A Personal Perspective on the Last Half-Century of Critical Phenomena

One of the crowning achievements of mathematical, statistical physics over the past half century has been the discovery of the many aspects of structure of the critical point. It has been an exciting time and was only possible through the combined efforts of many excellent people. This article contains brief reviews of some of the parts in which I have been most interested and to which I have made some contributions.     

Periodic solutions of non-linear discrete Volterra equations with finite memory

In this paper we discuss the existence of periodic solutions of discrete (and discretized) non-linear Volterra equations with finite memory. The literature contains a number of results on periodic solutions of non-linear Volterra integral equations with finite memory, of a type that arises in biomathematics. The “summation” equations studied here can arise as discrete models in their own right but are (as we demonstrate) of a type that arise from the discretization of such integral equations. Our main results are in two parts: (i) results for discrete equations and (ii) consequences for quadrature methods applied to integral equations. The first set of results are obtained using a variety of fixed-point theorems. The second set of results address the preservation of properties of integral equations on discretizing them. The effect of weak singularities is addressed in a final section. The detail that is presented, which is supplemented using appendices, reflects the differing prerequisites of functional analysis and numerical analysis that contribute to the outcomes.     

Gas chromatography/flame ionisation detection mass spectrometry for the detection of endogenous urine metabolites for metabonomic studies and its use as a complementary tool to nuclear magnetic resonance spectroscopy

Metabonomics is a relatively new field of research in which the total pool of metabolites in body fluids or tissues from different patient groups is subjected to comparative analysis. Nuclear magnetic resonance (NMR) spectroscopy is the technology that is currently most widely used for the analysis of these highly complex metabolite mixtures, and hundreds of metabolites can be detected without any upfront separation. We have investigated in this study whether gas chromatography (GC) separation in combination with flame ionisation detection (FID) and mass spectrometry (MS) detection can be used for metabolite profiling from urine. We show that although GC sample preparation is much more involved than for NMR, hundreds of metabolites can reproducibly be detected and analysed by GC. We show that the data quality is sufficiently high--particularly if appropriate baseline correction and time-warping methods are applied--to allow for data comparison by chemometrics methods. A sample set of urines from eleven healthy human volunteers was analysed independently by GC and NMR, and subsequent chemometrics analysis of the two datasets showed some similar features. As judged by NIST database searches of the GC/MS data some of the major metabolites that are detected by NMR are also visible by GC/MS. Since in contrast to NMR every peak in GC corresponds to a single metabolite, the electron ionisation spectra can be used to quickly identify metabolites of interest if their reference spectra are present in a searchable database. In summary, we show that GC is a method that can be used as a complementary tool to NMR for metabolite profiling of urine samples.     

Reactions of group 3 transition metal atoms with CS2 and OCS: Matrix isolation infrared spectra and density-functional calculations of SMCS, SM-(eta2-CS), SMCO, and SM-(eta2-CO) in solid argon

Laser-ablated scandium, yttrium, and lanthanum atoms were reacted with CS2 and OCS molecules in an argon matrix. Products of the type SMCX and S-M(eta2-CX) (X = S or O) were formed on sample deposition. Photolysis favored the S-M(eta(2)-CX) complex, while annealing increased the more stable SMCX isomer. Product absorptions are identified by density-functional frequency calculations and isotopic substitutions. This work reports the first vibrational spectroscopic characterization of Sc, Y, and La reaction products with CS2 and OCS and the subsequent interconversion between SMCX and S-M(eta2-CX) structural isomers.     

Biosensing with conically shaped nanopores and nanotubes

In this review we consider recent results from our group that are directed towards developing "smart" synthetic nanopores that can mimic the functions of biological nanopores (transmembrane proteins). We first discuss the preparation and characterization of conical nanopores synthesized using the track-etch process. We then consider the design and function of conical nanopores that can rectify the ionic current that flows through these pores under an applied transmembrane potential. Finally, two types of sensors that we have developed with these conical nanopores are described. The first sensor makes use of molecular recognition elements that are bound to the nanopore mouth to selectively block the nanopore tip, thus detecting the presence of the analyte. The second sensor makes use of conical nanopores in a resistive-pulse type experiment, detecting the analyte via transient blockages in ionic current.     

