Search results for: eigenmode

Authors: Olga S. Volodko, Lidiya A. Kompaniets, Ludmila V. Gavrilova

Abstract:

The method of empirical orthogonal functions is the method of data analysis with a complex spatial-temporal structure. This method allows us to decompose the data into a finite number of modes determined by empirically finding the eigenfunctions of data correlation matrix. The modes have different scales and can be associated with various physical processes. The empirical orthogonal function method has been widely used for the analysis of hydrophysical characteristics, for example, the analysis of sea surface temperatures in the Western North Atlantic, ocean surface currents in the North Carolina, the study of tropical wave disturbances etc. The method used in this study has been applied to the analysis of temperature and velocity measurements in saline Lake Shira (Southern Siberia, Russia). Shira is a shallow lake with the maximum depth of 25 m. The lake Shira can be considered as a closed water site because of it has one small river providing inflow and but it has no outflows. The main factor that causes the motion of fluid is variable wind flows. In summer the lake is strongly stratified by temperature and saline. Long-term measurements of the temperatures and currents were conducted at several points during summer 2014-2015. The temperature has been measured with an accuracy of 0.1 ºC. The data were analyzed using the empirical orthogonal function method in the real version. The first empirical eigenmode accounts for 70-80 % of the energy and can be interpreted as temperature distribution with a thermocline. A thermocline is a thermal layer where the temperature decreases rapidly from the mixed upper layer of the lake to much colder deep water. The higher order modes can be interpreted as oscillations induced by internal waves. The currents measurements were recorded using Acoustic Doppler Current Profilers 600 kHz and 1200 kHz. The data were analyzed using the empirical orthogonal function method in the complex version. The first empirical eigenmode accounts for about 40 % of the energy and corresponds to the Ekman spiral occurring in the case of a stationary homogeneous fluid. Other modes describe the effects associated with the stratification of fluids. The second and next empirical eigenmodes were associated with dynamical modes. These modes were obtained for a simplified model of inhomogeneous three-level fluid at a water site with a flat bottom.

Keywords: Ekman spiral, empirical orthogonal functions, data analysis, stratified fluid, thermocline

Procedia PDF Downloads 135

Authors: Victor I. Ilgisonis, Ludmila V. Konovaltseva, Vladimir P. Lakhin, Ekaterina A. Sorokina

Abstract:

The analytical solutions for geodesic acoustic eigenmodes in tokamak plasmas with circular concentric magnetic surfaces are found. In the frame of ideal magnetohydrodynamics the dispersion relation taking into account the toroidal coupling between electrostatic perturbations and electromagnetic perturbations with poloidal mode number |m| = 2 is derived. In the absence of such a coupling the dispersion relation gives the standard continuous spectrum of geodesic acoustic modes. The analysis of the existence of global eigenmodes for plasma equilibria with both off-axis and on-axis maximum of the local geodesic acoustic frequency is performed.

Keywords: tokamak, MHD, geodesic acoustic mode, eigenmode

Procedia PDF Downloads 733

Authors: Babak Eslami

Abstract:

Bimodal and trimodal AFM have provided additional capabilities to scanning probe microscopy characterization techniques. These capabilities have specifically enhanced material characterization of surfaces and provided subsurface imaging in addition to conventional topography images. Bimodal and trimodal AFM, being different techniques of multifrequency AFM, are based on exciting the cantilever’s fundamental eigenmode with second and third eigenmodes simultaneously. Although higher eigenmodes provide a higher number of observables that can provide additional information about the sample, they cause experimental challenges. In this work, different experimental approaches for enhancing AFM images in multifrequency for different characterization goals are provided. The trade-offs between eigenmodes including the advantages and disadvantages of using each mode for different samples (ranging from stiff to soft matter) in both air and liquid environments are provided. Additionally, the advantage of performing conventional single tapping mode AFM with higher eigenmodes of the cantilever in order to reduce sample indentation is discussed. These analyses are performed on widely used polymers such as polystyrene, polymethyl methacrylate and air nanobubbles on different surfaces in both air and liquid.

Keywords: multifrequency, sensitivity, soft matter, polymer

Procedia PDF Downloads 134

Authors: Ajay R, Rammohan B, Sridhar K S S, Gurusharan N

Abstract:

The objective of the work is to develop a numerical method to solve the inverse mode shape problem by determining the cross-sectional area of a structure for the desired mode shape via the vibration response study of the humerus bone, which is in the form of a cantilever beam with anisotropic material properties. The humerus bone is the long bone in the arm that connects the shoulder to the elbow. The mode shape is assumed to be a higher-order polynomial satisfying a prescribed set of boundary conditions to converge the numerical algorithm. The natural frequency and the mode shapes are calculated for different boundary conditions to find the cross-sectional area of humerus bone from Eigenmode shape with the aid of the inverse mode shape algorithm. The cross-sectional area of humerus bone validates the mode shapes of specific boundary conditions. The numerical method to solve the inverse mode shape problem is validated in the biomedical application by finding the cross-sectional area of a humerus bone in the human arm.

Keywords: Cross-sectional area, Humerus bone, Inverse mode shape problem, Mode shape

Procedia PDF Downloads 123