by the neuronal SNAREs that mediate neurotransmitter release and synaptotagmin-1, the Ca2+ sensor that triggers release. Since the 1H NMR signal of a tBu group attached to a large protein or complex can be observed with high sensitivity if the group retains high mobility, we have explored the use of this strategy to analyze presynaptic complexes involved in neurotransmitter release. For this purpose, we attached tBu groups at single cysteines of fragments of synaptotagmin-1, complexin-1 and the neuronal SNAREs by reaction with 5-(tert-butyldisulfaneyl)-2-nitrobenzoic acid (BDSNB), tBu iodoacetamide or tBu acrylate. The tBu resonances of the tagged proteins were generally sharp and intense, although tBu groups attached with BDSNB had a tendency to exhibit somewhat broader resonances that likely result because of the shorter linkage between the tBu and the tagged cysteine. Incorporation of the tagged proteins into complexes on nanodiscs led to severe broadening of the tBu resonances in some cases. However, sharp tBu resonances could readily be observed for some complexes of more than 200 kDa at low micromolar concentrations. Our results show that tagging of proteins with tBu groups provides a powerful approach to study large biomolecular assemblies of limited stability and/or solubility that may be applicable even at nanomolar concentrations. [ABSTRACT FROM AUTHOR]

We report the synthesis, structures and magnetic properties of two Dy3+ heteroleptic complexes [Dy(BH4)2(THF)5][BPh4] (1) and [Dy(BH4)2(tBu4Carb)(THF)] (2) (tBu4Carb=1,3,6,8‐tetra‐tert‐butyl‐9H‐carbazole). Both complexes show a κ3‐coordination mode of the borohydride anion but distinct geometries. Whereas the cationic complex 1 does not exhibit a slow relaxation of the magnetization, the neutral complex 2 behaves as a field‐induced single‐molecule magnet. [ABSTRACT FROM AUTHOR]

A mononuclear Co(II) complex of a Schiff base ligand derived from 5-Bromo-vanillin and 4-aminoantipyrine, that has a compressed tetragonal bipyramidal geometry and exhibiting field-induced slow magnetic relaxation, has been synthesized and characterized by single crystal X-ray diffraction, elemental analysis and molecular spectroscopy. In the crystal packing, a hydrogen-bonded dimer structural topology has been observed with two distinct metal centers having slightly different bond parameters. The complex has been further investigated for its magnetic nature on a SQUID magnetometer. The DC magnetic data confirm that the complex behaves as a typical S = 3/2 spin system with a sizable axial zero-field splitting parameter D/hc = 38 cm−1. The AC susceptibility data reveal that the relaxation time for the single-mode relaxation process is τ = 0.16(1) ms at T = 2.0 K and BDC = 0.12 T.

The combination of Co(III) and Dy(III) with a compartmental Schiff base ligand (H3L=3‐[(2‐Hydroxy‐3‐methoxy‐benzylidene)‐amino]‐propane‐1,2‐diol), presenting three different coordinating pockets, has allowed the synthesis of two novel Co(III)−Dy(III) complexes: [Co2Dy(HL)4]NO3 ⋅ 2CH3CN (1), a rare example of trinuclear linear CoIII2DyIII complex (and the first with slow relaxation of magnetization in absence of a DC field) and [Co2Dy2(μ3−OH)2(HL)2(OAc)6] ⋅ 4.6H2O (2), the first tetranuclear CoIII2DyIII2 cluster with a rhomb‐like structure where the Co(III) ions are connected along the short diagonal of the rhomb. 1 presents two different relaxation processes: a fast relaxation dominated by Quantum tunnelling (QT) and a slow relaxation with an energy barrier of 40 K. 2 shows two close relaxation processes without applied DC fields that follow QT and Orbach mechanisms whereas for HDC=500 Oe, the QT is cancelled and a direct term appears. Here we present the synthesis, X‐ray structure and magnetic characterization of these two Co(III)−Dy(III) single‐ion/molecule magnets. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • We studied a series of mononuclear Ln thiocyanate complexes with terpy as auxiliary ligand. • The sensitization of the luminescence of Eu and Tb derivatives due to the terpy ligands was demonstrated. • Features of the Ln environment affect both the luminescence and SMM behavior of the complexes. Abstract Novel mononuclear lanthanide thiocyanates with 2,2′;6′,2″-terpyridine (terpy), namely isomorphic complexes [Ln(terpy) 2 (NCS) 3 ] (Ln = Y , Eu , Tb and Dy) were prepared and studied. The effective luminescence sensitization of the Eu , Tb and Dy ions owing to the terpy ligands was observed and corresponding values of the absolute quantum yields were determined. The influence of structural features of the complexes studied on their luminescent properties was analyzed. Slow magnetic relaxation indicating SMM behavior was found for Dy complex. [ABSTRACT FROM AUTHOR]

