VictorJuiz/thesis huggingface dataset:
Some properties of liquid helium

The theoretical picture of liquid helium 3 which is currently accepted is due to Landau (1957 a). According to this theory, the propagation of sound in He5 should show a new phenomenon, called zero sound, if the liquid is excited at a high acoustic frequency and at low temperatures. This thesis describes theoretical and experimental investigations into this phenomenon.
We have attempted a measurement of the acoustic impedance of liquid He5 at a frequency of 10 000 Mo/s. In the method of measurement adopted, a travelling sound wave is reflected up and down inside a quarts crystal immersed in liquid He5. The acoustic impedance of the liquid is found by measuring the loss of energy from the crystal due to the radiation of sound out into the liquid. In order to obtain useful accuracy, it is necessary to obtain a crystal in which the sound wave can be reflected bank and forth at least 250 times. Preliminary experiments performed with various crystals showed that it was not hard to obtain a crystal which would give 100 echoes, but that obtaining a larger number presented unexpected difficulties. Various attempts were made to improve the performance of the apparatus, but the experiment was eventually abandoned as our theoretical analysis appeared to be more promising.
For the theoretical work, we have analysed measurements of the acoustic impedance of liquid He5 at a frequency of 1000 Mo/s which have been made by Keen, Matthews, and Wilks (1965). The theoretical expressions used are an extension of those given by Bekarevich and Khalatnikov (1961), who give expressions related to the acoustic impedance as part of a calculation of the Kapitza thermal boundary resistance. Using the same assumptions as Bekarevich and Khalatnikov we find that the acoustic impedance Z divided by the density ρ should rise from 183 m/s to about 190 m/s when the temperature is reduced through 0·09°K. The experimentally observed rise in Z/ρ is 19 ± 6 m/s, so the theory appears to underestimate the change in Z/ρ, and we have considered how the theory should be modified to account for the discrepancy.
In the theory of a Fermi liquid due to Landau (1957 a), the forces of interaction between the particles of the liquid are taken into account by introducing certain parameters F0, F1, F2, … which are determined from experimental measurements. Bekarevich and Khalatnikov include only two parameters (F0, F1) as these are the ones most easily derived from experiment. We have been able to estimate a third parameter (F2), and have used this to obtain revised values of the acoustic impedance. These values of Z/ρ are still a little smaller than the experimental points, but we regard the agreement as satisfactory. We conclude that the experimental results of Keen, Matthews, said Wilks are consistent with Landau's theory of a Fermi liquid, and provide valuable support for the existence of zero sound.
The spectral distribution of thermal radiation in the earth's atmosphere

The humidity of the stratosphere is, from the point of view of radiation transfer studies, a subject of some importance to the meteorologist. It has, nevertheless, presented many problems to the experimentalist. Owing to the extreme dryness of air above the tropopause, compared with that at ground level, great care has to be taken to avoid the contamination of any measuring instrument by water carried up during an ascent into the stratosphere. An indirect method of approach, which to a large extent overcomes these difficulties, is the subject of the work described in this thesis.
Measurements of stratospheric humidity which have been made to date by other workers, are reviewed together with some of the theoretical arguments which have been put forward to account for various water vapour distributions. Good evidence, both theoretical- and experimental, exists in favour of a water vapour mixing ratio in the region of 3 × 10−6 gm/gm in the lower stratosphere. Above about 50,000 ft experimental results have shown considerable diversity, and somewhat larger mixing ratios have been found in many cases. Recent measurements which suggest that the dry region of the stratosphere extends to much greater heights, have thrown doubt on a lot of the early work.
The instrument which is the subject of the present study measures the night emission from the 6.3 μ water vapour band in the atmosphere, using a liquid air cooled gold-doped germanium detector. By utilising the variation with height of the boiling point of liquid air, and with it the change in sensitivity of the detector, measurements of emission over about four orders of magnitude have been possible during an ascent. Calibration is performed by means of a black body at a measured temperature. The detector responds to the total incident radiation within a pass band from about 5.5 μ to 7 μ. Since no information is obtained regarding the spectral distribution of radiation within the pass band, but only the combined effect of the whole, a somewhat lengthy analysis has been necessary in order to interpret ascent data in terms of water vapour mixing ratios.
Results from one ascent, which was by far the most successful, are discussed in detail. Mixing ratios obtained from the analysis show good agreement with values deduced from radiosonde humidity data below 300 mb and with the well established value a few kilometers above the tropopause. Above this the mixing ratio is found to. vary between 2 × 10−6 and 4 × 10−6 up to 25 km. Interpretation of data at greater heights than this presented difficulties due to the presence of a large background component in the measured downward emission. Whilst the exact nature of this emission is not known, it has with some justification been assumed in the analysis that it is not due to water vapour.
Some problems in the theory of solids

