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The first-order input and output edge transfer matrix elements of the magnetic sector in a static mass spectrometer are derived based on the conservation law of the generalized momentum of ions in a magnetic field. The structure of the edge matrix is shown to be ambiguous and dependent on the effective model, which considers the displacement of ion trajectories in the edge field. A comparison of the results obtained with traditional methods, such as expanding the edge field components and trajectory equations into asymptotic series and integrating successive approximations, reveals significant differences in the first-order edge matrix elements in the effective model of the magnetic sector, where the ideal uniform field is bounded by Herzog boundaries, compared to the published data. Algorithms for matching the input and output axes of the magnetic sector, taking into account the action of the edge fields, are given. [ABSTRACT FROM AUTHOR]

This study aims to compare the Food and Agriculture Organization (FAO) framework as a common model and gene expression programming (GEP) model for predicting the irrigated wheat production by using land properties in Khajeh area, Iran. First, 80 representative soil profiles were described in wheat fields. Then, the soil samples were collected from each horizon, and soil properties were determined in the laboratory for obtaining the model input data. After that, wheat production models were developed by FAO and GEP models. Sensitivity analysis indicated that total N, available P, slope, coarse fragment, electrical conductivity, pH, and organic matter are important soil properties for wheat production. Based on the results, the value of predicted wheat production by GEP model (981–5382) is closer to the actual production (1000–5600) compared to the FAO models (1284–6123). The geometric mean error ratio (GMER), root mean square error (RMSE), and coefficient of determination (R2) between predicted and actual production for FAO and GEP models were calculated 1.24, 18.6, and 0.84 and 0.83, 15.4, and 0.91, respectively. The overall agreement was recognized between wheat predicted production by using FAO and GEP and actual production by composite operator. This agreement was 71.5 and 82.2% for FAO and GEP models, respectively. Therefore, gene expression programming model was introduced as an effective model for predicting the wheat production. This more accuracy was obtained due to good choosing and lack of interaction among land properties as input variables. [ABSTRACT FROM AUTHOR]

A neuron's firing correlates are defined as the features of the external world to which its activity is correlated. In many parts of the brain, neurons have quite simple such firing correlates. A striking example are grid cells in the rodent medial entorhinal cortex: their activity correlates with the animal's position in space, defining 'grid fields' arranged with a remarkable periodicity. Here, we show that the organization and evolution of grid fields relate very simply to physical space. To do so, we use an effective model and consider grid fields as point objects (particles) moving around in space under the influence of forces. We reproduce several observations on the geometry of grid patterns. This particle-like behavior is particularly salient in a recent experiment in which two separate grid patterns merge. We discuss pattern formation in the light of known results from physics of two-dimensional colloidal systems. Notably, we study the limitations of the widely used 'gridness score' and show how physics of 2d systems could be a source of inspiration, both for data analysis and computational modeling. Finally, we draw the relationship between our 'macroscopic' model for grid fields and existing 'microscopic' models of grid cell activity and discuss how a description at the level of grid fields allows to put constraints on the underlying grid cell network. [ABSTRACT FROM AUTHOR]

With an effective chiral flavour SU(3) model we show the effect of hadronic resonances on the QCD phase diagram. We state that varying the resonance couplings to the scalar and vector fields affects the order and location of the phase transition, the possible existence of a critical end point (CEP), and the thermodynamic properties. We present (strange) quark number susceptibilities at zero baryochemical potential and at three different points at the phase transition. Comparing results to lattice QCD, we state that reasonable large vector couplings limit the phase transition to a smooth crossover ruling out a CEP. [ABSTRACT FROM AUTHOR]

We propose a new method for the homogenization of hysteresis models of plasticity. For the one-dimensional wave equation with an elasto-plastic stress-strain relation we derive averaged equations and perform the homogenization limit for stochastic material parameters. This generalizes results of the seminal paper by Franců and Krejčí. Our approach rests on energy methods for partial differential equations and provides short proofs without recurrence to hysteresis operator theory. [ABSTRACT FROM AUTHOR]

The effective behaviour of stationary micromagnetic phenomena is modelled by a convexified Landau–Lifshitz minimization problem for the limit of large and soft magnets Ω with no exchange energy. The numerical simulation of the resulting minimization problem has to overcome difficulties caused by the pointwise side-constraint $$|\bf{m}|\leq 1$$ and the stray-field energy on the unbounded domain $$\mathbb{R}^{d}$$ . A penalty method models the side-constraint and the exterior Maxwell equation is recast via a nonlocal integral operator $$\mathcal{L}$$ . This paper gives an overview of the available results and implementational details. [ABSTRACT FROM AUTHOR]