Time reversal for obstacle location in elastodynamics from acoustic recording

The Note is concerned with a feasibility study of time reversal in a non-homogeneous elastic medium, from data recorded in an acoustic medium. Our aim here is to determine the presence and some physical properties of elastic “inclusions” (unknown, not observable solid objects, characterized by their elastic properties) from partial observations of acoustic waves scattered by these inclusions. A finite element numerical method, based on a variational acousto-elastodynamics formulation, is derived and used to solve the forward, and then, the time-reversed problem. A criterion, derived from the reverse time migration framework, is introduced, to help construct images of the inclusions to be determined. Numerical illustrations on configurations that mimic the breast cancer configuration are proposed, and show that one can differentiate between two inclusions, even with different properties.     

Solubilization of silica nanoparticles in alkanes and poly(α-olefin)s by functionalized polyisobutylene oligomers

Covalent and noncovalent chemical methods that use oligomeric lipophilic agents to solubilize silica nanoparticles in heptane and poly(α-olefin) (EPAO) solvents are described. While only modest solubilization efficiencies are seen with an octadecyl group, a variety of terminally functionalized polyisobutylene (PIB) derivatives are more efficient. Both covalent and noncovalent chemistry was found to be effective. Covalent modification solubilized up to 34 wt% of silica nanoparticles (SiNPs) as stable solutions in heptane or PAOs. Noncovalent modification was however more effective, solubilizing up to 70% of SiNPs in heptane or PAOs. The most successful covalent approach used PIB oligomers containing terminal triethoxysilane groups to covalently modify SiNPs. Alternatively, SiNPs that were first functionalized with amine groups could be solubilized in heptane or PAOs with polyisobutylene containing sulfonic acid groups using acid–base chemistry. Studies of these and other solubilization chemistry was also carried out using fluorescent labels, studies that confirmed the gravimetric analyses of the heptane-solubilized SiNPs. Transmission electron microscopy of a PAO solution of these solutions showed that these SiNPs were present as small aggregates dispersed in the PAOs.     

On balking from an empty queue

The intuition while observing the economy of queueing systems, is that one’s motivation to join the system, decreases with its level of congestion. Here we present a queueing model where sometimes the opposite is the case. The point of departure is the standard first-come first-served single server queue with Poisson arrivals. Customers commence service immediately if upon their arrival the server is idle. Otherwise, they are informed if the queue is empty or not. Then, they have to decide whether to join or not. We assume that the customers are homogeneous and when they consider whether to join or not, they assess their queueing costs against their reward due to service completion. As the whereabouts of customers interact, we look for the (possibly mixed) join/do not join Nash equilibrium strategy, a strategy that if adopted by all, then under the resulting steady-state conditions, no one has any incentive not to follow it oneself. We show that when the queue is empty then depending on the service distribution, both ‘avoid the crowd’ (ATC) and ‘follow the crowd’ (FTC) scenarios (as well as none-of-the-above) are possible. When the queue is not empty, the situation is always that of ATC. Also, we show that under Nash equilibrium it is possible (depending on the service distribution) that the joining probability when the queue is empty is smaller than it is when the queue is not empty. This research was supported by The Israel Science Foundation Grant No. 237/02.     

The O(N) vector model in the large-N limit revisited: multicritical points and double scaling limit

The multicritical points of the O(N)-invariant N vector model in the large-N limit are re-examined. Of particular interest are the subtleties involved in the stability of the phase structure at critical dimensions. In the limit N → ∞ while the coupling g → g_c in a correlated manner (the double scaling limit) a massless bound state O(N) singlet is formed and powers of 1/N are compensated by IR singularities. The persistence of the N → ∞ results beyond the leading order is then studied with particular interest in the possible existence of a phase with propagating small mass vector fields and a massless singlet bound state. We point out that under certain conditions the double scaled theory of the singlet field is non-interacting in critical dimensions.     

Determination of Economic Packaging Set-up Frequency of Jointly Replenished Items

This paper deals with the problem of determining the economic operating policy for inventory items which are manufactured jointly but packaged individually. The proposed new approach is very simple and efficient. An extensive simulation study is presented so that the results of several heuristics (based on a wide range of data, measuring the number of optimal solutions, average error and maximum error) can be compared.     