This thesis is concerned with the application of lattice dynamical theories to problems of current physical interest. The first sort is a calculation of the lattice dynamics of calcium fluoride, with a detailed discussion of the various types of model which may be used. On the basis of this discussion the Bern model is used in the numerical calculation and the results are presented in the form of dispersion curves and density-of-states curves.
The second part of the thesis deals with the theory of the vibrations of crystal lattices perturbed by the introduction of defects. The object is to develop the theory into a form such that it becomes easy to perform numerical calculations, using existing lattice dynamical calculations, so that physical properties of defects which involve changes of force constants as well as mass changes may be computed.
The third part deals with such a defect which has received some experimental attention recently, namely, the hydrogenation in calcium fluoride crystals. This is an interesting theoretical problem as not only is the theory of defects in crystal lattices concerned, but also that of anharmonicity. From the optical observations it is possible to calculate some of the anharmonic force constants involved.
Some properties of elementary particles or a determination of the lifetime of the neutral pi meson

Theoretical estimates of the lifetime of the neutral π meson have indicated a value of the order of 10−17 secs. In order to determine the lifetime by flight distance measurements a method employing very fine resolution is required. Nuclear emulsions provide a medium for resolution of distances of the order of a micron.
This experiment uses the same principle as that first tried by Harris et al.(1957). The decay at rest of the K+ meson in the Kπ2 mode (π+π0) provides a π0 of unique velocity and a direction directly opposite to that of the π+; the latter being charged, leaves a track in the emulsion. The decay of the π0 is detected in emulsion if it takes place in the Dalitz mode:-
π0 γ+e++e− (br. ratio 1.2%)
Detection is possible because of the emission of charged particles.
A stack of Ilford L4 emulsions was exposed to a beam of stopping K mesons. After processing, the stack was scanned for Kπ2 decays with the emission of a Dalitz pair. Other π0 producing decays of the K+ (Kμ3, Ke3, τ′) were at first indistinguishable from the desired Kπ2 decays.
In order to reduce this contamination, grain density measurements were made on the charged secondary from the K+ decay. By rejecting events in which g* was greater than 1.3 all τ′ and 30% of the Kμ3 events were rejected. A correction factor was calculated to account for the remaining decays.
The co-ordinates of the grains composing the events were measured relative to axes fixed in the field of view. A bifilar micrometer eyepiece was used which has the motions of the cross-wires digitised to enable rapid measurement. The co-ordinates were automatically punched out on to tape ready for input to the computer.
The tracks of the particles were obtained by fitting straight lines to the measured co-ordinates. The decay point of the π0 was defined as the intersection of the electron tracks with the line of flight of the π+. The point of production was taken as the foot of the perpendicular from the measured position of the K+ on to the π+ trajectory.
The effects of errors due to measurement, "grain noise" and grain size were thoroughly investigated. Use was made of co-ordinate measurements on τ decays of the K+ (π+π+π−) where it is known that the three tracks converge on the point of decay of the K+.
An estimation of the lifetime was made using a likelihood calculation. It was discovered that the presence of events giving anomalous flight distances affected the estimate considerably. A suitable cutoff criterion was applied to reject these events.
The result after allowing for the effect of contamination events referred to earlier was:-
τπ0 = (1.56 + 0.55 ) × 10−16 secs.
− 0.45
Some electron spin resonance experiments on exchange interactions

