476 research outputs found
An Invariance Principle of G-Brownian Motion for the Law of the Iterated Logarithm under G-expectation
The classical law of the iterated logarithm (LIL for short)as fundamental
limit theorems in probability theory play an important role in the development
of probability theory and its applications. Strassen (1964) extended LIL to
large classes of functional random variables, it is well known as the
invariance principle for LIL which provide an extremely powerful tool in
probability and statistical inference. But recently many phenomena show that
the linearity of probability is a limit for applications, for example in
finance, statistics. As while a nonlinear expectation--- G-expectation has
attracted extensive attentions of mathematicians and economists, more and more
people began to study the nature of the G-expectation space. A natural question
is: Can the classical invariance principle for LIL be generalized under
G-expectation space? This paper gives a positive answer. We present the
invariance principle of G-Brownian motion for the law of the iterated logarithm
under G-expectation
Shear flow effects on phase separation of entangled polymer blends
We introduce an entanglement model mixing rule for stress relaxation in a polymer blend to a modified Cahn-Hilliard equation of motion for concentration fluctuations in the presence of shear flow. Such an approach predicts both shear-induced mixing and demixing, depending on the relative relaxation times and plateau moduli of the two components
Familial breast cancer: management of ‘lower risk' referrals
Up to 40% of referrals from primary care to ‘breast cancer family clinics' prove to be of women whose assessed risk falls below the guidelines' threshold for management in secondary or tertiary care, despite recommendations that they should be screened out at primary care level. A randomised trial, involving 87 such women referred to the Tayside Familial Breast Cancer Service compared two ways of communicating risk information, letter or personal interview. Both were found to be acceptable to referred women and to their family doctors, although the former expressed a slight preference for interview. Only four women returned to their family doctors with continuing concerns about breast cancer. Nevertheless, understanding of information provided by either route was unsatisfactory, with apparent confusion about both absolute and relative risks of breast cancer. Substantial minorities appear to believe that they are at no increased risk at all, or even below the population level of risk, while others remain convinced that their personal risk has been underestimated. Family history record forms, completed by the referred women, preferably with the assistance of relatives, are crucial to full assessment of familial risk but one quarter of women referred to the Tayside Familial Breast Cancer Service currently do not complete and return these forms ahead of their clinic appointment. Further collaboration between primary care and the Breast Cancer Family Service is required to improve provision for concerned women whose risks fall below the threshold for special surveillance and to maximise effective use of the family history record form
Molecular observation of contour-length fluctuations limiting topological confinement in polymer melts
In order to study the mechanisms limiting the topological chain confinement in polymer melts, we have performed neutron-spin-echo investigations of the single-chain dynamic-structure factor from polyethylene melts over a large range of chain lengths. While at high molecular weight the reptation model is corroborated, a systematic loosening of the confinement with decreasing chain length is found. The dynamic-structure factors are quantitatively described by the effect of contour-length fluctuations on the confining tube, establishing this mechanism on a molecular level in space and time
Coarse-grained model of entropic allostery
Many signaling functions in molecular biology require proteins to bind to substrates such as DNA in response to environmental signals such as the simultaneous binding to a small molecule. Examples are repressor proteins which may transmit information via a conformational change in response to the ligand binding. An alternative entropic mechanism of "allostery" suggests that the inducer ligand changes the intramolecular vibrational entropy, not just the mean static structure. We present a quantitative, coarse-grained model of entropic allostery, which suggests design rules for internal cohesive potentials in proteins employing this effect. It also addresses the issue of how the signal information to bind or unbind is transmitted through the protein. The model may be applicable to a wide range of repressors and also to signaling in trans-membrane proteins
Kramers rate theory of ionization and dissociation of bound states
Calculating the microscopic dissociation rate of a bound state, such as a
classical diatomic molecule, has been difficult so far. The problem was that
standard theories require an energy barrier over which the bound particle (or
state) escapes into the preferred low-energy state. This is not the case when
the long-range repulsion responsible for the barrier is either absent or
screened (as in Cooper pairs, ionized plasma, or biomolecular complexes). We
solve this classical problem by accounting for entropic memory at the
microscopic level. The theory predicts dissociation rates for arbitrary
potentials and is successfully tested on the example of plasma, where it yields
an estimate of ionization in the core of Sun in excellent agreement with
experiments. In biology, the new theory accounts for crowding in
receptor-ligand kinetics and protein aggregation
Spinodal-assisted crystallization in polymer melts
Recent experiments in some polymer melts quenched below the melting temperature have reported spinodal kinetics in small-angle x-ray scattering before the emergence of a crystalline structure. To explain these observations we propose that the coupling between density and chain conformation induces a liquid-liquid binodal within the equilibrium liquid-crystalline solid coexistence region. A simple phenomenological theory is developed to illustrate this idea, and several experimentally testable consequences are discussed. Shear is shown to enhance the kinetic role of the hidden binodal
Theoretical prediction and experimental measurement of isothermal extrudate swell of monodisperse and bidisperse polystyrenes
Phase Separation of Rigid-Rod Suspensions in Shear Flow
We analyze the behavior of a suspension of rigid rod-like particles in shear
flow using a modified version of the Doi model, and construct diagrams for
phase coexistence under conditions of constant imposed stress and constant
imposed strain rate, among paranematic, flow-aligning nematic, and log-rolling
nematic states. We calculate the effective constitutive relations that would be
measured through the regime of phase separation into shear bands. We calculate
phase coexistence by examining the stability of interfacial steady states and
find a wide range of possible ``phase'' behaviors.Comment: 23 pages 19 figures, revised version to be published in Physical
Review
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