On the Motion of a Charged Particle Interacting with an Infinitely Extended System

 We study the time evolution of a charged particle moving in a medium under the action of a constant electric field E. In the framework of fully Hamiltonian models, we discuss conditions on the particle/medium interaction which are necessary for the particle to reach a finite limit velocity. We first consider the case when the charged particle is confined in an unbounded tube of ℝ³. The electric field E is directed along the symmetry axis of the tube and the particle also interacts with an infinitely many particle system. The background system initial conditions are chosen in a set which is typical for any reasonable thermodynamic (equilibrium or non-equilibrium) state. We prove that, for large E and bounded interactions between the charged particle and the background, the velocity v(t) of the charged particle does not reach a finite limit velocity, but it increases to infinite as: |v(t)−Et|≤C ₀ (1+t), where C ₀ is a constant independent of E. As a corollary we obtain that, if the initial conditions of the background system are distributed according to any Gibbs state, then the average velocity of the charged particle diverges as time goes to infinite. This result is obtained for E large enough in comparison with the mean energy of the Gibbs state. We next study the one-dimensional case, in which the estimates can be improved. We finally discuss, at an heuristic level, the existence of a finite limit velocity for unbounded interactions, and give some suggestions about the case of small electric fields. Received: 7 March 2002 / Accepted: 23 September 2002 Published online: 8 January 2003 RID="*" ID="*" Work partially supported by the GNFM-INDAM and the Italian Ministry of the University. Communicated by J.L. Lebowitz     

Confined polymer melts studied by atomic force microscopy

Using an atomic force microscope (AFM) the interaction between an AFM tip and different planar solid surfaces have been measured across a long-chain poly(dimethyl siloxane) (PDMS, M_W = 18,000 g/mol), a short-chain PDMS (M_W = 4200 g/mol), a poly(ethylmethyl siloxane) (PEMS, M_W = 16,800 g/mol), and a diblock copolymer consisting of one PDMS and one PEMS block (PDMS-b-PEMS, M_W = 15,100 g/mol). The interaction changed significantly during the first 10 h after immersing the solids in the polymer melt. This demonstrates that the time scale of structural changes at a solid surface is much slower than in the bulk. On mica and silicon oxide both polymers formed an immobilized “pinned” layer beyond which a monotonically decaying repulsive force was observed. Attractive forces were observed with short-chain PDMS on silicon oxide and PEMS on mica and silicon oxide. On the basal plane of graphite PEMS caused a stable, exponentially decaying oscillatory force.     

Chromatographic behavior of a polyclonal antibody mixture on a strong cation exchanger column. Part II: Adsorption modelling

The adsorption of a polyclonal IgG mixture on a strong cation exchanger column is characterized using a detailed multi-component pore model. This model is explicit in all transport parameters and includes salt dependent isotherms. As discussed in the first part of this work, the IgG mixture can be simplified by considering two pseudo-variants only. Linear gradient experiments are used to fit the salt dependent adsorption isotherms and the mass transport parameters for the two pseudo-variants. Using the model, breakthrough curves are predicted with good accuracy. The model is also implemented to visualize the axial and radial concentration profiles of the two pseudo-variants in the column during a loading experiment.     

Investigation of the activation-parameters of low-temperature slip in cubic metals

The macroscopic critical resolved shear stress (CRSS)τ of 9 body-centred cubic (BCC) and 5 face-centred cubic (FCC) metals has been found to vary with temperatureT in the range 0 to 300 K as given by: lnτ=A − BT, whereA andB are positive constants. Theτ−T data have been analysed within the framework of a kink-pair nucleation (KPN) model of plastic flow in crystals. The microscopic parameters of the unit activation process of yielding, e.g. the initial length of the glide dislocation segment, the critical height of the kink-pair nucleated in it, the activation volume associated with the CRSS, and the binding energy per interatomic spacing along the glide dislocation in the slip plane etc., have been evaluated. A consistent picture of the dislocation kinetics involved in the yielding of BCC and FCC metals emerges, which is adequately described by the KNP model of plastic flow in crystals.     

Mössbauer study of corrosion of mild steel induced by acid rain

Room temperature corrosion studies have been made on the rust of commercially available mild steel in a simulated acid rain environment using the method of transmission Mössbauer spectroscopy. The main corrosion products identified are α-FeOOH, γ-FeOOH, and a product with unfamiliar parameters which seems to be amorphous in nature (being very large linewidth ?2.5 mm/s) and may be considered as an intermediate phase. A small amount of γ-Fe₂O₃ (6–8%) is also observed.     

