1,522 research outputs found
Dynamics of the Tippe Top -- properties of numerical solutions versus the dynamical equations
We study the relationship between numerical solutions for inverting Tippe Top
and the structure of the dynamical equations. The numerical solutions confirm
oscillatory behaviour of the inclination angle for the symmetry
axis of the Tippe Top. They also reveal further fine features of the dynamics
of inverting solutions defining the time of inversion. These features are
partially understood on the basis of the underlying dynamical equations
Stationary problems for equation of the KdV type and dynamical -matrices.
We study a quite general family of dynamical -matrices for an auxiliary
loop algebra related to restricted flows for equations of
the KdV type. This underlying -matrix structure allows to reconstruct Lax
representations and to find variables of separation for a wide set of the
integrable natural Hamiltonian systems. As an example, we discuss the
Henon-Heiles system and a quartic system of two degrees of freedom in detail.Comment: 25pp, LaTe
Preliminary engineering report for design of a subscale ejector/diffuser system for high expansion ratio space engine testing
The design of a subscale jet engine driven ejector/diffuser system is examined. Analytical results and preliminary design drawings and plans are included. Previously developed performance prediction techniques are verified. A safety analysis is performed to determine the mechanism for detonation suppression
Elastic properties of cubic crystals: Every's versus Blackman's diagram
Blackman's diagram of two dimensionless ratios of elastic constants is
frequently used to correlate elastic properties of cubic crystals with
interatomic bondings. Every's diagram of a different set of two dimensionless
variables was used by us for classification of various properties of such
crystals. We compare these two ways of characterization of elastic properties
of cubic materials and consider the description of various groups of materials,
e.g. simple metals, oxides, and alkali halides. With exception of intermediate
valent compounds, the correlation coefficients for Every's diagrams of various
groups of materials are greater than for Blackaman's diagrams, revealing the
existence of a linear relationship between two dimensionless Every's variables.
Alignment of elements and compounds along lines of constant Poisson's ratio
, ( arbitrary perpendicular to ) is
observed. Division of the stability region in Blackman's diagram into region of
complete auxetics, auxetics and non-auxetics is introduced. Correlations of a
scaling and an acoustic anisotropy parameter are considered.Comment: 8 pages, 9 figures, presented on The Ninth International School on
Theoretical Physics "Symmetry and Structural Properties of Condensed Matter",
5 - 12 September 2007, Myczkowce, Polan
Additional Constants of Motion for a Discretization of the Calogero--Moser Model
The maximal super-integrability of a discretization of the Calogero--Moser
model introduced by Nijhoff and Pang is presented. An explicit formula for the
additional constants of motion is given.Comment: 7 pages, no figure
Coherent population oscillations with nitrogen-vacancy color centers in diamond
We present results of our research on two-field (two-frequency) microwave
spectroscopy in nitrogen-vacancy (NV-) color centers in a diamond. Both fields
are tuned to transitions between the spin sublevels of the NV- ensemble in the
3A2 ground state (one field has a fixed frequency while the second one is
scanned). Particular attention is focused on the case where two microwaves
fields drive the same transition between two NV- ground state sublevels (ms=0
-> ms=+1). In this case, the observed spectra exhibit a complex narrow
structure composed of three Lorentzian resonances positioned at the pump-field
frequency. The resonance widths and amplitudes depend on the lifetimes of the
levels involved in the transition. We attribute the spectra to coherent
population oscillations induced by the two nearly degenerate microwave fields,
which we have also observed in real time. The observations agree well with a
theoretical model and can be useful for investigation of the NV relaxation
mechanisms.Comment: 17 page
Mpemba effect and phase transitions in the adiabatic cooling of water before freezing
An accurate experimental investigation on the Mpemba effect (that is, the
freezing of initially hot water before cold one) is carried out, showing that
in the adiabatic cooling of water a relevant role is played by supercooling as
well as by phase transitions taking place at 6 +/- 1 oC, 3.5 +/- 0.5 oC and 1.3
+/- 0.6 oC, respectively. The last transition, occurring with a non negligible
probability of 0.21, has not been detected earlier. Supported by the
experimental results achieved, a thorough theoretical analysis of supercooling
and such phase transitions, which are interpreted in terms of different
ordering of clusters of molecules in water, is given.Comment: revtex, 4 pages, 2 figure
Precision surface characterization for finish cylindrical milling with dynamic tool displacements model
In this work a new approach to surface roughness parameters estimation during finish cylindrical end milling is presented. The proposed model includes the influence of cutting parameters, the tool’s static run out and dynamic phenomena related to instantaneous tool deflections. The modeling procedure consists of two parts. In the first stage, tool working part instantaneous displacements are estimated using an analytical model which considers tool dynamic deflections and static errors of the machine – tool-holder – tool system. The obtained height of the tool’s displacement envelope is then applied in the second stage to the calculation of surface roughness parameters. These calculations assume that in the cylindrical milling process, two different mechanisms of surface profile formation exist. Which mechanism is present is dependent on the feed per tooth and the maximum height of the tool’s displacement envelope. The developed model is validated during cylindrical milling of hardened hot-work tool steel 55NiCrMoV6 using a stylus profiler and scanning laser vibrometer over a range of cutting parameters. The surface roughness values predicted by the developed model are in good agreement with measured values. It is found that the employment of a model which includes only the effect of static displacements gives an inferior estimation of surface roughness compared to the model incorporating dynamic tool deflection
The Lax pairs for the Holt system
By using non-canonical transformation between the Holt system and the
Henon-Heiles system the Lax pairs for all the integrable cases of the Holt
system are constructed from the known Lax representations for the Henon-Heiles
system.Comment: 7 pages, LaTeX2e, a4.st
Dynamics of the Tippe Top—Properties of numerical solutions versus the dynamical equations
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