Uncertainty principle for proper time and mass

We review Bohr's reasoning in the Bohr-Einstein debate on the photon box experiment. The essential point of his reasoning leads us to an uncertainty relation between the proper time and the rest mass of the clock. It is shown that this uncertainty relation can be derived if only we take the fundamental point of view that the proper time should be included as a dynamic variable in the Lagrangian describing the system of the clock. Some problems and some positive aspects of our approach are then discussed.Comment: 15 pages, accepted for publication in J. Math. Phy

Can randomness alone tune the fractal dimension?

We present a generalized stochastic Cantor set by means of a simple {\it cut and delete process} and discuss the self-similar properties of the arising geometric structure. To increase the flexibility of the model, two free parameters, $m$ and $b$, are introduced which tune the relative strength of the two processes and the degree of randomness respectively. In doing so, we have identified a new set with a wide spectrum of subsets produced by tuning either $m$ or $b$. Measuring the size of the resulting set in terms of fractal dimension, we show that the fractal dimension increases with increasing order and reaches its maximum value when the randomness is completely ceased.Comment: 6 pages 2-column RevTeX, Two figures (presented in the APCTP International Symposium on Slow Dynamical Processes in Nature, Nov. 2001, Seoul, Korea

Fragmentation with a Steady Source

We investigate fragmentation processes with a steady input of fragments. We find that the size distribution approaches a stationary form which exhibits a power law divergence in the small size limit, P(x) ~ x^{-3}. This algebraic behavior is robust as it is independent of the details of the input as well as the spatial dimension. The full time dependent behavior is obtained analytically for arbitrary inputs, and is found to exhibit a universal scaling behavior.Comment: 4 page

Competitive random sequential adsorption of point and fixed-sized particles: analytical results

We study the kinetics of competitive random sequential adsorption (RSA) of particles of binary mixture of points and fixed-sized particles within the mean-field approach. The present work is a generalization of the random car parking problem in the sense that it considers the case when either a car of fixed size is parked with probability q or the parking space is partitioned into two smaller spaces with probability (1-q) at each time event. This allows an interesting interplay between the classical RSA problem at one extreme (q=1), and the kinetics of fragmentation processes at the other extreme (q=0). We present exact analytical results for coverage for a whole range of q values, and physical explanations are given for different aspects of the problem. In addition, a comprehensive account of the scaling theory, emphasizing on dimensional analysis, is presented, and the exact expression for the scaling function and exponents are obtained.Comment: 7 pages, latex, 3 figure

Computer simulation and study of the IR spectra of irradiated polymer materials

Within the framework of MDDP the calculations of IR spectra have been performed for the initial polyethylene terephthalate (PET) and its state with the cation which satisfactorily describing experimental data. The calculations were made using the MDDP (modified neglect of diatomic differential overlap), implemented in the program MOPAC 2012. A feature of the method is that the overlap integrals are replaced by the [delta]-function, single-site Coulomb and exchange integrals are calculated by atomic parameters Slater-Condon. In recent years the studies of the structure and physico-chemical properties of polyethylene terephthalate and composites made on it basis have got the intensive development. Comparison of calculations with experimental data gives their satisfactory agreement

Solution and bulk properties of branched polyvinyl acetates IV--Melt viscosity

The melt viscosities of some randomly branched and some comb shaped branched polyvinyl acetate fractions were compared to the viscosities of linear polymer over a range of molecular weights. The melt viscosity of the branched polymer was usually higher than that of linear polymer of the same weight average molecular weight. The extent of this increase was related to the molecular weight of the branches but no correlation could be found which included the number of branches per molecule. This unusual behaviour is believed to be due to the fact that the length of the branches in the polymers of this study was above the critical chain length for polyvinyl acetate which made it possible for the branches to be engaged in intermolecular chain entanglements.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32168/1/0000223.pd

Multivalency in healable supramolecular polymers: the effect of supramolecular cross-link density on the mechanical properties and healing of non- covalent polymer networks

Polymers with the ability to heal themselves could provide access to materials with extended lifetimes in a wide range of applications such as surface coatings, automotive components and aerospace composites. Here we describe the synthesis and characterisation of two novel, stimuli-responsive, supramolecular polymer blends based on p-electron-rich pyrenyl residues and p-electron-deficient, chain-folding aromatic diimides that interact through complementary p–p stacking interactions. Different degrees of supramolecular “cross-linking” were achieved by use of divalent or trivalent poly(ethylene glycol)-based polymers featuring pyrenyl end-groups, blended with a known diimide–ether copolymer. The mechanical properties of the resulting polymer blends revealed that higher degrees of supramolecular “cross-link density” yield materials with enhanced mechanical properties, such as increased tensile modulus, modulus of toughness, elasticity and yield point. After a number of break/heal cycles, these materials were found to retain the characteristics of the pristine polymer blend, and this new approach thus offers a simple route to mechanically robust yet healable materials