In the work described in this thesis, the exchange interactions between neighbouring magnetic ions in semidilute crystals have been measured from their paramagnetic resonance spectra. The results of these measurements are compared with the magnetic bulk properties of the concentrated crystals. The relationships between these bulk properties and the exchange interactions are considered in chapter 1, where a brief account of the origin of antiferromagnetic exchange is also given.
The experimental measurements have mainly been made using a Q band (λ = 0.85 cm) spectrometer, which is described in chapter 2.
In chapter 3, experiments are described on n.n. pairs of Mn++ ions in the face centred cubic MgO crystal lattice. The interaction between two n.n. spins s1 and s2 can be divided into two parts, an isotropic and an anisotropic part.
The isotropic exchange interaction is taken to be,
ℋ = J(s1 ⋅ s2) - j(s1 ⋅ s2)2 + …
The spins are strongly coupled together by this interaction and act as a single unit with spin S = s1 + s2, which can take the values 0, 1, 2, 3, 4, and 5. For purely first order exchange (j, etc = 0), the energy levels for the different S states are spaced according to a Lande interval rule, with S = 0 lowest. In earlier measurements on these pairs, Coles (Thesis 1959) measured the energy splitting between the S = 0 and S = 1 levels, and interpreted it in terms of a first order exchange term, J⁄k = 28°K, which could not be reconciled with the bulk magnetic properties. In the present work the intervals up to S = 4 have been measured by comparing the temperature variations of intensity for lines from different S states. The measurements of Coles have been confirmed, but it is found that the intervals to not follow a Lande rule, and the present results are interpreted in terms of a first order exchange term, J⁄k ≈ 15°K, and a second order term such that j ≈ .05 J. This is now in good agreement with bulk magnetic properties which suggest J⁄k ≈ 11°K. The difference is consistent with the difference in lattice spacings for the dilute and concentrated crystals. Further evidence for this second order biquadratic exchange in the concentrated crystals is provided by the anomalous sublattice magnetization below the transition temperature (Sievers and Tinkham 1963) and by the low temperature transverse susceptibility measured by Jacobs (private communication).
The anisotropy of the exchange interaction is reflected in the anisotropy of the pair resonance lines. The anisotropic exchange is given by,
ℋ = De(3s1zs2z - s1⋅s2) + Ee(s1xs2x - s1ys2y) + higher order terms.
[This is the start of the abstract. For the full abstract, please consult the PDF.]
A crystallographic study of the structure of some antibiotics

The crystal structure of 6-aminopenicillanic acid (C8, H12, N2, O3, S) (I) and cephalosporin Cc (C14, H17, O6, N3, S; CH3CO2H), (II) have been determined by X-ray crystallographic analysis.
6-aminopenicillanic acid crystallises in flat orthorhombic plates,
Crystal data.
a = 6.24 ± .02 Å, b = 14.83 ± .04 Å, c = 10.49 ± .03Å
space group P212121 Z=4.
Using copper Kα radiation layers okl - 4kl and hkO to hk8 were recorded on equi-inclination Wissenberg photographs. A total of 988 reflections were measured visually out of a possible 1170 in the copper sphere. A Patterson function was calculated using data sharpened by the finction 1⁄f2 exp.(3 Sin2θ), where f was the scattering factor for carbon; from this a superposition function was calculated. It was possible to obtain all atomic positions from this. These were refined using anistropic and isotropic least squares procedures, the final positions have calculated deviations of about .01Å. The final agreement factor was 11.6% using isotropic and 9.7%, anistropic temperature factors.
The structure is similar to that reported by Crowfoot, Bunn, Rogers-Low and Turner-Jones for potassium benzyl penicillin except that in the thiazolidine ring the atom out of the plane of the other four is the nitrogen instead of the carbon to which the carboxyl group is attached, as in the other penicillins. The bond between the sulphur and the gem-dimethyl group is longer in all the penicillins than the generally accepted value for a C - S single bond (1.86 Å compared with 1.81 - 1.82 Å). The length of the C - N bond in the β-lactam group falls between that of a C - N single bond and that of an ordinary C - N peptide bond; this is probably caused by the lack of resonance in the fused β-lactam ring.
Cephalosporin Cc crystalises in flat orthorhombic needles (a = 5.04 ± .0 Å, b = 7.00 ± .02 Å, c = 54.6 ± .2 Å), space group P212121. 1521 Reflections out of a possible 2580 in the copper sphere were measured visually on equi-inclination Wissenberg films (layers okl - 3kl and hol - h51). The structure was determined and refined in a similar fashion to 6-aminopenicillanic acid, though because of the larger size of the molecule three rounds of Fourier refinement were needed before it was possible to use the least square procedure. The final agreement after eight rounds of least squares refinement was 10.6%, with calculated standard deviations of about .01 Å.
The structure was identical to that proposed by Abraham and Newton. The bond distances were all within the expected range of values. The α-amino group of the side chain together with the acetic acid of crystallisation formed a hydrogen bond system around the screw axis parallel to b. There was no significant difference between the lengths bonds of the β-lactam group in cephalosporin Cc and in 6-aminopenicillanic acid.
[For the diagrams to accompany this abstract, please consult the PDF.]
Identical relations in simple groups

