Debye formulas for a relaxing system with memory

Rate (master) equations are ubiquitous in statistical physics, yet, to the best of our knowledge, a rate equation with memory has previously never been considered. We write down an integro-differential rate equation for the evolution of a thermally relaxing system with memory. For concreteness we adopt as a model a single-domain magnetic particle driven by a small ac field and derive the modified Debye formulas. For any memory time Θ the in-phase component of the resultant ac susceptibility is positive at small probing frequencies ω, but becomes negative at large ω. The system thus exhibits frequency induced diamagnetism. For comparison we also consider particle pairs with dipolar coupling. The memory effect is found to be enhanced by ferromagnetic coupling and suppressed by antiferromagnetic coupling. Numerical calculations support the prediction of a negative susceptibility which arises from a phase shift induced by the memory effect. It is proposed that the onset of frequency induced diamagnetism represents a viable experimental signature of correlated noise

Thermally activated escape rates of uniaxial spin systems with transverse field

Classical escape rates of uniaxial spin systems are characterized by a prefactor differing from and much smaller than that of the particle problem, since the maximum of the spin energy is attained everywhere on the line of constant latitude: theta=const, 0 =< phi =< 2*pi. If a transverse field is applied, a saddle point of the energy is formed, and high, moderate, and low damping regimes (similar to those for particles) appear. Here we present the first analytical and numerical study of crossovers between the uniaxial and other regimes for spin systems. It is shown that there is one HD-Uniaxial crossover, whereas at low damping the uniaxial and LD regimes are separated by two crossovers.Comment: 4 PR pages, 3 figures, final published versio

Magnetic relaxation in finite two-dimensional nanoparticle ensembles

We study the slow phase of thermally activated magnetic relaxation in finite two-dimensional ensembles of dipolar interacting ferromagnetic nanoparticles whose easy axes of magnetization are perpendicular to the distribution plane. We develop a method to numerically simulate the magnetic relaxation for the case that the smallest heights of the potential barriers between the equilibrium directions of the nanoparticle magnetic moments are much larger than the thermal energy. Within this framework, we analyze in detail the role that the correlations of the nanoparticle magnetic moments and the finite size of the nanoparticle ensemble play in magnetic relaxation.Comment: 21 pages, 4 figure

Monte Carlo simulation with time step quantification in terms of Langevin dynamics

For the description of thermally activated dynamics in systems of classical magnetic moments numerical methods are desirable. We consider a simple model for isolated magnetic particles in a uniform field with an oblique angle to the easy axis of the particles. For this model, a comparison of the Monte Carlo method with Langevin dynamics yields new insight in the interpretation of the Monte Carlo process, leading to the implementation of a new algorithm where the Monte Carlo step is time-quantified. The numeric results for the characteristic time of the magnetisation reversal are in excellent agreement with asymptotic solutions which itself are in agreement with the exact numerical results obtained from the Fokker-Planck equation for the Neel-Brown model.Comment: 5 pages, Revtex, 4 Figures include

Statistical Mechanics of Nonuniform Magnetization Reversal

The magnetization reversal rate via thermal creation of soliton pairs in quasi-1D ferromagnetic systems is calculated. Such a model describes e.g. the time dependent coercivity of elongated particles as used in magnetic recording media. The energy barrier that has to be overcome by thermal fluctuations corresponds to a soliton-antisoliton pair whose size depends on the external field. In contrast to other models of first order phase transitions such as the phi^4 model, an analytical expression for this energy barrier is found for all values of the external field. The magnetization reversal rate is calculated using a functional Fokker-Planck description of the stochastic magnetization dynamics. Analytical results are obtained in the limits of small fields and fields close to the anisotropy field. In the former case the hard-axis anisotropy becomes effectively strong and the magnetization reversal rate is shown to reduce to the nucleation rate of soliton-antisoliton pairs in the overdamped double sine-Gordon model. The present theory therefore includes the nucleation rate of soliton-antisoliton pairs in the double sine-Gordon chain as a special case. These results demonstrate that for elongated particles, the experimentally observed coercivity is significantly lower than the value predicted by the standard theories of N\'eel and Brown.Comment: 21 pages RevTex 3.0 (twocolumn), 6 figures available on request, to appear in Phys Rev B, Dec (1994

Runoff and sediment monitoring in an agricultural watershed in the Ethiopian Highlands

Land degradation due to soil erosion is a major issue in the Ethiopian Highlands. Deforestation leads to ongoing gully erosion during the rainy season (June to September) and thus the hydrology of a watershed changes as dense gully networks cause direct drainage of rain water. To better understand watershed scale gully processes in the Ethiopian Highlands, three gauging stations were installed in the 56 km2 large Gumara-Maksegnit catchment in the northern Amhara region, to monitor discharge and sediment load in the gullies during rainy season. Various weirs respectively a fixed cross section was installed: Two v-notched weirs were built in two approximately 30 ha large sub catchments. Discharge was determined based on continuously logged water level data (ultrasonic sensor respectively pressure sensor) and using a calibrated weir equation. Sediment concentration was estimated based on continuously logged turbidity sensor data. In the main outlet discharge was calculated based on water level data (pressure sensor) and by using a calibrated rating curve which was derived by means of spatial distributed flow velocity measurements within the fixed and rectangular shaped cross section. Sediment concentration was estimated by turbidity sensor equipment. To validate the continuously logged turbidity sensors data additional manually taken runoff samples were used. Additionally, rainfall data was logged at three gauging stations distributed in the watershed. Observed data from the rainy season 2012 showed that the runoff in the sub catchments as well as in the main outlet was mainly controlled by heavy single storm events. Although baseflow and interflow was observed in the main outlet, the portion of surface runoff dominated the runoff in the gully. As a consequence of the surface runoff driven regime in the gullies, huge amounts of sediment were observed during heavy rainfall events. The hydrological study at Gumara-Maksegnit watershed is part of an entire watershed monitoring program and provides local runoff and sediment yield data as a basis for regional soil conservation planning. Moreover watershed specific relations between precipitation, runoff and sediment concentration in the channels can support predictions of future event scenarios