Tomographic reconstruction of high-energy-density plasmas with picosecond temporal resolution

Three-dimensional reconstruction of the electron density in a plasma can be obtained by passing multiple beams at different field angles simultaneously through a plasma and performing a tomographic reconstruction of the measured field-dependent phase profiles. A relatively simple experimental setup is proposed and simulations are carried out to verify the technique. The plasma distribution is modeled as a discrete number of phase screens, and a Zernike polynomial representation of the phase screens is used to reconstruct the plasma profile.     

A single-shot pixellated phase-shifting interferometer utilizing a liquid-crystal spatial light modulator

We introduce a novel phase-shifting pixellated interferometer based on a liquid-crystal spatial light modulator and simulate the expected performance. The phase-shifted frames are captured simultaneously, which reduces problems arising from vibrations and air turbulence. The liquid-crystal spatial light modulator is flexible and can be configured to provide a large number of phase-shift levels and geometries to reduce measurement error.     

Subsurface probing of calcifications with spatially offset Raman spectroscopy (SORS): future possibilities for the diagnosis of breast cancer

Breast calcifications are often the only mammographic features indicating the presence of a cancerous lesion. Calcium oxalate (type I) may be found in and around benign lesions, however calcium hydroxyapatite (type II) is usually found within proliferative lesions, which can include both benign and malignant pathologies. However, the composition of type II calcifications has been demonstrated to vary between benign and malignant proliferative lesions, and could be an indicator for the possible disease state. Raman spectroscopy has previously been demonstrated as a powerful tool for non-destructive analysis of tissues, utilising laser light to probe chemical composition. Raman spectroscopy is traditionally a surface technique. However, we have recently developed methods that permit its application for obtaining sample composition to clinically relevant depths of many mm. We report the first demonstration of spatially offset Raman spectroscopy (SORS) for potential in vivo breast analysis. This study evaluates the possibility of utilising SORS for measuring calcification composition through varying thicknesses of tissues (2 to 10 mm), which is about one to two orders of magnitude deeper than has been possible with conventional Raman approaches. SORS can be used to distinguish non-invasively between calcification types I and II (and carbonate substitution of phosphate in calcium hydroxyapatite) within tissue of up to 10 mm deep. This result secures the first step in taking this technique forward for clinical applications seeking to use Raman spectroscopy as an adjunct to mammography for early diagnosis of breast cancer, by utilising both soft tissue and calcification signals. Non-invasive elucidation of calcification composition, and hence type, associated with benign or malignant lesions, could eliminate the requirement for biopsy in many patients.     

Modeling and device parameter design to improve reset time in binary-oxide memristors

A simulation-based analysis is conducted to study the set and reset times of TiO₂-based memristor device. This analysis uses nonlinear device model that captures the effects of large electric field inside memristor devices. Previous studies report strong asymmetry between reset and set times with reset time being several orders of magnitude higher than set time. The aim of this work was to investigate the effect of the device length and oxygen vacancies profile on the switching time. Our results show that a device model with a length of 10 nm and accurate parameters can result in more realistic device characteristics. Also, oxygen vacancies profile can be tuned to improve the reset time. MATLAB is used to simulate a 10-nm device, and the initial vacancy profile is chosen to look like inverted parabola. The results show reduced ratio between reset and set times from several orders of magnitude presented in the literature to not more than 1.5×. Thus, the proposed oxygen vacancies profile and quantitative results derived from it can be used to suggest a physical memristor device. In addition, the tuned parameters and model that matches actual device behavior can be factored in memristor fabrication.