A One Dimensional Crystal With Nearest Neighbors Coupled Through Their Velocities

1981 ◽  
Vol 103 (3) ◽  
pp. 293-296 ◽  
Author(s):  
J. N. Boyd ◽  
P. N. Raychowdhury

We consider a circular array of point masses connected by springs of non-negligible mass. In the Lagrangian for the harmonic motions of this system, the movements of neighboring point masses are coupled through both the kinetic and potential energies. By use of transformations derived from the theory of projection operators, we simplify the Lagrangian and obtain the natural frequencies of the motions of the system as functions of the number of particles present. We note that for large numbers of particles, the results for our circular array will yield the frequencies of a one dimensional crystal.

1995 ◽  
Vol 74 (06) ◽  
pp. 1533-1540 ◽  
Author(s):  
Pål André Holme ◽  
Nils Olav Solum ◽  
Frank Brosstad ◽  
Nils Egberg ◽  
Tomas L Lindahl

SummaryThe mechanism of formation of platelet-derived microvesicles remains controversial.The aim of the present work was to study the formation of microvesicles in view of a possible involvement of the GPIIb-IIIa complex, and of exposure of negatively charged phospholipids as procoagulant material on the platelet surface. This was studied in blood from three Glanzmann’s thrombasthenia patients lacking GPIIb-IIIa and healthy blood donors. MAb FN52 against CD9 which activates the complement system and produces microvesicles due to a membrane permeabilization, ADP (9.37 μM), and the thrombin receptor agonist peptide SFLLRN (100 μM) that activates platelets via G-proteins were used as inducers. In a series of experiments platelets were also preincubated with PGE1 (20 μM). The number of liberated microvesicles, as per cent of the total number of particles (including platelets), was measured using flow cytometry with FITC conjugated antibodies against GPIIIa or GPIb. Activation of GPIIb-IIIa was detected as binding of PAC-1, and exposure of aminophospholipids as binding of annexin V. With normal donors, activation of the complement system induced a reversible PAC-1 binding during shape change. A massive binding of annexin V was seen during shape change as an irreversible process, as well as formation of large numbers of microvesicles (60.6 ±2.7%) which continued after reversal of the PAC-1 binding. Preincubation with PGE1 did not prevent binding of annexin V, nor formation of microvesicles (49.5 ± 2.7%), but abolished shape change and PAC-1 binding after complement activation. Thrombasthenic platelets behaved like normal platelets after activation of complement except for lack of PAC-1 binding (also with regard to the effect of PGE1 and microvesicle formation). Stimulation of normal platelets with 100 μM SFLLRN gave 16.3 ± 1.2% microvesicles, and strong PAC-1 and annexin V binding. After preincubation with PGE1 neither PAC-1 nor annexin V binding, nor any significant amount of microvesicles could be detected. SFLLRN activation of the thrombasthenic platelets produced a small but significant number of microvesicles (6.4 ± 0.8%). Incubation of thrombasthenic platelets with SFLLRN after preincubation with PGE1, gave results identical to those of normal platelets. ADP activation of normal platelets gave PAC-1 binding, but no significant annexin V labelling, nor production of microvesicles. Thus, different inducers of the shedding of microvesicles seem to act by different mechanisms. For all inducers there was a strong correlation between the exposure of procoagulant surface and formation of microvesicles, suggesting that the mechanism of microvesicle formation is linked to the exposure of aminophospholipids. The results also show that the GPIIb-IIIa complex is not required for formation of microvesicles after activation of the complement system, but seems to be of importance, but not absolutely required, after stimulation with SFLLRN.


2020 ◽  
Vol 25 (2) ◽  
pp. 29
Author(s):  
Desmond Adair ◽  
Aigul Nagimova ◽  
Martin Jaeger

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.


Physica ◽  
1966 ◽  
Vol 32 (7) ◽  
pp. 1274-1282 ◽  
Author(s):  
Maria Stȩślicka ◽  
K.F. Wojciechowski

2021 ◽  
pp. 146808742110344
Author(s):  
José Galindo ◽  
Andrés Omar Tiseira ◽  
Luis Miguel García-Cuevas ◽  
Nicolás Medina

The current paper presents the validation of some hypotheses used for developing a one-dimensional twin-entry turbine model with experimental measurements. A Laser Doppler Anemometry (LDA) technique has been used for measuring the axial Mach number and for counting the number of particles downstream of the rotor outlet. These measurements have been done for different mass flow ratio (MFR) and reduced turbocharger speed conditions. The flow coming from each turbine entry does not fully mix with the other within the rotor since, downstream of the rotor, they can still be differentiated. Thus, the hypothesis of studying twin-entry turbines as two separated single-entry turbines in one-dimensional models is corroborated. Moreover, the rotor outlet area corresponding to each flow branch has linear trends with the MFR value. Therefore, the rotor outlet effective area used for one-dimensional models should vary linearly with the MFR value.


Author(s):  
Osvaldo Pinheiro de Souza e Silva ◽  
Severino Fonseca da Silva Neto ◽  
Ilson Paranhos Pasqualino ◽  
Antonio Carlos Ramos Troyman

This work discusses procedures used to determine effective shear area of ship sections. Five types of ships have been studied. Initially, the vertical natural frequencies of an acrylic scale model 3m in length in a laboratory at university are obtained from experimental tests and from a three dimensional numerical model, and are compared to those calculated from a one dimensional model which the effective shear area was calculated by a practical computational method based on thin-walled section Shear Flow Theory. The second studied ship was a ship employed in midshipmen training. Two models were made to complement some studies and vibration measurements made for those ships in the end of 1980 decade when some vibration problems in them were solved as a result of that effort. Comparisons were made between natural frequencies obtained experimentally, numerically from a three dimensional finite element model and from a one dimensional model in which effective shear area is considered. The third and fourth were, respectively, a tanker ship and an AHTS (Anchor Handling Tug Supply) boat, both with comparison between three and one dimensional models results out of water. Experimental tests had been performed in these two ships and their results were used in other comparison made after the inclusion of another important effect that acts simultaneously: the added mass. Finally, natural frequencies experimental and numerical results of a barge are presented. The natural frequencies numerical results of vertical hull vibration obtained from these approximations of effective shear areas for the five ships are finally discussed.


2011 ◽  
Vol 44 (1) ◽  
pp. 32-42 ◽  
Author(s):  
Thomas Vad ◽  
Wiebke F. C. Sager

Two simple iterative desmearing procedures – the Lake algorithm and the Van Cittert method – have been investigated by introducing different convergence criteria using both synthetic and experimental small-angle neutron scattering data. Implementing appropriate convergence criteria resulted in stable and reliable solutions in correcting resolution errors originating from instrumental smearing,i.e.finite collimation and polychromaticity of the incident beam. Deviations at small momentum transfer for concentrated ensembles of spheres encountered in earlier studies are not observed. Amplification of statistical errors can be reduced by applying a noise filter after desmearing. In most cases investigated, the modified Lake algorithm yields better results with a significantly smaller number of iterations and is, therefore, suitable for automated desmearing of large numbers of data sets.


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