Aminophenol Mannich base derivatives are versatile and flexible ligands for preparing a wide variety of homo- and heterometallic discrete coordination compounds, ranging from mononuclear to hexanuclear, which exhibit aesthetically pleasant structures with intricate topologies. These ligands are particularly adapted to obtain 3d/4f systems, where invariably the amino fragment is coordinated to the transition metal ion and the phenolate oxygen atoms bridge transition metal and lanthanide ions. Their coordination spheres are completed by donor atoms belonging either to methoxy and aldehyde groups of the Mannich base ligands or to terminal and bridging ancillary ligands. Moreover, robust 3d-4f dinuclear units can be assembled with either bridging ligands or complexes acting as bridging ligands to afford heterometallic complexes with increased nuclearity. The complexes containing one or two paramagnetic ions often exhibit appealing magnetic properties, alone or combined with other physical properties, that essentially arise from large local magnetic anisotropy and magnetic exchange coupling of the metal ions. This chapter provides an overview of recent results on single-molecule magnets (SMMs) based on aminophenol Mannich base ligands that illustrate the scope, state of the art and fruitful dynamism of this field of research. [ABSTRACT FROM AUTHOR]

In this work we review the Co2IIILn2III family of compounds reported up to date that shows SMM features. The vast majority of them show a butterfly arrangement with LnIII ions placed at the body positions. The number of DyIII examples constitutes the majority, probably because of the intrinsic properties of this lanthanide ion regarding SMMs characteristics. Butterfly complexes have a SAP geometry around LnIII ions with a variety of distortion degrees. However, when looking at the key Ueff parameter trend through this family of complexes, it becomes clear that a pure geometrical consideration is not enough to explain it. Ab initio based calculations provide evidence of highly anisotropic mJ ground states for complexes where LnIII = DyIII, pointing to exclusively mJ = 15/2 ground Kramers doublets. These calculations also agree with the thermally activated relaxation involving the first excited state and, in some examples where multiple relaxation pathways are observed, higher excited states. A few examples prove that Raman and/or direct mechanisms cannot be discarded a priori. Only two examples of isostructural LnIII families of the same Co2IIILn2III complex can be found. [ABSTRACT FROM AUTHOR]

Rock materials often display long-time relaxation, commonly termed aging or 'slow dynamics,' after the cessation of acoustic perturbations. In this paper, we focus on unconsolidated rock materials and propose to explain such nonlinear relaxation through the shear-transformation-zone theory of granular media, adapted for small stresses and strains. The theory attributes the observed relaxation to the slow, irreversible change of positions of constituent grains and posits that the aging process can be described in three stages: fast recovery before some characteristic time associated with the subset of local plastic events or grain rearrangements with a short time scale, log linear recovery of the elastic modulus at intermediate times, and gradual turnover to equilibrium steady state behavior at long times. We demonstrate good agreement with experiments on aging in granular materials such as simulated fault gouge after an external disturbance. These results may provide insights into observed modulus recovery after strong shaking in the near surface region of earthquake zones. [ABSTRACT FROM AUTHOR]

The paper presents the results of experimental research into the nonlinear acoustic properties of carbonate rocks depending on saturation. The linear acoustic properties of the same sample depending on saturation were presented earlier in Physical Acoustics. The previously obtained data point to the isotropy of the material, which makes it possible to restrict analysis to only two vibration modes. Responses for finite deformations were measured for the longitudinal and shear modes of an isotropic sample, which made it possible to analyze the nonlinear properties of macroscopic deformations with a change in volume and pure displacement. A heretofore unknown feature of the response was revealed for finite deformation values; it is related to the occurrence of a jumplike transition from classical nonlinearity to a hysteresis type of nonlinearity. As well, the deformation amplitude corresponding to the transition depends on fluid saturation. We studied the slow relaxation that occurs after long-term excitation of a sample with a deformation amplitude on the order of 10. Data are presented on relaxation for deformation from pure displacement and deformation with a change in volume, which made it possible to isolate features related to the type of deformation and to compare the obtained data with the earlier published theoretical model. These data are compared with the results of other research groups. [ABSTRACT FROM AUTHOR]

