J. L. González-Santander

Classification of flavonoid compounds by using entropy of information theory

A total of 74 flavonoid compounds are classified into a periodic table by using an algorithm based on the entropy of information theory. Seven features in hierarchical order are used to classify structurally the flavonoids. From these features, the first three mark the group or column, while the last four are used to indicate the row or period in a table of periodic classification. Those flavonoids in the same group and period are suggested to show maximum similarity in properties. Furthermore, those with only the same group will present moderate similarity. In this report, the flavonoid compounds in the table, whose experimental data in bioactivity and antioxidant properties have been previously published, are related.

Exact solution for the time-dependent temperature field in dry grinding: application to segmental wheels

We present a closed analytical solution for the time evolution of the temperature field in dry grinding for any time-dependent friction profile between the grinding wheel and the workpiece. We base our solution in the framework of the Samara-Valencia model Skuratov et al., 2007, solving the integral equation posed for the case of dry grinding. We apply our solution to segmental wheels that produce an intermittent friction over the workpiece surface. For the same grinding parameters, we plot the temperature fields of up- and downgrinding, showing that they are quite different from each other.

A Theorem for Finding Maximum Temperature in Wet Grinding

We consider the solutions found in the literature for heat transfer in surface grinding, assuming a constant heat transfer coefficient for the coolant acting on the workpiece surface and a constant or linear heat flux profiles entering into the workpiece. From the integral form of the time-dependent temperature field reached in the workpiece, assuming the previous conditions, we prove that the maximum temperature always occurs in the stationary regime on the workpiece surface within the contact zone between the wheel and the workpiece. This result assures a very rapid method for the theoretical computation of the maximum temperature.

Calculation of Some Integrals Arising in the Samara-Valencia Solution for Dry Flat Grinding

In the framework of the Samara-Valencia solution for heat transfer in grinding, two nontabulated integrals involving Macdonald’s function of zeroth order are calculated.

New analytical approximations for the liquid rise in a capillary tube

We present the ordinary differential equation (ODE) that governs the motion of a liquid rising in a capillary tube in such a way that we can easily derive the principal analytical approximations given in the literature. From this presentation, the numerical solution of the liquid rise over time could be computed very quickly and easily. Furthermore, we derive other analytical approximations not given in the literature, providing a mathematical justification for the cases in which such approximations are good. Some of the approximations found fit the experimental data better than the analytical approximations given in the literature.

Maximum Temperature and Relaxation Time in Wet Surface Grinding for a General Heat Flux Profile

We solve the boundary-value problem of the heat transfer modeling in wet surface grinding, considering a constant heat transfer coefficient over the workpiece surface and a general heat flux profile within the friction zone between wheel and workpiece. We particularize this general solution to the most common heat flux profiles reported in the literature, that is, constant, linear, parabolic, and triangular. For these cases, we propose a fast method for the numerical computation of maximum temperature, in order to avoid the thermal damage of the workpiece. Also, we provide a very efficient method for the numerical evaluation of the transient regime duration (relaxation time).

Positive Curvature Can Mimic a Quantum

We elaborate on the existing idea that quantum mechanics is an emergent phenomenon, in the form of a coarse—grained description of some underlying deterministic theory. We apply the Ricci flow as a technical tool to implement dissipation, or information loss, in the passage from an underlying deterministic theory to its emergent quantum counterpart. A key ingedient in this construction is the fact that the space of physically inequivalent quantum states (either pure or mixed) has positive Ricci curvature. This leads us to an interesting thermodynamical analogy of emergent quantum mechanics.

A NOTE ON THE QUANTUM OF TIME

Quantum mechanics rests on the assumption that time is a classical variable. As such, classical time is assumed to be measurable with infinite accuracy. However, all real clocks are subject to quantum fluctuations, which leads to the existence of a nonzero uncertainty in the time variable. The existence of a quantum of time modifies the Heisenberg evolution equation for observables. Here we propose and analyse a generalisation of Heisenbergs equation for observables evolving in real time (the time variable measured by real clocks), that takes the existence of a quantum of time into account. This generalisation of Heisenbergs equation turns out to be a delay-differential equation.

Closed-form expressions for derivatives of Bessel functions with respect to the order

Calculating the integrals involved in a recent integral representation of the derivative with respect to the order of the Bessel functions, we obtain closed form expressions of these derivatives in terms of generalized hypergeometric functions. Similar calculations can be carried out to the derivatives with respect to the order of the modified Bessel functions, obtaining closed-form expressions as well. As by-products, we obtain the calculation of two non-tabulated integrals.

Efficient Series Expansions of the Temperature Field in Dry Surface Grinding for Usual Heat Flux Profiles

In the framework of Jaeger’s model for heat transfer in dry surface grinding, series expansions for calculating the temperature field, assuming constant, linear, triangular, and parabolic heat flux profiles entering into the workpiece, are derived. The numerical evaluation of these series is considerably faster than the numerical integration of Jaeger’s formula and as accurate as the latter. Also, considering a constant heat flux profile, a numerical procedure is proposed for the computation of the maximum temperature as a function of the Peclet number and the depth below the surface. This numerical procedure has been used to evaluate the accuracy of Takazawa’s approximation.