An identical relation of a group G is an equation of the form w(x1, …, xn) = 1, where w is an element of the free group generated by x1, …, xn, which is satisfied by any substitution of elements of G for the variables x1, …, xn. A consequence of a given set of identical relations W is a relation which holds on every group on which each member of W holds. A set of identical relations is said to be closed if it contains all its consequences. As a special case of a theorem of G. Birkhoff, contained in his paper "On the Structure of Abstract Algebras", Proc. Cam. Phil. Soc. 31 (1935) 433-454, we have that there is a one-one correspondence between varieties of groups and closed sets of identical relations.
A set of identical relations is said to be finitely based if it is the set of consequences of a finite subset (which can be taken to consist of just one element, the direct product of the elements of this subset). In his paper "Identical Relations in Groups, I", Math. Ann. 14 (1937) 506-525, B. H. Neumann considers the question of whether the identical relations of a given variety (and, in particular, the variety generated by a finite group) are finitely based. He shows this to be true for a variety of abelian groups, and R. C. Lyndon, in "Two Notes on Nilpotent Groups", Proc. Amer. Math. Soc. 3 (1952) 579-583, extends this to nilpotent groups. [...]
[This is the start of the abstract. For the full abstract, please consult the PDF.]
Chemistry of [or polyacetylenes from/secondary metabolites of] the higher fungi

More than fifty polyacetylenic compounds produced by micro-organisms have been isolated and characterised since the discovery of the allenic polyacetylene, mycomycin, in 1952. A review of the sixteen natural allenic polyacetylenes which have been isolated and their structures elucidated, is included. this review is followed by a summary of the methods published by Brewster in 1959 for the correlation of observed optical rotations with the configurations of coat pound a having simple asymmetric centres.
Four allenic polyacetylenes (I-IV) have been isolated from the culture medium of the fungus Odontia bicolor.
HC≡C.C≡C.CH=C=CH.CH2.CH2.CH2OH
HC≡C.C≡C.CH=C=CH.CH2.CH2.CH2.CH2OH
HC≡C.C≡C.CH=C=CH.CH(OH).CH2.CH2OH
HC≡C.C≡C.CH=C=CH.CH(OH).CH2.CH2.CH2OH
In addition, substantial evidence has been presented for assigning the structure (V) to a non-allenic polyacetylene which is also produced by the fungus.
HC≡C.C≡C.CH=CH.CH=CH.CH2.CH2.CH2OH
The allenic metabolites isomerised readily in dilute alkali to fora triynes since the allene group in each case is conjugated to a diacetylene unit. The triynes formed from the diols had a terminal ethynyl group, whereas those formed from the alcohols had no terminal ethynyl group. The isomerised C10 alcohol (I) was shown to be identical to synthetical specimen with the structure (VI). The mechanisms of these isomerisations are discussed.
CH3.C≡C.C≡C.C≡C.CH2.CH2.CH2OH
An isopropylidene derivative of the C10 1,3-diol (III) was prepared and fully characterised. The absolute configuration of the C3 secondary alcohol centre in this diol was deduced to be (S) from a consideration of observed optical rotations and the use of Brewster's methods. Certain characteristics of the infrared spectra of the diols and the 1,3-isopropylidene derivatives have been noted.
Two polyacetylenes have been isolated from the culture medium of the fungus Clitocybe rhizophora and shown to have the structures (VII-VIII).
HOCH2.CH(OH).C≡C.C≡C.CH(OH).CH2.CH3
HOCH2.CH(OH).C≡C.C≡C.CO.CH2.CH3
They are unique among the polyacetylenes so far isolated from micro-organisms in being the first diacetylene and the first ketone to be isolated. The structural determination for the diyne-triol (VII) was confirmed by investigating the nuclear magnetic resonance spectrum of its isopropylidene derivative and of the products of hydrogenation and of sodium borohydride reduction of this derivative.
The absolute configurations of the secondary alcohol centres at C2 in both the natural compounds and at C7 in the triol were deduced to be (S) from observed optical rotations and the use of the methods of Brewster. Certain characteristic in the infrared spectra of the 1,2-isopropylidene derivative were noted and compared with the data from the 1,3-isopropylidene derivatives of the allenic C10 1,3-diol (III) from Odontia bicolor.
The synthesis of a polyacetylenic diacid (IX) from Merulius lachrymans has been described in an appendix.
HOOC.C≡C.C≡C.C≡C.CH2.CH2.COOH
An experimental study of spin interactions at very low temperatures

