New Developments in the Eight Vertex Model II. Chains of Odd Length

We study the transfer matrix of the 8 vertex model with an odd number of lattice sites N. For systems at the root of unity pointsη=mK/L with m odd the transfer matrix is known to satisfy the famous ‘‘TQ’’ equation where Q(υ) is a specifically known matrix. We demonstrate that the location of the zeroes of this Q(υ) matrix is qualitatively different from the case of evenN and in particular they satisfy a previously unknown equation which is more general than what is often called ‘‘Bethe’s equation.’’ For the case of even m where no Q(υ) matrix is known we demonstrate that there are many states which are not obtained from the formalism of the SOS model but which do satisfy the TQ equation. The ground state for the particular case of η=2K/3 and N odd is investigated in detail.     

Measurement of apex angle of the prism using total internal reflection

Total internal reflection technique is examined critically for the measurement of apex angle of the prism. Recognition of the critical boundary completely specifies the apex angle ‘A’ of the prism by keeping constant the ratio of refractive index of sample fluid (n₁=1.4) to that of glass (n₂=1.7). Recording of observations in the laboratory is dependent upon whether the apex angle ‘A’ of prism is greater than or less than or equal to critical angle ‘r_c’. The minimum value of error function ‘χ’ in the proximity of Abbe angle explain the choice of Abbe type instruments and shown invariant by relating positive ‘₊’ and the negative angle of emergence ‘₋’. Using ray-tracing technique, an expression for the length of the critical boundary ‘l’ is derived and is shown as a measure of the apex angle ‘A’ of the prism.

The choice of the realistic grazing condition leads us to two turning points for which error function ‘χ’ is minimal and yields appropriate option of the measurement of apex angle ‘A’ of the prism. It is further shown that the small error ‘ζ’ crept in the apex angle ‘A’ of the prism can lead to a significant error in the design of Pulfrich type instruments.

Experimental measurements are in-line with the predictions made.     

On the environmental decoherence and spin interference in mesoscopic loop structures

Mechanisms of ‘environmental decoherence’ such as surface scattering, Elliot–Yafet process and precession mechanisms, as well as their influence on the spin phase relaxation are considered and compared. It is shown that the ‘spin ballistic’ regime is possible, when the phase relaxation length for the spin part of the wave function (L^(s)) is much greater than the phase relaxation length for the ‘orbital part’ (L^(e)). In the presence of an additional magnetic field, the spin part of the electron's wave function (WF) acquires a phase shift due to additional spin precession about that field. If the structure length L is chosen to be L^(s)>L>L^(e), it is possible to ‘wash out’ the quantum interference related to the phase coherence of the ‘orbital part’ of the WF, retaining at the same time that related to the phase coherence of the spin part and, hence, to reveal corresponding conductance oscillations.     

Missing data in image and signal processing: The case of binary objects

I investigated which portions of the Fourier transform of binary signals, images and three-dimensional objects are necessary to correctly identify an object in the presence of noise. This is practically possible for very small binary data sets since the total number of possible objects is then very limited. There are for example 512 different binary images with 9 pixels. It is easy to see that this number soon becomes impractically large for bigger images or if one allows more than two possible pixel values. It turns out that even in the presence of large amounts of noise a relatively small portion of the Fourier transform is essential for deciding which of all possible binary objects the Fourier transform belongs to. These ‘decision experiments’ can be used as a standard for how well algorithms for retrieval of missing Fourier components perform. In another set of computer experiments I investigate the possibility of retrieving various missing Fourier components algorithmically. The main finding of this second set of computer experiments is that the simple retrieval algorithm (a limited form of ‘projection onto convex sets’) used falls very much short of what one might expect from the ‘decision experiments’.I conclude with a discussion what this discrepancy might be due to and some suggestions how to improve the performance of retrieval algorithms for binary objects.     

