Abstract:We study the effect of the simplest geometry which is imposed via the topology of the universe by gauging non-relativistic particle model on torus and 3-torus with the help of symplectic formalism of constrained systems. Also, we obtain generators of gauge transformations for gauged models. Extracting corresponding Poisson structure of existed constraints, we show the effect of the shape of the universe on canonical structure of phase-spaces of models and suggest some phenomenology to prove the topology of the universe and probable non-commutative structure of the space. In addition, we show that the number of extra dimensions in the phase-spaces of gauged embedded models are exactly two. Moreover, in classical form, we talk over modification of Newton's second law in order to study the origin of the terms appeared in the gauged theory.

In order to address the overall properties of the Brazilian agricultural commodity market and the intricate effects of political and economic instabilities, in this work, we provide a comprehensive study of the multifractal properties of the Brazilian commodities using multifractal detrended fluctuation analysis (MFDFA). We focus on the daily price of 12 Brazilian agricultural commodities over the last two decades, and four commodities (sugar, soybean, coffee and cattle) are also studied in terms of time-dependent MFDFA to address the effects of particular political and economic instability events. All commodities exhibit multifractal properties, which are then used to evaluate market efficiency. We find that all commodities except coffee show lower market efficiency for prices in Brazilian Reals (BRL) than in US Dollars (USD) reflecting the presence of constrains in domestic agricultural market, such as minimum price policy. From time-dependent MFDFA, we find that after the 2007/2008 food crisis, the market efficiency increases, as indicated by the changes in price dynamics towards lower persistency and weaker multifractality, with the dominance of small fluctuations.

Observations from the NASA MMS satellites show packages of ELF whistler‐mode waves localized inside the small‐scale irregularities of the magnetic field. These irregularities are formed by the narrow field‐aligned channels where the magnitude of the background magnetic field inside the channel is greater or less than outside. By analogy with the classical density ducts, we introduce the high‐B duct (HBD), where the magnitude of the field inside the channel is greater than the outside, and the low‐B duct (LBD), where the magnitude of the field inside the channel is less than the outside. We investigate the guiding of the ELF whistler‐mode waves by high‐B and low‐B ducts. We derive the analytical criteria for the wave ducting by these ducts and confirm them with two‐dimension, time‐dependent simulations of the electron‐MHD model. Also, we model ELF whistler‐mode waves observed inside the high‐B and low‐B ducts by MMS satellites.This article is protected by copyright. All rights reserved.

Two models with linear and nonlinear second class constraints are considered and gauged by embedding in an extended phase space. These models are studied by considering a free non-relativistic particle on the hyper plane and hyper sphere in the configuration space. The gauged theory of the first model is obtained by converting the very second class system to the first class one, directly. In contrast, the first class system related to the free particle on the hyper sphere is derived with the help of the infinite BFT embedding procedure. We propose a practical formula, based on the simplified BFT method, which is practical in gauging linear and some nonlinear second class systems. As a result of gauging these two models, we show that in the conversion of second class constraints to the first class ones, the minimum number of phase space degrees of freedom for both systems is a pair of phase space coordinates. This pair is made up of a coordinate and its conjugate momentum for the first model, but the corresponding Poisson structure of the embedded non-relativistic particle on hyper sphere is a non-trivial one. We derive infinite correction terms for the Hamiltonian of the nonlinear constraints and an interacting gauged Hamiltonian is constructed by summing over them. At

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