This thesis is divided into three parts. Part One contains a description of a method for measuring the magnetization entropy of a paramagnetic salt near 1°K, and a study of the low temperature thermal and magnetic properties of ferric methylammonium alum. Part Two contains an account of heat capacity measurements below 1°K made to examine the hyperfine coupling in ferromagnetic materials. Results are given for a range of iron-cobalt alloys, and for uranium hydride. Part Three contains an account of low temperature heat capacity measurements for titanium-iron, and for mixed zinc-manganese fluoride crystals.
On certain problems in homotopy theory

John Milnor has given a construction [J. Milnor. Construction of Universal Bundles, II. Ann. Math. 63 (1956) 430-436] which associates with each topological group G a sequence of spaces GP(i) [our notation] which can be regarded as generalizations of the classical projective spaces RP(i) = S0P(i), CP(i) = S1P(i) and QP(i) = S3P(i). If one considers H-spaces instead of topological groups, one finds that additional homotopy structure is necessary to imitate this construction. Intuitively, an An-space X is an H-space with sufficient additional structure to permit the construction for i ≤ n of spaces XP(i) with properties similar to those of the spaces GP(i). An An-map can be thought of as a map from one An-space to another which up to homotopy respects the An-structure.
The principal goals of this study are 1) to investigate the multiplication on an An-space in terms of the geometry of the projective spaces and 2) to analyse the algebra of the homology of an An-space. In the first direction we observe that in the classical case there exist maps RP(r) × RP(s) → RP(r+s) and CP(r) × CP(s) → CP(r+s) which restricted to either factor are the usual imbeddings RP(r) ⊂ RP(r+s) and CP(r) ⊂ CP(r+s). Working with An-spaces we find that the existence of such maps is implied by the multiplication's being itself an Ar+s-map. In particular, an H-space (X,m) is homotopy abelian if and only if there is a map of SX × SX → XP(2) which is the inclusion on either factor.
The second direction is guided by William Massey's definition of cohomology products. The essential properties of the singular chain complex on an An-space are embodied in the concept of an A(n)-algebra. Other algebraic objects called stacks are defined which give rise to spectral sequences of topological significance. Applied to An-spaces, these spectral sequences yield homology operations which serve as criteria for An-maps, and are related to the homology of the protective spaces.
The two paths of study are re-united in application to ΩCP(3) the loop space on complex projective 3-space. We find that ΩCP(3 is homotopy abelian and that there exists a homotopy equivalence f : S1 × ΩS7 → ΩCP(3) which is an H-map but not an A4-map.