Ever Ready to Go: The Multiple Exiles of Leo Szilard

I argue that to understand the life and work of Leo Szilard (1898–1964) we have to understand, first, that he was driven by events to numerous departures, escapes, and exiles, changing his religion, his language, his country of residence, and his scientific disciplines; second, that he was a man haunted by major moral dilemmas throughout his life, burdened by a sincere and grave sense of responsibility for the fate of the world; and third, that he experienced a terrible sense of déjà vu: his excessive sensitivity and constant alertness were products of his experiences as a young student in Budapest in 1919. The mature Szilard in Berlin of 1933, and forever after, was always ready to move. I proceed as follows:After a brief introduction to his family background, youth, and education in Budapest, I discuss the impact of his army service in the Great War and of the tumultous events in Hungary in 1918–1919 on his life and psyche, forcing him to leave Budapest for Berlin in late 1919. He completed his doctoral degree under Max von Laue (1879–1960) at the University of Berlin in 1922 and his Habilitationsschrift in 1925. During the 1920s and early 1930s, he filed a number of patents, several of them jointly with Albert Einstein (1879–1955). He left Berlin in March 1933 for London where he played a leading role in the rescue operations for refugee scientists and scholars from Nazi Germany. He also carried out notable research in nuclear physics in London and Oxford before immigrating to the United States at the end of 1938. He drafted Einstein’s famous letter of August 2, 1939, to President Franklin D. Roosevelt, worked in the Manhattan Project during World War II, initiated a petition to President Harry S. Truman not to use the bomb on Japan, and immediately after the war was a leader in the scientists’ movement that resulted in civilian control of nuclear energy. In 1946 he turned to biology, in which his most significant contribution was to formulate a theory of aging. In 1956 von Laue led an effort to invite him to head a new institute for nuclear physics in West Berlin, which he ultimately declined at the end of 1959. He remained in the United States, becoming a highly visible public figure, speaking, writing, and traveling extensively, and even corresponding with Soviet Premier Nikita S.Khrushchev and President John F. Kennedy to promote the international control of nuclear weapons. In retrospect, although Szilard was a man of many missions, his life story could be read as that of a man of conscience with but a single mission, to save mankind.     

CO2 laser treatment system of tinea pedis

The CO₂ laser treatment system ‘Melase 1000’ has been developed for the treatment of Tinea pedis and the efficacy of the treatment using the system and its optimum irradiation condition are studied. The present system enables us to make the healing time of Tinea pedis treatment far shorter than conventional pharmaceuticals. This is in spite of using heat levels low enough for patients not to feel discomfort. Features offered by the system are a safe-and-easy operation and a stable laser power for a prolonged use. The efficacy of the present therapy is excellent; only two treatments a week for three weeks, i.e. six consecutive treatments, attained an improvement rate of 71.8% in the skin findings and a ‘usefulness’ of 66.2% determined from cases rated as ‘useful’ or ‘better’. The optimum laser irradiation condition for a single treatment found in this experiment is a light fluence of about 3 J/cm² and four laser pulses with a time interval between pulses of 1 s for a typical horny layer thinner than 0.5 mm.     

Stretched exponential relaxation and dispersive conductivity behavior in lithium bismuth silicate glasses

Glasses having compositions xLi₂O∙(85 − x)Bi₂O₃∙15SiO₂ (x = 35, 40, and 45 mol%) were prepared by normal melt quenching technique. Electrical relaxation and conductivity in these glasses were studied using impedance spectroscopy in the frequency range from 20 Hz to 1 MHz and in the temperature range from 453 to 603 K. The ac and dc conductivities, activation energy of the dc conductivity and relaxation frequency were extracted from the impedance spectra. The dc conductivity increases with increase in Li₂O content providing modified glass structure and large number of mobile lithium ions. Similar values of activation energy for dc conduction and for conductivity relaxation time indicate that the ions overcome the same energy barrier while conducting and relaxing. The non-exponential character of relaxation processes increases with decrease in stretched exponential parameter ‘β’ as the composition parameter ‘x’ increases. The observed conductivity spectra follow a power law with exponent ‘s’ which increases regularly with frequency and approaches unity at higher frequencies. Nearly constant losses (NCL) characterize this linearly dependent region of the conductivity spectra. A deviation from the ‘master curve’ for various isotherms of conductivity spectra was also observed in the high-frequency region and at low temperatures, which supports the existence of different dynamic processes like NCL in addition to the ion hopping processes in the investigated glass system.     

