Here is a summary of activities in our research group.(updated May 14, 2015)

**Former members of the research group (1997-2001):**

Horst Meyer, professor - now emeritus.

Fang Zhong, research scientist - now staff member at the Jet Propulsion Laboratory, CalTech, Pasadena, CA.

Andrei B. Kogan, graduate student - now Associate Professor in the
Physics Department, U. of Cincinnati,

Cincinnati, OH.

**1) Equilibration dynamics of a pure fluid near the liquid-vapor
critical point. (F.Zhong, A.B. Kogan and H. Meyer).**

A fluid layer with fixed volume at the critical density is contained
inside a cell bounded by two horizontal flat copper plates. We are
investigating the density response inside this fluid to a perturbation by
a temperature step or by an oscillatory temperature change of the copper
boundary plates. This is an interesting problem that is relevant to
experiments under microgravity where stratification is absent, and where
the whole fluid layer can reach the critical point (Under the earth's
gravity conditions, in presence of stratification, only a very small
fraction of the fluid in the middle of the cell will remain at the
critical density that permits the critical point to be realised). It turns
out that both temperature and density equilibration are strongly
influenced by a rapid perturbation through the fluid after the initial
temperature step, called the "piston effect" that is a result of the
strong density change at the boundary layers resulting from the diverging
thermal expansion. The study of this effect is important because the
thermal diffusivity slows down as the critical point is approached.
Accounts have been published in Phys. Rev **E 51**,3223 (1995); **E53**,
5935 (1996), J. Low Temp. Phys. **108,** 161 (1997). More recent
experiments with a new cell, where equilibration and the effect of
convection onset were studied, are published in an article by Kogan and
Meyer, J. Low Temp. Phys. **112**, 417 (1998).

**2) Heat Transport in a pure fluid near the critical point: Steady
state and relaxation dynamics in 3He.(F. Zhong and H. Meyer) **

Near the critical point, where the compressibility diverges, density
stratification in a fluid layer is introduced not only by the gravity
field, but also by a heat flow through this layer. Both effects cause the
measured thermal conductivity along the critical isochore to be smaller
than predicted from mode-coupling and renormalization-group theories in
zero gravity and in the limit of zero heat flow. Furthermore they shorten
the thermal relaxation time compared with predictions. Calculations, done
both in closed-form and also by numerical simulations have given
quantitatively the effect from the stratification for both these effects
on the thermal conductivity and relaxation time as a function of the heat
current. They were compared with experiments and good agreement was
obtained. A paper has appeared in the J. Low Temp. Phys. **114**, 231
(1999)

**3)Crossover behavior in 3-He and Xe near their liquid-vapor critical
point. Work done in collaboration with E. Luijten (presently at the
University of Illinois).**

A detailed discussion is presented of the crossover from mean-field to
Ising critical behavior upon approach of the critical point. By combining
different sets of experimental data, we are able to cover an unusually
large temperature range on either side of the critical temperature Tc.
Below Tc, we can thus make an accurate comparison with a recent
calculation (by Luijten) for the crossover of the coexistence curve. For
the regime above Tc, an analysis of the compressibility demonstrates that
the crossover regime in 3-He is unexpectedly widened by a subtle interplay
between quantum and critical fluctuations. From the analysis, the
corresponding Ginzburg numbers for each property are deduced. Also the
first correction amplitudes for the confluent singularities are obtained
from the fit of the data. The respective ratios of these numbers and those
obtained for the coexistence curves for 3-He and Xe are discussed in terms
of predictions by Bagnuls et al. E. Luijten and H. Meyer, Phys. Rev. E**62**,3257
(2000), H. Meyer, Proc. 2000 NASA/JPL Workshop on Fundamental Physics in
Microgravity NASA Document D-21522(2001), **cond-mat/0105333**

**4) Onset of convection in a Rayleigh-Benard cell in ^{3}He
along the critical isochore : steady-state and transients (A.Kogan and
H. Meyer **(experiments)

As the critical point is approached, fluids become very compressible. Then the onset of convection, calculated from the "Rayleigh" transition, is to take place at a temperature difference across the fluid layer that tends rapidly to zero. The increasing compressibility introduces another effect, the "adiabatic temperature gradient" ("Schwarzschild criterion"), which is usually unimportant in laboratory Rayleigh-Benard convection experiments. It is known by geophysicists because this effect is important in atmospheric phenomena for large air columns. However near the critical point this effect becomes important and dominates in fluid layers with conventional heights (order of 1 mm). We have observed this effect for 3- He, and as the temperature is increased away from the critical point, the Rayleigh condition for the convection onset eventually dominates. This is the first systematic study of the crossover from the Rayleigh to the Schwarzschild regime, and the experiments are in good agreement with the predictions. Another result of this study is the slope of the convective heat current versus Rayleigh number. This slope turns out to be independent of the compressibility for 3-He along the critical isochore, and to be the same as in much less compressible fluids such as liquid 4-He and water in R-B cells of similar aspect ratios.

