The exponential power law: partial wetting kinetics and dynamic contact angles

An equation for the kinetics of partial drop spreading is proposed. This equation was empirically derived from experimental data for the spreading kinetics of partially wetting liquids in terms of the wet area versus time. The equation has the form of an exponential power law (EPL), and transforms into the well-known power law for complete wetting, when the equilibrium contact angle approaches zero. The EPL fits very well available experimental data. To lend additional support to the validity of this generalized equation, it will be demonstrated that when it is transformed to present the dynamic contact angle (DCA), it fits very well DCA experimental data for other wetting processes, such as capillary flow and tape coating.     

Evaluation of the drag force by integrating the energy dissipation rate in stokes flow for 2D domains using the FEM

The total drag force on the surface of a body, which is the sum of the form drag and the skin friction drag in a 2D domain, is numerically evaluated by integrating the energy dissipation rate in the whole domain for an incompressible Stokes fluid. The finite element method is used to calculate both the energy dissipation rate in the whole domain as well as the drag on the boundary of the body. The evaluation of the drag and the energy dissipation rate are post-processing operations which are carried out after the velocity field and the pressure field for the flow over a particular profile have been obtained. The results obtained for the flow over three different but constant area profiles—a circle, an ellipse and a cross-section of a prolate spheroid—with uniform inlet velocity are presented and it is shown that the total drag force times the velocity is equal to the total energy dissipation rate in the entire finite flow domain. Hence, by calculating the energy dissipation rate in the domain with unit velocity specified at the far-field boundary enclosing the domain, the drag force on the boundary of the body can be obtained.     

Low detection limit spectrophotometry

An efficient, more sensitive and accurate spectrophotometric process is possible and can be used to obtain qualitative or quantitative results for analytes at limiting concentrations lower than usual. Transmission measurements (incident light power, P₀, or transmitted, P) are performed with a fluorescence spectrometer. One cell only is used to measure standards or unknown solutions, placed between the standard holder cuvette and the emission monochromator of the instrument. The source of the radiant power (P₀) is not the xenon lamp but the fluorescence or scattered radiation from the holder cuvette filled with an appropriate solution. The analyte concentration is found from a calibration graph, based upon Beer’s law or the approximate formula P₀−P=2.303P₀εbc, which is valid for dilute solutions. Determination of iron in a reference material, using 1,10-phenanthroline as the chromogenic reagent, was chosen as an example to demonstrate the suitability of the proposed method and clarify several important statistical questions. Also discussed is why and to what extent molecular fluorescence methods are more sensitive than molecular absorption methods.     

武定县地域功能区划分方法研究

县级功能区划作为综合区划,既是落实省级主体功能区规划,又是编制县域空间发展规划的基础。首先探讨县级功能区划方法,然后以武定县为例运用主导因素法划分出城镇区、资源开发区、开发预留区、农业区、生态区等功能区。研究发现：(1)县级功能区划既要考虑县域资源环境本底与发展愿景,又要兼顾省级主体功能区对本县定位;(2)区划评价单元须考虑基础数据可获得性及各单项指标评价单元的统一;(3)指标体系选取以省级主体功能区划指标体系为参照,具有可行性;(4)单一区划方法无法合理区划县级各功能区单元,需多种方法相结合。     

Some optical specificity of ultrathin crystalline films

The changes of optical properties under boundary presence in molecular crystal nanofilm were theoretically investigated in this work. The dispersion law and states of excitons as well as their space distribution along boundary direction have been determined using adjusted Green's function method and also by combined analytical and numerical calculations. On the basis of real and imaginary part of relative permittivity, both absorption and refraction indices were determined, and the influences of boundary parameters on occurrence of a very selective and strictly discrete absorption were analyzed.     

The difference between Newtonian and relativistic forces

This paper discusses a new turn in the 148-year old electrodynamic force law controversy between the 1822 Ampère force law of the Newtonian electrodynamics and Grassmann's 1845 law which has become the electrodynamic force law of relativistic electromagnetism. Faced with the infallibility of Ampère's empirical law, defenders of relativity theory now argue that Ampère's law is equivalent to the relativistic law. This paper demonstrates that, far from being equivalent, the laws require two different mechanics of solid bodies, disagree on internally generated stresses, and predict different force distributions.     

How does the Entropy/Information Bound Work?

According to the universal entropy bound, the entropy (and hence information capacity) of a complete weakly self-gravitating physical system can be bounded exclusively in terms of its circumscribing radius and total gravitating energy. The bound’s correctness is supported by explicit statistical calculations of entropy, gedanken experiments involving the generalized second law, and Bousso’s covariant holographic bound. On the other hand, it is not always obvious in a particular example how the system avoids having too many states for given energy, and hence violating the bound. We analyze in detail several purported counterexamples of this type, and exhibit in each case the mechanism behind the bound’s efficacy. In memoriam Asher Peres.     

Occurrence, Repetition and Matching of Patterns in the Low-temperature Ising Model

We continue our study of the exponential law for occurrences and returns of patterns in the context of Gibbsian random fields. For the low-temperature plus-phase of the Ising model, we prove exponential laws with error bounds for occurrence, return, waiting and matching times. Moreover we obtain a Poisson law for the number of occurrences of large cylindrical events and a Gumbel law for the maximal overlap between two independent copies. As a by-product, we derive precise fluctuation results for the logarithm of waiting and return times. The main technical tool we use, in order to control mixing, is disagreement percolation     

Long-term correlations in hourly wind speed records in Pernambuco, Brazil

We study the statistical properties of hourly wind speed time series detected at four weather stations in the state of Pernambuco, Brazil, in the period 2008-2009. We find that the average and maximum hourly wind speeds deviate from a mutual linear relationship, and that they may be well explained individually by a Weibull distribution, however, with different shape parameter values. On the other hand, the long-term correlations of both of these observables obey the same power-law behavior, with two distinct scaling regimes. Our results agree with previous studies on wind speed series correlations in other regions of the world, which is suggestive of universal behavior.     

The optimal path of piston motion for Otto cycle with linear phenomenological heat transfer law

An Otto cycle engine with internal and external irreversibilities of friction and heat leakage, in which the heat transfer between the working fluid and the environment obeys linear phenomenological heat transfer law [q ∝△(T -1)], is studied in this paper. The optimal piston motion trajectory for maximizing the work output per cycle is derived for the fixed total cycle time and fuel consumed per cycle. Optimal control theory is applied to determine the optimal piston trajectories for the cases of with and w...