We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model reduction, and build a mathematical framework for analyzing the reduced models. We introduce the notions of universal and asymptotic filters to characterize 'optimal' model reductions for sloppy linear models. We illustrate our methods by applying them to the practically important problem of modeling evaporation in oil spills. [ABSTRACT FROM AUTHOR]

In recent years, studies of long-range interacting (LRI) systems have taken center stage in the arena of statistical mechanics and dynamical system studies, due to new theoretical developments involving tools from as diverse a field as kinetic theory, non-equilibrium statistical mechanics, and large deviation theory, but also due to new and exciting experimental realizations of LRI systems. In the first, introductory, Section 1, we discuss the general features of long-range interactions, emphasizing in particular the main physical phenomenon of non-additivity, which leads to a plethora of distinct effects, both thermodynamic and dynamic, that are not observed with short-range interactions: Ensemble inequivalence, slow relaxation, broken ergodicity. In Section 2, we discuss several physical systems with long-range interactions: mean-field spin systems, self-gravitating systems, Euler equations in two dimensions, Coulomb systems, one-component electron plasma, dipolar systems, free-electron lasers. In Section 3, we discuss the general scenario of dynamical evolution of generic LRI systems. In Section 4, we discuss an illustrative example of LRI systems, the Kardar-Nagel spin system, which involves discrete degrees of freedom, while in Section 5, we discuss a paradigmatic example involving continuous degrees of freedom, the so-called Hamiltonian mean-field (HMF) model. For the former, we demonstrate the effects of ensemble inequivalence and slow relaxation, while for the HMF model, we emphasize in particular the occurrence of the so-called quasistationary states (QSSs) during relaxation towards the Boltzmann-Gibbs equilibrium state. The QSSs are non-equilibrium states with lifetimes that diverge with the system size, so that in the thermodynamic limit, the systems remain trapped in the QSSs, thereby making the latter the effective stationary states. In Section 5, we also discuss an experimental system involving atoms trapped in optical cavities, which may be modelled by the HMF system. In Section 6, we address the issue of ubiquity of the quasistationary behavior by considering a variety of models and dynamics, discussing in each case the conditions to observe QSSs. In Section 7, we investigate the issue of what happens when a long-range system is driven out of thermal equilibrium. Conclusions are drawn in Section 8. [ABSTRACT FROM AUTHOR]

The electrocapillarity and zero-frequency differential capacitance, C d , have been studied using pendant drop method, at the Hg interface of an ionic liquid (IL), 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)amide, [C 2 mim + ][TFSA − ], and have been compared with those of [C 2 mim + ]BF 4 − , an IL with the common cation and a different anion, to focus on the anion dependence of zero-frequency C d . The Hg interface of [C 2 mim + ][TFSA − ], the IL of the larger anion in the present study, exhibits greater zero-frequency C d than that of [C 2 mim + ]BF 4 − , the IL of the smaller anion. This behavior contradicts a simple expectation in which larger ion leads to smaller C d . This apparent contradiction is explained by proximity of the charged moiety of TFSA − to the electrode surface compared with that of BF 4 − . The potential dependence of zero-frequency C d for the two ILs both exhibits one-hump camel shape around the potential of zero charge ( E pzc ), which has been predicted to be specific behavior of the electrical double layer of ILs by theory and simulation. The humps are located at potentials more negative than E pzc . From a mean-field lattice-gas theory for the EDL in ILs, this negative shift can be interpreted that the charged moiety for C 2 mim + is more easily condensed in the EDL than those for BF 4 − and TFSA − . [ABSTRACT FROM AUTHOR]

