Crossover Critical Behavior in the Three-Dimensional Ising Model

The character of critical behavior in physical systems depends on the range of interactions. In the limit of infinite range of the interactions, systems will exhibit mean-field critical behavior, i.e., critical behavior not affected by fluctuations of the order parameter. If the interaction range is finite, the critical behavior asymptotically close to the critical point is determined by fluctuations and the actual critical behavior depends on the particular universality class. A variety of systems, including fluids and anisotropic ferromagnets, belongs to the three-dimensional Ising universality class. Recent numerical studies of Ising models with different interaction ranges have revealed a spectacular crossover between the asymptotic fluctuation-induced critical behavior and mean-field-type critical behavior. In this work, we compare these numerical results with a crossover Landau model based on renormalization-group matching. For this purpose we consider an application of the crossover Landau model to the three-dimensional Ising model without fitting to any adjustable parameters. The crossover behavior of the critical susceptibility and of the order parameter is analyzed over a broad range (ten orders) of the scaled distance to the critical temperature. The dependence of the coupling constant on the interaction range, governing the crossover critical behavior, is discussed.     

Whirling frequencies and amplitudes due to deviations of generator shape

Earlier measurements in large synchronous generators indicate the existence of backward whirling motion, and also relatively large deviations of shape in both the rotor and the stator. These non-symmetric geometries produce an attraction force between the rotor and the stator, called unbalanced magnetic pull (UMP). The target of this paper is to analyse the whirling frequencies and amplitude of the response for large synchronous generators with a high number of poles, due to deviations of shape in the rotor and stator. A mathematical model is developed to describe the shapes of the rotor and stator, and the corresponding UMP is obtained by using the law of energy conservation. The UMP is analysed due to different deviations of shape. The result gives the average angular frequency and the magnitude of the UMP for certain deviations of shape. From this result, the whirling frequency and the amplitude of the corresponding response can be approximated. Simulations of the response of a Jeffcott rotor model show good agreement with the theoretical results of the UMP for some generator geometries. The conclusion is that different whirling frequencies, both backward and forward whirling, can occur in these machines due to deviations in shape of the generator. Therefore, the shape of the generator can excite resonance vibrations on several other frequencies than the rotation frequency. During maintenance of hydropower generators the shapes of the rotor and stator are frequently measured. The results from this paper can be used to evaluate such measurements and to explain the existence of complicated whirling motion.     

ContributionsSign-balanced covering matrices

A q × n array with entries from 0, 1,…,q − 1 is said to form a difference matrix if the vector difference (modulo q) of each pair of columns consists of a permutation of [0, 1,… q − 1]; this definition is inverted from the more standard one to be found, e.g., in Colbourn and de Launey (1996). The following idea generalizes this notion: Given an appropriate δ (-[−1, 1]^t, a λq × n array will be said to form a (t, q, λ, Δ) sign-balanced matrix if for each choice C₁, C₂,…, C_t of t columns and for each choice = (₁,…,_t) Δ of signs, the linear combination ∑_j=1^t _jC_j contains (mod q) each entry of [0, 1,…, q − 1] exactly λ times. We consider the following extremal problem in this paper: How large does the number k = k(n, t, q, λ, δ) of rows have to be so that for each choice of t columns and for each choice (₁, …, _t) of signs in δ, the linear combination ∑_j=1^t _jC_j contains each entry of [0, 1,…, q t- 1] at least λ times? We use probabilistic methods, in particular the Lovász local lemma and the Stein-Chen method of Poisson approximation to obtain general (logarithmic) upper bounds on the numbers k(n, t, q, λ, δ), and to provide Poisson approximations for the probability distribution of the number W of deficient sets of t columns, given a random array. It is proved, in addition, that arithmetic modulo q yields the smallest array - in a sense to be described.     

Q value related mass determinations using a Penning trap

We report here about measurements of reaction and decay Q values by precise determination of pairs of atomic masses. These were performed with the Penning trap mass spectrometer SMILETRAP. Measurements with Penning traps give reliable and accurate masses, in particular Q values, due to the fact that certain systematic errors to a great deal cancel in the mass difference between the two atoms defining the Q value. Some Q values that are of fundamental interest will be discussed here, for example, a new Q value for the ⁶Li (n,γ) ⁷Li reaction, for the β-decay of tritium, related to properties of the electron neutrino mass, and for the neutrino-less double β-decay of ⁷⁶Ge, related to the question of whether the neutrino is a Majorana particle or not. In case of the latter two we report the most accurate Q values, namely 18,589.8(12) eV for the tritium decay and 2,038.997(46) keV for the neutrino-less double β-decay of ⁷⁶Ge.     

PARTIAL VERSUS GENERAL STORAGE POLICY: COMMODITIES AND RESOURCES

This paper examines joint storage considerations when both commodities and resources can be stored, e.g., grain and water for irrigation. Results suggest that when separate agencies control public resource and commodity storage, suboptimal storage rules occur unless (i) each agency is sensitive to the policies of the other, (ii) commodity inventories are adjusted in response to prices, and (iii) resource inventories are adjusted in response to both commodity demand and resource supply conditions. For example, the common case where water storage depends on weather and reservoir conditions alone is not sufficiently general. The results imply that water management agencies that tend to be dominated by engineers and hydrological considerations need to incorporate economic considerations into decision processes.     

Thermal characterisation of micro-hotplates used in sensor structures

Micro-hotplates operated at elevated temperature form the basic element in several sensor devices, such as integrated calorimetric or Taguchi-type gas sensors and flow-rate sensors. In all of these applications thermal properties of the sensing elements play a determining role in functional operation, therefore, their accurate characterisation is essential. The micro-hotplates investigated were developed by one side porous silicon micro-machining technology, forming Pt micro-filaments embedded in non-stoichiometric silicon nitride, and suspended across a cavity. This work is dealing with the accurate temperature detection in the micro-scale by different measurement methods for the deduction of steady state and transient thermal properties from the results. Transient properties of the structure were investigated by application of a simplified thermal equivalent circuit model.     

Peripheral spectrum of positive quasi-compact operators onC 0(X)

LetX be a locally compact space, andT, a quasi-compact positive operator onC ₀(X), with positive spectral radius,r. Then the peripheral spectrum ofT is a finite set of poles containingr, and the residue of the resolvent ofT at each peripheral pole is of finite rank. Using the concept of closed absorbing set, we develop an iterative process that gives the order,p, ofr, some special bases of the algebraic eigenspaces ker(T-r) ^p and ker(T ^*-r) ^p , and finally the dimension of the algebraic eigenspace associated to each peripheral pole.