Nonholonomic constraints in kk-symplectic Classical Field Theories

A $k$-symplectic framework for classical field theories subject to nonholonomic constraints is presented. If the constrained problem is regular one can construct a projection operator such that the solutions of the constrained problem are obtained by projecting the solutions of the free problem. Symmetries for the nonholonomic system are introduced and we show that for every such symmetry, there exist a nonholonomic momentum equation. The proposed formalism permits to introduce in a simple way many tools of nonholonomic mechanics to nonholonomic field theories.Comment: 27 page

A semi-infinite matrix analysis of the BFKL equation

The forward BFKL equation is discretised in virtuality space and it is shown that the diffusion into infrared and ultraviolet momenta can be understood in terms of a semi-infinite matrix. The square truncation of this matrix can be exponentiated leading to asymptotic eigenstates sharing many features with the BFKL gluon Green's function in the limit of large matrix size. This truncation is closely related to a representation of the XXX Heisenberg spin $= - \frac{1}{2}$ chain with SL(2) invariance where the Hamiltonian acts on a symmetric double copy of the harmonic oscillator. A simple modification of the BFKL matrix suppressing the infrared modes generates evolution with energy compatible with unitarity.Comment: Small changes, same conclusions, matching the published version in EPJ

Relationship between the Mathematical Quotient and Emotional Quotient as a Driven Factor to Improve the Social Profile Characteristics of Students

This study investigated the profile, emotional and mathematical quotients of 323 college students in the Philippines. The researcher gathered the data through the EQ Map questionnaire and Scholastic Ability Test for Adults. Results indicated that the respondents' emotional quotient level is moderately well, and their mathematical quotient is poor. Results also showed that the number of hours studying their lesson among the respondents' profile variables affect their emotional quotient. On the other hand, the place where respondents learn their lessons affects their mathematical quotient. This study also signified that the mathematical quotient has no significant relationship to the emotional quotient. This study can show students how social profile characteristics influence their emotional and mathematical quotients. It is recommended that a local study be conducted to evaluate whether or not there is a substantial association between students' emotional quotients and their academic achievement. The results of this study might then be concluded. In addition, a study on the factors affecting the emotional and mathematical capacity of the student may also be undertaken in a specific group within the institution, and the results may then be compared to those obtained from studies conducted at other universities. In a similar sense, it is also recommended to carry out research that will serve the needs of both private and government institutions regarding the aspects that influence emotional intelligence

On the Hamilton-Jacobi Theory for Singular Lagrangian Systems

We develop a Hamilton-Jacobi theory for singular lagrangian systems using the Gotay-Nester-Hinds constraint algorithm. The procedure works even if the system has secondary constraints.Comment: 36 page

Symmetries in Classical Field Theory

The multisymplectic description of Classical Field Theories is revisited, including its relation with the presymplectic formalism on the space of Cauchy data. Both descriptions allow us to give a complete scheme of classification of infinitesimal symmetries, and to obtain the corresponding conservation laws.Comment: 70S05; 70H33; 55R10; 58A2

Hamiltonian Dynamics of Linearly Polarized Gowdy Models Coupled to Massless Scalar Fields

The purpose of this paper is to analyze in detail the Hamiltonian formulation for the compact Gowdy models coupled to massless scalar fields as a necessary first step towards their quantization. We will pay special attention to the coupling of matter and those features that arise for the three-handle and three-sphere topologies that are not present in the well studied three torus case -in particular the polar constraints that come from the regularity conditions on the metric. As a byproduct of our analysis we will get an alternative understanding, within the Hamiltonian framework, of the appearance of initial and final singularities for these models.Comment: Final version to appear in Classical and Quantum Gravit

A Generalization of Chetaev's Principle for a Class of Higher Order Non-holonomic Constraints

The constraint distribution in non-holonomic mechanics has a double role. On one hand, it is a kinematic constraint, that is, it is a restriction on the motion itself. On the other hand, it is also a restriction on the allowed variations when using D'Alembert's Principle to derive the equations of motion. We will show that many systems of physical interest where D'Alembert's Principle does not apply can be conveniently modeled within the general idea of the Principle of Virtual Work by the introduction of both kinematic constraints and variational constraints as being independent entities. This includes, for example, elastic rolling bodies and pneumatic tires. Also, D'Alembert's Principle and Chetaev's Principle fall into this scheme. We emphasize the geometric point of view, avoiding the use of local coordinates, which is the appropriate setting for dealing with questions of global nature, like reduction.Comment: 27 pages. Journal of Mathematical Physics (to zappear

Morphological Characterization of Brazilian Organ Clays Using AFM and SEM Studies

A combination of SEM (Scanning Electron Microscopy) and AFM (Atomic Force Microscopy) techniques was used to characterise the morphology of Brazilian montmorillonites before and after intercalation of some organic compounds. AFM revealed that the layers are staked over above the others. The surface of the particles consisted of layers bounded with smooth flat basal planes and larger edges ending in some cascade-like steps 184 µm wide. Some micro and macro valleys (0.6 µm deep) are distributed throughout the whole area and irregularities on basal planes may be attributed to the crystallographic conditions of the genesis of these Brazilian montmorillonites. The mapping performed over 20 x 40 areas showed adhesion forces of 11 nN magnitude on bare clay mineral in the Na+ form and 40 nN for the calcium form. Forces between 10 and 6 nN were found after organic intercalation. In general, the intercalation caused significant changes in the surface properties of clay mineral. The combination of AFM and SEM studies provided evidence about the poorl crystallinity of the Brazilian montmorillonites.A combination of SEM (Scanning Electron Microscopy) and AFM (Atomic Force Microscopy) techniques was used to characterise the morphology of Brazilian montmorillonites before and after intercalation of some organic compounds. AFM revealed that the layers are staked over above the others. The surface of the particles consisted of layers bounded with smooth flat basal planes and larger edges ending in some cascade-like steps 184 µm wide. Some micro and macro valleys (0.6 µm deep) are distributed throughout the whole area and irregularities on basal planes may be attributed to the crystallographic conditions of the genesis of these Brazilian montmorillonites. The mapping performed over 20 x 40 areas showed adhesion forces of 11 nN magnitude on bare clay mineral in the Na+ form and 40 nN for the calcium form. Forces between 10 and 6 nN were found after organic intercalation. In general, the intercalation caused significant changes in the surface properties of clay mineral. The combination of AFM and SEM studies provided evidence about the poorl crystallinity of the Brazilian montmorillonites