Syntheses, Structures and Magnetic Properties of M2 (M = Fe, Co) Complexes with N6 Coordination Environment: Field-Induced Slow Magnetic Relaxation in Co2

Two dinuclear complexes [M2(H2L)2](ClO4)4·2MeCN (M = Co for Co2 and Fe for Fe2) were synthesized using a symmetric hydrazone ligand with the metal ions in an N6 coordination environment. The crystal structures and magnetic properties were determined by single-crystal X-ray diffraction and magnetic susceptibility measurements. The crystal structure study revealed that the spin centers were all in the high-spin state with a distorted octahedron (Oh) geometry. Dynamic magnetic properties measurements revealed that complex Co2 exhibited field-induced single-molecule magnet properties with two-step relaxation in which the fast relaxation path was from QTM and the slow relaxation path from the thermal relaxation under an applied field.

Justifying Born’s Rule Pα = |Ψα|2 Using Deterministic Chaos, Decoherence, and the de Broglie-Bohm Quantum Theory

In this work, we derive Born’s rule from the pilot-wave theory of de Broglie and Bohm. Based on a toy model involving a particle coupled to an environment made of “qubits” (i.e., Bohmian pointers), we show that entanglement together with deterministic chaos leads to a fast relaxation from any statistical distribution ρ(x) of finding a particle at point x to the Born probability law |Ψ(x)|2. Our model is discussed in the context of Boltzmann’s kinetic theory, and we demonstrate a kind of H theorem for the relaxation to the quantum equilibrium regime.

How control and relaxation interventions and virus mutations influence the resurgence of COVID-19

After a year of the unprecedented COVID-19 pandemic in 2020, the world has been overwhelmed by COVID-19 resurgences in 2021. Resurgences usually cause longer, broader and higher waves of infection, with greater threat to societies and economies compared to first waves. They may be caused by late implementation or early relaxation of non-pharmaceutical interventions (NPIs) such as social restrictions, ineffective interventions, or virus mutations. Here we provide quantitative evidence to characterize epidemiological differences between waves, evaluate possible causes, and predict potential trends under virus mutations. We use an event-driven dynamic epidemiological model embedded with time-dependent intervention interactions to compare two waves of COVID-19 outbreaks, and we quantify the impacts of control or relaxation interventions (called events) on wave patterns. We show the second waves in late 2020 in Germany, France and Italy could have been better contained by either carrying forward the effective interventions from their first waves or implementing better controls and timing. We also obtain the quantitative effects of enforcing or relaxing interventions on various transmissibility levels of coronavirus mutants (like delta or lambda) in the second waves and in the next 30 days. Comprehensive analyses at four levels - vertical (between waves), horizontal (across countries), what-if (scenario simulations on second waves) and future (30-day trend) - in the two 2020 waves in Germany, France and Italy show that (1) intervention fatigue (government and community reluctance to interventions), early relaxations and lagging interventions may be common reasons for the resurgences observed in many countries; (2) timely strong interventions such as full lockdown will contain resurgence; and (3) in the absence of sufficient vaccination, herd immunity and effective antiviral pharmaceutical treatments and with more infectious mutations, the widespread early or fast relaxation of interventions including public activity restrictions will result in a COVID-19 resurgence.

Slow and intermittent stress relaxation of biomass granular media

In the present work, the relaxation of several wood powders has been investigated in an annular shear cell. It is found that the slow logarithmic relaxation commonly observed for various materials including granular materials is interrupted by large events. Their frequency and amplitude are investigated with respect to particle size and stress-history by measuring stresses and strain. These large events during the relaxation appear to be controlled by the deformation. The coarser the particles are, the bigger is the deformation of the powder bed between two fast relaxation events and during the event.

Nonlinear Approximations to Critical and Relaxation Processes

We develop nonlinear approximations to critical and relaxation phenomena, complemented by the optimization procedures. In the first part, we discuss general methods for calculation of critical indices and amplitudes from the perturbative expansions. Several important examples of the Stokes flow through 2D channels are brought up. Power series for the permeability derived for small values of amplitude are employed for calculation of various critical exponents in the regime of large amplitudes. Special nonlinear approximations valid for arbitrary values of the wave amplitude are derived from the expansions. In the second part, the technique developed for critical phenomena is applied to relaxation phenomena. The concept of time-translation invariance is discussed, and its spontaneous violation and restoration considered. Emerging probabilistic patterns correspond to a local breakdown of time-translation invariance. Their evolution leads to the time-translation invariance complete (or partial) restoration. We estimate the typical time extent, amplitude and direction for such a restorative process. The new technique is based on explicit introduction of origin in time as an optimization parameter. After some transformations, we arrive at the exponential and generalized exponential-type solutions (Gompertz approximants), with explicit finite time scale, which is only implicit in the initial parameterization with polynomial approximation. The concept of crash as a fast relaxation phenomenon, consisting of time-translation invariance breaking and restoration, is advanced. Several COVID-related crashes in the time series for Shanghai Composite and Dow Jones Industrial are discussed as an illustration.