Mass spectrometry as a tool for the selective profiling of destruxins; their first identification in Lecanicillium longisporum

Mass spectrometry was applied to the identification of the destruxins (dtxs), cyclic peptides that are commonly produced by the fungal insect‐pathogen, Metarhizium anisopliae. The aim of the study was to optimise a methodology in order to firstly determine whether these compounds were present in other species and to determine the effect of differing growth conditions upon the dtx content detected. Matrix‐assisted laser desorption/ionisation time‐of‐flight mass spectrometry (MALDI‐ToF‐MS) was initially used to analyse the dtxs, but limitations were indicated. Nano‐scale high‐performance liquid chromatography/electrospray ionisation mass spectrometry (HPLC/ESI‐MS) and automated ‘data‐dependent’ tandem mass spectrometric (MS/MS) analysis were also applied, utilising characteristic neutral losses during fragmentation to confirm the presence of the dtxs. This latter approach distinguished the dtx E and B isoforms by retention time and diagnostic neutral losses during fragmentation allowing extraction of the destruxin data from a complex dataset. This process revealed the presence of a number of dtxs in the fungal species Lecanicillium longisporum, a species previously not known to produce dtxs, and dtx production in this species was shown to be significantly higher in aerated cultures compared with still cultures. Copyright © 2009 John Wiley & Sons, Ltd.     

Measuring single small molecule binding via rupture forces of a split aptamer

The rupture force of a split (bipartite) aptamer that forms binding pockets for adenosine monophosphate (AMP) was measured by atomic force spectroscopy. Changes in the rupture force were observed in the presence of AMP, while this effect was absent when mutant aptamers or inosine were used. Thus, changes in the rupture force were a direct consequence of specific binding of AMP to the split aptamer. The split aptamer concept allowed the detection of nonlabeled AMP and enabled us to determine the dissociation constant on a single-molecule level.     

Effect of the molecular structure on the hierarchical self-assembly of semifluorinated alkanes at the air/water interface

Semifluorinated alkanes (C(n)F(2n+1)C(m)H(2m+1)), short FnHm display local phase separation of mutually incompatible hydrocarbon and fluorocarbon chain moieties, which has been utilized as a structure-forming motif in supramolecular architectures. The packing of semifluorinated alkanes, nominally based on dodecyl subunits, such as perfluoro(dodecyl)dodecane (F12H12) and perfluoro(dodecyl)eicosane (F12H20), as well as a core extended analogue, 1,4-dibromo-2-((perfluoroundecyl)methoxy)-5-(dodecyloxy)benzene) (F11H1-core-H12), was studied at the air/water interface. Langmuir monolayers were investigated by means of neutron reflectivity directly at the air/water interface and scanning force microscopy after transfer to silicon wafers. Narrowly disperse surface micelles formed in all three cases; however, they were found to bear different morphologies with respect to molecular orientation and assembly dimensionality, which gives rise to different hierarchical aggregate topologies. For F12H12, micelles of ca. 30 nm in diameter, composed of several circular or "spherical cap" substructures, were observed and a monolayer model with the fluorocarbon block oriented toward air is proposed. F12H20 molecules formed larger (ca. 50 nm diameter) hexagonally shaped surface micelles that were hexagonally, densely packed, besides more elongated but tightly interlocked wormlike structures. Conversely, F11H1-core-H12 films organized into linear rows of elongated surface micelles with comparable width, but an average length of ca. 400 nm, apparently formed by antiparallel molecular packing.     

Nonlinear Instability of the Two-Dimensional Striation Model About Smooth Steady States

The two-dimensional striation model consists of a nonlinear system of PDE's which arises in the modeling of the ionospheric plasma. The local-in-time existence of strong solutions is first proved using Banach's fixed point theorem. Then, under physically relevant assumptions, the system is shown to be nonlinearly unstable as soon as it is linearly unstable. Moreover, the instability occurs before the possible blow-up time of the solution. The proof relies on an earlier work of Hwang and Guo (2003 Hwang , H. J. , Guo , Y. ( 2003 ). On the dynamical Rayleigh–Taylor instability . Arch. of Rat. Mech. Anal. 167 : 235 – 253 .[Crossref], [Web of Science ®] , [Google Scholar]). The first step of the proof is to investigate under which conditions the linearized system is unstable and to prove that its spectrum is bounded, by means of a variational formulation. The second one consists in constructing a family of solutions depending on the parameter δ measuring the smallness of the perturbation to the steady-state. Thanks to the boundedness of the linearized spectrum, this family of solutions is shown to be unstable by means of a power series expansion in δ.