A spatial filtering technique for improved holographic character recognition

Conventional holographic pattern recognition systems suffer from the disadvantage that, in dealing with highly ordered patterns such as Arabic numerals or the letters of the Roman alphabet it is sometimes impossible to distinguish between patterns with a high degree of similarity (eg the capital letters ‘E’ and ‘F’ or ‘B’ and ‘P’).The present paper analyzes a simple case and shows how the insertion of a suitable spatial filter in the Fourier transform plane can reduce the unwanted cross-correlation signal between dissimilar patterns to zero, without removing the desired auto-correlation signal between similar patterns. Although no attempt is made to generalize the analysis, it seems probable that in cases involving the recognition of a small number of patterns with a strong ‘family resemblance’ a compromise filtering arrangement could be developed which would lead to a substantially improved performance.     

The Order Parameter of the Chiral Potts Model

An outstanding problem in statistical mechanics is the order parameter of the chiral Potts model. An elegant conjecture for this was made in 1983. It has since been successfully tested against series expansions, but there is as yet no proof of the conjecture. Here we show that if one makes a certain analyticity assumption similar to that used to derive the free energy, then one can indeed verify the conjecture. The method is based on the ‘‘broken rapidity line’’ approach pioneered by Jimbo et al. (J. Phys. A 26:2199--2210 (1993).).     

Global noise characteristics of a laser Doppler vibrometer-II. Experiments using beam dynamics

The use of a laser Doppler vibrometer to obtain velocity information from vibrating structures has gained wide acceptance in recent years. Although use of such an instrument can yield a spatially dense matrix of velocity information, several users have noted ‘noise’ at certain points in the spatial field. The technique by which the SLDV system operates results in occasional velocity ‘drop-outs’ which are unidirectional, always estimating the velocity response closer to zero than reality. These ‘drop-out’ areas occur more predominately at points of maximum velocity response with small rotational components. Alternatively, points exhibiting minimum velocity response with large rotational components are less susceptible to the ‘noise’. In this paper, an experiment to visualize the speckle pattern motions received by the photo-detectors during these vibration conditions is presented. Theories regarding the source(s) of the ‘noise’ are developed.     

Observations and modeling of lightning leaders

The development of atmospheric lightning is initiated by a ‘leader’ phase during which ionized channels appear in virgin air. The use of rapid cameras, the measure of fields and currents associated with the discharge allow one to compare the propagation of laboratory leaders with those of natural or artificially triggered lightning. The corresponding physical processes can be analyzed with the help of models developed for laboratory leaders provided that the non linear effects due to the intense current circulation leading to lightning leader thermalization are taken into account. A self-coherent simulation of triggered lightning leaders for both polarities is presented is this paper. Furthermore, these models make it possible to define the ‘stabilization field’ concept, equal to the minimum ambient field allowing the stable progress of a leader from a ground structure, expressed as a height and curvature function of this structure. This concept can be validated through triggered lightning tests. Finally, the stabilization field analysis is completed by a simplified analytical model based upon an electrostatic approach of propagation equilibrium. To cite this article: P. Lalande et al., C. R. Physique 3 (2002) 1375–1392.     

Probing the coherent transport through coupled quantum dots

We investigate the photoconductance through a double quantum dot or ‘artificial molecule’ induced by a broadband millimeter wave source. This source functions as a heterodyne interferometer, consisting of two nonlinear transmission lines generating harmonic output in the range of 2–400 GHz, and, being coherent, allows tracking of the induced current of the sample in both magnitude and phase. This enables us to monitor effects related to coherent electronic transport through these ‘artificial molecules’.     

Un coronographe interférentiel achromatique coaxial

We present a new type of stellar interfero-coronagraph, the ‘CIAXE’, which is a variant of the ‘AIC’, the Achromatic Interfero-Coronagraph. The CIAXE is characterized by a very simple, compact and fully coaxial optical combination. Indeed, contrarily to the classical AIC which has a Michelson interferometer structure, the CIAXE delivers its output beam on the same axis as the input beam. This will ease its insertion in the focal instrumentation of existing telescopes or next generation ones. Such a device could be a step forward in the field of instrumental search for exoplanets. To cite this article: J. Gay et al., C. R. Physique 6 (2005).     

