Nonlinearity of muscle stiffness

In this letter, a comparison between three types (two linear and one nonlinear) of models of skeletal muscle stiffness is shown. Results are compared with experimental data for biceps brachii in the case of muscle stretching and with the Hill equation for a biological muscle. It is shown that results for nonlinear stiffness model in case of length-force relationship fits to the experimental data.     

Experimental and numerical investigation of chaotic regions in the triple physical pendulum

The experimental and numerical analysis of triple physical pendulum is performed. The experimental setup of the triple pendulum with the first body externally excited by the square function and the widely used LabView measure-programming system, which is designed especially for measure data processing and acquisition, are described. The mathematical model of the system is then introduced. The parameters of the model are estimated by minimization of the sum of squares of deviations between the signal from the simulation and the signal from the experiment. A good agreement between results from experiment and from simulation is shown in few examples, including periodic as well as chaotic solutions.     

Prediction of multicomponent liquid adsorption using excess quantities. III. Calculations for the liquid/air interface

The utilization of excess quantities as the basis of a thermodynamic approach can simplify the prediction of multicomponent data from binary ones. Whereas in Part II the excess formalism was applied to the prediction of liquid phase adsorption on solids, in this paper, the liquid/air interface is investigated. In order to show the generality of the suggested approach, thermodynamic equations are developed in analogy to Part II. Surface tensions are predicted by different excess models and compared with experimental data. From predicted surface tensions, ternary adsorption isotherms on the liquid/air interface are calculated.     

Seasonal and Annual Tritium Variations in Belgrade Natural Waters

Characteristics of seasonal and annual variations of tritium concentration completed with hydrological long-term data from 1976–1989 for the Belgrade alluvial aquifer are presented. The highest tritium concentration in precipitation of an average year appears at the beginning of summer with a maximum in June (9 Bq/l) when the amount of precipitation is also high (102 l/m²). The quantity of tritium precipitating in this area was also the largest in the summer, especially in June (922 Bq/M²). Similar variations of tritium concentration was found in the waters of the Danube and the Sava with maxima 11.3 Bq/l (July) and 9 Bq/l (June) respectively. Tritium concentrations orginated from snowmelt influence to the occurrence of higher values during that period which is more distinct in the Sava. The groundwaters and particularly ones in the Ranney wells follow changes of levels, temperature and tritium content in the alluvial of Sava with a time lag from a few days to a month. During the period of observation tritium content was decreasing in all studied waters. The decrease was faster in precipitation (11.2 to 3.0 Bq/l) and the Sava and Renney wells (10.6 to 3.0 Bq/l) than in the Danube (13.1 to 5.2 Bq/l).     

Dynamical response of a pendulum driven horizontally by a DC motor with a slider–crank mechanism

Nonlinear Dynamics - The pendulum is excited horizontally by a system of a DC motor and a slider–crank mechanism. Mathematical modeling is realistic and based on experimental rig, taking into...     

Modeling, numerical analysis and application of triple physical pendulum with rigid limiters of motion

The mathematical model of a triple physical pendulum harmonically forced with rigid limiters of motion is presented together with the model of stability based on the Aizerman–Gantmakher theory. Some examples of numerical simulations are given for the system of three coupled rods with a horizontal barrier. The system behavior near the grazing incidence is presented; in particular the spectra of Lyapunov exponents are calculated using the presented model of stability.     

Double mode model of size-dependent chaotic vibrations of nanoplates based on the nonlocal elasticity theory

Nonlinear Dynamics - In this paper vibrations of the isotropic micro/nanoplates subjected to transverse and in-plane excitation are investigated. The governing equations of the problem are based on...     

Dynamics Investigation of Three Coupled Rods with a Horizontal Barrier

This report is a part of the larger project of non-linear dynamics investigation of three coupled physical pendulums with damping and with arbitrary situated barriers, and externally driven. The set of differential equations and the set of algebraic inequalities (representing a barrier) governing the motion of three coupled rods are presented in the non-dimensional form. The system of governing equations is integrated between two successive impacts, and the discontinuity points are detected (by halving time step until a required precision is obtained). In each impact time, the state of the system is transformed using the extended restitution coefficient rule. The theory of Aizerman and Gantmakher is used to calculate the fundamental solution matrices in the analyzed system exhibiting discontinuities. The fundamental matrices are used during calculation of Lyapunov exponents, during stability analysis of periodic solutions (Floquet multipliers) and in shooting method applied to detect and trace periodic orbits. Some examples for three coupled identical rods with horizontal barrier are reported.     

Determination of Water Force Constants with Fuzzy Methods

The paper proposes a new approach to the determination of moleculare force fields from observed vibrational frequencies for the case, that observed frequencies are only given in more or less sharp expectation ranges (intervals). Starting from a physically reasonable force constant space, we determine force fields so that the calculated eigenfrequencies are near by the experimental ones. However, in contrast to classical least squaress methods, we will model the uncertainty expressed by the statement “near by” with special triangle functions where the experimental values stand in the head of the triangles. In the sense of the fuzzy set theory, these functions are interpreted as membership functions. Within the force constant space we carry out Normal Coordinate Analyses in the usual way and determine a force field so that the eigenfrequencies have the least possible deviation from the experimental values. The deviation is evaluated with the help of the triangle membership functions. Hence, the selected force field with least deviation is called a fuzzy-optimal one. The water molecule is selected as a model case, because its least-squares force field is precisely known. Following the Born-Oppenheimer-Approximation, we treat all water isotopes in the same manner and select fuzzy-optimal force fields so that the evaluations for each water isotope are approximately similar and as high as possible. We will see that the fuzzy approach is always applicable, even if the assumptions for application of least squares methods are failed. This is a main advantage of the fuzzy method.