The isomorphism problem for some universal operator algebras

This paper addresses the isomorphism problem for the universal (non-self-adjoint) operator algebras generated by a row contraction subject to homogeneous polynomial relations. We find that two such algebras are isometrically isomorphic if and only if the defining polynomial relations are the same up to a unitary change of variables, and that this happens if and only if the associated subproduct systems are isomorphic. The proof makes use of the complex analytic structure of the character space, together with some recent results on subproduct systems. Restricting attention to commutative operator algebras defined by a radical ideal of relations yields strong resemblances with classical algebraic geometry. These commutative operator algebras turn out to be algebras of analytic functions on algebraic varieties. We prove a projective Nullstellensatz connecting closed ideals and their zero sets. Under some technical assumptions, we find that two such algebras are isomorphic as algebras if and only if they are similar, and we obtain a clear geometrical picture of when this happens. This result is obtained with tools from algebraic geometry, reproducing kernel Hilbert spaces, and some new complex-geometric rigidity results of independent interest. The C^?-envelopes of these algebras are also determined. The Banach-algebraic and the algebraic classification results are shown to hold for the wot-closures of these algebras as well.     

Sub-100-nm laser-induced periodic surface structures upon irradiation of titanium by Ti:sapphire femtosecond laser pulses in air

The formation of laser-induced periodic surface structures (LIPSS) on titanium upon irradiation with linearly polarized femtosecond (fs) laser pulses (τ=30 fs, λ=790 nm) in an air environment is studied experimentally and theoretically. In the experiments, the dependence on the laser fluence and the number of laser pulses per irradiation spot has been analyzed. For a moderate number of laser pulses (N<1000) and at fluences between ～0.09 and ～0.35 J/cm², predominantly low-spatial-frequency-LIPSS with periods between 400 nm and 800 nm are observed perpendicular to the polarization. In a narrow fluence range between 0.05 and 0.09 J/cm², high-spatial-frequency-LIPSS with sub-100-nm spatial periods (～λ/10) can be generated with an orientation parallel to the polarization (N=50). These experimental results are complemented by calculations based on a theoretical LIPSS model and compared to the present literature.     

X‐Tream quality assurance in synchrotron X‐ray microbeam radiation therapy

Microbeam radiation therapy (MRT) is a novel irradiation technique for brain tumours treatment currently under development at the European Synchrotron Radiation Facility in Grenoble, France. The technique is based on the spatial fractionation of a highly brilliant synchrotron X‐ray beam into an array of microbeams using a multi‐slit collimator (MSC). After promising pre‐clinical results, veterinary trials have recently commenced requiring the need for dedicated quality assurance (QA) procedures. The quality of MRT treatment demands reproducible and precise spatial fractionation of the incoming synchrotron beam. The intensity profile of the microbeams must also be quickly and quantitatively characterized prior to each treatment for comparison with that used for input to the dose‐planning calculations. The Centre for Medical Radiation Physics (University of Wollongong, Australia) has developed an X‐ray treatment monitoring system (X‐Tream) which incorporates a high‐spatial‐resolution silicon strip detector (SSD) specifically designed for MRT. In‐air measurements of the horizontal profile of the intrinsic microbeam X‐ray field in order to determine the relative intensity of each microbeam are presented, and the alignment of the MSC is also assessed. The results show that the SSD is able to resolve individual microbeams which therefore provides invaluable QA of the horizontal field size and microbeam number and shape. They also demonstrate that the SSD used in the X‐Tream system is very sensitive to any small misalignment of the MSC. In order to allow as rapid QA as possible, a fast alignment procedure of the SSD based on X‐ray imaging with a low‐intensity low‐energy beam has been developed and is presented in this publication.     

Linear response in the strong field domain

We show that, while it is well-known that first-order perturbation theory leads to linear response (of, e.g., a material system to an external field), the reverse is not true: linear response does not necessarily imply the validity of first-order perturbation theory, nor does it follow from it that the external perturbation is weak. We do so by analyzing the intensity dependence in the photoexcitation followed by dissociation or isomerization of a bound molecular system by a shaped broadband laser pulse. We show that, in certain cases where strong field effects are definitely present, the observed photoexcitation yield as a function of intensity may exhibit linear dependence over a wide range of intensities. The behavior is shown to coexist with a rather extensive range of coherent control over the branching ratios, an effect that was shown in the past to be impossible in the single precursor state (e.g., in the first-order perturbation theory) domain. For example, we demonstrate computationally that when (flat continuum-mediated) Raman transitions are present, appropriate pulse shaping can lead to a linear yield with intensity over a wide range of intensities, while coherent control over the branching ratio is significant. Thus, it is not necessary to invoke external bath effects (as is currently being done) to explain present-day experiments where coherent control is observed in the linear response regime.