High-p jets in diffractive electroproduction

The diffractive production of high-p jets in deep-inelastic scattering is studied in the semiclassical approach. The p-spectra of and diffractive final states are found to be qualitatively different. For fina states, which are produced by ‘hard’ colour-singlet exchange, the p-spectrum is much softer than for final states, where the colour neutralization is ‘soft’. Furthermore, the two different final states can be clearly distinguished by their diffractive mass distributions.     

Dark matter problem and effective curvature Lagrangians

A ‘radical’ conservative unifying model of scalar dark matter and modified gravity is proposed here. After a conformal mapping, the dependence of the effective Lagrangian on the curvature is not only singular but also bifurcates into several almost Einsteinian spaces, distinguished only by a different gravitational strength and cosmological constant. A swallow tail or butterfly catastrophe in the bifurcation set indicates the possibility for the coexistence of different Einsteinian domains in our Universe. This finding may shed new light on the nature and large scale distribution not only of dark matter but also on ‘dark energy’, regarded as an effective cosmological constant.     

Linear and nonlinear optical properties of CdSexS1−x microcrystallites

Microcrystals of CdSe_xS_1−x (x≈0.6) with nanometer dimensions have been investigated experimentally by a range of optical techniques. This system of ‘quantum dot’ consists of nanometer sized semiconductor particles embedded within an insulating glass matrix. The existence of microscopic CdSeS crystals within the glass matrix is demonstrated by the observation of Raman scattering from the ‘CdSe-like’ and ‘CdS-like’ LO phonons. The nature of the electronic states within these three dimensionally confined systems is investigated by linear absorption and photoluminescence spectroscopy. The photoluminescence spectra show features which are attributed to direct electron-hole recombination and recombination via states within the ‘blue shifted’ energy gap (which are possibly surface related). Carrier relaxation is also investigated by a pump-probe experiment whereby the absorption is partially bleached by a short pump pulse then probed some variable time later by a delayed probe pulse of much lower intensity. Fast and slow components in the carrier relaxation process are identified, and a relationship is suggested between the carrier relaxation and the features observed in the photoluminescence spectra. The well known ‘photodarkening’ properties of such materials are also investigated by the above techniques.     

Ultrastructure and cytochemistry of lipid granules in the many-celled magnetotactic prokaryote, 'Candidatus Magnetoglobus multicellularis'

Conspicuous cytoplasmic granules are reported in a magnetotactic multicellular prokaryote named ‘Candidatus Magnetoglobus multicellularis’. Unfortunately, this microorganism, which consists of an assembly of gram-negative bacterial cells, cannot yet be cultivated, limiting the biochemical analysis of the granules and preventing in vitro studies with starvation/excess of nutrients. In this scenario, light and electron microscopy techniques were used to partially address the nature of the granules. Besides magnetosomes, three types of inclusions were observed: small (mean diameter = 124 nm) polyhydroxyalkanoate-like (PHA) granules, large (diameters ranging from 0.11 to 2.5 μm) non-PHA lipid granules, and rare phosphorus-rich granules, which probably correspond to polyphosphate bodies. The PHA granules were rounded in projection, non-reactive with OsO₄, and suffered the typical plastic deformation of PHAs after freeze fracturing. The nature of the large granules, consisting of round globular structures (mean diameter = 0.76 μm), was classified as non-PHA based on the following data: (a) multilayered structure in freeze-fracture electron microscopy, typical of non-PHA lipids; (b) Nile blue fluorescence imaging detected non-PHA lipids; (c) imidazole buffered osmium tetroxide and ruthenium red cytochemistry stained the globules, which appeared as electron-dense granules instead of electron lucent as PHAs do. Most likely, ‘Candidatus Magnetoglobus multicellularis’ stores carbon mainly as unusual lipid granules, together with smaller amounts of PHAs.     

Scaling and long-range dependence in option pricing III: A fractional version of the Merton model with transaction costs

A model for option pricing of fractional version of the Merton model with ‘Hurst exponent’ H being in [1/2,1) is established with transaction costs. In particular, for H(1/2,1) the minimal price C_min(t,S_t) of an option under transaction costs is obtained, which displays that the timestep δt and the ‘Hurst exponent’ H play an important role in option pricing with transaction costs.