We present the mathematical analysis of bi-cluster flocking phenomenon for the short-ranged Cucker-Smale model with some well-prepared initial data. For this, we derive a system of differential inequalities for the functionals measuring the local spatial and velocity fluctuations and differences of local velocity averages, and then estimate the upper bound of spatial fluctuations and the lower bound of the difference between local velocity averages. We explicitly present an admissible class of initial configurations leading to the asymptotic emergence of bi-cluster flocking phenomenon. Unlike global flocking (a mono-cluster flocking configuration in velocity), where the convergence rate is always exponential, the asymptotic convergence to bi-cluster flocking configurations is affected by the far-field decay rate of communication weights so that it can be algebraic. [ABSTRACT FROM AUTHOR]

Three new Dy complexes have been prepared according to a complex-as-ligand strategy. Structural determinations indicate that the central Dy ion is surrounded by two LZn units (L2− is the di-deprotonated form of the N2O2 compartmental N, N′-2,2-dimethylpropylenedi(3-methoxysalicylideneiminato) Schiff base. The Dy ions are nonacoordinate to eight oxygen atoms from the two L ligands and to a water molecule. The Zn ions are pentacoordinate in all cases, linked to the N2O2 atoms from L, and the apical position of the Zn coordination sphere is occupied by a water molecule or bromide or chloride ions. These resulting complexes, formulated (LZnX)-Dy-(LZnX), are tricationic with X=H2O and monocationic with X=Br or Cl. They behave as field-free single-molecule magnets (SMMs) with effective energy barriers ( Ueff) for the reversal of the magnetization of 96.9(6) K with τ0=2.4×10−7 s, 146.8(5) K with τ0=9.2×10−8 s, and 146.1(10) K with τ0=9.9×10−8 s for compounds with ZnOH2, ZnBr, and ZnCl motifs, respectively. The Cole-Cole plots exhibit semicircular shapes with α parameters in the range of 0.19 to 0.29, which suggests multiple relaxation processes. Under a dc applied magnetic field of 1000 Oe, the quantum tunneling of magnetization (QTM) is partly or fully suppressed and the energy barriers increase to Ueff=128.6(5) K and τ0=1.8×10−8 s for 1, Ueff=214.7 K and τ0=9.8×10−9 s for 2, and Ueff=202.4 K and τ0=1.5×10−8 s for 3. The two pairs of largely negatively charged phenoxido oxygen atoms with short DyO bonds are positioned at opposite sides of the Dy3+ ion, which thus creates a strong crystal field that stabilizes the axial MJ=±15/2 doublet as the ground Kramers doublet. Although the compound with the ZnOH2 motifs possesses the larger negative charges on the phenolate oxygen atoms, as confirmed by using DFT calculations, it exhibits the larger distortions of the DyO9 coordination polyhedron from ideal geometries and a smaller Ueff value. Ab initio calculations support the easy-axis anisotropy of the ground Kramers doublet and predict zero-field SMM behavior through Orbach and TA-QTM relaxations via the first excited Kramers doublet, which leads to large energy barriers. In accordance with the experimental results, ab initio calculations have also shown that, compared with water, the peripheral halide ligands coordinated to the Zn2+ ions increase the barrier height when the distortions of the DyO9 have a negative effect. All the complexes exhibit metal-centered luminescence after excitation into the UV π-π* absorption band of ligand L2− at λ=335 nm, which results in the appearance of the characteristic DyIII (4F9/2→6H J/2; J=15/2, 13/2) emission bands in the visible region. [ABSTRACT FROM AUTHOR]

A series of six-coordinate lanthanide complexes {(H3O)[Ln(NA)2]⋅H2O} n (H2NA=5-hydroxynicotinic acid; Ln=GdIII ( 1⋅Gd); TbIII ( 2⋅Tb); DyIII ( 3⋅Dy); HoIII ( 4⋅Ho)) have been synthesized from aqueous solution and fully characterized. Slow relaxation of the magnetization was observed in 3⋅Dy. To suppress the quantum tunneling of the magnetization, 3⋅Dy diluted by diamagnetic YIII ions was also synthesized and magnetically studied. Interesting butterfly-like hysteresis loops and an enhanced energy barrier for the slow relaxation of magnetization were observed in diluted 3⋅Dy. The energy barrier (Δ τ) and pre-exponential factor ( τ0) of the diluted 3⋅Dy are 75 K and 4.21×10−5 s, respectively. This work illustrates a successful way to obtain low-coordination-number lanthanide complexes by a framework approach to show single-ion-magnet-like behavior. [ABSTRACT FROM AUTHOR]