893 research outputs found
Minimal model for beta relaxation in viscous liquids
Contrasts between beta relaxation in equilibrium viscous liquids and glasses
are rationalized in terms of a double-well potential model with
structure-dependent asymmetry, assuming structure is described by a single
order parameter. The model is tested for tripropylene glycol where it accounts
for the hysteresis of the dielectric beta loss peak frequency and magnitude
during cooling and reheating through the glass transition.Comment: Phys. Rev. Lett. (in press
Charge and momentum transfer in supercooled melts: Why should their relaxation times differ?
The steady state values of the viscosity and the intrinsic ionic-conductivity
of quenched melts are computed, in terms of independently measurable
quantities. The frequency dependence of the ac dielectric response is
estimated. The discrepancy between the corresponding characteristic relaxation
times is only apparent; it does not imply distinct mechanisms, but stems from
the intrinsic barrier distribution for -relaxation in supercooled
fluids and glasses. This type of intrinsic ``decoupling'' is argued not to
exceed four orders in magnitude, for known glassformers. We explain the origin
of the discrepancy between the stretching exponent , as extracted from
and the dielectric modulus data. The actual width of the
barrier distribution always grows with lowering the temperature. The contrary
is an artifact of the large contribution of the dc-conductivity component to
the modulus data. The methodology allows one to single out other contributions
to the conductivity, as in ``superionic'' liquids or when charge carriers are
delocalized, implying that in those systems, charge transfer does not require
structural reconfiguration.Comment: submitted to J Chem Phy
Relation between the High Density Phase and the Very-High Density Phase of Amorphous Solid Water
It has been suggested that high-density amorphous (HDA) ice is a structurally
arrested form of high-density liquid (HDL) water, while low-density amorphous
(LDA) ice is a structurally arrested form of low-density liquid (LDL) water.
Recent experiments and simulations have been interpreted to support the
possibility of a second "distinct" high-density structural state, named very
high-density amorphous (VHDA) ice, questioning the LDL-HDL hypothesis. We test
this interpretation using extensive computer simulations, and find that VHDA is
a more stable form of HDA and that in fact VHDA should be considered as the
amorphous ice of the quenched HDL.Comment: 5 pages, 4 fig
Welfare guarantees for proportional allocations
According to the proportional allocation mechanism from the network
optimization literature, users compete for a divisible resource -- such as
bandwidth -- by submitting bids. The mechanism allocates to each user a
fraction of the resource that is proportional to her bid and collects an amount
equal to her bid as payment. Since users act as utility-maximizers, this
naturally defines a proportional allocation game. Recently, Syrgkanis and
Tardos (STOC 2013) quantified the inefficiency of equilibria in this game with
respect to the social welfare and presented a lower bound of 26.8% on the price
of anarchy over coarse-correlated and Bayes-Nash equilibria in the full and
incomplete information settings, respectively. In this paper, we improve this
bound to 50% over both equilibrium concepts. Our analysis is simpler and,
furthermore, we argue that it cannot be improved by arguments that do not take
the equilibrium structure into account. We also extend it to settings with
budget constraints where we show the first constant bound (between 36% and 50%)
on the price of anarchy of the corresponding game with respect to an effective
welfare benchmark that takes budgets into account.Comment: 15 page
Time-temperature superposition in viscous liquids
Dielectric relaxation measurements on supercooled triphenyl phosphite show
that at low temperatures time-temperature superposition (TTS) is accurately
obeyed for the primary (alpha) relaxation process. Measurements on 6 other
molecular liquids close to the calorimetric glass transition indicate that TTS
is linked to an high-frequency decay of the alpha loss, while
the loss peak width is nonuniversal.Comment: 4 page
Anisotropic Local Stress and Particle Hopping in a Deeply Supercooled Liquid
The origin of the microscopic motions that lead to stress relaxation in
deeply supercooled liquid remains unclear. We show that in such a liquid the
stress relaxation is locally anisotropic which can serve as the driving force
for the hopping of the system on its free energy surface. However, not all
hopping are equally effective in relaxing the local stress, suggesting that
diffusion can decouple from viscosity even at local level. On the other hand,
orientational relaxation is found to be always coupled to stress relaxation.Comment: 4 pages, 3 figure
The relationship between fragility, configurational entropy and the potential energy landscape of glass forming liquids
Glass is a microscopically disordered, solid form of matter that results when
a fluid is cooled or compressed in such a fashion that it does not crystallise.
Almost all types of materials are capable of glass formation -- polymers, metal
alloys, and molten salts, to name a few. Given such diversity, organising
principles which systematise data concerning glass formation are invaluable.
One such principle is the classification of glass formers according to their
fragility\cite{fragility}. Fragility measures the rapidity with which a
liquid's properties such as viscosity change as the glassy state is approached.
Although the relationship between features of the energy landscape of a glass
former, its configurational entropy and fragility have been analysed previously
(e. g.,\cite{speedyfr}), an understanding of the origins of fragility in these
features is far from being well established. Results for a model liquid, whose
fragility depends on its bulk density, are presented in this letter. Analysis
of the relationship between fragility and quantitative measures of the energy
landscape (the complicated dependence of energy on configuration) reveal that
the fragility depends on changes in the vibrational properties of individual
energy basins, in addition to the total number of such basins present, and
their spread in energy. A thermodynamic expression for fragility is derived,
which is in quantitative agreement with {\it kinetic} fragilities obtained from
the liquid's diffusivity.Comment: 8 pages, 3 figure
Energy landscape - a key concept for the dynamics of glasses and liquids
There is a growing belief that the mode coupling theory is the proper
microscopic theory for the dynamics of the undercooled liquid above a critical
temperature T_c. In addition, there is some evidence that the system leaves the
saddlepoints of the energy landscape to settle in the valleys at this critical
temperature. Finally, there is a microscopic theory for the entropy at the
calorimetric glass transition T_g by Mezard and Parisi, which allows to
calculate the Kauzmann temperature from the atomic pair potentials.
The dynamics of the frozen glass phase is at present limited to
phenomenological models. In the spirit of the energy landscape concept, one
considers an ensemble of independent asymmetric double-well potentials with a
wide distribution of barrier heights and asymmetries (ADWP or Gilroy-Phillips
model). The model gives an excellent description of the relaxation of glasses
up to about T_g/4. Above this temperature, the interaction between different
relaxation centers begins to play a role. One can show that the interaction
reduces the number of relaxation centers needed to bring the shear modulus down
to zero by a factor of three.Comment: Contribution to the III Workshop on Nonequilibrium Phenomena in
Supercooled Fluids, Glasses and Amorphous Materials, 22-27 September 2002,
Pisa; 14 pages, 3 figures; Version 3 takes criticque at Pisa into account;
final version 4 will be published in J.Phys.: Condens.Matte
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