Plots for the Nusselt- versus Rayleigh number are presented for early-stage convective turbulence. Data sets with Prandtl numbers up to about 100 follow approximately the 2/7 power law. However there are unexpected results for higher Pr numbers, the largest being approx. 590.

The evolution of the temporal transients in the temperature difference
Delta T(t) across the fluid layer before the steady-state is reached has
also been investigated in detail, and some quite unexpected effects were
observed. Among them are damped oscillations of the temperature difference
across the fluid layer that follow the first peak after starting the heat
current. These oscillatory profiles have been compared with recent
computer simulations by Chiwata & Onuki and Furukawa & Onuki(Kyoto
University), which appeared in PRL'01 and in PR-E '02, and also with those
by Amiroudine and Zappoli in PRL **90**, 105303 (2003).

Fig.1 Selected portion of the temperature difference Delta T(t)
across the fluid layer after the heat flow was started at time t=0. It
defines the times t_{p} and t_{osc}. The relaxation time
tau_{asymp} is obtained from an exponential fit of the observed
recording to the asymptotic Delta T, shown by a straight horizontal
dashed line.

A detailed analysis has been made of certain characteristic
times in the time profile of the temperature difference across the fluid
layer mentioned
above.
These times are 1) the period of the damped oscillations t_{osc},
2) the relaxation time tau_{asymp} with which the transient tends
asymptotically to the steady state in an exponential way and 3) the time t_{p}
from the heat flow onset to the peak of Delta T(t). These times are
defined in the figure below what demonstrates the evolution of Delta
T(t) after the start of the heat flow

For all the data at various reduced
temperatures, the scaled ratios t_{osc}/tau_{D},
tau_{asymp}/tau_{D} and t_{p}/tau_{D}
were found to fall each on one "universal" curve, when plotted versus the
Rayleigh number. Here tau_{D} is the diffusion relaxation
time which is a function of L the height of the fluid layer (0.1 cm in our
experiment), and D the thermal diffusion constant as mesured in separate
experiments.

( Phys. Rev. Lett **82**, 4635 (1999), Physica **284**, 208
(2000), Phys Rev.E.**63** 056310 (2001), **cond-mat/0209495**, Phys
Rev.E.**66** 056310 (2002) and in Physica **B**329-333, 114(2003).

Comparison of the
numerical simulations by A. Furukawa and A. Onuki with
experimental data showed good agreement for the scaling of the steady
state convection current and of t(osc) versus the Rayleigh number, but
systematic discrepancies for t(p), where t(p) from simulation is larger
than from experiments, indicating that the onset of convection in
simulations is delayed in time in comparison with experiments (Furukawa,
Meyer, Onuki and Kogan,(PR E **68** 056309 (2003)).

Introduction of
temperature perturbation with a lateral periodicity of 2L into
the simulations has shown that the onset of convection occurs
significantly earlier, hence gives a lower t(p), and for a given amplitude
brings experiment and simulations into near agreement. (Furukawa, Meyer
and Onuki (PR E 71 067301 (2005).

Fig.2 The time of the first peak, t

The most recent article in collaboration with G. Accary (Accary and Meyer, PR-E 74, 046308 (2006)) describes numerical simulations with a time-independent space-periodic perturbation applied to the top plate, aiming to represent the various sources of noise in the experiments. It was found that a single amplitude of this additional perturbation reproduces the noise level of the experiments for all used combinations of the temperature and heating power. this simple operation removes the systematic discrepancy reported in an earlier paper and brings the simulations in good agreement with the measurements.

a)"Equilibration and Other Dynamic Properties of Fluids near the
Liquid-Vapor Critical Point" by H. Meyer and F. Zhong, Comptes Rendus de
l'Academie des Sciences-Mecanique,**332**, 327 (2004)

b) "Time scaling in the convection onset of a supercritical fluid, by H.
Meyer and G. Accary, Actes XIXème CFM 2009, Marseille article #1325 ISSN
0395 5437 (2009) [pdf]

8) Invited Presentations at
"March"meetings of the American Physical Society:

a) "Fritz London's Legacy at Duke University" in "Low Temperature
Physics: A Historical Perspective, Session U5, March 16, 2006, http://www.phy.duke.edu/history/DistinguishedFaculty/WilliamFairbank/Londonlegacy.pdf

b) "Van Vleck and the magnetic susceptibilities of gaseous molecules" in
"J.H. Van Vleck: Quantum theory and Magnetism" Session L8, March 22, 2011,
http://www.phy.duke.edu/~hm/vanVleck/

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