Osmotic force resisting chain insertion in a colloidal suspension

We consider the problem of inserting a stiff chain into a colloidal suspension of particles that interact with it through excluded volume forces. The free energy of insertion is associated with the work of creating a cavity devoid of colloid and sufficiently large to accommodate the chain. The corresponding work per unit length is the force that resists the entry of the chain into the colloidal suspension. In the case of a hard sphere fluid, this work can be calculated straightforwardly within the scaled particle theory; for solutions of flexible polymers, on the other hand, we employ simple scaling arguments. The forces computed in these ways are shown, for nanometer chain and colloid diameters, to be of the order of tens of pN for solution volume fractions of a few tenths. These magnitudes are argued to be important for biophysical processes such as the ejection of DNA from viral capsids into the cell cytoplasm. Received 18 December 2002 Published online: 16 April 2003 RID="a" ID="a"e-mail: castel@chem.ucla.edu RID="b" ID="b"Present address: Courant Institute of Mathematical Sciences, NYU, New York, New York 10012, USA     

The sharp Hausdorff measure condition for length of projections

In a recent paper, Pertti Mattila asked which gauge functions have the property that for any Borel set with Hausdorff measure 0$">, the projection of to almost every line has positive length. We show that finiteness of , which is known to be sufficient for this property, is also necessary for regularly varying . Our proof is based on a random construction adapted to the gauge function.

     

Synthesis and biological evaluation of gramicidin S dimers

The design and synthesis of analogues of the cyclic beta-sheet gramicidin S (GS), having additional functionalities in their turn regions, is reported. The monomeric GS analogues were transformed into dimers and their activities towards biological membranes, through antimicriobial and hemolytic assays, were evaluated. Finally, conductivity measurements have been performed to elucidate ion channel forming properties.     

“Magic Relation” Between the Structures of Coexisting Phases at a First-Order Phase Transition in a Hard Sphere System

In the statistical geometry of a hard sphere system of any number of dimensions, V _o and S _o, the so-called available space and the area of the interface between the available and unavailable space, respectively, can be used as surrogates for chemical potential and pressure. It is shown exactly that, if a first-order transition occurs, the relation dV _o/dS _o=–/2D, where is the diameter of a sphere and D is the dimensionality of the system, must hold for densities in the phase coexistence region. This relation is remarkable in that –/2D is the ratio of the volume to the surface area of a sphere. Also, it is shown that it is possible for the system to have two successive first-order transitions, but that the occurrence of a continuous transition (even in two dimensions) is unlikely. It is argued that this unlikelihood is substantially strengthened by the absence of temperature (except as a trivial factor) as a variable in hard-sphere systems. This suggests that the findings of the KTHNY theory, recent simulations, and colloid experiments (specialized to sticky hard disks) can be extended to true hard disks. The fundamental physics underlying the magic relation is yet to be exposed. The author continues to search for the underlying reason and hopes that the present paper will stimulate others to join the search.     

A note on uniform approximation to distributions of extreme order statistics

Summary The error bound of an approximation to the distribution of thekth largest order statistic as established by Reiss (1981,Adv. Appl. Prob.,13, 533–547) is improved by making use of an asymptotic expansion of length two in Reiss (the same as above).     

Asymptotic independence of distributions of normalized order statistics of the underlying probability measure

Let n denote the sample size, and let r_i ∈ {1,…,n} fulfill the conditions r_i ? r_i?1 ≥ 5 for i = 1,…,k. It is proved that the joint normalized distribution of the order statistics Z_ri:n, i = 1,…,k, is independent of the underlying probability measure up to a remainder term of order $\text{O((}\text{k}\text{n}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$. A counterexample shows that, as far as central order statistics are concerned, this remainder term is not of the order $\text{O((}\text{k}\text{n}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$ if r_i ? r_i?1 = 1 for i = 2,…,k.     

Investigation of the level schemes of 73,75,77As via the (3He,d) reaction

The reactions ^{72, 74, 76}Ge(³He, d) were investigated at E_lab = 23 MeV with a multigap and a Q3D magnetic spectrograph. Some 30 new levels up to $\text{E}{}^1\text{≈ 4}\text{MeV}$ have been found. The level schemes of the odd As isotopes ^{73, 75, 77}As up to $\text{E}{}^1\text{≈ 4}\text{MeV}$ seem to be rather independent of the neutron number. The good agreement of the low-lying level structure with the Coriolis-coupling model including a pairing force was verified and the vacancies of low-lying shell model states were extracted and compared with the simple pairing theory.